Earthquake Engineering Handbook

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EARTHQUAKE ENGINEERING HANDBOOK

New Directions in Civil Engineering Series Editor

W. F. CHEN Hawaii University Published Titles Advanced Analysis of Steel Frames: Theory, Software, and Applications W.F. Chen and Shouji Toma Analysis and Software of Cylindrical Members W.F. Chen and Shouji Toma Artificial Intelligence and Expert Systems for Engineers C.S. Krishnamoorthy and S. Rajeev Cold Weather Concreting Boris A. Krylov Concrete Beams with Openings: Analysis and Design M.A. Mansur and Kiang-Hwee Tan Concrete Buildings: Analysis for Safe Construction W.F. Chen and K.H. Mosallam Flexural-Torsional Buckling of Structures N.S. Trahair Flood Frequency Analysis Ramachandro A. Rao and Khaled Hamed Fracture Processes of Concrete Jan G.M. van Mier Fracture and Size Effect in Concrete and Other Quasibrittle Materials Zdenek P. Bazant and Jaime Planas Introduction to Environmental Geotechnology Hsai-Yang Fang Limit Analysis and Concrete Plasticity M.P. Nielsen LRFD Steel Design Using Advanced Analysis W.F. Chen and Seung-Eock Kim Response Spectrum Method in Seismic Analysis and Design of Structures Ajaya Kumar Gupta Simulation-Based Reliability Assessment for Structural Engineers Pavel Marek, Milan Gustar, and Thalia Anagnos Stability Design of Steel Frames W.F. Chen and E.M. Lui Stability and Ductility of Steel Structures under Cyclic Loading Yuhshi Fukumoto and George C. Lee The Finite Strip Method Y.K. Cheung and L.G. Tham Theory of Adaptive Structures: Incorporating Intelligence into Engineered Products Senol Utku Unified Theory of Reinforced Concrete Thomas T.C. Hsu Water Treatment Processes: Simple Options S. Vigneswaran and C. Visvanathan ˆ

ˆ

Forthcoming Titles Earthquake Engineering Handbook W.F. Chen and Charles Scawthorn Transportation Systems Planning: Methods and Applications Konstandinos Goulias

EARTHQUAKE ENGINEERING HANDBOOK EDITED BY

Wai-Fah Chen Charles Scawthorn

CRC PR E S S Boca Raton London New York Washington, D.C.

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Library of Congress Cataloging-in-Publication Data Earthquake engineering handbook / edited by Wai-Fah Chen, Charles Scawthorn. p. cm.—(New directions in civil engineering) Includes bibliographical references and index. ISBN 0-8493-0068-1 (alk. paper) 1. Earthquake engineering—Handbooks, manuals, etc. I. Chen, Wai-Fah, 1936- II. Scawthorn, Charles, III. Series. TA654.6 .E374 2002 624.1'762—dc21

2002073647

This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the authors and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. All rights reserved. Authorization to photocopy items for internal or personal use, or the personal or internal use of specific clients, may be granted by CRC Press LLC, provided that $1.50 per page photocopied is paid directly to Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923 USA The fee code for users of the Transactional Reporting Service is ISBN 0-8493-0068-1/03/$0.00+$1.50. The fee is subject to change without notice. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe.

Visit the CRC Press Web site at www.crcpress.com © 2003 by CRC Press LLC Information contained in this work has been obtained from sources believed to be reliable. ICBO®, NCSEA, or their memberships shall not be responsible for any errors, omissions, or damages arising out of this information. This work is published with the understanding that ICBO and NCSEA, as copublishers, are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought. No claim to original U.S. Government works International Standard Book Number 0-8493-0068-1 Library of Congress Card Number 2002073647 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper

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Foreword

The International Conference of Building Officials® (ICBO®) is proud to join CRC Press to co-publish the Earthquake Engineering Handbook. Known internationally for its development and publication of the Uniform Building Code™ (UBC™), ICBO’s reputation as a leader in seismic codes traces its origin back to 1927 with its release of the nation’s first complete model building code. The Earthquake Engineering Handbook is not only timely, reflecting the most recent research in earthquake engineering, but also comprehensive, covering more than 30 topics. Written by a panel of internationally known experts, the Handbook provides applications and practical information to help solve real-world problems faced by civil, structural, geotechnical, and environmental engineers. The Handbook also serves as an excellent resource for researchers and students wishing to extend their knowledge of earthquake engineering. Editors Wai-Fah Chen, and Charles Scawthorn have done a masterful job of assembling a “blue ribbon” panel of authors from both academic and professional engineering communities. The result is a book that more than lives up to the reputation of the long and outstanding line of engineering handbooks from CRC Press. The Earthquake Engineering Handbook does not just review standard practices, but also brings readers quickly up to date on new approaches and innovative techniques. CRC Press and ICBO would like to thank the National Council of Structural Engineers Associations (NCSEA) for co-sponsoring this Handbook. NCSEA was founded for the purpose of improving the level of standard practice for the structural engineering profession throughout the United States and to represent the profession on a national level. Mark A. Johnson Director of Publications and Product Development, ICBO

© 2003 by CRC Press LLC

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Preface

The Handbook of Earthquake Engineering is a comprehensive reference and resource work covering the spectrum of disciplines required for mitigation of earthquake effects and design of earthquake-resistant structures. It has been written with the practitioner in mind. The focus is on a graduate engineer with a need for a single reference source to keep abreast of new techniques and practices, as well as review standard practices. Earthquake engineering requires first of all knowledge of the geologic causes of, and expected shaking, liquefaction, and other effects that result from, a strong earthquake. It also requires a good understanding of the impacts these natural effects have on humankind, ranging from our buildings and other structures to the entire built and even social environment. In this regard, earthquakes are an almost unique natural phenomenon, in that they affect virtually everything within a region — even to furnishings within a building, and underground structures. To this end, the Handbook is divided into five parts. Initially, Part I reviews the basic problem of earthquakes from a historical perspective, provides an overview of the framework within which earthquake risk is managed and an introduction to dynamics, since earthquakes are most fundamentally a dynamic process and problem. Part II of the Handbook addresses the geoscience aspects, covering geology, tectonics, liquefaction and tsunamis, focusing especially on earthquake strong ground motion. Parts III and IV cover the broad spectrum of structures, from buildings built of steel, concrete, wood and masonry, to special structures such as bridges and equipment, to the variety of infrastructure called lifelines — that is, the water, power, transportation and other systems and components without which modern urban society cannot function. Earthquake structural engineering in the last decade has also seen a burst of new technology intended to avoid rather than resist the forces of earthquakes. These topics, base isolation and structural control, are also included. Because earthquakes affect not only the built but also the social environment, in all its aspects, Part V addresses special topics that the earthquake engineer must be cognizant of, if not indeed be expert in. An important aspect of this is the social and economic impacts of earthquakes, which in recent years have assumed increasing importance. We wish to thank all the authors for their contributions and also to acknowledge the support of CRC Press. Wai-Fah Chen Charles Scawthorn


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Editors

Wai-Fah Chen is presently Dean of the College of Engineering at the University of Hawaii. He was a George E. Goodwin Distinguished Professor of Civil Engineering and Head of the Department of Structural Engineering at Purdue University from 1976 to 1999. He received his B.S. in civil engineering from the National ChengKung University, Taiwan, in 1959, M.S. in structural engineering from Lehigh University, Pennsylvania, in 1963, and Ph.D. in solid mechanics from Brown University, Rhode Island, in 1966. He received the Distinguished Alumnus Award from the National Cheng-Kung University in 1988 and the Distinguished Engineering Alumnus Medal from Brown University in 1999. Dr. Chen’s research interests cover several areas, including constitutive modeling of engineering materials, soil and concrete plasticity, structural connections, and structural stability. He is the recipient of several national engineering awards, including the Raymond Reese Research Prize and the Shortridge Hardesty Award, both from the American Society of Civil Engineers, and the T. R. Higgins Lectureship Award from the American Institute of Steel Construction. In 1995, he was elected to the U.S. National Academy of Engineering. In 1997, he was awarded Honorary Membership by the American Society of Civil Engineers. In 1998, he was elected to the Academia Sinica (National Academy of Science) in Taiwan. A widely respected author, Dr. Chen authored and coauthored more than 20 engineering books and 500 technical papers. His books include several classical works such as Limit Analysis and Soil Plasticity (Elsevier, 1975), the two-volume Theory of Beam-Columns (McGraw-Hill, 1976–77), Plasticity in Reinforced Concrete (McGraw-Hill, 1982), and the two-volume Constitutive Equations for Engineering Materials (Elsevier, 1994). He currently serves on the editorial boards of more than 10 technical journals. He has been listed in more than 20 Who’s Who publications. Dr. Chen is the editor-in-chief for the popular 1995 Civil Engineering Handbook, the 1997 Handbook of Structural Engineering, and the 1999 Bridge Engineering Handbook. He currently serves as the consulting editor for McGraw-Hill’s Encyclopedia of Science and Technology. He has been a longtime member of the Executive Committee of the Structural Stability Research Council and the Specification Committee of the American Institute of Steel Construction. He has been a consultant for Exxon Production Research on offshore structures, for Skidmore, Owings, and Merrill in Chicago on tall steel buildings, and for the World Bank on the Chinese University Development Projects, among many others. Dr. Chen has taught at Lehigh University, Purdue University, and the University of Hawaii.


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Charles Scawthorn is a Senior Vice President with an international risk consulting firm. He received his Bachelor of Engineering from The Cooper Union for the Advancement of Science and Art, New York; M.S. in structural engineering from Lehigh University, Bethlehem, Pennsylvania; and Doctor of Engineering in seismic risk analysis from Kyoto University, Kyoto, Japan. In more than 30 years of practice, Dr. Scawthorn has designed and analyzed buildings and industrial structures and engaged in planning projects and research in the United States and internationally. These projects have included structural design of high-rise buildings, offshore platforms, and critical facilities such as LNG plants and data processing and emergency operating centers. These activities have progressed from the assessment of individual structure risk to that of complex systems risk and the development of integrated risk reduction programs. Dr. Scawthorn has assessed organizational and community risk due to earthquake and other hazards for the Federal Emergency Management Agency (FEMA), the Office of Emergency Services, and other agencies in the United States, and for national governments and the World Bank internationally. These projects have ranged from analysis of portfolio risks for multinational corporations and insurance companies, and regional loss assessments for government, to analysis of enterprise-wide risk for multinationals, and design of national insurance programs. These projects have ranged across the United States, Mid-East, Far East, and Europe. Under funding from the National Science Foundation, the U.S. Geological Survey, FEMA and the insurance industry, Dr. Scawthorn has developed innovative approaches for the analysis of fires following earthquakes, optimizing urban land use with respect to natural hazards risk, and seismically reinforcing low-strength masonry buildings. Much of his decision-oriented and emergency management work on the spread and mitigation of fires following earthquakes has been performed in conjunction with fire departments in California, particularly San Francisco. He has been a principal in the development of techniques for the rapid assessment of seismic vulnerability, is the original author of the EQEHAZARDTM software for seismic risk assessment, and was technical lead on the development of a national Flood Loss Estimation Model for HAZUS, for the National Institute of Building Sciences and FEMA. Dr. Scawthorn has investigated natural disasters in the United States, Canada, Mexico, Japan, Turkey, and the former Soviet Union. Dr. Scawthorn is a Fellow of the American Society of Civil Engineers and a member of various other professional organizations. He has served on the Scientific Advisory Committee of the National Center for Earthquake Engineering Research, received the Applied Technology Council’s Award of Excellence for Extraordinary Achievement in Seismic Evaluation of Buildings, and is on the Editorial Board of Engineering Structures and the Natural Hazards Review (ASCE). He is the author of over 100 technical papers as well as a contributor to the McGraw-Hill Yearbook of Science and Technology.


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Contributors

Jorma K. Arros

Lian Duan

James J. Johnson

ABS Consulting Oakland, California

California Department of Transportation Sacramento, California

James J. Johnson and Associates Alamo, California

Donald B. Ballantyne ABS Consulting Seattle, Washington

Horst G. Brandes

Eser Durukal ˇ ¸ University Bogacizi Kandilli Observatory Istanbul, Turkey

Department of Civil Engineering University of Hawaii Honolulu, Hawaii

ImageCat, Inc. Long Beach, California

Gilles J. Bureau

Mustafa Erdik

Consulting Engineer Piedmont, California

ˇ ¸ University Bogacizi Kandilli Observatory Istanbul, Turkey

Kenneth W. Campbell ABS Consulting and EQECAT, Inc. Portland, Oregon

Kuo-Chun Chang Department of Civil Engineering National Taiwan University Taiwan, China

Wai-Fah Chen University of Hawaii Honolulu, Hawaii

J. Daniel Dolan Brooks Forest Product Research Center Department of Wood Science and Forest Products Virginia Polytechnic Institute and State University Blacksburg, Virginia


Ronald T. Eguchi

Ronald O. Hamburger Simpson Gumpertz & Heger, Inc. San Francisco, California

Mahmoud Khater ABS Consulting Oakland, California

Richard E. Klingner Department of Civil Engineering The University of Texas Austin, Texas

Howard Kunreuther Wharton School University of Pennsylvania Philadelphia, Pennsylvania

David L. McCormick ABS Consulting Oakland, California

Susumu Iai Port and Airport Research Institute Yokosuka, Japan

Hirokazu Iemura Graduate School of Civil Engineering Department of Civil Engineering Systems Kyoto University Kyoto, Japan

Gayle S. Johnson Han-Padron Associates Oakland, California

Y. L. Mo Department of Civil and Environmental Engineering University of Houston Houston, Texas

Niaz A. Nazir DeSimone Consulting Engineers San Francisco, California

Michael J. O’Rourke Department of Civil Engineering Rensselaer Polytechnic Institute Troy, New York

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Keith A. Porter

Hope A. Seligson

Yeong-Bin Yang

Civil Engineering Department California Institute of Technology Pasadena, California

ABS Consulting Irvine, California

Department of Civil Engineering National Taiwan University Taiwan, China

Mulyo Harris Pradono Structural Dynamics Laboratory Department of Civil Engineering Systems Kyoto University Kyoto, Japan

Richard Roth, Jr. Consulting Casualty Actuary Huntington Beach, California

Charles Scawthorn Consulting Engineer Berkeley, California

Anschel J. Schiff Stanford University Stanford, California


Guna Selvaduray Materials Engineering Department San Jose State University San Jose, California

Kimberly I. Shoaf School of Public Health University of California at Los Angeles Los Angeles, California

Costas Synolakis Department of Civil Engineering University of Southern California Los Angeles, California

Paul C. Thenhaus ABS Consulting Evergreen, Colorado

Jong-Dar Yau Department of Architecture and Building Technology Tamkang University Taiwan, China

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Contents

SECTION I

1

Earthquakes: A Historical Perspective 1.1 1.2

2

Jorma K. Arros Introduction Single-Degree-of-Freedom System Multidegree-of-Freedom Systems

SECTION II

5

Charles Scawthorn

Introduction Overview of Earthquake Risk Identifying the Assets at Risk Earthquake Hazard Earthquake Damage and Loss Mitigation Alternatives Earthquake Risk Management Decision-Making Earthquake Risk Management Program Summary

Dynamics of Structures 3.1 3.2 3.3

4

Charles Scawthorn

Introduction Review of Historical Earthquakes

Earthquake Risk Management: An Overview 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9

3

Fundamentals

Geoscience Aspects

Earthquakes: Seismogenesis, Measurement, and Distribution Charles Scawthorn 4.1 4.2 4.3 4.4 4.5

Introduction Causes of Earthquakes and Faulting Measurement of Earthquakes Global Distribution of Earthquakes Characterization of Seismicity

Engineering Models of Strong Ground Motion 5.1 5.2

Introduction The Attenuation Relation


Kenneth W. Campbell

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5.3 5.4 5.5 5.6 5.7

Model Parameters Statistical Methods Theoretical Methods Engineering Models Engineering Evaluation

6

Simulation Modeling of Strong Ground Motion

7

Geotechnical and Foundation Aspects Horst G. Brandes

8

Seismic Hazard Analysis

6.1 6.2 6.3 6.4 6.5 6.6

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8

8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 8.13 8.14 8.15 8.16 8.17 8.18

Mustafa Erdik and Eser Durukal Introduction Earthquake Source Models Time Domain Characteristics of Strong Ground Motion Frequency Domain Characteristics of Strong Ground Motion Radiation Pattern and Directivity Simulation of Strong Ground Motion

Introduction Seismic Hazards Strong Ground Motion Dynamic Soil Behavior Liquefaction Seismic Analysis of Slopes and Dams Earthquake-Resistant Design of Retaining Walls Soil Remediation Techniques for Mitigation of Seismic Hazards Paul C. Thenhaus and Kenneth W. Campbell Introduction Probabilistic Seismic Hazard Methodology Constituent Models of the Probabilistic Seismic Hazard Methodology Definition of Seismic Sources Earthquake Frequency Assessments Maximum Magnitude Assessments Ground Motion Attenuation Relationships Accounting for Uncertainties Typical Engineering Products of PSHA PSHA Disaggregation PSHA Case Study The Owen Fracture Zone–Murray Ridge Complex Makran Subduction Zone Southwestern India and Southern Pakistan Southeastern Arabian Peninsula and Northern Arabian Sea Ground Motion Models Soil Amplification Factors Results


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8.19 Conclusions 8.20 PSHA Computer Codes

9

10

Tsunami and Seiche 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9

Costas Synolakis Introduction Tsunamis vs. Wind Waves Tectonic Tsunami Sources Initial Waves Generated by Submarine Landslides Exact Solutions of the Shallow-Water (SW) Equations Numerical Solutions for Calculating Tsunami Inundation Harbor and Basin Oscillations Tsunami Forces Producing Inundation Maps

Soil–Structure Interaction 10.1 10.2 10.3 10.4 10.5

James J. Johnson Soil–Structure Interaction: Statement of the Problem Specification of the Free-Field Ground Motion Modeling of the Soil Soil–Structure Interaction Analysis Soil–Structure Interaction Response

SECTION III

11

Structural Aspects

Building Code Provisions for Seismic Resistance 11.1 11.2 11.3 11.4

Ronald O. Hamburger

Introduction Historical Development 2000 NEHRP Recommended Provisions Performance-Based Design Codes

12

Seismic Design of Steel Structures

13

Reinforced Concrete Structures

Ronald O. Hamburger and Niaz A. Nazir 12.1 Introduction 12.2 Historic Development and Performance of Steel Structures 12.3 Steel Making and Steel Material 12.4 Structural Systems 12.5 Unbraced Frames Appendix A: Design Procedure for a Typical Reduced Beam Section-Type Connection

13.1 Introduction 13.2 Basic Concepts


Y. L. Mo

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13.3

14

Seismic Behavior 13.4 Analytical Models 13.5 Seismic Design 13.6 Seismic Retrofit

Precast and Tilt-Up Buildings 14.1 14.2 14.3 14.4 14.5

15

Wood Structures 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8

16

J. Daniel Dolan Introduction Wood As a Material Seismic Performance of Wood Buildings Design Considerations Resistance Determination Diaphragms Shear Walls Connections

Seismic Behavior, Design, and Retrofitting of Masonry 16.1 16.2 16.3 16.4 16.5 16.6 16.7

17

Charles Scawthorn and David L. McCormick Introduction Precast and Tilt-Up Buildings Performance of Precast and Tilt-Up Buildings in Earthquakes Code Provisions for Precast and Tilt-Up Buildings Seismic Evaluation and Rehabilitation of Tilt-Up Buildings

Richard E. Klingner Introduction Masonry in the United States Performance of Masonry in U.S. Earthquakes Fundamental Basis for Seismic Design of Masonry in the United States Masonry Design Codes Used in the United States Analysis Approaches for Modern U.S. Masonry Seismic Retrofitting of Historical Masonry in the United States

Base Isolation 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9

Yeong-Bin Yang, Kuo-Chun Chang, and Jong-Dar Yau Introduction Philosophy behind Seismic Isolation Systems Basic Requirements of Seismic Isolation Systems Design Criteria for Isolation Devices Design of High Damping Rubber Bearings Design of Lead Rubber Bearings Design of Friction Pendulum Systems Design Examples Concluding Remarks


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18

Bridges 18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8

19

Structural Control 19.1 19.2 19.3 19.4 19.5

20

Hirokazu Iemura and Mulyo Harris Pradono Introduction Structural Control Concepts Structural Control Hardware and Software Examples of the Application of Semiactive Control Concluding Remarks

Equipment and Systems 20.1 20.2 20.3 20.4 20.5 20.6 20.7

21

Lian Duan and Wai-Fah Chen Introduction Earthquake Damages to Bridges Seismic Design Philosophies Seismic Conceptual Design Seismic Performance Criteria Seismic Design Approaches Seismic Analysis and Modeling Seismic Detailing Requirements

Gayle S. Johnson Introduction Importance of Equipment Seismic Functionality Historical Performance Design Practices Code Provisions Assessment of Existing Facilities Nonstructural Damage

Seismic Vulnerability 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8

Keith A. Porter Introduction Method 1: Statistical Approach Method 2: Expert Opinion Analytical Methods: General Validation of Vulnerability Functions Catalog of Vulnerability Functions Uses of Vulnerability Functions Closing Remarks

SECTION IV

22

Infrastructure Aspects

Lifeline Seismic Risk

Ronald T. Eguchi 22.1 Introduction 22.2 Brief History of Lifeline Earthquake Engineering in the United States


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22.3 22.4 22.5 22.6 22.7

23

Buried Pipelines 23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.8 23.9 23.10

24

Donald B. Ballantyne Introduction Performance Objectives Analysis Overview Hazards Pipe Vulnerability and Damage Algorithms System Component Vulnerability System Assessment Mitigation Alternatives Summary and Conclusions

Electrical Power Systems 25.1 25.2 25.3 25.4 25.5 25.6 25.7 25.8 25.9

26

Michael J. O’Rourke Introduction Pipeline Performance in Past Earthquakes PGD Hazard Quantification Wave Propagation Hazard Quantification Pipe Failure Modes and Failure Criterion Pipeline Response to Faulting Pipeline Response to Longitudinal PGD Pipeline Response to Transverse PGD Pipeline Response to Wave Propagation Countermeasures to Mitigate Seismic Damage

Water and Wastewater Systems 24.1 24.2 24.3 24.4 24.5 24.6 24.7 24.8 24.9

25

Nonlinearity of Earthquakes Indirect Economic Losses Cost-Effective Mitigation Strategies Federal and Industry Lifeline Initiatives Lifeline Seismic Risk

Anschel J. Schiff Introduction Historical Response of Electrical Power Systems to Earthquakes Code Provision, Standards and Guidelines for Electrical Systems Earthquake Preparedness Earthquake Hazard and System Vulnerability Evaluation Earthquake Preparedness — Disaster-Response Planning Earthquake Preparedness — Earthquake Mitigation Earthquake Preparedness — Mitigation Closing Remarks

Dams and Appurtenant Facilities 26.1 Introduction 26.2 Dams and Earthquakes


Gilles J. Bureau

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26.3 26.4 26.5 26.6 26.7

27

Seismic Vulnerability of Existing Dams Seismic Evaluation of Dams Seismic Upgrade of Existing Dams Seismic Design of New Dams Seismic Instrumentation of Dams

Port Structures 27.1 27.2 27.3 27.4 27.5 27.6 27.7

Susumu Iai Introduction Seismic Response of Port Structures Current Seismic Provisions for Port Structures Seismic Performance-Based Design Seismic Performance Evaluation and Analysis Methods for Analysis of Retaining/Earth Structures Analysis Methods for Open Pile/Frame Structures

SECTION V

28

Human Impacts of Earthquakes 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8

29

Hope A. Seligson and Kimberley I. Shoaf Introduction Casualties in Historic Earthquakes A Standardized Earthquake Injury Classification Scheme Casualty Estimation Methodology Casualty Mitigation and Prevention Public Health Impacts Shelter Requirements Closing Remarks

Fire Following Earthquakes 29.1 29.2 29.3 29.4 29.5

30

Special Topics

Charles Scawthorn Introduction Fires following Selected Earthquakes Analysis Mitigation Conclusion

Hazardous Materials: Earthquake-Caused Incidents and Mitigation Approaches Guna Selvaduray 30.1 30.2 30.3 30.4 30.5

Introduction and Significance of Earthquake-Caused Hazardous Materials Incidents The Loma Prieta Earthquake The Northridge Earthquake The Hanshin-Awaji Earthquake Earthquake-Caused HAZMAT Incidents at Educational Institutions and Laboratories


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30.6 30.7 30.8 30.9 30.10

31

Loss Estimation 31.1 31.2 31.3 31.4 31.5 31.6 31.7 31.8 31.9

32

Damage and Corrective Actions at Japanese Petroleum Facilities Lessons Learned Mitigation Approaches Problem Areas That Must Be Addressed Conclusions Mahmoud Khater, Charles Scawthorn and James J. Johnson Introduction and Overview Why Do We Need Loss Estimation? History of Loss Estimation Loss Modeling The Hazard Module Seismic Vulnerability Models Damage and Loss Estimation HAZUS® Earthquake Loss Estimation Software Applications of Loss Estimation

Insurance and Financial Risk Transfer

Charles Scawthorn, Howard Kunreuther,

and Richard Roth, Jr. 32.1 Introduction 32.2 Insurance and the Insurance Industry 32.3 Earthquake Insurance 32.4 Earthquake Insurance Risk Assessment 32.5 Government Earthquake Insurance Pools 32.6 Alternative Risk Transfer 32.7 Summary

33

Emergency Planning

34

Developing an Earthquake Mitigation Program

Charles Scawthorn 33.1 Introduction 33.2 Planning for Emergencies 33.3 Writing the Emergency Plan 33.4 The Emergency Operations Center (EOC) 33.5 Training and Maintenance of the Emergency Plan 33.6 Summary: Developing an Emergency Plan Appendix A Appendix B

34.1 34.2 34.3 34.4 34.5

Introduction Overview of an Earthquake Mitigation Program Phase 0: Pre-Program Activities Phase 1: Assessing the Problem Phase 2: Developing the Program


Charles Scawthorn

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34.6 Phase 3: Implementing the Program 34.7 Maintaining the Program


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Fundamentals


I

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1

Earthquakes: A Historical Perspective 1.1

Introduction Global Earthquake Impacts

1.2

Review of Historical Earthquakes Pre-Twentieth Century Events · Early Twentieth Century Events · Mid-Century Events · First Turning Point · Second Turning Point

Charles Scawthorn Consulting Engineer Berkeley, CA

Defining Terms References Further Reading

Let us look at the facts. – Terence Adelphoe, l. 796

1.1 Introduction Earthquakes are a major problem for mankind, killing thousands each year. A review of Table 1.1 shows, for example, that an average of almost 17,000 persons per year were killed in the twentieth century.1 Earthquakes are also multifaceted, sometimes causing death and destruction in a wide variety of ways, from building collapse to conflagrations, tsunamis, and landslides. This chapter therefore reviews selected earthquakes and the damage they have caused, to inculcate in the reader the magnitude and complexity of the problem earthquakes pose for mankind. To do this, we first review in this introduction some basic statistics on damage. Section 1.2, the heart of this chapter, then reviews selected earthquakes, chosen for their particular damaging effects, or because the earthquake led to a significant advance in mitigation. This review is focused. It is relatively brief on earlier earthquakes, which are mentioned largely for historical interest or because you should be aware of them as portents for future events; however, the review is lengthier on selected recent events, especially U.S. events, because these provide the best record on the performance of modern structures. Table 1.2 shows selected U.S. earthquakes. Based on this review, the next section then extracts important lessons, following which we conclude with a brief history of the response to earthquakes.

1

The average is still more than 10,000 if the single largest event (Tangshan, 1976) is omitted.


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TABLE 1.1

Selected Earthquakes Since 1900 (Fatalities Greater than 1,000)a

Year

Day-Month

Location

Latitude

Longitude

Deaths

M

1902

19-Apr 16-Dec 19-Apr 28-Apr 04-Apr 08-Sep 31-Jan 16-Mar 18-Apr 17-Aug 14-Jan 21-Oct 28-Dec 23-Jan 09-Aug 13-Jan 21-Jan 30-Jul 13-Feb 16-Dec

Guatemala Turkestan Turkey Turkey India, Kangra Italy, Calabria Colombia Taiwan, Kagi San Francisco, CA Chile, Santiago Jamaica, Kingston Central Asia Italy, Messina Iran Turkey, Marmara Sea Italy, Avezzano Indonesia, Bali China China, Canton China, Gansu

14N 40.8N 39.1N 39.1N 33.0N 39.4N 1N 23.6N 38N 33S 18.2N 38N 38N 33.4N 40.5N 42N 8.0S 28.0N 23.5N 35.8N

91W 72.6E 42.4E 42.5E 76.0E 16.4E 81.5W 120.5E 123W 72W 76.7W 69E 15.5E 49.1E 27E 13.5E 115.4E 104.0E 117.0E 105.7E

2,000 4,500 1,700 2,200 19,000 2,500 1,000 1,300 2,000+ 20,000 1,600 12,000 70,000 5,500 1,950 29,980 15,000 1,800 10,000 200,000

7.5 6.4

24-Mar 25-May 01-Sep 16-Mar 07-Mar 22-May 01-May 06-May 23-Jul 31-Mar 25-Dec 02-Mar 25-Aug 15-Jan 20-Apr 30-May 16-Jul 25-Jan 26-Dec 10-Nov 26-Nov 20-Dec

China Iran Japan, Kanto China, Yunnan Japan, Tango China, nr Xining Iran Iran Italy Nicaragua China, Gansu Japan, Sanriku China India, Bihar-Nepal Formosa Pakistan, Quetta Taiwan Chile, Chillan Turkey, Erzincan Romania Turkey Turkey, Erbaa

31.3N 35.3N 35.0N 25.5N 35.8N 36.8N 38N 38.0N 41.1N 13.2N 39.7N 39.0N 32.0N 26.6N 24.0N 29.6N 24.4N 36.2S 39.6N 45.8N 40.5N 40.9N

100.8E 59.2E 139.5E 100.3E 134.8E 102.8E 58E 44.5E 15.4E 85.7W 97.0E 143.0E 103.7E 86.8E 121.0E 66.5E 120.7E 72.2W 38E 26.8E 34.0E 36.5E

5,000 2,200 143,000 5,000 3,020 200,000 3,300 2,500 1,430 2,400 70,000 2,990 10,000 10,700 3,280 30,000 2,700 28,000 30,000 1,000 4,000 3,000

7.3 5.7 8.3 7.1 7.9 8.3 7.4 7.2 6.5 5.6 7.6 8.9 7.4 8.4 7.1 7.5 6.5 8.3 8 7.3 7.6 7.3

10-Sep 26-Nov 15-Jan

Japan, Tottori Turkey Argentina, San Juan

35.6N 41.0N 31.6S

134.2E 33.7E 68.5W

1,190 4,000 5,000

7.4 7.6 7.8

01-Feb 07-Dec 12-Jan 27-Nov 31-May 10-Nov

Turkey Japan, Tonankai Japan, Mikawa Iran Turkey Peru, Ancash

41.4N 33.7N 34.8N 25.0N 39.5N 8.3S

32.7E 136.2E 137.0E 60.5E 41.5E 77.8W

2,800 1,000 1,900 4,000 1,300 1,400

7.4 8.3 7.1 8.2 6 7.3

20-Dec

Japan, Tonankai

32.5N

134.5E

1,330

8.4

1903 1905 1906

1907 1908 1909 1912 1915 1917 1918 1920 1923

1925 1927 1929 1930 1931 1932 1933 1934 1935

1939 1940 1942

1943 1944

1945 1946


6.3 8.6 7.9 8.9 7.1 8.3 8.6 6.5 8.1 7.5 7.3 7.8 7.5 6.5 7.3 8.6

Comments/Damage ($ millions)

Conflagration Conflagration Conflagration Deaths possibly 100,000

Major fractures, landslides

$2800, conflagration

Large fractures

Deaths possibly 60,000 $100

Some reports of 1,000 killed

Deaths possibly 8,000 Deaths possibly 5,000

Landslides, great destruction

0068_C01_fm Page 3 Tuesday, July 30, 2002 8:18 AM

TABLE 1.1 (CONTINUED) Selected Earthquakes Since 1900 (Fatalities Greater than 1,000)a Year

Day-Month

1948

28-Jun 05-Oct 05-Aug 15-Aug

1949 1950 1954 1957

1960 1962 1963 1966 1968 1969 1970

1972 1974 1975 1976

1977 1978 1980 1981 1982 1983 1985 1986 1987 1988 1990 1991 1992 1993 1995 1997

Location

Latitude

Longitude

Deaths

M

Japan, Fukui Turkmenistan Ecuador, Ambato India, Assam; Tibet

36.1N 38.0N 1.2S 28.7N

136.2E 58.3E 78.5E 96.6E

5,390 110,000 6,000 1,530

7.3 7.3 6.8 8.7

09-Sep 27-Jun 02-Jul 13-Dec 29-Feb 22-May 01-Sep 26-Jul

Algeria, Orleansvl. USSR (Russia) Iran Iran Morocco, Agadir Chile Iran, Qazvin Yugoslavia, Skopje

36N 56.3N 36.2N 34.4N 30N 39.5S 35.6N 42.1N

1.6E 116.5E 52.7E 47.6E 9W 74.5W 49.9E 21.4E

1,250 1,200 1,200 1,130 10,000 4,000 12,230 1,100

6.8 7.4 7.3 5.9 9.5 7.3 6

19-Aug 31-Aug 25-Jul 04-Jan 28-Mar 31-May 10-Apr 23-Dec 10-May 28-Dec 04-Feb 06-Sep 04-Feb 06-May 25-Jun 27-Jul

Turkey, Varto Iran Eastern China Yunnan, China Turkey, Gediz Peru Iran, southern Nicaragua China Pakistan China Turkey Guatemala Italy, northeastern New Guinea China, Tangshan

39.2N 34.0N 21.6N 24.1N 39.2N 9.2S 28.4N 12.4N 28.2N 35.0N 40.6N 38.5N 15.3N 46.4N 4.6S 39.6N

41.7E 59.0E 111.9E 102.5E 29.5E 78.8W 52.8E 86.1W 104.0E 72.8E 122.5E 40.7E 89.1W 13.3E 140.1E 118.0E

2,520 12,000 3,000 10,000 1,100 66,000 5,054 5,000 20,000 5,300 10,000 2,300 23,000 1,000 422 255,000

7.1 7.3 5.9 7.5 7.3 7.8 7.1 6.2 6.8 6.2 7.4 6.7 7.5 6.5 7.1 8

16-Aug 24-Nov 04-Mar 16-Sep 10-Oct 23-Nov 11-Jun 28-Jul 13-Dec 30-Oct 19-Sep 10-Oct 06-Mar 20-Aug 07-Dec 20-Jun 16-Jul 19-Oct 12-Dec

Philippines Iran-USSR border Romania Iran, Tabas Algeria, El Asnam Italy, southern Iran, southern Iran, southern W. Arabian Peninsula Turkey Mexico, Michoacan El Salvador Colombia-Ecuador Nepal-India border Armenia, Spitak Iran, western Philippines, Luzon India, northern Indonesia, Flores

6.3N 39.1N 45.8N 33.2N 36.1N 40.9N 29.9N 30.0N 14.7N 40.3N 18.2N 13.8N 0.2N 26.8N 41.0N 37.0N 15.7N 30.8N 8.5S

124.0E 44.0E 26.8E 57.4E 1.4E 15.3E 57.7E 57.8E 44.4E 42.2E 102.5W 89.2W 77.8W 86.6E 44.2E 49.4E 121.2E 78.8E 121.9E

8,000 5,000 1,500 15,000 3,500 3,000 3,000 1,500 2,800 1,342 9,500 1,000 1,000 1,450 25,000 40,000 1,621 2,000 2,500

7.9 7.3 7.2 7.8 7.7 7.2 6.9 7.3 6 6.9 8.1 5.5 7 6.6 7 7.7 7.8 7 7.5

29-Sep 16-Jan 27-May 10-May

India, southern Japan, Kobe Sakhalin Island Iran, northern

18.1N 34.6N 52.6N 33.9N

76.5E 135E 142.8E 59.7E

9,748 6,000 1,989 1,560

6.3 6.9 7.5 7.5


Comments/Damage ($ millions) Conflagration Large landslides Great topographical changes

Deaths possibly 15,000 Deaths possibly 5,000 Shallow depth just under city Deaths possibly 20,000

Great rockslide; $500 Managua

$6,000 West Irian Deaths possibly 655,000; $2,000 Mindanao

$11

Deaths possibly 30,000

$16,200 Deaths possibly 50,000 Landslides, subsidence Tsunami wave height 25 m $100,000, conflagration 4,460 injured; 60,000 homeless


1-4

Earthquake Engineering Handbook

TABLE 1.1 (CONTINUED) Selected Earthquakes Since 1900 (Fatalities Greater than 1,000)a Year

Day-Month

1998

04-Feb 30-May 17-Jul 25-Jan 17-Aug 20-Sep 26-Jan

1999

2001

Location

Latitude

Longitude

Deaths

M

Afghanistan Afghanistan Papua New Guinea Colombia Turkey Taiwan

37.1N 37.1N 2.96S 4.46N 40.7N 23.7N

70.1E 70.1E 141.9E 75.82W 30.0E 121.0E

2,323 4,000 2,183 1,185 17,118 2,297

6.1 6.9 7.1 6.3 7.4 7.6

India, Bhuj

23.3 N

70.3 E

19,988

7.7

Total Events = 108

Comments/Damage ($ millions) Also Tajikistan Also Tajikistan Tsunami 50,000 injured; $7,000 8,700 injured; 600,000 homeless 166,812 injured; 600,000 homeless

Total Deaths = 1,762,802

a

Magnitude scale varies. Source: National Earthquake Information Center, Golden, CO, http://neic.usgs.gov/neis/eqlists/eqsmajr.html.

TABLE 1.2

Selected U.S. Earthquakesa

Year

Month

Day

1755 1774 1791

11 2 5

18 21 16

1811 1812

12 1 2 10

16 23 7 5

36N 36.6N 36.6N

6 6 1 10 4 10 3 9 2 4 5 5 9 4 10 6 11 3 12 10 5 9 4 8 7 12 3 7 8 8 3 4 2 3

10 0 9 8 3 21 26 1 24 19 16 31 4 18 3 29 4 11 31 19 19 5 13 21 21 16 9 10 18 30 28 29 9 28

38N 37.5N 35N 37N 19N 37.5N 36.5N 32.9N 31.5N 38.5N 14N

122W 123W 119W 122W 156W 122W 118W 80W 117W 123W 143W

60N 38N 40.5N 34.3N 34.5N 33.6N 31.8N 46.6N 32.7N 44.7N 47.1N 19.7N 35N 39.3N 51.3N 58.6N 44.8N 41.8N 61N 47.4N 34.4N 42.1N

142W 123W 118W 120W 121W 118W 116W 112W 116W 74.7W 123W 156W 119W 118W 176W 137W 111W 112W 148W 122W 118W 113W

1817 1836 1838 1857 1865 1868 1872 1886 1892

1897 1899 1906 1915 1925 1927 1933 1934 1935 1940 1944 1949 1951 1952 1954 1957 1958 1959 1962 1964 1965 1971 1975

Latitude

Longitude

M

MMI

Fatalities

Damage US $ (millions)

8 7 8


90W 89.6W 89.6W

8.6 8.4 8.7

8.3

6.8 8.5 7.7

5.8 8.3 8.3 7.8 6.2 7.5 6.3 7.1 6.2 7.1 5.6 7 6.9 7.7 7 8.6 7.9 7.7 5.8 8.3 6.5 6.7 6.2

12 12 8 10 10 7 9 10 10 10 9 10 9

81 3 50 60

5

2,000

400

13

8

115

40

10

2 9

8

8

19 6 2 25

11 10

13

60

8 11

9 10

3 5

7 11 8

131 7 65

2 540 13 553 1

Locale Massachusetts, Nr Cape Ann Eastern Virginia (MMI from Sta) Connecticut, E. Haddam (MMI from Sta) Missouri, New Madrid Missouri, New Madrid Missouri, New Madrid Massachusetts, Woburn (MMI from Sta) California California California, Central California, San Jose, Santa Cruz Hawaii California, Hayward California, Owens Valley South Carolina, Charleston California, San Diego County California, Vacaville, Winters Guam, Agana Virignia, Giles County (Mb from Sta) Alaska, Cape Yakataga California, San Francisco (fire) Nevada, Pleasant Valley California, Santa Barbara California, Lompoc California, Long Beach California, Baja, Imperial Valley Montana, Helena California, southeast of El Centro New York, Massena Washington, Olympia Hawaii California, Kern County Nevada, Dixie Valley Alaska Alaska, Lituyabay (landslide) Montana, Hebgen Lake Utah Alaska Washington, Seattle California, San Fernando Idaho, Pocatello Valley


1-5

Earthquakes: A Historical Perspective

TABLE 1.2 (CONTINUED) Selected U.S. Earthquakesa

Year

Month

Day

Latitude

1975

8 11 1 5 7 11 5 10 11 4 7 10 11 6 10 2

1 29 24 25 27 8 2 28 16 24 8 1 24 26 18 28

39.4N 19.3N 37.8N 37.6N 38.2N 41.2N 36.2N 43.9N 19.5N 37.3N 34N 34.1N 33.2N 19.4N 37.1N 34.1N

122W 155W 122W 119W 83.9W 124W 120W 114W 155W 122W 117W 118W 116W 155W 122W 118W

6.1 7.2 5.9 6.4 5.2 7 6.5 7.3 6.6 6.2 6.1 6 6.3 6.1 7.1 5.5

4 4 6 6 6 3 9 1 1 2 10

23 25 28 28 29 25 21 16 17 3 6

34N 40.4N 34.2N 34.2N 36.7N 45N 42.3N 40.3N 34.2N 42.8N 65.2N

116W 124W 117W 116W 116W 123W 122W 76W 119W 111W 149W

6.3 7.1 6.7 7.6 5.6 5.6 5.9 4.6 6.8 6 6.4

1980

1983

1984 1986 1987 1989 1990 1992

1993 1994

1995

Longitude

M

MMI

Fatalities

9 7 7

2 1

7 8

5 2

8 7 7 8 6 6 9 7 7 8 8 9 7 7 5 9 7

8 2 62

Damage US $ (millions) 6 4 4 2 1 3 31 13 7 8 5 358

6,000 13 66

3

92

2 57

30,000

Locale California, Oroville Reservoir Hawaii California, Livermore California, Mammoth Lakes Kentucky, Maysville California, northern coast California, central, Coalinga Idaho, Borah Peak Hawaii, Kapapala California, Morgan Hill California, Palm Springs California, Whittier California, Superstition Hills Hawaii California, Loma Prieta California, southern, Claremont, Covina California, Joshua Tree California, Humboldt, Ferndale California, Big Bear California, Landers, Yucca Valley California-Nevada border T.S. Washington-Oregon Oregon, Klamath Falls Pennsylvania (felt Canada) California, Northridge Wyoming, Afton Alaska (oil pipeline damaged)

a

Magnitude scale varies. Source: National Earthquake Information Center (1996). Database of Significant Earthquakes Contained in Seismicity Catalogs, Golden, CO.

1.1.1 Global Earthquake Impacts Globally, earthquakes have caused massive death and destruction up to the present day. Table 1.1 provides a list of selected twentieth century earthquakes with fatalities of approximately 1,000 or more, and Table 1.3 provides a list of earthquakes with fatalities of approximately 50,000 or more prior to the twentieth century. All the earthquakes are in the Trans-Alpide belt or the circum-Pacific Ring of Fire (Figure 1.1), and the great loss of life is almost invariably due to low-strength masonry buildings and dwellings. Exceptions to this rule are few in number but include the 1923 Kanto (Japan) earthquake, where most of the approximately 140,000 fatalities were due to fire; the 1970 Peru earthquake, where large landslides destroyed whole towns; the 1988 Armenian event, where 25,000 were killed in Spitak and Leninakan, mostly due to poor quality, precast construction; and the 1999 Marmara (Turkey) earthquakes, where 17,000 were killed in a rapidly urbanizing area where many mid-rise, soft story, reinforced concrete buildings collapsed, due largely to inadequate code enforcement [Scawthorn, 2000]. The absolute trend for earthquake fatalities is not decreasing, as indicated in Figure 1.2, although if population increase is taken into account, some relative decrease is occurring. Economic and insured losses for all sources, as indicated in Figure 1.3, are increasing. The 1995 Kobe (Japan) earthquake, with unprecedented losses of $100 billion,2 may only be a harbinger of even greater losses if an earthquake strikes Tokyo, Los Angeles, San Francisco, or some other large urban region. To understand how these losses occur and how they might be reduced, it is valuable to review some important earthquakes from previous centuries as well as very recent earthquakes. 2 The largest previous loss due to any natural hazard was in the 1994 Northridge earthquake, estimated at about $40 billion.



1-6


TABLE 1.3

Selected Pre-Twentieth Century Earthquakes (Fatalities Greater than 50,000)

Year

Month

Day

Location

Deaths

856 893 1138 1268 1290 1556 1667 1693 1727 1755 1783

12 3 8

22 23 9

Iran, Damghan Iran, Ardabil Syria, Aleppo Asia Minor, Silicia China, Chihli China, Shansi Caucasia, Shemakha Italy, Sicily Iran, Tabriz Portugal, Lisbon Italy, Calabria

200,000 150,000 230,000 60,000 100,000 830,000 80,000 60,000 77,000 70,000 50,000

9 1 11 1 11 11 2

23 11 18 1 4

M

Comments

8.7

Great tsunami, fires

Source: National Earthquake Information Center, Golden, CO, http://neic.usgs.gov/neis/eqlists/eqsmosde.html.

Earthquakes of 20th Century Number of Deaths 100,000 - 255,000

(5)

50,000 - 100,000

(3)

20,000 - 50,000

(9)

10,000 - 20,000 (14) 5,000 - 10,000 (14) 2,000 - 5,000 (31) 1,000 - 2,000 (32) 1,000 or less (1)

FIGURE 1.1 Selected earthquakes since 1900 (fatalities greater than 1000).

1.2 Review of Historical Earthquakes This section presents a review of selected historical earthquakes. The review is divided into several parts: pre-twentieth century, early and mid-twentieth century, and two periods termed first and second turning points, respectively. Magnitudes (M, see Chapter 4) are indicated but, especially for the earlier events, are necessarily estimated rather than measured, and are therefore quite approximate; later events are indicated on the moment magnitude scale (Mw) where possible. Similarly, seismic intensity maps are provided when available, in most cases using the Modified Mercalli Intensity scale (MMI, see Chapter 4). © 2003 by CRC Press LLC


1-7


10,000,000 1,000,000 100,000 10,000 1,000 100 10 1

1

2

3

4

5

6

7

8

9

10

FIGURE 1.2 Twentieth century global earthquake fatalities, by decade.

US$ 160bn 80 70 60 50 40 30 20 10 0 1950

1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

Economic losses (2000 values) of which insured losses (2000 values) Trend of economic losses Trend of insured losses (Amounts in US$ bn)

FIGURE 1.3 Trend of worldwide economic and insured losses. (From Munich Reinsurance.)

1.2.1 Pre-Twentieth Century Events As Table 1.3 indicates, truly catastrophic earthquakes have occurred for many centuries. Herein we review very briefly only a few of these events, selected for their historical importance. 1.2.1.1 1755: November 1, Lisbon, Portugal (M9) The earthquake began at 9:30 on November 1, 1755, and was centered in the Atlantic Ocean, about 200 km WSW of Cape St. Vincent.3 Lisbon, the Portuguese capital, was the largest and most important of the cities damaged; however, severe shaking also was felt in France, Switzerland, and Northern Italy, and in North Africa shaking was felt with heavy loss of life in Fez and Mequinez. A devastating fire following the earthquake raged for five days and destroyed a large part of Lisbon. 3

The following discussions are largely drawn from Kozak and James [n.d.].


0068_C01_fm Page 8 Tuesday, August 13, 2002 10:59 AM

1-8


FIGURE 1.4 Lisbon, Portugal, ruins of Praca de Patriarcal (Patriarchal Square) (copper engraving, Paris, 1757), Le Bas series, Bibliothèque Nationale. Colleção de algunas ruinas de Lisboa, 1755. Drawings executed by Messrs Paris et Pedegache. Paris: Jacques-Phillippe Le Bas, 1757. (From the Kozak Collection of Images of Historical Earthquakes, National Information Service for Earthquake Engineering, University of California, Berkeley. With permission.)

A very strong tsunami caused heavy destruction along the coasts of Portugal, southwestern Spain, and western Morocco. About 30 min after the quake, a large wave swamped the area near Bugie Tower on the mouth of the Tagus. The area between Junqueria and Alcantara in the western part of the city was the most heavily damaged by a total of three waves with maximum height estimated at 6 m, each dragging people and debris out to sea and leaving exposed large stretches of the river bottom. In Setubal, 30 km south of Lisbon, the water reached the first floor of buildings. The destruction was greatest in Algarve, southern Portugal, where the tsunami dismantled some coastal fortresses and, in the lower levels, razed houses. In some places, the waves crested at more than 30 m. The tsunami reached, with less intensity, the coasts of France, Great Britain, Ireland, Belgium, and Holland. In Madeira and in the Azores, damage was extensive and many ships were in danger of being wrecked. The tsunami crossed the Atlantic Ocean, reaching the Antilles in the afternoon. Reports from Antigua, Martinique, and Barbados note that the sea first rose more than a meter, followed by large waves. The oscillation of suspended objects at great distances from the epicenter indicates an enormous area of perceptibility. The observation of seiches as far away as Finland suggests a magnitude approaching 9.0. Between the earthquake and the fires and tsunami that followed (which were probably more damaging than the actual earthquake), approximately 10,000 to 15,000 people died (population: 275,000) [Kendrick, 1956]. As Kozak and James [n.d.] note, most depictions of damaged Lisbon are fanciful; Figure 1.4, however, is an accurate depiction of a portion of central Lisbon following the earthquake. The 1755 Lisbon earthquake was felt across broad parts of Europe. It occurred at the height of the Enlightenment and on the eve of the Industrial Revolution. Its massive death and destruction of one of the largest and most beautiful cities in Europe shook thinkers such as Voltaire, whose inherent optimism was deeply shaken by the event, as can be seen in his poem, Poeme sur le desastre de Lisbonne: Did Lisbon, which is no more, have more vices Than London and Paris immersed in their pleasures? Lisbon is destroyed, and they dance in Paris! Rousseau disagreed with Voltaire’s change in philosophy, taking a more pragmatic view: …it was not Nature that collected twenty thousand houses on the site … if the inhabitants of this big city had been more equally dispersed and more lightly housed, the damage would have been much less. [Quoted in Goldberg, 1989] From a scientific viewpoint, changes were made in building construction in Lisbon following the earthquake, such as the gaiola (an internal wooden cage for masonry buildings), as well as in the planning of reconstructed Lisbon; however, while the gaiola survived to the 1920s in Portugal, it was little publicized and not utilized elsewhere [Tobriner, 1984]. Together with the 1783 Calabrian earthquakes, the Lisbon earthquake strengthened nascent European efforts at construction of seismological instruments [Dewey and Byerly, 1969]. 1.2.1.2 1755: November 18, Cape Ann, MA (M7) The heaviest damage due to this earthquake occurred in the region around Cape Ann and Boston. At Boston, much of the damage was confined to an area of infilled land near the wharfs. There, about 100 © 2003 by CRC Press LLC



1-9

chimneys were leveled with the roofs of houses, and many others (1200 to 1500) were shattered and partly thrown down. Stone fences were thrown down throughout the countryside, particularly on a line extending from Boston to Montreal. New springs formed, and old springs dried up. Water and fine sand issued from ground cracks at Pembroke. This earthquake was felt from Lake George, NY, to a point at sea 200 miles east of Cape Ann, and from Chesapeake Bay to the Annapolis River, Nova Scotia, about 300,000 mi2 [Stover and Coffman, 1993]. Due to the proximity in dates, and observations of a tsunami in the eastern Atlantic caused by the Lisbon earthquake, effects at distance between the two events are sometimes confused. 1.2.1.3 1811–1812: New Madrid, MO, Sequence The 1811–1812 sequence of earthquakes centered around New Madrid, on the Mississippi River in the central United States, south of St. Louis and north of Memphis, are of note due to their being some of the largest magnitude earthquakes ever recorded in North America, and definitely the largest earthquakes east of the Rockies. Between 1811 and 1812, four catastrophic earthquakes, with magnitude estimates greater than 7.0, occurred during a 3-month period. Nuttli [1973] determined a 7.2 mb body-wave magnitude for the 2:15 a.m., December 16, 1811 event; and Street [1982] used the spatial attenuation of intensities for all four events to show magnitudes of 7.0 for the 8:15 a.m., December 16, 1811 event; 7.1 for the January 23, 1812 event; and 7.3 for the February 7, 1812 event. Hundreds of aftershocks followed over a period of several years. The total energy released by the principal shocks and their larger-magnitude aftershocks is estimated to be equivalent to that of an mb = 7.5 (or MS = 8.0) earthquake, approximately equivalent to the 1906 San Francisco earthquake. The largest earthquakes to have occurred since then were on January 4, 1843 and October 31, 1895, with magnitude estimates of 6.0 and 6.2, respectively, and considerable uncertainty exists as to the likelihood of large earthquakes in this region. Figure 1.5 shows MMI observations for the December 16, 1811 event, in which it can be seen that extremely violent shaking occurred in the Mississippi Valley, and the event was felt from Connecticut to Illinois to South Carolina. In 1811–1812, however, these areas were quite sparsely populated, with very few significant structures of any kind. If such events were to occur today, considering the enormous development in the central United States, including, for example, the massive navigational improvements constructed over the last 100 years along the Mississippi and tributary rivers, the potential loss of life, damage, and economic disruption would be catastrophic. No comprehensive loss estimates have been performed for a repeat of the 1811–1812 sequence; however, losses have been estimated for impacts to lifelines and ensuing economic impacts [Applied Technology Council, 1991], and for annualized losses to buildings (structures only) [Federal Emergency Management Agency, 2000], from which it can be approximately estimated that a repeat of the 1811–1812 events today would cause economic losses in the range of $50 to $100 billion. Fuller [1912] provides detailed information on topographical and geological effects, and Hopper [1985] provides estimates of intensity if similar events were to occur today. 1.2.1.4 1857: January 9, Fort Tejon, CA (M7) This earthquake occurred on the San Andreas fault, which ruptured from near Parkfield (in the Cholame Valley) almost to Wrightwood (a distance of about 300 km) (Figure 1.6). Horizontal displacement of as much as 9 m was observed on the Carrizo Plain. A comparison of this shock to the San Francisco earthquake, which occurred on the San Andreas fault on April 18, 1906, shows that the fault break in 1906 was longer but that the maximum and average displacements in 1857 were larger. Property loss was heavy in the sparsely populated area, and one person was killed in the collapse of an adobe house at Gorman. Strong shaking lasted from 1 to 3 min. Instances of seiching, fissuring, sandblows, and hydrologic changes were reported from Sacramento to the Colorado River delta. Sandblows occurred at Santa Barbara and in the flood plain of the Santa Clara River. The shock was felt from Marysville south to San Diego and east to Las Vegas, NV. Several slight to moderate foreshocks preceded the main shock by 1 to 9 h. Many aftershocks occurred, and two (January 9 and 16) were large enough to have been widely felt [Stover and Coffman, 1993]. © 2003 by CRC Press LLC


1-10


F

F

F NF NF NF NF

NF 4

5

5

F

F

5

NF

6

4

7−8

6 5−6

7 6−7 8

8

5−6

5 5

6 6 7 7 6−7

6 6

NF

F 5 F NF 6

NF

5 6

5

5

5

7 5

7

NF

5

5

7 6 7 7−8 11 8 11

6

NF

6−7 4 6 7

5 7

5−6

4

4

5−6 F 6−7 6 5−6 5−6

5

6 4 5

6 5−6

F

NF DEC. 16, 1811 (02:15 A.M.) 0

KM

300

FIGURE 1.5 Isoseismal map of the December 16, 1811 earthquake. The arabic numbers give the Modified Mercalli Intensities at each data point. (From Nuttli, O.W. 1979. “Seismicity of the Central United States,” in Geology in the Siting of Nuclear Power Plants, Hatheway, A.W. and McClure, C.R., Eds., Geological Society of America, Rev. Eng. Geol, 4, 67–94. With permission.)

1.2.1.5 1886: Charleston, SC The largest and by far the most destructive earthquake in the southeast United States occurred on August 31, 1886, with epicenter about 15 miles northwest of Charleston, SC (32.9 N, 80.0 W). The first shock was at 21:51, with magnitude of 7.6 [Johnston, 1991], and the second about 8 min later. The earthquake was felt over 2.5 million mi2 (from Cuba to New York, and Bermuda to the Mississippi), equivalent to a © 2003 by CRC Press LLC


1-11


124°

122°

120°

118°

116°

114°

40°

Reno

UTAH

NEVADA Sacramento

38° San Francisco

Monterey

CALIFORNIA Las Vegas

36°

Bakersfield

II-VI

VII-IX

ARIZONA 34° Los Angeles

P A C I F I C San Diego

O C

ATES UNITED ST MEXICO

Blythe

E A N

32° EXPLANATION Epicenter IX Intensity 9

0

100 KILOMETERS

GULF OF CALIFORNIA

FIGURE 1.6 Modified Mercalli Intensity map, 1857 Fort Tejon, CA, earthquake. (From Stover, C.W. and Coffman, J.L. 1993. Seismicity of the United States, 1568–1989 (revised). U.S. Geological Survey Professional Paper 1527, Government Printing Office, Washington, D.C.)

radius of more than 800 mi; the strongly shaken portion extended to 100 mi. Approximately 110 persons lost their lives and 90% of the brick structures in Charleston were damaged [Dutton, 1889]. Damaging secondary effects were fires, ruptured water and sewage lines, damaged wells, flooding from a cracked dam in Langley, SC, and in the highest intensity area bent railroad tracks, throwing one train off the tracks. Dollar damage estimates in 1886 dollars were about $5.5 million. Four decades later, Freeman [1932] made a careful study of the damage, concluding that “taking the city as a whole, the ratio of earthquake damage to sound value was small in Charleston, and probably averaged little if any more than 10%.” The bending of rails and lateral displacement of tracks due to ground displacements were very evident in the epicentral region, though not at Charleston. There were severe bends of the track in places and sudden and sharp depressions of the roadbed. At one place, there was a sharp S-curve. At a number of locations, the effect on culverts and other structures demonstrated strong vertical force in action at the © 2003 by CRC Press LLC


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Jedburg

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FIGURE 1.7 Effects in the epicentral area of the 1886 Charleston, SC, earthquake. (From Algermissen, S.T. 1983. An Introduction to the Seismicity of the United States, Earthquake Engineering Research Institute, Berkeley, CA. With permission.)

time of the earthquake. Figure 1.7 is a map of effects in the epicentral area, while Figure 1.8 shows damage in central Charleston, bent rails due to ground movement, and large sand boils, indicating liquefaction, in the surrounding hinterland. This and the 1755 Cape Ann, MA, earthquakes demonstrate the potential for large, damaging earthquakes in the eastern United States.

1.2.2 Early Twentieth Century Events 1.2.2.1 1906: April 18, San Francisco (Mw 7.9) This earthquake is the most devastating in the history of California, and one of the most important in the history of earthquake engineering. The region of destructive intensity extended over a distance of © 2003 by CRC Press LLC


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FIGURE 1.8 (A) Damage in central Charleston, (B) bent rails due to ground movement, and (C) large sand boils indicating liquefaction. (From Peters, K.E. and Herrmann, R.B., Eds. n.d. First-Hand Observations of the Charleston Earthquake of August 31, 1886 and Other Earthquake Materials, South Carolina Geological Survey Bulletin 41.)

600 km. The total felt area included most of California and parts of western Nevada and southern Oregon (Figure 1.9). This earthquake caused the most lengthy fault rupture observed in the contiguous United States, i.e., from San Juan Bautista to Point Arena, where it passes out to sea, with additional displacement observed farther north at Shelter Cove in Humbolt County, indicating a potential total length of rupture of 430 km. Fault displacements were predominantly right lateral strike-slip, with the largest horizontal displacement — 6.4 m — occurring near Point Reyes Station in Marin County (Figure 1.10). The surface of the ground was torn and heaved into furrow-like ridges. Roads crossing the fault were impassable, and pipelines were broken. On or near the San Andreas fault, some buildings were destroyed but other buildings, close to or even intersected by the fault, sustained nil to only light damage (Figure 1.11). South of San Francisco, the concrete block gravity-arch dam of the Crystal Springs Reservoir (dam only 100 to 200 yards from the fault, reservoir on the fault) was virtually undamaged by the event, and the San Andreas earthen dam, whose abutment was intersected by the fault rupture, was also virtually undamaged, although surrounding structures sustained significant damage or were destroyed [Lawson et al., 1908]. The earthquake and resulting fires caused an estimated 3000 deaths and $524 million in property loss. One pipeline that carried water from San Andreas Lake to San Francisco was broken, shutting off the water supply to the city. However, distorted ground within the city resulted in hundreds of breaks in water mains, which were the actual source of lack of water supply for firefighting (Figure 1.12). Fires that ignited in San Francisco soon after the onset of the earthquake burned for three days because of the lack of water to control them (Figure 1.13). Damage in San Francisco was devastating, with 28,000 buildings destroyed, although 80% of the damage was due to the fire, rather than the shaking (Figure 1.14). Fires also intensified the loss at Fort Bragg and Santa Rosa. Damage was severe at Stanford University, south of San Francisco (Figure 1.15). Although Santa Rosa lies about 30 km from the San Andreas fault, © 2003 by CRC Press LLC


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122°

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FIGURE 1.9 MMI map of 1906 San Francisco earthquake. (From Stover, C.W. and Coffman, J.L. 1993. Seismicity of the United States, 1568–1989 (revised). U.S. Geological Survey Professional Paper 1527, U.S. Government Printing Office, Washington, D.C.)

damage to property was severe and 50 people were killed. The earthquake also was severe in the Los Banos area of the western San Joaquin Valley, where the MMI was IX more than 48 km from the fault zone. The maximum intensity of XI was based on geologic effects, but the highest intensity based on damage was IX. Several foreshocks probably occurred, and many aftershocks were reported, some of which were severe [Stover and Coffman, 1993]. © 2003 by CRC Press LLC



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FIGURE 1.10 Fence about 1 km northwest of Woodville on the E.R. Strain farm. This fence was offset 2.6 m by the main fault. Note the swerve in the fence as it approaches the fault-trace. The total displacement of the straight portions of the fence is about 3.3 m. (From National Geophysical Data Center, wysiwyg://122/http:/ /www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/2/ 2_slides.html.)

FIGURE 1.11 At W.D. Skinner’s farm near Olema, a fence south of this barn was offset 4.7 m. The barn, beneath which the fault-trace passed, remained attached to the foundation on the southwest side, but was broken from it on the northwest side and dragged 4.8 m. The fault-trace at this location also showed vertical offset, most likely caused by local soil conditions. The maximum vertical displacement of the faulting was 1.2 m. (Photo: G.K. Gilbert, U.S. Geological Survey. From National Geophysical Data Center, wysiwyg://122/http:/ /www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/2/ 2_slides.html.)

FIGURE 1.12 Union Street, San Francisco, not more than a quarter of a block in length between Pierce and Steiner Streets, had been filled to equalize the street grade, and the sides of the streets were not supported. During the earthquake, the north sidewalk was shifted about 3.0 m to the north and depressed about 3.0 m below its original level. The south sidewalk was depressed a few centimeters and shifted to the north as much as 1 m. The paving and cable conduit in this area incurred more severe damage than at any other point in the city. (From National Geophysical Data Center, wysiwyg://122/ http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/2/2_slides.html.)

The devastation in San Francisco was so enormous, and so largely due to fire (Figure 1.16), however, that some of the lessons of the event were lost. Studies on the effects of the earthquake and fire on structures and structural materials [USGS, 1907] focused as much on the fire as on the earthquake. A detailed review of a number of engineered buildings found that many had not been badly damaged by the earthquake and even, if well-fireproofed, had survived the fire in reasonable shape. Enough buildings © 2003 by CRC Press LLC


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FIGURE 1.13 This row of two-story buildings tilted away from the street when the ground beneath the foundations slumped. Such ground failures contributed to the shaking intensity and to the subsequent building damage. This photo was taken before fire destroyed the entire block. Note billowing smoke in the sky. (Photo: NOAA/ NGDC, wysiwyg://122/http://www.ngdc.noaa.gov/seg/ hazard/slideset/earthquakes/2/2_slides.html.)

(A)

(B)

(C)

FIGURE 1.14 (A) Collapsed San Francisco City Hall; (B) the “damn’dest finest ruins,” this view looks east toward Market Street in San Francisco. Wooden buildings, one to three stories high, with brick or stone-work fronts, were closely interspersed with two- to eight-story brick buildings. Mingled with these were modern office buildings. Here the fire burned fiercely. In its aftermath, the streets were heaped with rubble to a depth of a meter or more and were nearly impassible. Because of the heat of the fire, much of the damage due directly to the shock was concealed or obliterated in this part of the city. (Photo: Eric Swenson, U.S. Geological Survey.) (C) One of the camps set up for earthquake victims is depicted. Similar camps were established on the hills, parks, and open spaces of the city. Five days after the earthquake rains brought indescribable suffering to the tens of thousands of people camped in the open. Few people had waterproof covering initially. The downpour aggravated the unsanitary conditions of the camps and added numbers of pneumonia cases to the already crowded regular and temporary hospitals of the city. Eventually tents such as these were provided to the 300,000 homeless. (Photo: Eric Swenson, U.S. Geological Survey. From National Geophysical Data Center, wysiwyg://122/http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/2/ 2_slides.html.) © 2003 by CRC Press LLC


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FIGURE 1.15 Memorial Church as seen from the inner quadrangle at Stanford University, Palo Alto. The stone tower of the church fell and destroyed the parts of the roof immediately around the tower. The gable on the north end of the church was thrown outward into the quadrangle. (Photo: W.C. Mendenhall, U.S. Geological Survey, wysiwyg://122/http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/2/2_slides.html.)

Principal distribution mains. Salt-water system. Old shore line. Boundary line of burned district. Principal earthquake breaks in streets. Districts covered largely by brick structures. Cisterns in service.

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FIGURE 1.16 Map of San Francisco showing district burned in 1907. (From U.S. Geological Survey. 1907. The San Francisco Earthquake and Fire of April 18, 1906 and Their Effects on Structures and Structural Materials. Bulletin 324, Washington, D.C.)

of various construction types were present that the study drew clear lessons from the event: that wellengineered steel and reinforced concrete buildings could survive shaking of this intensity with little damage. It was also noted that “great earthquakes are followed by … an interval of 50 or 100 years during which no earthquakes occur” [USGS, 1907] (which turned out to be true; see below). As a result, for many years the event was more popularly known as “the Fire,” and earthquake provisions were not especially emphasized in building codes in California until after the 1925 Santa Barbara and 1933 Long Beach events (see Section 1.2.2.3). © 2003 by CRC Press LLC


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FIGURE 1.17 San Francisco Bay area seismicity, showing pattern of seismicity leading up to 1906 earthquake, subsequent quiescence, and initial stages of new cycle. (From U.S. Geological Survey. 1907. The San Francisco Earthquake and Fire of April 18, 1906 and Their Effects on Structures and Structural Materials. Bulletin 324, Washington, D.C.)

The San Francisco earthquake resulted in the largest urban fire in history, only exceeded in peacetime by the 1923 Tokyo earthquake and fire (see below). It was the largest insurance loss in history up to that time; and it resulted in the first modern study and documentation of earthquake effects [Lawson et al., 1908] and in the publication and dissemination of Reid’s theory of elastic rebound [Reid et al., 1910]. This theory was vital to the understanding of earthquakes, as it clearly and simply explained that an earthquake was the sudden reaction of the Earth’s overly strained crust “snapping back” along the fault. Coupled with advances in the study of the Earth’s structure, observations from the 1906 and other large earthquakes in the early to mid-twentieth century increasingly provided an understanding of earthquake sources, finally unified by the theory of plate tectonics in the 1960s. An outcome of this is the ability to understand the earthquake cycle, as shown in Figure 1.17, from which it can be seen that the 1906 earthquake was the final (and by far largest) release of strain energy stored in the Earth’s crust due to plate motion (in the case of California and the 1906 earthquake, the North American and Pacific plates; see Chapter 4). That is, as the plates move past each other, the Earth’s crust is deformed, storing strain energy, not unlike a spring as it is stretched. As the plates are deformed, there are internal localized failures (i.e., small to intermediate earthquakes) and partial slippages (i.e., earthquakes), until finally the entire fault, strained to the breaking point, ruptures along its entire length, and snaps back the several meters the plates had displaced during the previous several hundred years. The previous cycle in the San Francisco Bay area is seen in Figure 1.17 to have begun with the 1838 earthquake,4 with an increasing rate of seismicity until 1906. From 1906 to the 1979 M5.7 Coyote Lake earthquake, there were relatively few earthquakes, and then an increasing number, with the 1989 Loma Prieta event (discussed below) being the analog of the 1838 event. The implications of this for the San Francisco Bay area are, of course, ominous. Another result of the 1906 earthquake was the founding of the Seismological Society of America. However, given the magnitude of the event and resulting damage, it would seem that a more comprehensive

4 Note that historic records in the San Francisco Bay area, although incomplete, date from the founding of the Mission Dolores in San Francisco in 1776.




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program of investigation into seismology and earthquake engineering would have emerged from the 1906 event. However, as Maher5 observes [Carder, 1965]: The great San Francisco earthquake of Apr. 18, 1906, resulted in a temporary impetus in earthquake investigation. However, after the excitement had died down, interest in research on earthquakes declined, partly because of activity by pressure groups who considered that the dissemination of information about earthquakes was detrimental to business. The existence of “pressure groups” is confirmed by Branner [1913].6 1.2.2.2 1923: September 1, Kanto, Japan (M 7.9) The M7.9 Kanto earthquake occurred at 11:58 a.m., September 1, 1923, with epicenter beneath Sagami Bay (Figure 1.18). The Tokyo region (actually, Mt. Fuji) is the junction of four tectonic plates (Philippine Sea, Pacific, Eurasian, and North American), and the subduction of the Pacific plate beneath the Eurasian plate was the seismogenesis of the event. Figure 1.18 shows contours of shaking damage percentage for Japanese wooden houses, contours of uplift and subsidence, locations of tsunami, and other effects in the most severely affected region [Hamada et al., 1992]. Seismic intensity on the Japan Meteorological Agency scale (JMA, see Chapter 4) is also indicated on the figure. Damage was heaviest in the Yokohama and Tokyo urbanized areas, although the shore of Sagami Bay and parts of the Boso peninsula also sustained heavy damage, a 3- to 6-m tsunami, and major geologic effects, with maximum crustal uplift of 2 m. The death toll in Kanagawa and Tokyo prefectures was 97,000, including about 60,000 in Tokyo city. The total number of dead and missing reached about 143,000, with 104,000 people listed as injured. About 128,000 houses and buildings were destroyed, another 126,000 heavily damaged, and as many as 447,000 lost to fire (Figures 1.19 and 1.20). Fire accounted for the majority of houses destroyed in Tokyo, and about 50% of houses lost in Kanagawa prefecture could be attributed to fire [Hamada et al., 1992]. The conflagration as a result of this fire is the largest peacetime conflagration in history, with combined fire and earthquake fatalities exceeding those of the incendiary attacks on Tokyo in World War II, and also probably exceeding the immediate fatalities in either of the atomic bombings of Hiroshima or Nagasaki. The conflagration was initially a mass fire (Figure 1.21), although self-generated winds resulted in large vortices or “firestorm” conditions in several locations, most notably at the Military Clothing Depot in Honjo Ward, where many refugees had gathered. Most of them carried clothing, bedrolls, and other flammables rescued from their homes, which served as a ready fuel source, and the engulfing flames suffocated an estimated 40,000 people. The enormous conflagration was due to hot, dry, windy conditions (although there had been some rain recently), combined with the time of the earthquake, just before noon, when the population was preparing its lunch. Coal or charcoal cooking stoves were in use throughout Tokyo and Yokohama for the noontime meal, and fires sprang up everywhere within moments of the quake. Firespread was very rapid, due to high winds as well as lack of water for firefighting because of broken water mains [ASCE, 1929].

5

Thomas J. Maher was a captain of the U.S. Coast and Geodetic Survey, and inspector-in-charge of the Survey's San Francisco field station from 1928 to 1936. He retired in 1946, and died in June 1964. 6 “… Another and more serious obstacle is the attitude of many persons, organizations, and commercial interests toward earthquakes in general. The idea back of this false position — for it is a false one — is that earthquakes are detrimental to the good repute of the West Coast, and that they are likely to keep away business and capital, and therefore the less said about them the better. This theory has led to the deliberate suppression of news about earthquakes, and even of the simple mention of them. Shortly after the earthquake of April 1906, there was a general disposition that almost amounted to concerted action for the purpose of suppressing all mention of that catastrophe. When efforts were made by a few geologists to interest people and enterprises in the collection of information in regard to it, we were advised and even urged over and over again to gather no such information, and above all not to publish it. ‘Forget it,’ ‘the less said, the sooner mended,’ and ‘there hasn't been any earthquake,’ were the sentiments we heard on all sides…” © 2003 by CRC Press LLC

Tsunami

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Uplift (cm) Subsidence (cm) Break of Electric Cable Observed Faulting

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FIGURE 1.18 Map of distribution of damage, 1923 Kanto earthquake. (From Hamada, M., Wakamatsu, K., and Yasuda, S. 1992. “Liquefaction-Induced Ground Deformation during the 1923 Kanto Earthquake,” in Case Studies of Liquefaction and Lifeline Performance during Past Earthquakes, Vol. I, Japanese Case Studies, Hamada, M. and O’Rourke, T.D., Eds., Technical report NCEER-92–0001, February, National Center for Earthquake Engineering Research, State University of New York, Buffalo. With permission.)



City Boundary between Prefectures 1% Percentage of Totally Damaged 10% Houses due to Ground Motion 50%


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EXPLANATION



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FIGURE 1.19 Tokyo (Ginza) ruins. (From Home Office. 1926. The Great Earthquake of 1923 in Japan, Bureau of Social Affairs, Home Office, Tokyo. With permission.)

FIGURE 1.20 Tokyo (Ginza) ruins. (From Home Office. 1926. The Great Earthquake of 1923 in Japan, Bureau of Social Affairs, Home Office, Tokyo. With permission.)

FIGURE 1.21 1923 Kanto earthquake conflagration, banks of Sumida River (aerial photo). (From Home Office. 1926. The Great Earthquake of 1923 in Japan, Bureau of Social Affairs, Home Office, Tokyo. With permission.)

As Cameron and James note: The Great Kanto earthquake ushered in the modern age of earthquake engineering …, [as exemplified in] … the World Engineering Congress of 1929 … [where] an early base isolation technique … by Riuitchi Oka …, promoting the use of “spherical rockers” at the base of columns … . Also of note was a paper by Kenzaburo Mashima, entitled “Earthquakes and Building Construction,” in which flexible construction was strongly endorsed. … Mashima also concluded that masonry structures were the most dangerous during an earthquake, followed by reinforced concrete buildings. He gave steel and wood structures the highest marks for seismic resistance. … Strongly in favor of rigid construction was Dr. Taichu Naito, Professor of Architecture at Waseda University in Tokyo. Naito noted three important elements in seismic resistant design: structural rigidity, a rational distribution of lateral force, and the reduction of the natural period of elastic oscillation to one smaller than the probable period of an earthquake … immediate changes in building codes followed the 1923 earthquake and were in effect in the rebuilding of Tokyo and Yokohama, including mandated maximum height and added bracing for wood buildings; increased requirements for masonry buildings, including parapet bracing; addition of brackets or braces to increase rigidity for connections between columns and girders in steel buildings; and improved detailing for reinforced concrete structures [Cameron and James, n.d., paraphrased]. © 2003 by CRC Press LLC


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FIGURE 1.22 MMI isoseismal map, 1933 Long Beach earthquake. (From Stover, C.W. and Coffman, J.L. 1993. Seismicity of the United States, 1568–1989 (revised). U.S. Geological Survey Professional Paper 1527, U.S. Government Printing Office, Washington, D.C.)

1.2.2.3 1925: Santa Barbara; 1933: Long Beach Earthquakes The M6.2 Santa Barbara earthquake occurred on June 29, 1925 and caused $8 million damage and 13 fatalities from an offshore shock in the Santa Barbara Channel, on an extension of the Mesa Fault or the Santa Ynez system. On State Street, the principal business thoroughfare, few buildings escaped damage; several collapsed. The shock occurred at 6:42 a.m., before many people had reported for work and when streets were uncrowded, reducing death and injury. The M6.3 Long Beach earthquake of March 10, 1933 had its epicenter offshore, southeast of Long Beach, on the Newport-Inglewood fault, and caused $40 million property damage and 115 lives lost (Figure 1.22). The major damage occurred in the thickly settled district from Long Beach to the industrial section south of Los Angeles, where unfavorable geological conditions (made land, water-soaked alluvium) combined with much poor structural work to increase the damage. At Long Beach, buildings collapsed, tanks fell through roofs, and houses displaced on foundations. School buildings were among those structures most generally and severely damaged (Figure 1.23), and it was clear that a large number of children would have been killed and injured had the earthquake occurred during school hours. These two earthquakes are discussed not so much for the size or peculiarities of damage, but due to advances in engineering and building code requirements instituted following these two events (see Chapter 11, this volume, for a more detailed discussion of this aspect): © 2003 by CRC Press LLC



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FIGURE 1.23 Walls crumbled at Alexander Hamilton Jr. High School on State Street, Long Beach. Great loss of life would have occurred if the shock had taken place during school hours.

• Following the 1925 event, the first modern code containing seismic provisions was published: the first edition of the Uniform Building Code, published by the Pacific Coast Building Officials in 1927 (see Chapter 11, this volume). Its seismic requirements were not mandatory and appeared in an appendix. • As a result of the 1925 event [SEAOC, 1980] and the efforts by a number of parties,7 a Seismological Field Survey was created in 1932 within the the U.S. Coast and Geodetic Survey (USC&GS), with offices in San Francisco. A strong motion accelerometer designed in 1931 by McComb and Parkhurst of the USC&GS, and Wenner of the National Bureau of Standards [Cloud, in Carder, 1965], modeled after the Wood-Anderson instrument [EERI, 1997], was deployed in 1932. During the 1933 Long Beach earthquake the first-ever recordings of earthquake strong ground motions were thus made (actually three recordings of the main shock, at Long Beach, Vernon, and Los Angeles [Maher, in Carder, 1965]). “This was a milestone, as it was the first time any such records had been made anywhere in the world” [EERI, 1997]. Following the 1933 Long Beach earthquake, which caused extensive damage to unreinforced masonry buildings and, in particular, several public schools, the State of California adopted regulations: • Further construction of unreinforced masonry buildings was prohibited. • The Riley Act was required that all building in California be provided with a lateral strength equal to 3% of the weight of the structure, making seismic design mandatory. • The Field Act established and charged the Office of the State Architect with responsibility for the regulation of public school construction. Schools had been especially damaged in the 1933 event. The Office of the State Architect established rigorous standards for structural design, plan review, and inspection of construction that would affect structural engineering practice throughout California and eventually find its way into the building code requirements applicable to all forms of construction.

1.2.3 Mid-Century Events 1.2.3.1 July 21, 1952: Kern County, CA (M7.7) This earthquake was the largest in the conterminous United States since the San Francisco shock of 1906 (Figure 1.24) and received considerable study by the earthquake community. Jenkins and Oakeshott [1955] edited a volume focused on the geology, seismology, and structural damage specific to the event, and the Bulletin of the Seismological Society of America published a special issue on data collected by

7

Sources vary. Housner [EERI, 1997] gives John Freeman full credit, indicating Freeman literally had to lobby President Herbert Hoover and his Secretary of Commerce, while Maher [in Carder, 1965] cites efforts by a citizens’ group, including Levison (president of Firemans Fund Insurance Company), Dewell (a practicing structural engineer in San Francisco), Baily Willis, and others. © 2003 by CRC Press LLC


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FIGURE 1.24 Modified Mercalli Intensity map, 1952 Kern County earthquake. (From Stover, C.W. and Coffman, J.L. 1993. Seismicity of the United States, 1568–1989 (revised). U.S. Geological Survey Professional Paper 1527, U.S. Government Printing Office, Washington, D.C.)

the Pacific Fire Rating Bureau [Steinbrugge and Moran, 1954]. It claimed 12 lives and caused property damage estimated at $60 million. It was unusual in that an aftershock (August 22, M5.8) actually caused more damage in Bakersfield than the main shock, although the damage was to structures already somewhat damaged by the main shock. The generally moderate damage in Bakersfield was confined mainly to isolated parapet failure. Cracks formed in many brick buildings, and older school buildings were damaged somewhat. In contrast, however, the Kern General Hospital was damaged heavily. Multistory steel and concrete structures sustained minor damage, which commonly was confined to the first story. MMI XI was assigned to a small area on the Southern Pacific Railroad southeast of Bealville. There, the earthquake cracked reinforced-concrete tunnels having walls 46 cm thick, shortened the distance between portals of two tunnels about 2.5 m, and bent the rails into S-shaped curves. Reports of long-period wave effects from the earthquake were widespread. Water splashed from swimming pools as far distant as the Los Angeles area, where damage to tall buildings was nonstructural but extensive. Water also splashed in pressure tanks on tops of buildings in San Francisco [Stover and Coffman,1993]. The 1952 Kern County earthquake was investigated by a new generation of structural engineers and earth scientists, who moved over the next several years to create the first edition of the Structural Engineers Association of California’s Recommended Lateral Force Requirements, or “Blue Book,” which




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FIGURE 1.25 1960 Chile Mw 9.5 earthquake. The ship in the photo was wrecked by the tsunami on Isla Mocha (north of Valdivia). Note the raised beach and landslides. Large landslides and massive flows of earthen debris and rock occurred on the island. The tsunami runup on Isla Mocha was 25 m (more than 82 ft). (From NOAA/ NGDC, http://www.ngdc.noaa.gov/seg/hazard/slideset/ tsunamis.)

FIGURE 1.26 1960 Chile Mw 9.5 earthquake. The fishing village of Queule (north of Valdivia and south of Lebu) before and after the catastrophe of May 1960. The bottom photo was taken after the land subsidence and after the tsunami. The town was destroyed. The houses, together with the remains of fishing boats and uprooted trees, were washed as much as 2 km inland by a tsunami 4.5 m high. The sinking of the land also brought about a permanent rise of the sea. The meandering creek bed in the foreground has been changed into an estuary. The trees that dot the river bank in the top photo are the only ones that remain in the bottom photo. Also the linear feature next to the solitary tree in the bottom photo can be found in the top photo marked with smaller trees that later disappeared in the wave. (From NOAA/NGDC, http://www.ngdc.noaa.gov/seg/hazard/slideset/tsunamis/.)

was the first uniform code for seismic areas in the United States [SEAOC, 1980]. This was a critical development, as the Blue Book became the model for seismic requirements and building codes around the world. 1.2.3.2 1960: May 22, Chile (Mw 9.5) On May 22, 1960, a Mw 9.5 earthquake, the largest earthquake ever instrumentally recorded, occurred in southern Chile. The series of earthquakes that followed ravaged southern Chile and ruptured over a period of days a 1000-km section of the fault, one of the longest ruptures ever reported. The number of fatalities associated with both the tsunami and the earthquake has been estimated between 490 and 5,700. Reportedly there were 3,000 injured, and initially there were 717 missing. The Chilean government estimated 2,000,000 people were left homeless and 58,622 houses were completely destroyed. Damage (including tsunami damage) was more than U.S. $500 million. The main shock set up a series of seismic sea waves (tsunamis) that not only was destructive along the coast of Chile (Figures 1.25 and 1.26), but that also caused numerous casualties and extensive property damage in © 2003 by CRC Press LLC


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Epicenter X Intensity 10

FIGURE 1.27 MMI map, 1964 Alaska earthquake. (From NOAA/NGDC, http://www.ngdc.noaa.gov/seg/hazard/ slideset/earthquakes/7/7_slides.html.)

Hawaii and Japan, and that was noticeable along shorelines throughout the Pacific Ocean area. There were several other geologic phenomena besides tsunamis associated with this event. Subsidence caused by the earthquake produced local flooding and permanently altered the shorelines of much of the area in Chile impacted by the earthquake. Landslides were common on Chilean hillsides. The Puyehue volcano erupted 47 h after the main shock [NOAA/NGDC, n.d.].

1.2.4 First Turning Point This section briefly describes salient points from selected earthquakes between 1964 and 1971, a period that ended with a major change in the thinking of earthquake engineers and that, within a few years, led to a National Earthquake Hazards Reduction Program in the United States, and heightened activity in other countries. 1.2.4.1 1964: March 28, Alaska (Mw 8.3) This great earthquake and ensuing tsunami took 125 lives (tsunami 110, earthquake 15), and caused about $311 million in property loss. Earthquake effects were heavy in many towns, including Anchorage, Chitina, Glennallen, Homer, Hope, Kasilof, Kenai, Kodiak, Moose Pass, Portage, Seldovia, Seward, Sterling, Valdez, Wasilla, and Whittier (Figure 1.27). Anchorage, about 120 km northwest of the epicenter, sustained the most severe damage to property. About 30 blocks of dwellings and commercial buildings were damaged or destroyed in the downtown area. The J.C. Penney Company building was damaged beyond repair (Figure 1.28); the Four Seasons apartment building, a new six-story structure, collapsed (Figure 1.29); and many other multistory © 2003 by CRC Press LLC



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FIGURE 1.28 This slide shows the five-story J.C. Penney building at 5th Avenue and Downing Street in Anchorage, where two people died and one was injured. Concrete facing fell on automobiles in front of the building. Although the building was approximately square, the arrangement of effective shear-resisting elements was quite asymmetrical, consisting principally of the south and west walls that were constructed of poured concrete for the full building height. The north and east sides of the building faced the street. The north side of the building had no shear wall but was covered by a facade composed of 4-inch (10.2-cm) thick precast, nonstructural reinforced concrete panels. The east wall, also covered with the precast panels, had poured-concrete shear walls between columns in the two northerly bays and in the bottom three stories of the two southerly bays. The rotational displacement induced by the earthquake apparently caused failure of this east wall shear-resistant element, the building became more susceptible to rotational distortion, and the south and west shear walls failed. (From NOAA/NGDC, http:// www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/7/7_slides.html.)

FIGURE 1.29 The Four Seasons Apartments in Anchorage was a six-story, lift-slab reinforced concrete building that crashed to the ground during the earthquake. The building was structurally complete but unoccupied at the time of the earthquake. The main shear-resistant structural elements of the building, a poured-in-place, reinforced-concrete stairwell and a combined elevator core and stairwell, fractured at the first floor and toppled over, and came to rest on top of the rubble of all six floors and the roof. The concrete stairwell is in the center of the picture. (From NOAA/ NGDC, http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/7/7_slides.html.)

buildings were damaged heavily. The schools in Anchorage were heavily damaged. The Government Hill Grade School, sitting astride a huge landslide, was almost a total loss. Anchorage High School and Denali Grade School were damaged severely. Duration of the shock was estimated at 3 min. Landslides in Anchorage caused heavy damage. Huge slides occurred in the downtown business section (Figure 1.30), at Government Hill, and especially at Turnagain Heights (Figure 1.31), where an area of about 130 acres was devasted by displacements that broke the ground into many deranged blocks that were collapsed and tilted at all angles. This slide destroyed about 75 private homes. Water mains and gas, sewer, telephone, and electrical systems were disrupted throughout the area. The earthquake was accompanied by vertical displacement over an area of about 52,000 km2. The major area of uplift trended northeast from southern Kodiak Island to Prince William Sound and trended © 2003 by CRC Press LLC


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FIGURE 1.30 This view of damage to Fourth Avenue buildings in downtown Anchorage shows the damage resulting from the slide in this area. Before the earthquake, the sidewalk in front of the stores on the left, which are in the graben, was at the level of the street on the right, which was not involved in the subsidence. The graben subsided 11 feet (3.3 m) in response to 14 feet (4.2 m) of horizontal movement of the slide block during the earthquake. Lateral spreading produced a fan-shaped slide 1800 feet (545.5 m) across that covered about 36 acres (14.6 ha) and moved a maximum of 17 feet (5.1 m). Movement on the landslide began after about 1 to 2 min of ground shaking and stopped when the shaking stopped. (From NOAA/NGDC, http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/7/7_slides.html.)

FIGURE 1.31 The Turnagain Heights landslide in Anchorage. Seventy-five homes twisted, slumped, or collapsed when liquefaction of subsoils caused parts of the suburban bluff to move as much as 2000 feet (606 m) downward toward the bay, forming a complex system of ridges and depressions. The slide developed because of a loss in strength of the soils, particularly of lenses of sand, that underlay the slide. The motion involved the subsidence of large blocks of soil, the lateral displacement of clay in a 25-foot (7.6-m) thick zone, and the simultaneous lateral translation of the slide debris on liquefied sands and silts. (From NOAA/NGDC, http://www.ngdc.noaa.gov/seg/hazard/slideset/ earthquakes/7/7_slides.html.)

east–west to the east of the sound. Vertical displacements ranged from about 11.5 m of uplift to 2.3 m of subsidence relative to sea level. Off the southwest end of Montague Island, there was absolute vertical displacement of about 13 to 15 m. Uplift also occurred along the extreme southeast coast of Kodiak Island, Sitkalidak Island, and over part or all of Sitkinak Island. The zone of subsidence covered about 285,000 km2, including the north and west parts of Prince William Sound, the west part of the Chugach Mountains, most of Kenai Peninsula, and almost all the Kodiak Island group. This shock generated a tsunami that devastated many towns along the Gulf of Alaska (Figure 1.32), and left serious damage at Alberni and Port Alberni, Canada, along the West Coast of the United States (15 killed), and in Hawaii. The maximum wave height recorded was 67 m at Valdez Inlet. Seiche action in rivers, lakes, bayous, and protected harbors and waterways along the Gulf Coast of Louisiana and Texas caused minor damage. It was also recorded on tide gages in Cuba and Puerto Rico. This great earthquake was felt over a large area of Alaska and in parts of western Yukon Territory and British Columbia, Canada [Stover and Coffman, 1993]. © 2003 by CRC Press LLC



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FIGURE 1.32 This photo was taken at Seward at the north end of Resurrection Bay, showing an overturned ship, a demolished Texaco chemical truck, and a torn-up dock strewn with logs and scrap metal after the tsunamis. The waves left a shambles of houses and boats in the lagoon area, some still looking relatively undamaged and some almost completely battered. The total damage to port and harbor facilities at Seward was estimated at more than $15,000. Most of this damage was the result of the tsunamis. Eleven persons lost their lives due to the sea waves at Seward. (From NOAA/NGDC, http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/7/ 7_slides.html.)

The Alaska earthquake had two significant influences: (1) its truly remarkable size, area affected, and geologic effects greatly stimulated the earth sciences in the United States, and led to a major documentation of the event [U.S. Coast and Geodetic Survey, 1967]; and (2) the impacts on modern structures, such as the J.C. Penney and Four Seasons Apartment buildings, alarmed structural engineers and started a thought process that would lead to major building code changes within a decade. 1.2.4.2 1964: June 16, Niigata, Japan (M7.5) The city of Niigata, on the Japan Sea coast of the island of Honshu, Japan, was struck by a M7.5 earthquake at 1:25 p.m, June 16, 1964, resulting in widespread damage (Figure 1.33) (see Chapter 4 for an explanation of the JMA intensity scale). Many buildings, bridges, quay walls, and lifeline systems suffered severe damage, and it was fortunate that only 26 persons were killed. The real significance of this event was the technical investigation and identification of the cause of some remarkable building failures, which were caused by liquefaction. Being a natural phenomenon, liquefaction had occurred in most larger earthquakes since time immemorial (see Figure 1.8, for example), but had not been specifically identified and investigated. At the Kawagishi-cho apartments in Niigata city, liquefaction occurred, resulting in the overturning collapse of the buildings (Figure 1.34). Note the quality of the construction; even though overturned, these buildings remained intact. Koizumi [1965] identified liquefaction and its cause and, combined with the major examples of liquefaction observed in Alaska earlier the same year, this led to a major research effort into the analysis and mitigation of liquefaction over the next several decades. 1.2.4.3 1971: February 9, San Fernando, CA (M6.5) This destructive earthquake occurred in a sparsely populated area of the San Gabriel Mountains, near San Fernando, killing 65, injuring more than 2000, and causing property damage estimated at $505 million [NOAA, 1973] (Figure 1.35). The earthquake created a zone of discontinuous surface faulting, named the San Fernando fault zone, which partly follows the boundary between the San Gabriel Mountains and the San Fernando-Tujunga Valleys and partly transects the northern salient of the San Fernando Valley. This latter zone of tectonic ruptures was associated with some of the heaviest property damage sustained in the region. Within the entire length of the surface faulting, which extended roughly east–west for about 15 km, the maximum vertical offset measured on a single scarp was about 1 m, the maximum lateral offset about 1 m, and the maximum shortening (thrust component) about 0.9 m.



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N

Aomori

Hachinohe

2 II

1

III Morioka 3 Miyako

Akita 4

4 IV

3 Ofunato

Sakata 5 Sendai

3 V

Yamagata V

5

4

Niigata

Aikawa 5

5

4

4

Wakamatsu Wajima

4 Shirakawa

IV

4 4 2 Kanazawa 1 Fukui

3

Nagano 4 2 Matsushiro

3

1 Takayama II

Maebashi 4 3

3

3

3

Mito 4 2

4 Onahama

Kakioka

3

III

Tokyo 3 Kofu

Iida 2

2

2

3 3

Choshi

Yokohama 1

I

1 Shizuoka

Tomizaki

3 Cape Omaezaki

FIGURE 1.33 Japan Meteorological Agency intensity map of 1964 Niigata, Japan, earthquake. (From Japan Meteorological Agency. With permission.)

FIGURE 1.34 1964 Niigata earthquake, overturning of apartment buildings, Kawagishi-cho, Niigata. (From NOAA/NGDC, available online at http://www.ngdc.noaa.gov/seg/hazard/slideset/ earthquakes/.) © 2003 by CRC Press LLC


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122°

120°

118°

116°

114°

Tonopah

38° Stockton

UTAH

NEVADA

II-IV

Fresno

Monterey

I-IV Las Vagas

36°

V

California

Barstow

Santa Maria

ARIZONA

c

ifi

c Pa VII-XI

34°

VII

VI

Los Angeles

Oc n

ea

II-IV

0 32°

100

KILOMETERS

EXPLANATION Epicenter 1X Intensity 11

San Diego

United States Mexico

Yuma

FIGURE 1.35 Modified Mercalli Intensity map of 1971 San Fernando earthquake. (From NOAA/NGDC, available online at http://neic.usgs.gov/neis/eqlists/USA/1971_02_09_iso.html.)

The most spectacular damage included the destruction of major structures at the Olive View and the Veterans’ Administration Hospitals, and the collapse of freeway overpasses (Figure 1.36). The newly built earthquake-resistant buildings at the Olive View Hospital in Sylmar were destroyed; four five-story wings pulled away from the main building and three stair towers toppled (Figure 1.37). Although newly built and complying with the building code, the building’s columns lacked confinement due to widely spaced lateral ties. Older, unreinforced masonry buildings collapsed at the Veterans’ Administration Hospital at San Fernando, killing 49 people (Figure 1.38). Many older buildings in the Alhambra, Beverly Hills, Burbank, and Glendale areas were damaged beyond repair, and thousands of houses and chimneys were damaged in the region (Figure 1.39). A large number of one-story commercial buildings, termed tilt-ups, were found to have a common design flaw, involving the roof-wall connection putting the wood ledger in cross-grain bending, which is discussed in Chapter 14 of this volume. Public utilities and facilities of all kinds were damaged, both above and below ground. Severe ground fracturing and landslides were responsible for extensive damage in areas where faulting was not observed. The most damaging landslide occurred in the Upper Lake area of Van Norman Lakes, where highway overpasses, railroads, pipelines, and almost all structures in the path of the slide were damaged severely. Several overpasses collapsed. Two dams were damaged severely (Lower Van Norman Dam and Pacoima Dam) (Figure 1.40), and three others sustained minor damage. Lower Van Norman Dam came very close to overtopping, which would have resulted in a sudden release of the impounded water and probable mass casualties for the 80,000 people living below the dam [Stover and Coffman, 1993]. The impact of the San Fernando earthquake on engineers was out of all proportion to the number killed, or even the monetary costs. Engineers were shocked to observe that modern structures, such as Olive View Hospital, Van Norman Dam, highway bridges, and tilt-up buildings, were failing under a moderate-sized earthquake. Of note also was the recording during the event of about 100 strong ground motion records, which effectively doubled the number of new records then in existence! © 2003 by CRC Press LLC


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FIGURE 1.36 The I-5 (Golden State) and I-210 (Foothills) Freeway Exchange. There was damage to both roadway and structures on the completed portion of this freeway, from its intersection with Route 5 to the Maclay Street separation. Throughout this section, the freeway appeared to settle on a somewhat uniform grade line. The settling was especially noticeable at the bridges, where it varied from 6 to 24 inches. Pavement was buckled and broken for several hundred feet on each side of the damaged structures. Structural damage varied, from minor damage to wing walls and slope paving, to rotation and settlement of abutments, splaying and cracking of columns, displacement of wing walls, and contortion of the sides of fills. Street sections beneath the various undercrossings suffered damage to curbs, sidewalks, slope paving, and roadway sections. (Photo: E.V. Leyendecker, U.S. Geological Survey. From NOAA/NGDC, available online at http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/20/20_slides.html.)

(A)

(B)

FIGURE 1.37 Damage sustained in the 1971 San Fernando, California, earthquake. (A) This building, known as the Medical Treatment and Care Building (in the Olive View Hospital complex) was completed in 1970 at a cost of $25 million. The four towers containing the stairs and day-room areas were built to be structurally separated four inches from the main building. The three towers that failed were supported by concrete columns. When these columns failed, the towers overturned. Note that the base of the tower in this photo has fallen in the basement. After the shock, the building leaned as much as 2 feet in a northerly direction with nearly all of this drift in the first story. Note also the broken columns on the first floor. The first story nearly collapsed, and the building was ultimately demolished. The structure was located in a band that incurred heavy damage during the 1971 earthquake. (Photo: E.V. Leyendecker, U.S. Geological Survey.) (B) Close-up of first-story column failure at Olive View Hospital. The column was located at the west end of Wing B on the first story of the five-story hospital. This is a typical first-story tied corner column, and the damage is characteristic of column damage found on the first floor in all wings of the hospital. These corner columns were square with a corner notch out, giving the appearance of a thick L-shaped column. Note the broken ties, the spacing of the ties, and the bent rebar. The building was laterally displaced about 2 feet to the north in the earthquake. (Photo: E.V. Leyendecker, U.S. Geological Survey. From NOAA/NGDC, available online at http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/20/20_slides.html.) Shown as Color Figure 1.37. © 2003 by CRC Press LLC



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FIGURE 1.38 Aerial view of the damage to the San Fernando Veterans’ Administration Hospital and complex. This complex was located in the band of accentuated damage found along the base of the San Gabriel Mountains. The collapsed structure was built in 1926, before earthquake building codes were in effect. Fortyseven of the 65 deaths attributed to the earthquake occurred as a result of the collapse of this structure. (Photo: E.V. Leyendecker, U.S. Geological Survey. From N OA A / N G D C , a v a i l a b l e o n l i n e a t h t t p : / / www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/20/ 20_slides.html.)

FIGURE 1.39 A home in Crestview Park on Almetz Street. More than 700 dwellings were evacuated and declared unsafe after the San Fernando earthquake. (Photo: E.V. Leyendecker, U.S. Geological Survey. From N OA A / N G D C , a v a i l a b l e o n l i n e a t h t t p : / / www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/20/ 20_slides.html.)

FIGURE 1.40 Van Norman Dam (Lower San Fernando Dam). For a length of about 1800 feet, the embankment (including the parapet wall, dam crest, most of the upstream slope, and a portion of the downstream slope) slid into the reservoir. A loss of about 30 feet of dam height resulted when as much as 800,000 cubic yards of dam embankment was displaced into the reservoir. This material slid when liquefaction of the hydraulic fill on the upstream side of the embankment occurred. The dam was about half full at the time. Eighty-thousand people living downstream of the dam were immediately ordered to evacuate, and steps were taken to lower the water level in the reservoir as rapidly as possible. The Los Angeles Dam was constructed to replace the Van Norman Reservoir. (Photo: E.V. Leyendecker, U.S. Geological Survey. From NOAA/NGDC, available online at http:// www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/20/ 20_slides.html.)

1.2.4.4 New Directions The 1971 San Fernando earthquake, coming within a few years of the 1964 Alaska, 1964 Niigata (Japan), 1967 Caracas (Venezuela), and 1968 Tokachi-oki (Japan) earthquakes (the latter two events are not discussed here), brought a realization among geotechnical and structural engineers that major changes were needed in the building codes, as well as that other earthquake mitigation measures were required to deal with existing structures. During the 1970s: • The Uniform Building Code was revised in the 1973 and 1976 editions to increase lateral force requirements, correct the defective detail for roof-wall connections in tilt-up and similar buildings, © 2003 by CRC Press LLC


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• •

•

• •

and require adequate lateral spacing in reinforced concrete columns (see Hamburger, Chapter 11, this volume). A major reshaping of building code earthquake provisions was undertaken [Applied Technology Council, 1978]. Investigation of liquefaction, which was the root of the failure of the Lower Van Norman Dam, had begun following the 1964 events, and practical engineering tools soon emerged to analyze the potential for liquefaction (see Brandes, Chapter 7, this volume). The failures of power, water, and other infrastructure led to the birth of lifeline earthquake engineering (see Eguchi, Chapter 22, this volume) to address seismic vulnerabilities in urban infrastructure. The United States instituted a national dam-safety program (see Bureau, Chapter 26, this volume). In 1977, the National Earthquake Hazards Reduction Act of 1977, Public Law 95–124, was passed, culminating thinking that had begun prior to the 1964 Alaska earthquake and evolved into a series of studies and high-level reports [see EERI, 1999; also available online at http://quake.wr.usgs.gov/ research/history/wallace-VI.html] leading to the passage of the NEHRP.

1.2.5 Second Turning Point 1.2.5.1 1985: September 19, Michoacan, Mexico (M7.9) The earthquake occurred in the state of Michoacan, Mexico, on Thursday, September 19, 1985 at 7:18 a.m. local time. The epicenter was approximately 40 miles west of El Infiernillo Dam on the Balsas River, near the town of Lazaro Cardenas on the Pacific coast. The next day, an aftershock of magnitude 7.5 struck approximately 70 miles to the southwest, 15 miles north of Zihuatenejo, in the state of Guerrero, at 7:37 p.m. local time. At least 9,500 people were killed, about 30,000 were injured, more than 100,000 people were left homeless, and severe damage was caused in parts of Mexico City and in several states of central Mexico. It is widely rumored in Mexico that the death toll from this earthquake may have been as high as 35,000. It is estimated that the quake seriously affected an area of approximately 825,000 km2, caused between U.S. $3 and $4 billion of damage, and was felt by almost 20 million people. Four hundred twelve buildings collapsed and another 3,124 were seriously damaged in Mexico City. About 60% of the buildings were destroyed at Ciudad Guzman, Jalisco. Damage also occurred in the states of Colima, Guerrero, Mexico, Michoacan, Morelos, parts of Veracruz, and in other areas of Jalisco. This event was extremely remarkable and received wide attention because the epicenter was about 400 km from central Mexico City, where the greatest loss of life occurred. Earthquakes do not usually cause significant damage at this distance, and the major damage in Mexico City was due to an unfortunate combination of circumstances: 1. It was a large, distant event, resulting in higher frequencies being largely attenuated, with peak ground accelerations (PGA) of only 0.03 to 0.04 g on firm soils in Mexico City (CU station, see Figure 1.41), but with lower frequencies (longer periods) still having significant energy when the seismic waves reached Mexico City. 2. The Valle de Mexico has unusual geology. It is an enclosed basin, surrounded by active volcanoes, in which all drainage is trapped (a shallow lake still existed at the time of the Spanish Conquest, ca. 1500). There are three zones: (1) a foothill zone consisting of firm volcanic deposits mostly west of downtown; (2) a lake zone consisting of ash from the volcanoes which has fallen on the basin for thousands of years and slowly settled (pluviated) in the central lake of the basin, formed by the runoff trapped in the basin. The center of the basin is therefore a very deep, soft deposit of saturated ash; and (3) intermediate between these two zones is a transition zone. The soft ashwater deposits in the lake zone are very soft, but elastic over a large strain range, with a natural period of about 2 sec. 3. The oldest part of the city, and many of the high rises, are in the Lake zone. Settlement of buildings built in this zone is extreme, if not properly founded. A rule-of-thumb is that the natural period © 2003 by CRC Press LLC


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C = V/W

ξ = 5% Response Spectrum EW ComponetZat SCT NS Componet at SCT EW Componet at CU

1.0

0.8

0.6

0.4

0.2

0.0

1

2 T (Seconds)

3

4

FIGURE 1.41 Response spectra (5% damped), Mexico City CU (firm) and SCT (soft) stations, September 19, 1985 Michoacan earthquake.

of buildings, T, = 0.1N, where N is the number of stories, i.e., a 10-story building normally has a period of about 1 sec, a 20-story building 2 sec, etc.8 4. The long period motion from the large distant event therefore tuned in, i.e., matched the period (of about 2 sec) on the deep, soft deposits of the Lake zone, resulting in resonance of the input ground motion, with unusually strong amplification; PGA of 0.18 g was recorded at the SCT station near the edge of the Transition-Lake zones (see Figure 1.41). 5. On the soft soils the amplified ground motions with response spectra (for an explanation of response spectra, see Chapter 4) tuned in on buildings with periods of about 1.0 to 1.5 sec (i.e., 10- to 15-story buildings). As these buildings were damaged and weakened, their period softened, i.e., became longer, and thus moved toward the peak amplification region at 2 sec in the already amplified response spectra, resulting in a double resonance. As buildings in the 10- to 15-story range weakened, they were being more strongly loaded to collapse. As they weakened, taller buildings (longer periods) were moving into the downhill side of Figure 1.41, and thus shedding load. The result was that damage was highly selective and occurred most in buildings in the 10- to 15-story range. Figure 1.42 shows results of a survey by teachers and students at the Autonomous University of Mexico [UNAM, 1985], in which it can be seen that 9- to 12-story buildings were found to be most heavily damaged. The damage was truly devastating. Figure 1.43 shows the Pino Suarez 23-story building,9 the tallest building to collapse for any reason prior to September 11, 2001. In all three 23-story towers, the columns were welded box columns that buckled at the fourth floor, leading to a story mechanism and collapse [Osteraas and Krawinkler, 1989] of one of the 23-story towers onto the southern 16-story tower, both towers finally collapsing into the street. Figure 1.43A shows the elevation of the complex: three central 8 Specific building data for Mexico City buildings indicated the relationship was T = 0.12 + 0.086N [Scawthorn et al., 1986). 9 The Pino Suarez complex consisted of a 2-story, reinforced concrete base building supporting three 21-story and two 14-story, steel-framed towers (one 14-story at the north and one at the south end of the row of towers). The buildings are sometimes referred to as being 21 stories tall [e.g., Osteraas and Krawinkler, 1989], when in fact they were 23 stories above the ground (21 stories + 2-story base).



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DAMAGED BLDGS (%)

DAMAGED BLDGS. VS. HGT, UNAM SURVEY Central Mexico City, 19 Sept 1966 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 N = 1 to 2

FIGURE 1.42

3 to5

6 to 8 No. FLOORS

9 to 12

> 12

Damage survey. (From Scawthorn, C. et al. 1986, after UNAM, 1985. With permission.)

23-story towers with two 16-story towers each at each end, all steel framed; Figure 1.43B shows the collapsed towers; Figure 1.43B shows the remaining towers, with the southernmost one with cladding removed, exposing the steel framing; Figures 1.43C and D show the buckled box column (note the welded C-section around the buckle, placed following the earthquake to stabilize the buildings). In both remaining 23-story towers, the pattern of buckled columns at the fourth floor was remarkably consistent. Figure 1.44 shows the collapse of the 14-story reinforced concrete Nuevo Leon building in the Tlatelolco complex. As can be seen in Figure 1.44A, the building had an unusual X-bracing scheme in the transverse direction. Inspection indicated (1) columns sheared in the longitudinal direction at the sky-lobbies, and (2) failed X-bracing connections in the transverse direction. Figure 1.45 shows examples of other damage in this event. Figure 1.46 shows the Hotel Regis, which partially collapsed in the earthquake. An immediate ignition quickly engulfed the building and trapped occupants, and spread over the next 24 hours to all other buildings in the block, including several important government buildings. The Mexico City event was perhaps the first earthquake, with the exception of the 1967 Caracas, Venezuela, event (not discussed here), to cause the collapse of numerous major modern high-rise buildings. This was largely due to it being the first earthquake (Caracas excepted) to strongly shake major, modern high-rise buildings. 1.2.5.2 1988: December 7, Armenia (M7.0) On December 7, 1988, at 11:41 a.m. local time, a M7.0 earthquake struck northwest Armenia, at the time a Soviet republic with 3.5 million people. Armenia occupies approximately 30,000 km2 in the southern Caucasus Mountains, generally considered the boundary between Europe and Asia (Figure 1.47). The event caused catastrophic damage that resulted in 25,000 deaths and $16 billion loss in a 400-km2 epicentral region occupied by approximately 700,000 people. Damage and several deaths also occurred in the Kars region of Turkey, 80 km southwest of the earthquake’s epicenter. The Armenian earthquake was a disaster of modern concrete buildings designed and constructed in the 1970s, not of old, unreinforced stone masonry buildings, the predominant type of construction.



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(A)

(B)

(C)

(D)

FIGURE 1.43 Pino Suarez collapse, September 19, 1985 Mexico City earthquake. (A) Collapsed 23-story and 16story Pino Suarez towers. (Photo: E.V. Leyendecker. NOAA/NGDC.) (B) Elevation of two remaining 23-story and one remaining 16-story tower, showing framing. (C) Buckled box column, Pino Suarez tower. (D) Close-up of buckled box column, Pino Suarez tower. (Photos B, C, D: C. Scawthorn.) Shown as Color Figure 1.43.

Faced with a housing shortage and a wave of urbanization in the 1970s, Soviet urban planners relaxed standards for new multistory buildings and raised the height limit from five stories to nine. Failure of these new buildings claimed the most lives. When these buildings collapsed, they fell straight down, either crushing occupants in the compact piles of rubble or suffocating them. In Spitak, there were no undamaged buildings because of the strong epicentral shaking and the shallow (15 km) depth (Figure 1.48). In Leninakan (now called Gyumri), approximately 80% of the building stock was damaged, with many schools, hospitals, apartment buildings, and factories collapsing (Figure 1.49). The predominant building type (unreinforced stone masonry bearing-wall construction) performed poorly overall, although most low-rise unreinforced masonry buildings performed well. Nine-story precast, nonductile concrete frame buildings performed poorly, with less than 12 of the more than 50 buildings remaining standing after the earthquake. In contrast, a group of nine-story buildings having precast concrete wall and floor panels performed well. Of two lift-slab buildings, a 10-story collapsed and a 16-story (the tallest) exhibited severe torsion effects and heavy damage to the first floor.



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(A)

(B)

(C)

FIGURE 1.44 Nuevo Leon collapse, Tlatelolco complex, September 19, 1985 Mexico City earthquake. (A) Overview of the collapse site. Building still standing is virtually identical to collapsed structure. (B) Overview of the wreckage. (C) Search and rescue workers in the wreckage. (Photos: C. Scawthorn.) Shown as Color Figure 1.44.

(A)

(B)

FIGURE 1.45 Examples of Mexico City building damage, September 19, 1985 earthquake. Parts (A), (B), (D), and (G) shown as Color Figure 1.45.



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(D)

(C)

(F)

(E)

(H)

(G)

(I)

FIGURE 1.45 (CONTINUED) © 2003 by CRC Press LLC


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(A)

(B)

FIGURE 1.46 Hotel Regis, Mexico City building damage, September 19, 1985 earthquake. (A) Before earthquake; (B) afterward.

Both the 1985 Mexico City and 1988 Armenia events were now raising serious questions about the safety of high-rise buildings. 1.2.5.3 1989: October 17, Loma Prieta (Mw 7.1) At 5:04 p.m., Tuesday, October 17, 1989, an Mw 7.1 earthquake struck the San Francisco Bay area. The 20-second earthquake was centered about 60 miles south of San Francisco on the San Andreas fault, was largely strike-slip motion, and was felt from Eureka to Los Angeles and east as far as Fallon, NV. It was felt in high-rise buildings in San Diego. Maximum intensity was IX in parts of Oakland and San Francisco (Figure 1.50), numerous landslides occurred in the epicentral area, liquefaction occurred in some areas of Oakland and San Francisco, and a small tsunami with maximum wave height (peak-to-trough) of 40 cm was recorded at Monterey. Among the most catastrophic seismic-induced events were: • The collapse of the double-deck elevated Cypress Street section of Interstate 880 in Oakland (Figure 1.51) • The collapse of a section of the roadbed of the San Francisco-Oakland Bay Bridge (Figure 1.52) • Multiple building collapses in San Francisco’s Marina district, as well as a major fire (see Chapter 29) (Figure 1.53) • The collapse of several structures in the town of Santa Cruz at the Pacific Garden Mall and in other areas around the epicentral region Ground motions were amplified in soft, water-saturated soils around the Bay’s margin, resulting in much of the dramatic damage in parts of San Francisco and Oakland. Fatalities were 62 people, a remarkably low number given the time and size of the earthquake. This was attributed to low traffic and many people having gone home early to watch the third game of the World Series between the San Francisco Giants and the Oakland Athletics. Most casualties were caused by the collapse of the Cypress Street section, which had much lighter traffic than usual for a rush hour, although the fall of a parapet from one building accounted for eight deaths of persons not even in the building (Figure 1.54). The earthquake received extraordinary media attention due to the disruption of the World Series, with national media already focused on the Bay area. Many people across the United States were seeing damage live on TV, such as the collapsed Cypress Street elevated highway, before people only a few blocks away from the damage were aware of it. Damage was estimated at $5.6 billion. Areas outside of Santa Cruz, including the towns of Watsonville, Hollister, and Los Gatos, also suffered heavy damage. At least 3,700 people were reported injured and more than 12,000 were displaced. More than 18,000 homes were damaged and 963 were destroyed. More than 2,500 other buildings were damaged and 147 were destroyed. © 2003 by CRC Press LLC



FIGURE 1.47

Intensity map of December 7, 1988 Armenia earthquake. (Courtesy EQE International)

FIGURE 1.48 Damage in Spitak, December 7, 1988 Armenia earthquake. (Courtesy EQE International)


1-41


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(B)

(A)

FIGURE 1.49

Damage in Leninakan, December 7, 1988 Armenia earthquake. (Courtesy EQE International)

km 0 10 20 Santa Rosa

Vallejo 38°N

Stockton San Francisco X - Extreme Damage

Beverley Oakland

IX - Heavy Damage VIII - Moderate Damage VII - Light Damage VI - Minimal Damage

Half Menlo Park Sunnydale Moon San Jose Bay

V - Strongly Felt

Morgan Hill

II-IV - Lightly to Moderately Felt 37°N

I - Not Felt Undefined (White) 123°W

Santa Clara Hollister 122°W

FIGURE 1.50 Predictive intensity map, October 17, 1989 Loma Prieta earthquake. (http://quake.wr.usgs.gov/ research/strongmotion/intensity/1989.html.)

Downtown San Francisco was effectively closed for 3 days due to curtailment of electric power and gas service while the safety of those systems was restored. Restoration of the San Francisco Bay area following the earthquake was varied. The Bay Bridge was restored to service in 30 days and, surprisingly, impacts on commuter patterns during the disruption were much less than anticipated, due to BART (the regional subway system) and an emergency ferry system providing service. On the other hand, the Cypress Street elevated highway was a key link in the East Bay highway network; opposition over rebuilding the highway along the same route delayed rebuilding for 10 years, while an alternative route was found and the highway rebuilt. Chinatown in San Francisco had major business losses compared to prior to the earthquake, due to the loss of the Embarcadero Freeway. This elevated highway was very similar to the Cypress and sustained similar but not as severe damage (there was no collapse of the Embarcadero Freeway). However, the Embarcadero Freeway had always had significant public opposition due to its route along the waterfront, and opponents seized the © 2003 by CRC Press LLC


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(A)

(B)

(C)

(D)

FIGURE 1.51 Collapse of Cypress Street double-deck elevated highway, Oakland, October 17, 1989 Loma Prieta earthquake. Various views. (Courtesy EQE International) Part (B) shown as Color Figure 1.51.

opportunity and the Freeway was demolished (and replaced by a gracious surface roadway). The freeway provided quick access to Chinatown, however, and when this access was lost, tourism and local patronage in Chinatown was slow to recover. Similarly, the pedestrian mall in Santa Cruz sustained significant and steady business drop-off, due to a lengthy decision-making process regarding rebuilding. 1.2.5.4 1994: January 17, Northridge (Mw 6.7) At 4:31 a.m., Pacific Standard Time, Monday, January 17, a moderate but very damaging earthquake with a moment magnitude of 6.7 struck the densely populated San Fernando Valley in northern Los Angeles. This event was similar in magnitude, time of year, time of day, and epicentral location to the 1971 San Fernando earthquake, and affected largely the same area. Thousands of aftershocks, many in the magnitude 4.0 to 5.0 range, occurred during the next few weeks, further damaging already affected structures. The earthquake was felt throughout much of southern California and as far away as Turlock, CA; Las Vegas, NV; Richfield, UT; and Ensenada, Mexico. The maximum recorded acceleration exceeded 1.0 g at several sites in the area, with the largest value of 1.8 g recorded at Tarzana, about 7 km south of the epicenter, with corresponding MMI of IX (Figures 1.55 and 1.56). A maximum uplift of about 15 cm occurred in the Santa Susana Mountains; many rockslides occurred in mountain areas, blocking some roads; ground cracks were observed at Granada Hills and in Potrero Canyon; and liquefaction occurred at Simi Valley and in some other parts of the Los Angeles basin. In all, these geologic effects were a contributing but not major source of damage. © 2003 by CRC Press LLC


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(A)

(B)

(C)

FIGURE 1.52 Collapse of portion of the east span of the San Francisco Oakland Bay Bridge, October 17, 1989 Loma Prieta earthquake. (A) Collapsed span. (Courtesy EQE International) (B) Close-up of collapsed span; note beam seat at lower left. (C) Close-up of beam seat, showing amount of movement. (Photos B, C: C. Scawthorn) Shown as Color Figure 1.52.

Damage to several major freeways serving Los Angeles choked the traffic system in the days following the earthquake. Major freeway damage occurred up to 32 km from the epicenter (Figure 1.57). Collapses and other severe damage forced closure of portions of 11 major roads to downtown Los Angeles. The death toll was 57, and more than 1,500 people were seriously injured. A few days after the earthquake, 9,000 homes and businesses were still without electricity; 20,000 were without gas; and more than 48,500 had little or no water. Fires caused additional damage in the San Fernando Valley and at Malibu and Venice (Figure 1.58). About 12,500 structures were moderately to severely damaged, leaving thousands of people temporarily homeless (Figure 1.59). Of the 66,546 buildings inspected, 6% were severely damaged (red tagged) and 17% were moderately damaged (yellow tagged). Commercial buildings, especially parking structures and tilt-ups, sustained major damage in a number of cases (Figure 1.60). A surprising find was the cracking of connections in welded steel moment-resistant frames (see Chapter 12). Total direct damage, business interruption, and other losses that could be documented amounted to U.S. $24 billion. Further, amounts that could not be documented were also estimated to arrive at a final estimated economic loss of U.S. $44 billion [EQE, 1997], making this the most expensive natural catastrophe in history up to that time. Significantly, insurance claims were finally10 totaled at $15 billion, leading to insurers foregoing future earthquake underwriting in California for a period. Northridge, following within a little more than 5 years of the Loma Prieta earthquake, marked a turning point in the United States. Given the magnitude of the losses, it was clear that a larger earthquake

10

It took several years for all accounting to be completed (see Chapter 32, this volume, or Scawthorn [1995]).



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(C)

(D)

FIGURE 1.53 Collapse of buildings in the Marina district of San Francisco, October 17, 1989 Loma Prieta earthquake. Shown as Color Figure 1.53.

FIGURE 1.54 Collapse of parapet at building on Bluxome Street, San Francisco. Eight people died under the brick falling from the parapet. Shown as Color Figure 1.54.

could be a severe catastrophe. Caltrans was funded to retrofit all bridges in California by 2000 (and very nearly did so); many utilities accelerated programs initiated following Loma Prieta; the federal government significantly funded research on mitigation, including a multimillion dollar research effort into steel connections; several universities (Stanford and the University of California at Berkeley) accelerated their retrofit programs, and numerous local governments and private enterprises did likewise. © 2003 by CRC Press LLC


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FIGURE 1.55 Trinet Shake Map: instrumental intensity map, January 17, 1994 Northridge earthquake. Rather than using the traditional method of postcard responses from postmasters, this map is generated from instrumental data. (Courtesy U.S. Geological Survey)

1.2.5.5 1995: January 17, Hanshin (Kobe), Japan (Mw 6.8) The earthquake occurred at 5:46 a.m. with moment magnitude of 6.9, about 20 km southwest of downtown Kobe, between the northeast tip of Awaji Island and the island of Honshu. The fault rupture was 30 to 50 km in length, bilateral strike-slip, and ran directly through central Kobe, which contributed to the high level of destruction. Total fatalities were 6,427 people confirmed killed, with 36,896 injured, and extensive damage (VII JMA) in the Kobe area and on Awaji-shima. Over 90% of the casualties occurred along the southern coast of Honshu between Kobe and Nishinomiya. At least 28 people were killed by a landslide at Nishinomiya. About 310,000 people were evacuated to temporary shelters. Over 200,000 buildings were damaged or destroyed. Numerous fires, gas and water main breaks, and power outages occurred in the epicentral area. The earthquake was felt along a coastal strip extending from © 2003 by CRC Press LLC



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FIGURE 1.56 Community Intensity map, January 17, 1994 Northridge earthquake. Rather than using the traditional method of postcard responses from postmasters, this map is generated from citizen voluntary intensity observation data, via the Web. Citizens in California have quickly become familiar with this system and, for a major event, thousands of contributed data will be received and a map generated within an hour or less. (Courtesy U.S. Geological Survey)

FIGURE 1.57 Collapse of freeways, northern Los Angeles County, January 17, 1994 Northridge earthquake (M 6.7). (Courtesy EQE International) Shown as Color Figure 1.57. © 2003 by CRC Press LLC


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FIGURE 1.58 Gas flare and burned home, Balboa Boulevard, January 17, 1994 Northridge earthquake. (Courtesy EQE International)

FIGURE 1.59 Collapsed residential apartment buildings, January 17, 1994 Northridge earthquake. (Courtesy EQE International) Shown as Color Figure 1.59.

(A)

(B)

FIGURE 1.60 Collapse of parking structures, January 17, 1994 Northridge earthquake. (Courtesy EQE International) Shown as Color Figure 1.60.

Suma Ward, Kobe, to Nishinomiya, and in the Ichinomiya area on Awaji-shima (VII JMA); at Hikone, Kyoto, and Toyooka (V JMA); at Nara, Okayama, Osaka, and Wakayama (IV JMA); at Iwakuni (V). The earthquake was also felt at Takamatsu, Shikoku (IV JMA). Right-lateral surface faulting was observed for 9 km with horizontal displacement of 1.2 to 1.5 m in the northern part of Awaji-shima (Figure 1.61). The number of buildings destroyed by the earthquake exceeded 100,000, or approximately one in five buildings in the strongly shaken area. An additional 80,000 buildings were badly damaged. The large numbers of damaged traditional-style Japanese residences and small, traditional commercial buildings of three stories or less account for a great deal of the damage. In sections where these buildings were © 2003 by CRC Press LLC


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17 January 1995 Hyogoken Nanbu Earthquake, M=6.9 135°E 163

35°N

Epicenter (JMA) active fault Kansai Committee JR Osaka Gas JMA aftershock zone (Kyoto U.)

195

Kyoto 263

113

323 601 229

270

481

Nojima Fault

561 819 833 616

Kobe

251 792 >318 >775 Nishinomiya 266

Osaka

245 145 113 220

240

Osaka Bay Awaji Island

149 0

20km

+ 200

FIGURE 1.61 Mainshock epicenter (JMA), aftershock zone, and peak ground motions (cm/s/s) of the 1995 Kobe earthquake, superimposed on a map of active faults, January 17, 1995 Hanshin earthquake. (From EERI [Earthquake Engineering Research Institute]. 1995. The Hyogo-Ken Nanbu Earthquake: Great Hanshin Earthquake Disaster, January 17, 1995. Preliminary Reconnaissance Report. Comartin, C.D., Greene, M., and Tubbesing, S.K., Tech. Eds. Earthquake Engineering Research Institute Report 95–04, sponsored by the Earthquake Engineering Research Institute, Oakland, CA, with support from the National Science Foundation and Federal Emergency Management Agency.)

concentrated, entire blocks of collapsed buildings were common. Several thousand buildings were also destroyed by the fires following the earthquake. Most of the heavily damaged wood-frame buildings were traditional one- or two-story residential or small commercial buildings of Shinkabe or Okabe construction. These buildings normally have very heavy mud and tile roofs (which are effective in preventing typhoon damage), supported by post-andbeam construction. Foundations are often stone or concrete blocks, and the wood framing is not well attached to the foundations. The Shinkabe construction has mud walls reinforced with a bamboo lattice. Okabe construction has thin-spaced wood sheathing that spans between the wood posts and is attached with limited nailing. The exterior plaster is not reinforced with wire mesh or well attached to the wood framing, so it falls off in sheets when cracked. In new (post-1981) construction, nominal diagonal bracing is required to resist lateral loads. Traditional wood-frame construction had the most widespread damage throughout the region, resulting in the largest number of casualties. Collapses led to the rupture of many gas lines. Failures in these buildings were typically caused by large inertial loads from the heavy roofs that exceeded the lateral earthquake load-resisting capacity of the supporting walls. The relatively weak bottom stories created by the open fronts typically collapsed. Unlike most U.S. homes, Japanese homes typically have few if any substantive interior partitions to help resist the earthquake loads. In this respect, the bottom stories are similar to the U.S. homes that are supported on unbraced cripple walls. In older homes, many framing members had been weakened by wood rot. Soil failures exacerbated the damage, because the foundations have virtually no strength to resist settlement, and connections between the residences and their foundations were weak (Figure 1.62). Mid-rise commercial buildings, generally 6 to 12 stories high, make up a substantial portion of the buildings in the Kobe business district. The highest concentration of damaged mid-rise buildings was © 2003 by CRC Press LLC


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(A)

(B)

FIGURE 1.62 Japanese house collapses, January 17, 1995 Hanshin earthquake. (Courtesy EQE International) Shown as Color Figure 1.62.

observed in the Sannomiya area of Kobe’s central business district. In this area, most of the commercial buildings had some structural damage, and a large number of buildings collapsed on virtually every block. Most collapses were toward the north, which was evidently the result of a long-period velocity pulse perpendicular to the fault. This effect has also been observed in other earthquakes. Failures of major commercial and residential buildings were noted as far away as Ashiya, Nishinomiya, and Takarazuka. In general, many newer structures performed quite well and withstood the earthquake with little or no damage. In the heavily damaged central sections of downtown Kobe, approximately 60% of the buildings had significant structural damage, and about 20% completely or partially collapsed. One survey of a 120,000-m2 area in downtown Kobe (the Sannomiya area) found that 21 of 116 buildings, or 18%, were visibly destroyed. Another report indicated that 22% of office buildings in a portion of the Kobe city center were unusable, while an additional 66% needed more than 6 months for complete restoration. City inspectors declared approximately 50% of the multifamily dwellings in Kobe unsafe to enter or unfit for habitation, leaving more than 300,000 people homeless (Figure 1.63). At the Ashiyama seaside town, 21 of 52 mid- and high-rise condominium structures built between 1975 and 1979 had severe damage to the structural steel framing. This innovative and unconventional structural system consisted of macro-steel moment frames in which the column and girder members were large steel trusses. Girders were typically located at every fifth floor. Housing units consisted of precast concrete assemblies that had been brought to the site by barge. Damage observed included the brittle fracture of square, tubular columns up to 50 cm wide with 5-cm-thick walls, and fracturing of steel wide-flange diagonal bracing elements. Residual horizontal offsets in column elements were observed to be as large as 2 cm in some cases. In general, it appeared that the brittle fractures had occurred in framing elements subjected to high combined tensile and shear stresses. In one of the units, six of the eight main steel columns forming the lateral-load-resisting system had fractured (Figure 1.64). Two limited-access highways service the Kobe-Osaka transportation corridor, the Hanshin and Wangan expressways. Built in the mid- to late 1960s, the Hanshin Expressway is the main through road and is almost entirely elevated for more than 40 km. Much of the roadway is supported by single, large reinforced concrete piers spaced every 32 m, many of which failed in shear or bending over a 20-km length. Similar failures of the roadway occurred at many locations, including complete toppling of large reinforced concrete pillars supporting a 500-m section. It was observed that the road deck changed from steel to a heavier concrete section at the location where this collapse occurred. These failures not only closed the Hanshin Expressway for an indefinite period, but severely impeded traffic on Route 43, a street-level highway beneath the expressway (Figure 1.65). Elevated railroad structures and railway stations were particularly hard hit. Three main lines (JR West, Hankyu, and Hanshin) run through the Kobe-Osaka transportation corridor, generally on elevated structures and embankments. All the lines had elevated structure and embankment failures, overpass collapses, distorted rails, and other severe damage. A large number of cars were damaged, and some fell © 2003 by CRC Press LLC


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(A)

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(C)

FIGURE 1.63 Japanese commercial building collapses, January 17, 1995 Hanshin earthquake. (Courtesy EQE International)

onto city streets. Several stations and several kilometers of reinforced concrete elevated structures were destroyed, and numerous spans collapsed. The Rokkomichi Station (built in 1972) of the JR West line was virtually destroyed (Figure 1.66). The Shinkansen (Bullet Train) was constructed ca. 1964. Most of its path in the Kobe area is through two long tunnels under Rokko Mountain. No information on the tunnels’ performance was immediately available. At the east portal of the tunnel, the line is carried on an elevated viaduct built in 1968. For a length of 3 km, this viaduct was severely damaged, with a number of the longer spans collapsing. In general, these collapses were caused by shear failure of the supporting concrete columns (Figure 1.66C). Damage to underground facilities, such as mines, tunnels, or subways, is rare in earthquakes. An unusual example of severe damage to this type of facility occurred in the Kobe subway system, a twotrack line running under central Kobe, which was generally built by cut-and-cover methods in the mid1960s. The double track is typically carried through a concrete tube 9 m wide by 6.4 m high, which widens to 17 m at the stations. The tube typically has about 5 m of overburden, which is supported by 0.4-m-thick walls and roof slabs. The walls and roof slab are supported midspan (between the tracks) by a series of 5-m tall, 1-m long, 0.4-m wide reinforced concrete columns, which failed in shear due to displacements imposed by ground strain. The Port of Kobe, one of the largest container facilities in the world, sustained major damage during the earthquake. In effect, the port was practically destroyed. The total direct damage to the port easily exceeded U.S. $11 billion. The port complex, constructed on three man-made islands — Maya Container © 2003 by CRC Press LLC


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(C)

FIGURE 1.64 Ashiyahama Steel Buildings and column failures, January 17, 1995 Hanshin earthquake. (Photos: C. Scawthorn)

(A)

(B)

FIGURE 1.65 Hanshin Expressway collapse, January 17, 1995 Hanshin earthquake. (Photo (B): C. Scawthorn) Shown as Color Figure 1.65.

Terminal, Port Island (with an area of 10 km2), and Rokko Island (with an area of 6 km2) — accounts for approximately 30% (2.7 million containers per year) of Japan’s container shipping. At the time of the earthquake, the three facilities included 27 active container berths and various other wharves, ferry terminals, roll-on facilities, and warehousing. In addition, the older parts of the port contain numerous other facilities, such as an extensive shipyard. Also, at the time of the earthquake, several new islands © 2003 by CRC Press LLC


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(A)

(B)

FIGURE 1.66

(C)

Railroad and subway damage, January 17, 1995 Hanshin earthquake. (Courtesy EQE International)

were under development, and new berths were under construction to the east of Rokko Island (Figure 1.67). Numerous fires broke out, exacerbated by loss of water supply throughout the affected region (Figure 1.68) (see Chapter 29). 1.2.5.6 1999: August 17, Turkey (Mw 7.4) Similar to the San Andreas fault being the North American-Pacific plate boundary, Turkey lies on a major boundary between the African and Eurasian plates. The North Anatolian Fault Zone (NAFZ) is the most prominent active fault in Turkey and has been the source of numerous large earthquakes throughout history, including a number of major earthquakes in the twentieth century [Ambraseys and Finkel, 1995] (Figure 1.69). The Mw 7.4 Marmara (also known as Kocaeli) earthquake occurred at 3:10 a.m. local time, August 17, 1999, on the east–west trending north strand of the NAFZ, about 100 km southeast of Istanbul. The 125-km-long fault and high damage area follows or is close to the south shore of Izmit Bay (Figure 1.70), and has predominantly 2.2 m right lateral displacement, from Adapazari in the east to Yalova in the west. Significant vertical fault scarps of as much as 2 m occur at several locations (Figure 1.71). Peak ground accelerations of approximately 0.4 g were recorded near the fault, and liquefaction and subsidence were observed on the shores of Izmit Bay and Lake Sapanca. Figure 1.72 presents the response spectra for the north–south (NS) component of the YPT record, recorded at the Yarimca petrochemical complex on the north shore of Izmit Bay, approximately 4 km from the fault trace. Substantial geotechnical effects occurred due to the earthquake, especially along the south shores of Izmit Bay and Lake Sapanca, where settlement and slumping were observed at numerous locations (Figure 1.73). In Adapazari, significant settlement and liquefaction were observed, resulting in very major damage to buildings (Figure 1.74). Adapazari (at the eastern terminus of faulting) is a soft soil site that exhibited © 2003 by CRC Press LLC


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(A)

(B)

(C)

FIGURE 1.67 Figure 1.67.

Port damage, January 17, 1995 Hanshin earthquake. (Courtesy EQE International) Shown as Color

FIGURE 1.68

Fires, January 17, 1995 Hanshin earthquake. Shown as Color Figure 1.68.



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Location of August 17, 1999 Turkish Earthquake 1992 1967 1957 1944

1951

1943

1942

1939

Black Sea Istanbul

7.3

Izmit

7.3 n Fault lla Anato Nor th Ankara 100km

7.1

7.1 7.0 1999 Epicenter

0

7.9

TURKEY

6.8

Historical earthquake epicenter and magnitude 1957 Extent of surface rupture Direction of relative motion on fault

FIGURE 1.69 turkey/.)

Progressive North Anatolian Fault rupture in adjacent earthquakes. (From quake.wr.usgs.gov/study/

29°

30°

BOGAZIC UNIVERSITY KANDILLI OBSERVATORY and EARTHQUAKE RESEARCH INSTITUTE SEISMOLOGY LABORATORY

31°

BLACK SEA

Istanbul 41°

41° Düzce Adapazan Hendek

Izmit

MARMARA SEA Yalova

Gölcük

Akyazi

Gernlik 17.08.1999 Izmit Earthquake (Mw = 7.4) Bursa Bileclk

5<M1.0 >1.0

0.15–0.25 0.15 1/3 to 1/2 PGA 1/2 PGA

>1.0 >1.15 >1.0 >1.0

Comments Major earthquake Great earthquake Standard of practice; somewhat larger for critical conditions Standard of practice With a 20% strength reduction With a 20% strength reduction

Source U.S. Army Corps of Engineers [1982] State of California Japan Seed [1979a] Marcuson and Franklin [1983] Hynes-Griffin and Franklin [1984]

Source: Adapted from Abramson, L.W., T.S. Lee et al. 2002. Slope Stability and Stabilization Methods. New York, John Wiley & Sons.

where c and φ are the Mohr-Coulomb strength parameters along the failure surface and the summation is carried out over all M slices. Compared to the nonseismic case, F h clearly results in a reduction of the FS. On the other hand, the effect of F v is less pronounced because it appears with the same sign in both the numerator and the denominator. As a result, it is common to neglect F v altogether. Most modern commercial limit equilibrium slope stability programs allow for this type of pseudostatic analysis. The difficulty arises in selecting appropriate values of kh and FS. Because kh represents the inertial shaking effects, it is reasonable to assume that it should be related in some fashion to the peak horizontal acceleration amax (PHA). In general, slope deposits are compliant to various degrees and amax only occurs over a very short period of time. Therefore, in practice kh is taken as a fraction of the maximum acceleration. Considerable judgment is required in selecting appropriate values of kh. A number of suggestions can be found in the literature [Seed, 1979a; U.S. Army Corps of Engineers, 1982; Marcuson and Franklin, 1983; Hynes-Griffin and Franklin, 1984; Abramson et al., 2002] and some of these are listed in Table 7.9. The value of kh is often prescribed in local codes. Although easy to conduct, the pseudostatic approach is quite simplistic. It attempts to represent complex dynamic behavior in terms of static forces. Stability is expressed in terms of an overall factor of safety. The implicit assumption is that the soil is rigid-perfectly plastic and unchanging. This does not represent an appropriate approach in cases where significant excess pore pressures may accumulate or where strength degradation due to seismic loading is in excess of approximately 15% [Kramer, 1996]. Displacements associated with time-varying inertial forces can be estimated, to a first degree, with the procedure proposed by Newmark [1965], which represents an extension of the pseudostatic approach. An analogy is made between failure along a given sliding surface in a slope and a block initially resting on an inclined surface (Figure 7.50). The block is subjected to horizontal inertial forces kh(t)W that © 2003 by CRC Press LLC

0068_C07_fm Page 46 Tuesday, August 13, 2002 1:58 PM

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A

kh(t)W

kh(t)W

W B

W

ay

C

t

FIGURE 7.50 Newmark sliding block method.

correspond to seismic motions propagating through the slope deposit. Displacement is initiated when the sum of the downslope static and inertial forces equals the strength developed at the interface between the block and the inclined plane. This condition occurs when the factor of safety is 1.0 and corresponds to a yield coefficient ky and a yield acceleration ay = kyg. When the block is subjected to an interval with acceleration larger than ay , it will begin to move relative to the plane (Figure 7.50). The corresponding velocities and displacements can be obtained through integration of the acceleration record in excess of ay . The assumption is that the sliding mass constitutes a rigid body. This assumption is only appropriate for slopes where soils are very stiff or where the motion is of low frequency. Where this is not the case careful consideration must be given in selecting an appropriate accelerogram. This may be done by carrying out a site response analysis and determining acceleration series at various points along the potential failure surface. An average horizontal equivalent acceleration (HEA) can be developed for use with the Newark sliding block method. With reference to Figure 7.50, this would be computed as: HEA (t ) =

m Aa A (t ) + mB aB (t ) + mC aC (t ) m A + mB + mC

(7.42)

where m represents the mass of soil in each slice above the point where the acceleration response a(t) is given. Conversely, a dynamic finite element analysis can be conducted to calculate average accelerations over finite lengths of the potential failure surface based on integration of the time-dependent stresses. These acceleration time series can in turn be used as input for the sliding block analysis. A number of computer programs are available that can carry out such an analysis, including QUAD-4 [Idriss et al., 1973] and FLUSH [Lysmer et al., 1975]. Makdisi and Seed [1978] developed a simplified procedure to estimate permanent horizontal displacements of earth dams and embankments. These are determined with the aid of the charts in Figure 7.51. The analysis is based on the dynamic response of embankments subjected to a range of ground motions representing earthquakes of various magnitudes. Makdisi and Seed calculated the distribution of average maximum acceleration with depth below the crest of the embankment (Figure 7.51A and B). Displacements were estimated by comparing the acceleration at depth to the corresponding yield acceleration by means of a Newmark-type sliding block analysis. The yield acceleration was taken as 80% of the undrained shear strength of the soil. Results of the sliding block analysis are summarized in Figure 7.51C, from which the horizontal displacement can be calculated for any failure surface extending a distance y below the crest. To is the fundamental period of the dam, which can be obtained by means of an approximate shear beam analysis [Gazetas, 1982] or other two-dimensional dynamic response modeling approach. Although widely used, it is important to note that the Makdisi-Seed procedure is based on a limited set © 2003 by CRC Press LLC


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Geotechnical and Foundation Aspects

of case studies and, strictly speaking, should only be applied to dams and embankment slopes with seismic motions corresponding to earthquake magnitudes in the range of 6.5 to 8.5 where the PGA at the base of the embankment is at least 0.2 g. A number of equivalent-linear procedures have been suggested to estimate approximate permanent displacements in dams and slopes [Lee, 1974; Serff et al., 1976]. Their most appealing quality is that they retain the simplicity of linear material behavior. They work well, provided that pore pressures remain relatively low and that seismic motions do not induce excessive levels of material nonlinearity [Finn, 2001]. However, it is likely that in the future more reliance will be placed on stress-based finite element and other similar numerical procedures that directly incorporate inelastic soil behavior. A sufficient number of two- and three-dimensional analyses have been conducted using constitutive models ranging from simple hysteretic to complex elasto-plastic models to validate this approach [Prevost et al., 1985; Finn, 1988; Griffiths and Prevost, 1988; Marcuson et al., 1992]. Computer codes such as TARA-3 [Finn et al., 1986], PLAXIS [Brinkgreve and Vermeer, 1988], and QUAKE/W [Quake/W, 2001] have been developed to carry out these types of analysis.

7.7 Earthquake-Resistant Design of Retaining Walls Soil pressures that act on retaining structures during earthquake shaking include both static and dynamic components. Dynamic forces vary as the shaking proceeds and reflect not only the type of wall and soil retained but also complex structure-interaction effects that in general are difficult to analyze. For example, motion components that are close to the natural period of the soil-structure system can induce very large transient pressures. Also, phase differences along the length of the retaining structure may induce significant shear forces and bending moments. In practice, however, most walls are designed using simplified pseudostatic methods similar to those described previously for natural and constructed slopes. The approach is to determine all static forces, along with pseudostatic seismic forces, and proceed with conventional stability checks for overturning, sliding, bearing capacity, and overall stability. Seismic effects are usually considered using the Mononobe–Okabe method [Mononobe and Matsuo, 1929; Okabe, 1929], which represents an extension of the Coulomb theory. The forces acting on active and passive wedges of cohesionless soil are shown in Figure 7.52. The pseudostatic forces are given in terms of the wedge weight W and the seismic coefficients kh and kv described earlier. For the active case (Figure 7.52A), the total lateral force on the wall corresponds to the maximum value of Pae exerted by any wedge with critical failure surface of inclination η. This force can be expressed as: Pae =

1 γH 2 (1 − kv )K ae 2

(7.43)

where K ae =

(

cos 2 φ − θ − β

) ( )

)

1/ 2     − − δ + φ φ α β sin sin ( )    cos 2 θ cos β cos δ + θ + β 1 +    cos δ + θ + β cos (α − θ)    

(

)

(

2

(7.44)

and  k  β = tan −1  h   1 − kv 


(7.45)

0068_C07_fm Page 48 Wednesday, July 31, 2002 8:20 AM

7-48


Y

H

(A) 0

F.E. Method 0.2 “Shear Slice” (range for all data) 0.4 y/h 0.6

Average of all data

0.8

10 0

0.2

(B)

0.4 0.6 kmax/ümax

0.8

1.0

10

M~8

1

M~8 7

U/kmax g To − seconds

M~7

6 0.1

M~6 0.01

0.001 (a)

(b)

0.0001 0

(C)

0.2

0.4

0.6 ky/kmax

0.8

1.0 0

0.2

0.4

0.6 ky/kmax

0.8

1.0

FIGURE 7.51 Simplified procedure to estimate permanent horizontal displacements of earth dams and embankments. (From Makdisi, F.I. and H.B. Seed. 1978. “Simplified Procedure for Estimating Dam and Embankment Earthquake-Induced Deformations,” J. Geotech. Eng. ASCE, 104(GT7), 849–867. Used by permission of the American Society of Civil Engineers.) © 2003 by CRC Press LLC


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A

C

α

C

α A

Fv

Fv

γ, φ c=0 Fh

θ

θ Fh W

φ

W

Ppe R

δ Pae

R

φ

δ

γ, φ c=0 η

η B

B (A) Active

(B) Passive

FIGURE 7.52 Mononobe–Okabe method. Forces acting on active (A) and passive (B) wedges of cohesionless soil.

Note that if φ – α – β < 0, Equation 7.44 cannot be evaluated. This means that equilibrium is not satisfied. For stability under seismic conditions it is therefore necessary that α ≤ φ – β . The location of the combined wall force Pae can be obtained by separating Pae into static and dynamic components: Pae = Pa + ∆ Pae

(7.46)

The static force Pa acts at a height of H/3 above the base of the wall. According to Seed and Whitman [1970], the dynamic component Pae acts at an approximate elevation of 0.6H above the base. Hence, the location of Pae can be calculated as: z=

Pa ( H 3) + ∆Pae (0.6 H ) Pae

(7.47)

The critical failure surface for seismic conditions is flatter than for the static case. An expression for the angle δ can be found in Kramer [1996]. The Mononobe–Okabe method for estimating Pae can also be applied to c-ϕ backfill soil [Prakash and Saran, 1966]. For the passive case (Figure 7.52B), the total lateral force on the wall is given by: Ppe =

1 γ H 2 (1 − kv )K pe 2

(7.48)

where K pe =

(

cos 2 φ + θ − β

) ( )

)

1/ 2      sin (δ + φ) sin φ + α − β   2 cos θ cos β cos δ − θ + β 1 −    cos δ − θ + β cos (α − θ)    

(

)

(

2

(7.49)

The Mononobe–Okabe method is subject to the limitations of the Coulomb theory and to the same uncertainties associated in selecting appropriate coefficients kh and kv as was discussed earlier. This method should not be used for soils that may liquefy or otherwise may lose strength due to the shaking. Wood [1973] showed that where the principal energy of the input motions approaches the fundamental frequency of the unrestrained backfill ( fo = Vs /4H), dynamic amplification becomes an important factor, which is not considered in any of the analysis procedures described in this section. © 2003 by CRC Press LLC


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Elastic soil

H L

Unyielding wall

1.2

ν = 0.5 ν = 0.4

1.0

0.8

ν = 0.3

0.8

ν = 0.5

ν = 0.2 Fp 0.6

0.6

0.4

Fm 0.4

0.2

0.2

ν = 0.4

ν = 0.3 ν = 0.2

0

0 0

2

4

6

8

10

0

L/H

2

4

6

8

10

L/H

Dimensionless thrust factor for various geometries and soil Poisson’s ratio values.

Dimensionless moment factor for various geometries and soil Poisson’s ratio values.

FIGURE 7.53 Dynamic loads on rigid retaining walls. (Modified from Wood, J. 1973. “Earthquake-Induced Soil Pressures on Structures,” Report EERL 73-05, California Institute of Technology, Pasadena, p. 311.)

Very large gravity walls and other retaining structures that are restrained may not yield sufficiently to reach active or passive plastic equilibrium states. Wood [1973] presents a method to calculate dynamic lateral forces and overturning moments for a rigid wall by assuming that the backfill soil behaves in a homogeneous, linearly elastic fashion, and that the seismic excitation is due to a uniform, constant, horizontal acceleration throughout the backfill. Wood actually considered two rigid walls separated by a distance L of sufficient magnitude to avoid interaction between the two of them (Figure 7.53). The dynamic force and moment are calculated as:


∆Poe = γ H 2

ah F g p

(7.50)

∆M oe = γ H 3

ah F g m

(7.51)


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where ah is the amplitude of the motion. The dimensionless factors F p and F m are shown in Figure 7.53. The point of application of ∆Poe, above the base of the wall, is given by: z=

∆M oe ≈ 0.63H ∆Poe

(7.52)

The previous methods assume that the backfill is not immersed in water. Although walls are typically built with provisions for proper drainage, this is not possible for retaining structures where water is found on either side, as is the case for many harbor and other shore-front structures. Extensive damage to such structures was observed during recent earthquakes in Turkey, Taiwan, and Japan and in many cases were attributed to dynamic water effects. Water influences the inertial forces in the backfill and may result in substantial hydrodynamic pressures. Also, a loose, saturated granular backfill may liquefy and cause undesirable settlements. If the permeability of the soil is sufficiently small (typically less than about 10–3 cm/sec), the solid and fluid fractions are likely to move in unison, whereas if the permeability is very large, the fluid will tend to move independently of the solid structure. In the former case, the inertial forces are dependent on the total unit weight of the soil, whereas in the latter case they will be a function of the submerged unit weight. If the type of backfill is such that water is restrained by the soil skeleton, the Monotobe–Okabe method can be modified to give the active total soil force on the wall by replacing the soil unit weight in Equation 7.43 according to: γ = γ b (1 − ru )

(7.53)

where r u is the pore pressure ratio, defined as the pore pressure divided by the effective confining pressure, and γb is the submerged unit weight. The seismic coefficient given in Equation 7.45 now becomes:   γ sat kh β = tan −1    γ b (1 − ru ) (1 − kv ) 

(7.54)

where γsat is the saturated unit weight of the soil. In addition to the hydrostatic water pressure in the absence of shaking, an additional equivalent hydrostatic term must be considered which is calculated using an equivalent fluid unit weight: γ w −eq = γ w + ru γ b

(7.55)

If the backfill is partially submerged to a height λH above the base of the wall (λ < 1.0), it is necessary to use an average soil unit weight:

(

)

γ = λ2 γ sat + 1 − λ2 γ d

(7.56)

where γd is the dry unit weight of the soil. The additional equivalent hydrostatic term calculated with the equivalent fluid unit weight in Equation 7.55 also must be included for partially submerged backfill. Permanent displacements of yielding walls are often a greater concern than outright failure because excessive deformations can severely limit their intended function. Richards and Elms [1979] use Newmark’s sliding block method to estimate permanent lateral displacement of gravity walls. Consider a gravity wall acted upon by a Monotobe–Okabe lateral force Pae during seismic shaking, as shown in Figure 7.54. Lateral displacement will be initiated on the verge of active failure, at which point plastic equilibrium dictates that:



7-52


θ khW

Pae δ

W

FIGURE 7.54 Forces acting on gravity wall during seismic shaking.

φb

N = W + Pae sin (δ + θ)

(7.57)

T = khW + Pae cos (δ + θ)

(7.58)

T = N tan φb

(7.59)

where φb is the friction angle between the base and the foundation soil. These expressions can be combined to obtain: kh =

ay g

= tan φb −

Pae cos (δ + θ) − Pae sin (δ + θ) tan φb W

(7.60)

The term ay represents the yield acceleration, beyond which lateral displacement occurs. Using the results of Newmark [1965] and Franklin and Chang [1977], Richards and Elms developed the following relationship to estimate permanent lateral displacement: d perm = 0.087

v p2 a3p a3y

(7.61)

In this equation vp is the peak velocity and ap the peak acceleration at the wall location. This type of analysis should not be used indiscriminately because it is rather simplistic and ignores several effects that may play an important role in some cases. Only accelerations in the direction normal to the length of the wall are considered. Neither vertical nor horizontal acceleration components in the direction of the length of the wall are accounted for. Also, the backfill and the wall are assumed to act as one and no amplification of input motions occurs in the retained soil. Only lateral sliding displacements are estimated but not tilting or vertical settlements. Whitman and Liao [1985] considered some of these effects and estimated errors associated with them. Kramer [1996] presents procedures for the design of various types of retaining structures that are based on the pseudostatic methods described in this section. A more rigorous approach to the design and analysis of retaining structures is possible by means of the finite element method. In fact, the finite element method is quickly becoming the method of choice for the design of all but the simplest of retaining structures. © 2003 by CRC Press LLC



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7.8 Soil Remediation Techniques for Mitigation of Seismic Hazards If seismic hazards are deemed to be unacceptably high because of poor soil conditions, it is often possible to achieve improved seismic performance through the use of one or more soil remediation techniques. Poor performance is the result of (1) inadequate strength, (2) low stiffness, or (3) insufficient drainage. Many remediation techniques have evolved over the years, mostly through trial and error, aimed at improving at least one of these properties. When selecting one or more mitigation methods, it is important to consider the effectiveness of the remediation approach for the particular situation at hand, cost, environmental consequences, regulatory requirements, and technical feasibility. Also, careful assessment of the degree of ground improvement achieved is essential. The subject of soil remediation is quite extensive and a number of excellent sources and case studies are available in the literature [Hausmann, 1990; Hryciw, 1995; Mitchell et al., 1995; Schaefer, 1997]. The purpose of this section is to highlight the most promising techniques for improving seismic performance. Excavation and replacement may be a cost-effective solution for sufficiently shallow deposits. Placing a structure at depth may bypass undesirable surface soils, although costs and construction difficulties increase rapidly with depth and with excavation below the water table, particularly in high-permeability soils. Surrounding deposits that have not been modified may still cause problems as lifelines and other connecting structures may be damaged during an earthquake. Compaction can be accomplished using a variety of techniques that are aimed at increasing the density of soil, thereby resulting in improved stiffness, strength, and liquefaction resistance. Vibrocompaction is most effective for clean, loose cohesionless soils with less than about 15% silt and less than about 3% clay content. It is achieved by vibration of the head of the vibration probe as it is withdrawn. Because compaction occurs only within a short range of the probe, the procedure must be repeated at regular spacings on the order of 5 to 10 ft. Of course, the spacing depends on the size of the probe and the soil type. During the past few years, larger and more powerful vibrators have been introduced, which allow larger spacings and deeper penetration (in some cases, up to 120 ft). When compaction is achieved by horizontal motion of the vibrator, it is referred to as vibroflotation. Vibratory techniques also exist that induce vertical vibration, such as Terra-Probe, Vibro-Wing, and Tri-Star or Y-Probe methods [Hryciw, 1995]. Wightman [1991] presents an overview of this technique. Dynamic compaction involves dropping a heavy weight from a large distance. The high energy upon impact is provided by heavy steel or concrete units (6 to 35 tons) that freefall from distances up to 100 ft or more. It often represents an alternative to vibrocompaction, especially for uncontrolled fills, municipal solid waste deposits, coal mine spoils, and other loose soils. Soils with significant amounts of fines (20% or more) can in some cases be densified quite effectively. The depth of improvement is related to the tamper weight and drop height but may reach up to 30 ft or more. A good reference on dynamic compaction is the FHWA publication by Lukas [1986], which was updated in 1996 as FHWA Geotechnical Engineering Circular No. 1. Blast densification is another high-energy ground improvement technique that achieves densification by destroying existing soil structure and forcing soil grains into a tighter configuration as a result of shock waves produced by the blast. Charges are placed in predrilled or jetted holes. The size of the charge must be selected carefully so that it is sufficiently large to be effective but not too intense to cause excessive vibrations that may cause damage to nearby structures. Liquefaction may develop and may have to be controlled by proper drainage means. Because of the potential of undesirable effects in surrounding areas, blast densification has not seen the same degree of use as the previous techniques. However, it has been shown effective in densifying soils to depths of approximately 130 ft [Narin van Court and Mitchell, 1995]. Compaction piles achieve densification by displacing the soil as the piles are driven into the ground. Because they typically densify the soil to distances on the order of a only few pile diameters, they must be placed close together to be effective. Improvements have been noted to depths of about 60 ft [Marcuson et al., 1991]. Grouting involves the injection of various grouting agents into the soil. Compaction grouting has been shown to be effective for mitigation of liquefaction potential [Graf, 1992; Boulanger and Hayden, 1995]. The technique consists of injecting a soil-cement grout of sufficient plasticity and friction under pressure, © 2003 by CRC Press LLC


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which displaces and densifies soil in a controlled fashion. Although the technique is widely used for a number of purposes, there is little in terms of a rational design methodology. Instead, the method has progressed based almost entirely on trial and error and a few empirical observations. Research is now under way to establish optimum grout characteristics, injection pressures, and effective pumping rates vs. soil characteristics [Schaefer, 1997]. Advances have been made recently in terms of equipment and monitoring, and particularly in terms of evaluating the degree of improvement through seismic testing. Whereas compaction grouting results in discrete bulbs of grout in the soil, permeation grouting uses low viscosity grouts that are able to penetrate into individual voids with minimal disturbance to the soil structure. The types of grouts used range from high-slump cements to various gels of very low viscosity, depending primarily on the void characteristics of the soil [Graf, 1992]. In jet grouting, a high-pressure fluid is used to erode soil in a predrilled hole and replace it with an engineered soil-grout mix to form a solid element sometimes referred to as soilcrete or grout column. The dimensions of the grouted cavities are controlled by the injection pressure, the type and operation of the injection nozzle, and the erosion susceptibility of the soil. Jet grouting is most successful in cohesionless soils and can be performed as deep as predrilled holes can be provided. This technique has been used successfully as a liquefaction countermeasure [Hayden, 1994]. Another soil improvement technique that can be used to mix underperforming soil with grouts and admixtures is to use large rotary augers to churn up soil and blend in cementitous agents that result in increased stiffness and strength. Soil-mixing can be used to provide support for overlaying structures or to reduce liquefaction hazards [Schaefer, 1997]. Vibrostone columns have been used to improve soils prone to liquefaction since the 1970s [Dobson, 1987]. Construction is accomplished by introducing a vibratory probe into the ground, which displaces the soil laterally through vibratory motion and therefore induces densification in the surrounding volume. The void that is created is backfilled with stone. The resulting column and surrounding soil provide for higher stiffness and strength. Also, the damaging effects of liquefaction are reduced because the stone columns provide a relief path for excess pore pressures to dissipate. A review of the performance of vibrostone columns for reduction of soil liquefaction is presented by Baez [1995]. Wick drains can also be used to dissipate excess pore pressures generated during earthquake shaking. They consist of either properly graded sand and gravel drains or of prefabricated geosynthetic materials. Figure 7.55 illustrates the general soil particle size ranges for applicability of various stabilization techniques. An excellent review of liquefaction remediation techniques is presented in PHRI [1997].

Defining Terms Amplification — Increase in ground motion due to the presence of soil deposits, usually expressed in terms of the ratio of ground surface to bedrock motion.

Attenuation — Rate of seismic ground motion decrease with distance. Backbone curve — Nonlinear stress-strain relationship for a soil that is loaded monotonically. Bracketed duration — Time between the first and last exceedance of a given threshold acceleration during a seismic event.

Cyclic resistance ratio — Cyclic stress ratio above which liquefaction is triggered. Cyclic strength — Shear stress during cyclic loading at which the resulting deformations are considered excessive.

Cyclic stress ratio — Ratio of earthquake-induced equivalent shear stress amplitude to effective overburden stress.

Damping curve — Relationship between viscous damping coefficient and shear strain for nonlinear soils.

Epicenter — Projection on the surface of the Earth directly above the location where the initial seismic disturbance occurred. Equivalent damping ratio — Ratio between the dissipated and stored energies within a hysteretic loop at a given shear strain. © 2003 by CRC Press LLC


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Gravel

Sand

Silt

Clay

Vibro-compaction Blasting Particulate Grout Chemical Grout Displacement Grout Pre-compression Dynamic Deep Compaction Electro-osmosis Reinforcement (tension, compression, shear) Thermal Treatment Admixtures

10

1.0

0.1

0.01 Particle Size (mm)

0.00 1

0.0001

FIGURE 7.55 Applicable grain size ranges for different stabilization methods. (Modified from Mitchell, J.K. 1981. “Soil Improvement: State-of-the-Art,” in Proc. Tenth International Conference on Soil Mechanics and Foundation Engineering, Stockholm, American Society of Civil Engineers, New York.)

Equivalent-linear soil model — A stress-strain model that uses elastic shear modulus and damping ratio parameters that are functions of shear strain. These parameters are updated iteratively during each incremental step until they match the target values corresponding to the level of strain in the soil. Flow failures — Soil failure due to liquefaction involving large lateral displacements that occur when the static shear stress along a potential failure plane is larger than the shear strength of the liquefied soil. Intensity — Strength of shaking from a particular earthquake at a given location. Lateral spreading — Small to moderate lateral displacements associated with liquefaction that occur due to seismic shaking when the static shear stress is less than the shear strength of the liquefied soil. Liquefaction — A process in which the soil loses shear strength and approaches the state of a liquid due to a transient accumulation of excess pore pressures. Magnitude — A measure of the energy released at the source of the earthquake. Magnitude scaling factors — Factors to be applied to the cyclic resistance ratio obtained from the standard penetration test, cone penetration test, and shear wave velocity liquefaction charts for earthquakes of magnitude other than 7.5. Modulus reduction curve — Relationship expressing the rate at which the maximum shear modulus of soil decreases with shear strain due to nonlinear effects. Near-field — Within a distance equal to the dimension of the fault section involved in the earthquake. Nonlinear cyclic model: — A stress-strain model that is truly nonelastic and that models the nonlinearity through an explicit relationship involving nonelastic material parameters. Peak ground acceleration (PGA) — Maximum recorded acceleration amplitude. © 2003 by CRC Press LLC


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Pseudostatic approach — Stability analysis procedure in which inertial forces caused by earthquake shaking are approximated by equivalent static forces that are a function of peak ground motion acceleration and soil weight. Residual shear strength — Soil shear strength after seismic shaking has stopped. Response spectrum — A plot of maximum acceleration, velocity, or displacement for a single-degreeof-freedom oscillator as a function of system period, for a given input motion and system damping (typically 5%). Sand boils — Sand and silt mounds deposited by spouting from crater-like vents as excess pore pressure dissipates from buried deposits that have liquefied. Seismic hazards — Possible types of damage from earthquake shaking. Seismic waves — Waves originating from an earthquake event and traveling through geologic media, including compressional p-waves, shear S-waves, surface Love waves, and long-period Rayleigh waves. Site-specific ground response analysis — Ground motion analysis that involves site-specific material distributions, dynamic soil response, and boundary conditions. It is usually carried out using a numerical approach. Strong motion — Seismic shaking that is of sufficient intensity to have a significant effect on engineering structures. Tsunami — Large tidal wave that follows from the sudden displacement of the seafloor or a submarine landslide, usually caused by an offshore earthquake. Yield acceleration — Acceleration corresponding to a pseudostatic safety factor equal to 1, above which permanent deformations accumulate.

References Abrahamson, N.A. and K.M. Shedlock. 1997. “Overview,” Seismol. Res. Lett., 68(1), 9–23. Abrahamson, N.A. and P.G. Somerville. 1996. “Effects of the Hanging Wall and Footwall on Ground Motions Recorded during the Northridge Earthquake,” Bull. Seismol. Soc. Am., 86, S93–S99. Abramson, L.W., T.S. Lee, et al. 2002. Slope Stability and Stabilization Methods, John Wiley & Sons, New York. Aki, K. 1988. “Local Site Effects on Strong Ground Motion,” in Earthquake Engineering and Soil Dynamics, Vol, II, Recent Advances in Ground Motion Evaluation, Geotechnical Special Publication No. 20, American Society of Civil Engineers, New York. Andrews, D.C.A. and G.R. Martin. 2000. “Criteria for Liquefaction of Silty Soils,” in Proc. 12th World Conference on Earthquake Engineering, Auckland, New Zealand. Andrus, R.D. and K.H. Stokoe. 1997. “Liquefaction Resistance Based on Shear Wave Velocity,” in Proc. NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Salt Lake City, NV, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. Arnold, C. and R. Reitherman. 1982. Building Configuration and Seismic Design. John Wiley & Sons, New York. Baez, J.I. 1995. “A Design Model for the Reduction of Soil Liquefaction by Vibro-Stone Columns,” University of Southern California, Los Angeles, p. 207. Bardet, J.-P., N. Mace, et al. 1999. “Liquefaction-Induced Ground Deformation and Failure,” University of California, Department of Civil Engineering, p. 125. Bolt, B.A. 1969. “Duration of Strong Motion,” in Proc. 4th World Conference on Earthquake Engineering, Santiago, Chile. Boore, D.M., W. Joyner, et al. 1997. “Empirical Near-Source Attenuation Relationships for Horizontal and Vertical Components of Peak Ground Acceleration, Peak Ground Velocity, and Pseudo-Absolute Acceleration Response Spectra,” Seismol. Res. Lett., 68(1), 154–179. Boulanger, R.W. and R.F. Hayden. 1995. “Aspects of Compaction Grouting of Liquefiable Soils,” ASCE J. Geotech. Eng., 12(121), 844–855. © 2003 by CRC Press LLC



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Brinkgreve, R.B.J. and P.A. Vermeer. 1988. “PLAXIS, Finite Element Code for Soil and Rock Analysis, Version 7, Balkema, Rotterdam. BSSC (Building Seismic Safety Council). 1997. NEHRP Recomme nded Provisions for Seismic Regulat ions for New Building s and Othe r Structures, National Institute of Building Sciences, p. 335. Castro, G. and S.J. Poulos. 1977. “Factors Affecting Liquefaction and Cyclic Mobility,” J. Geotech. Eng. Div. ASCE, 106(GT6), 501–506. Cetin, K.O. and R.B. Seed. 2000. “Nonlinear Shear Mass Participation Factor (Rd) for Cyclic Shear Stress Ratio Evaluation,” University of California, Berkeley. Chopra, A.K. 2001. Dynamic s of Structures, Theory and Applicat ions to Earthquak e Engineering. PrenticeHall, Upper Saddle River, NJ. Cruden, D.M. and D.J. Varnes. 1996. “Landslide Types and Processes,” in Landslides, Investigation and Mitigation, Transportation Research Board Special Report 247, pp. 36–75, A.K. Turner and R.L. Schuster, Eds., National Academy Press, Washington, D.C. Dobson, T. 1987. Case Histories of the Vibro Systems to Minimiz e the Risk of Liquefaction, Geotechnical Special Publication No. 12, American Society of Civil Engineers, New York, pp. 167–183. Faccioli, E. 1991. “Seismic Amplification in the Presence of Geologic and Topographic Irregularities,” in Proc. Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, St. Louis, MO. Finn, W.D.L. 1988. “Dynamic Analysis in Geotechnical Engineering,” in Earthquak e Engineering and Soil Dynamic s, Vol. II: Recent Advances in Ground-Motion Evaluat ion, Geotechnical Special Publication 20, American Society of Civil Engineers, New York. Finn, W.D.L. 1991. “Geotechnical Engineering Aspects of Microzonation,” in Proc. Fourth International Conference on Microzonation, Earthquake Engineering Research Institute, Stanford University, Palo Alto. Finn, W.D.L. 2000. “State-of-the-Art of Geotechnical Earthquake Engineering Practice,” Soil Dyn. Earthquake Eng., 20, 1–15. Finn, W.D.L. 2001. “Earthquake Engineering,” in Geotechnical and G eoenvironmental E ngineering Handbook, R.K. Rowe, Ed., Kluwer Academic, Boston, pp. 615–659. Finn, W.D.L., P.M. Byrne, et al. 1996. “Some Geotechnical Aspects of the Hyogo-ken-Nanbu (Kobe) Earthquake of January 17, 1995,” Can. J. Civil Eng., 23(3), 778–796. Finn, W.D.L., R.H. Ledbetter, et al. 1994. Liquefaction in Silty Soils: Design and Analysis, Geotechnical Publication No. 44, American Society of Civil Engineers, New York, pp. 51–76. Finn, W.D.L., M. Yogendrakumar, et al. 1986. “TARA-3: A Problem for Non-Linear Static and Dynamic Effective Stress Analysis,” Soil Dynamics Group, University of British Columbia, Vancouver. Franklin, A.G. and F.K. Chang. 1977. “Permanent Displacements of Earth Embankments by Newmark Sliding Block Analysis,” U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg, MS. Gazetas, G. 1982. “Shear Vibrations of Vertically Inhomogeneous Earth Dams,” Int. J. Num. Analyt. Meth. Geomech., 6(1), 219–241. Geist, E.L. 2000. “Origin of the 17 July 1998 Papua New Guinea Tsunami: Earthquake or Landslide?” Seismol. Res. Lett., 71(3), 344–351. Graf, E.D. 1992. Earthquak e Support Grouting in Sands , Geotechnical Special Publication No. 30, American Society of Civil Engineers, New York, pp. 265–274. Graves, R.W. 1993. “Modeling Three-Dimensional Site Response Effects in the Marina District Basin, San Francisco, California,” Bull. Seismol. Soc. Am., 83: 1042–1063. Graves, R.W., A. Pitarka et al. 1998. “Ground Motion Amplification in the Santa Monica Area: Effects of Shallow Basin Edge Structure,” Bull. Seismol. Soc. Am., 88(5), 1224–1242. Griffiths, D.V. and J.H. Prevost. 1988. “Two- and Three-Dimensional Finite Element Analysis of the Long Valley Dam,” National Center for Earthquake Engineering Research, University of New York, Buffalo.



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Harder, L.F. and R. Boulanger. 1997. “Application of Ksigma and Kalpha Correction Factors,” in Proc. NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Salt Lake City, NV, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. Harder, L.F. and H.B. Seed. 1986. “Determination of Penetration Resistance for Coarse-Grained Soils Using the Becker Hammer Drill,” Earthquake Engineering Research Center, University of California, Berkeley. Hausmann, M.R. 1990. Engineering Principles of Ground Modification. McGraw-Hill, New York. Hayden, R.F. 1994. “Utilization of Liquefaction Countermeasures in North America,” in Proc. Fifth U.S. National Conference on Earthquake Engineering, Chicago. Hryciw, R.D., Ed. 1995. Soil Improvement for Earthquake Hazard Mitigation, Geotechnical Special Publication No. 49, American Society of Civil Engineers, New York. Hynes-Griffin, M.E. and A.G. Franklin. 1984. “Rationalizing the Seismic Coefficient Method,” U.S. Army Corps of Engineers, Waterways Experiment Station 21, Vicksburg, MS. ICBO (International Conference of Building Officials). 1997. Uniform Building Code, International Conference of Building Officials, Whittier, CA. ICC (International Code Council). 2000. International Building Code, International Code Council, Falls Church, VA. Idriss, I.M. 1990. “Response of Soft Soil Sites during Earthquakes,” H. Bolton Seed Memorial Symposium, BiTech Publishers. Idriss, I.M., J. Lysmer, et al. 1973. “QUAD-4: A Computer Program for Evaluating the Seismic Response of Soil Structures by Variable Damping Finite Element Procedures,” Earthquake Engineering Research Center, University of California, Berkeley. Kramer, S.L. 1996. Geotechnical Earthquake Engineering, Prentice-Hall, Upper Saddle River, NJ. Lee, K.L. 1974. “Seismic Permanent Deformations in Earth Dams,” School of Engineering and Applied Science, University of California, Los Angeles. Lee, K.L. and J.A. Focht. 1976. “Strength of Clay Subjected to Cyclic Loading,” Mar. Geotechnol., 1(3), 165–188. Liao, S.S.C. and R.V. Whitman. 1986. “Overburden Correction Factors for SPT in Sand,” J. Geotech. Eng. ASCE, 112(3), 373–377. Lukas, R.G. 1986. Dynamic Compaction for Highway Construction, Vol. 1. Design and Construction Guidelines, Federal Highway Administration. Lysmer, J., T. Udaka, et al. 1975. “FLUSH: A Computer Program for Approximate 3-D Analysis of SoilStructure Interaction Problems,” Earthquake Engineering Research Center, University of California, Berkeley. Makdisi, F.I. and H.B. Seed. 1978. “Simplified Procedure for Estimating Dam and Embankment Earthquake-Induced Deformations,” J. Geotech. Eng. ASCE, 104(GT7), 849–867. Marcuson, W.F. and A.G. Franklin. 1983. Seismic Design, Analysis and Remedial Measures to Improve the Stability of Existing Earth Dams, Corps of Engineers Approach, Seismic Design of Embankments and Caverns, American Society of Civil Engineers, New York. Marcuson, W.F., P.F. Hadala, et al. 1991. Seismic Rehabilitation of Earth Dams, Geotechnical Publication No. 35, American Society of Civil Engineers, New York, pp. 430–466. Marcuson, W.F., M.E. Hynes, et al. 1992. “Seismic Stability and Permanent Deformation Analysis: The Last Twenty Five Years,” in ASCE Specialty Conference on Stability and Performance of Slopes and Embankments, Vol. II, Geotechnical Special Publication No. 31, American Society of Civil Engineers, New York. Mitchell, J.K. 1981. “Soil Improvement: State-of-the-Art,” in Proc. Tenth International Conference on Soil Mechanics and Foundation Engineering, Stockholm, American Society of Civil Engineers, New York. Mitchell, J.K., C.D.P. Baxter, et al. 1995. “Performance of Improved Ground During Earthquakes,” in Soil Improvement for Earthquake Mitigation, American Society of Civil Engineers, New York.




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Molas, G.L. and F. Yamazaki. 1995. “Attenuation of Earthquake Ground Motion in Japan Including Deep Focus Events,” Bull. Seismol. Soc. Am., 85(5), 1343–1358. Molas, G.L. and F. Yamazaki. 1996. “Attenuation of Response Spectra in Japan Using New JMA Records,” Bull. Earthquake Resistant Structure Research Center, Institute of Industrial Science, University of Tokyo (29), 115–28. Mononobe, N. and H. Matsuo. 1929. “On the Determination of Earth Pressures During Earthquakes,” in Proc. World Engineering Conference. Narin van Court, W.A. and J.K. Mitchell. 1995. New Insights into Explosive Compaction of Loose, Saturated, Cohesionless Soils, Special Geotechnical Publication No. 49, American Society of Civil Engineers, New York, pp. 51–65. NCEER (National Center for Earthquake Engineering Research). 1992. Case Studies of Liquefaction and Lifeline Performance during Past Earthquakes. Vol. 1, Japanese Case Studies; Vol. 2, United States Case Studies, National Center for Earthquake Engineering Research, State University of New York, Buffalo. NCEER (National Center for Earthquake Engineering Research). 1997. Proceedings of the NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Summary Report, T.L. Youd and I. Idriss, Eds., National Center for Earthquake Engineering Research, State University of New York, Buffalo. Newmark, N.M. 1965. “Effects of Earthquakes on Dams and Embankments,” Geotechnique, 15(2), 139–160. Newmark, N.M. and W.J. Hall. 1982. Earthquake Spectra and Design, Earthquake Engineering Research Institute, University of California, Berkeley, p. 103. Okabe, S. 1929. “General Theory of Earth Pressures,” J. Jpn. Soc. Civil Eng., 12(1). O’Rourke, T.D. 1992. The Loma Prieta, California, Earthquake of October 17, 1989: Marina District, United States Geological Service, Government Printing Office, Washington, D.C. Otani, S. 2000. “New Seismic Design Provisions in Japan,” Pacific Earthquake Engineering Research Center, University of California, Berkeley, pp. 3–14. PHRI (Port and Harbor Research Institute). 1997. Handbook on Liquefaction Remediation of Reclaimed Land, Port and Harbour Research Institute, Japan, Brookfield, VT. Poulos, S.J., G. Castro, et al. 1985. “Liquefaction Evaluation Procedure,” J. Geotech. Eng. ASCE, 111(6), 772–792. Prakash, S. and S. Saran. 1966. “Static and Dynamic Earth Pressure Behind Retaining Walls,” in Proc. Third Symposium on Earthquake Engineering, Roorkee, India. Prevost, J.H., A.M. Abdel-Ghaffar, et al. 1985. “Nonlinear Dynamic Analysis of Earth Dams: A Comparative Study,” J. Geotech. Eng. ASCE, 111(2), 882–897. Quake/W. 2001. “Quake/W for Finite Element Dynamic Earthquake Analysis: Users’ Guide,” GEO-SLOPE International Ltd., Calgary. Richards, R. and D.G. Elms. 1979. “Seismic Behavior of Gravity Retaining Walls,” J. Geotech. Eng. ASCE, 105(GT4), 449–464. Robertson, P.K. and C.E. Fear. 1995. “Liquefaction of Sand and its Evaluation,” in Proc. 1st International Conference on Earthquake Geotechnical Engineering, Tokyo. Robertson, P.K. and C.E. Wride. 1997. “Cyclic Liquefaction and its Evaluation Based on the SPT and CPT,” in Proc. NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Salt Lake City, NV, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. Rodriguez-Marek, A., J.D. Bray, et al. 1999. “Characterization of Site Response, General Site Categories,” Pacific Earthquake Engineering Research Center, University of California, Berkeley, p. 134. Romo, M.P. and H.B. Seed. 1986. “Analytical Modeling of Dynamic Soil Response in the Mexico Earthquake of September 19, 1985,” in Proc. ASCE International Conference on the Mexico Earthquakes 1985, Mexico City, American Society of Civil Engineers, New York. Schaefer, V.R., Ed. 1997. Ground Improvement, Ground Reinforcement, Ground Treatment, Geotechnical Special Publication No. 69, American Society of Civil Engineers, New York.



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Seed, H.B. 1979a. “Considerations in the Earthquake-Resistant Design of Earth and Rockfill Dams,” Geotechnique, 29(3), 215–263. Seed, H.B. 1979b. “Soil Liquefaction and Cyclic Mobility for Level Ground During Earthquakes,” J. Geotech. Eng. ASCE, 105(GT2), 201–255. Seed, H.B. 1983. “Earthquake Resistant Design of Earth Dams,” in Proc. Symposium on Seismic Design of Earth Dams and Caverns, New York. Seed, H.B. 1986. “Design Problems in Soil Liquefaction,” J. Geotech. Eng. ASCE, 113(8), 827–845. Seed, R.B. and L.F. Harder. 1990. “SPT-Based Analysis of Cyclic Pore Pressure Generation and Undrained Residual Strength,” H. Bolton Seed Memorial Symposium, BiTech Publishers. Seed, H.B. and I.M. Idriss. 1970. “Soil Moduli and Damping Factors for Dynamic Response Analysis,” Earthquake Engineering Research Center, University of California, Berkeley. Seed, H.B. and I.M. Idriss. 1971. “Simplified Procedure for Evaluating Soil Liquefaction Potential,” J. Soil Mech. Found. Div. ASCE, 97(SM9), 1249–1273. Seed, H.B. and I.M. Idriss. 1982. Ground Motions and Soil L iquefaction during Earthquak es, Monogr. 5, Earthquake Engineering Research Institute, University of California, Berkeley. Seed, H.B. and R.V. Whitman. 1970. “Design of Earth Retaining Structures for Dynamic Loads,” in Proc. ASCE Specialty Conference on Lateral Stresses in the Ground and Design of Earth Retaining Structures, American Society of Civil Engineers, New York. Seed, R.B., K.O. Cetin, et al. 2001. “Recent Advances in Soil Liquefaction Engineering and Seismic Site Response Evaluation,” in Proc. Fourth International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, University of Missouri, Rolla. Seed, R.B., S.W. Chang, et al. 1997. “Site-Dependent Seismic Response Including Recent Strong Motion Data,” Special Session on Earthquake Geotechnical Engineering, Proc. XIV Internat ional Conference on Soil Mechanics and Foundat ion Engineering, Balkema, Hamburg. Seed, R.B., S.E. Dickenson, et al. 1990. “Preliminary Report on the Principal Geotechnical Aspects of the October 17, 1989 Loma Prieta Earthquake,” Earthquake Engineering Research Center, University of California, Berkeley, p. 137. Seed, H.B., K. Tokimatsu et al. 1985. “The Influence of STP Procedures in Soil Liquefaction Resistance Evaluations,” J. Geotech. Eng. ASCE, 111(12), 1425–1445. Seed, H.B., C. Ugas, et al. 1976. “Site-Dependent Spectra for Earthquake-Resistant Design,” Bull. Seismol. Soc. Am., 66, 221–243. Serff, N., H.B. Seed, et al. 1976. “Earthquake-Induced Deformations of Earth Dams,” Earthquake Engineering Research Center, University of California, Berkeley, p. 140. Shabestari, K.T. and F. Yamazaki. 1998. “Attenuation Relationship of JMA Seismic Intensity Using JMA Records,” in Proc. Tenth Japan Earthquake Engineering Symposium, Kobe, Japan. Silver, M.L. and H.B. Seed. 1971. “Volume Changes in Sands during Cyclic Loading,” J. Soil Mech. Found. Div. ASCE, 97(9), 1171–1182. Somerville, P. 1998. “Emerging Art: Earthquake Ground Motion,” in Geotechnical E arthquak e Engineering and Soil D ynamic s, Vol. III, Geotechnical Special Publication No. 75, American Society of Civil Engineers, New York. Somerville, P.G. and R.W. Graves. 1996. “Strong Ground Motions of the Kobe, Japan Earthquake of January 17, 1995, and Development of a Model of Forward Rupture Directivity Applicable in California,” in Proc. Western Regional Technical Seminar on Earthquake Engineering for Dams, Association of State Dam Officials, Sacramento. Somerville, P.G., C.K. Saikia, et al. 1996. “Implications of the Northridge Earthquake for Strong Ground Motions from Thrust Faults,” Bull. Seismol. Soc. Am., 86, S115–S125. Stark, T.D. and G. Mesri. 1992. “Undrained Shear Strength of Sands for Stability Analysis,” J. Geotech. Eng. ASCE, 118(11), 1727–1747. Stone, W.C., F.Y. Yokel, et al. 1987. Engineering Aspects of the September 19, 1985 Mexico Earthquak e, NBS Building Science Series, 165, National Bureau of Science, Washington, D.C., p. 207.




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Sy, A. and R.G. Campanella. 1994. “Becker and Standard Penetration Tests (BPT-SPT) Correlations with Consideration of Casing Friction,” Can. Geotech. J., 31, 343–356. Tappin, D.R., T. Matsumoto et al. 1999. “Offshore Surveys Identify Sediment Slump as Likely Cause of Devastating Papua New Guinea Tsunami 1998,” Eos, 80(30), 329. Thiers, G.R. and H.B. Seed. 1978. Strength and S tress-Strain Char acteristics of Clays Subjected to Seismic Loading C onditions, ASTM Special Technical Publication 450, American Society for Testing and Materials, pp. 3–56. Tokimatsu, K. and H.B. Seed. 1987. “Evaluation of Settlements in Sand Due to Earthquake Shaking,” J. Geotech. Eng. ASCE, 113(8), 861–878. Trifunac, M.D. and A.G. Brady. 1975. “On the Correlation of Seismic Intensity with Peaks of Recorded Strong Ground Motion,” Bull. Seismol. Soc. Am., 65, 139–162. U.S. Army Corps of Engineers. 1982. Slope Stability Manual, Department of the Army, Office of the Chief of Engineers, Washington, D.C. Vucetic, M. and R. Dorby. 1991. “Effect of Soil Plasticity on Cyclic Response,” J. Geotech. Eng. ASCE, 117(1), 89–107. Whitman, R.V. and S. Liao. 1985. “Seismic Design of Retaining Walls,” U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg, MS. Wieczorek, G.F. 1996. “Landslide Triggering Mechanisms,” in Landslides, Investigation and Mitigation, A.K. Turner and R.L. Schuster, Eds., Transportation Research Board Special Report 247, National Academy Press, Washington, D.C., pp. 76–90. Wightman, A. 1991. “Ground Improvement by Vibrocompaction,” Geotech. News, 9(2), 39–41. Wood, J. 1973. “Earthquake-Induced Soil Pressures on Structures,” Report EERL 73-05, California Institute of Technology, Pasadena, p. 311. Youd, T.L. and S.N. Hoose. 1977. “Liquefaction Susceptibility and Geologic Setting,” in Proc. 6th World Conference on Earthquak e Engineering, Prentice-Hall, Englewood Cliffs, NJ. Youd, T.L. and I.M. Idriss. 2001. “Liquefaction Resistance of Soils: Summary Report from the 1996 NCEER and 1998 NCEER/NSF Workshops on Evaluation of Liquefaction Resistance of Soils,” J. Geotech. Eng. ASCE, 127(4), 297–313. Youd, T.L. and S.K. Noble. 1997. “Magnitude Scaling Factors,” in Proc. NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Salt Lake City, NV, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. Youd, T.L. and D.M. Perkins. 1978. “Mapping of Liquefaction-Induced Ground Failure Potential,” J. Geotech. Eng. Div. ASCE, 104(GT4), 433–446.

Further Reading Kramer’s book [Kramer, 1996] provides a detailed explanation of earthquake effects on geotechnical engineering parameters, as does Finn’s article on the state of the art of geotechnical earthquake engineering practice [Finn, 2001]. A series of U.S. and Japanese case studies of liquefaction effects on lifeline performance during earthquakes contains a wealth of information on lifeline performance during earthquakes [NCEER, 1992]. Another case study of interest is a USGS professional paper on the Marina district of San Francisco in the 1989 Loma Prieta earthquake [O’Rourke, 1992]. An excellent review of liquefaction remediation techniques is presented in a handbook on liquefaction remediation of reclaimed land [PHRI, 1997].



8

Seismic Hazard Analysis 8.1 8.2 8.3

Introduction Probabilistic Seismic Hazard Methodology Constituent Models of the Probabilistic Seismic Hazard Methodology Seismic Sources · Earthquake Recurrence Frequency · Ground Motion Attenuation · Ground Motion Probability

8.4

Definition of Seismic Sources

8.5

Earthquake Frequency Assessments

Area Sources · Fault Sources Historical Frequency Assessments · Geologic Earthquake Frequency Assessments · Conservation of Seismic Moment on Segmented Faults · Time-Dependent Probability Modeling

8.6

Maximum Magnitude Assessments Area Source Determinations · Individual Fault Determinations · Mixed Source Determinations

8.7

Ground Motion Attenuation Relationships Impact on Seismic Source Definition · Reference Site Class

8.8 Accounting for Uncertainties 8.9 Typical Engineering Products of PSHA 8.10 PSHA Disaggregation Scaling Empirical Earthquake Spectra

8.11 PSHA Case Study Tectonic Setting · Regional Seismicity · Great Earthquakes · Earthquake Source Characterization

8.12 The Owen Fracture Zone–Murray Ridge Complex Maximum Magnitude · Earthquake Recurrence Frequencies

8.13 Makran Subduction Zone Maximum Magnitude · Earthquake Recurrence Frequencies

8.14 Southwestern India and Southern Pakistan Maximum Magnitude · Earthquake Recurrence Frequencies

8.15 Southeastern Arabian Peninsula and Northern Arabian Sea Maximum Magnitude · Earthquake Recurrence Frequencies

8.16 Ground Motion Models Stable Continental Interior Earthquakes · Stable Oceanic Interior Earthquakes · Transform Plate Boundary Earthquakes · Subduction Zone Earthquakes

Paul C. Thenhaus ABS Consulting Evergreen, CO

Kenneth W. Campbell ABS Consulting and EQECAT Inc. Portland, OR © 2003 by CRC Press LLC

8.17 Soil Amplification Factors 8.18 Results 8.19 Conclusions 8.20 PSHA Computer Codes Defining Terms References Further Reading


8-2


8.1 Introduction Seismic hazard is a broad term used in a general sense to refer to the potentially damaging phenomena associated with earthquakes, such as ground shaking, liquefaction, landslides, and tsunami. In the specific sense, seismic hazard is the likelihood, or probability, of experiencing a specified intensity of any damaging phenomenon at a particular site, or over a region, in some period of interest. It is the latter, specific sense, that is the subject of this chapter. The methodology for assessing the probability of seismic hazards grew out of an engineering need for better designs in the context of structural reliability [Cornell, 1968, 1969], since such assessments are frequently made for the purpose of guiding decisions related to mitigating risk. However, the probabilistic method has also proven to be a compelling, structured framework for the explicit quantification of scientific uncertainties involved in the hazard estimation process. Uncertainty is inherent in the estimation of earthquake occurrence and the associated hazards of damaging ground motion, permanent ground displacements, and, in some cases, seiche and tsunami. Scientific knowledge for the accurate quantification of these hazards is always limited. The balance of the hazard assessment is comprised of informed technical judgment. Prior to the widespread use of probabilistic seismic hazard analysis (PSHA) for assessing earthquake hazards, deterministic methods dominated such assessments. Deterministic methods consider the effect at a site of either a single scenario earthquake, or a relatively small number of individual earthquakes. Difficulties surrounded the selection of a representative earthquake on which the hazard assessment would be based. These difficulties often involved the identification of an earthquake that satisfied a codified or regulatory definition. The probabilistic methodology reduces the need for such earthquake definitions, which typically are ambiguous at best. The probabilistic methodology quantifies the hazard at a site from all earthquakes of all possible magnitudes, at all significant distances from the site of interest, as a probability by taking into account their frequency of occurrence. Deterministic earthquake scenarios, therefore, are a subset of the probabilistic methodology. In principle, PSHA can address any natural hazard associated with earthquakes, including ground shaking, fault rupture, landslide, liquefaction, seiche, or tsunami. However, most interest is in the probabilistic estimation of ground-shaking hazard, since it causes the largest economic losses in most earthquakes. The presentation here, therefore, is restricted to the estimation of the earthquake ground motion hazard. Figure 8.1 illustrates elements of the probabilistic ground motion hazard methodology in the context of a complete program for establishing engineering seismic design criteria for a site of significant engineering importance. The process begins with the characterization of earthquake occurrence using two sources of data: observed seismicity (historical and instrumental) and geologic. The occurrence information is combined with data on the transmission of seismic shaking (termed attenuation, see Chapter 5) to form the seismotectonic model. Since uncertainty is inherent in the earthquake process, the parameters of the seismotectonic model are systematically varied via logic trees, Monte Carlo simulation, and other techniques, to provide the probabilistic seismic hazard model’s results. The results may be disaggregated (also known as deaggregation) to identify specific contributory parameters to the overall results. The results must also consider the site-specific soil properties. The final results, presented in many different ways depending on the user’s needs, are termed seismic design criteria, if the end use is the design of an engineering structure. Each of these aspects is discussed further below.

8.2 Probabilistic Seismic Hazard Methodology PSHA can be summarized as the solution of the following expression of the total probability theorem: λ[X ≥ x] ≈

M Max

∑ ν ∫ ∫ P [ X ≥ x M , R] f i

Sources i


Mo

R|M

M

(m) f R|M (r m) dr dm

(8.1)


8-3


FIGURE 8.1 Flowchart showing the elements of the probabilistic hazard methodology in the context of a seismic design criteria methodology.

where λ[X ≥ x ] is the annual frequency that ground motion at a site exceeds the chosen level X = x ; νi is the annual rate of occurrence of earthquakes on seismic source i, having magnitudes between Mo and MMax; Mo is the minimum magnitude of engineering significance; MMax is the maximum magnitude assumed to occur on the source; P[X ≥ x |M,R] denotes the conditional probability that the chosen ground motion level is exceeded for a given magnitude and distance; fM(m) is the probability density function of earthquake magnitude; fR|M(r |m ) is the probability density function of distance from the earthquake source to the site of interest. In application, this expression is solved for each seismic source i of a seismotectonic model. Once the annual exceedance rate λ[X ≥ x ] is known, the probability that an observed ground motion parameter X will be greater than or equal to the value x in the next t years (the exposure period) is easily computed from the equation:

(

)

P [ X ≥ x ] = 1 − exp −tλ [ X ≥ x ]

(8.2)

where the “return period” of x is defined as: RX ( x ) =


1 −t = λ [ X ≥ x ] ln 1 − P [ X ≥ x ]

(

)

(8.3)


8-4


Probability values commonly used and cited in PSHA are ground motions that have a 10% probability of being exceeded in a 50-year exposure period of engineering interest. From Equation 8.3, this gives a return period of: RX ( x ) =

−50 = 475 years ln (1 − 0.1)

(8.4)

Thus, these specific ground motions, which have a 10% probability of being exceeded during 50 years, are commonly termed to have an average 475-year return period. It is informative to note that setting the exposure period equal to the return period in Equations 8.2 and 8.3 results in a 63% probability that the ground motions will be exceeded in t years under the Poisson assumption used to develop these relationships.

8.3 Constituent Models of the Probabilistic Seismic Hazard Methodology Figure 8.2 schematically illustrates the constituent models of the probabilistic approach to estimating earthquake ground motion hazard. These are models of: 1. 2. 3. 4.

Seismic sources Earthquake recurrence frequency Ground motion attenuation Ground motion occurrence probability at a site

These models are introduced here and discussed in more detail in the following sections of this chapter.

8.3.1 Seismic Sources PSHA requires that the distribution of earthquakes be defined in space with each epicenter having a defined distance from the site of interest. This has been traditionally accomplished through the geographic delineation of seismic source zones and seismically active faults. Definitions of these sources are based on interpretations of available geological, geophysical, and seismological data with respect to earthquake mechanisms and source structures that are likely to be common within specific geographic regions (Figure 8.3). Seismic source delineation is generally premised on geoscience knowledge that relates earthquakes to geological structure. However, where causative earthquake faults and structure are not known with certainty, seismic source interpretations are not unique [Thenhaus, 1983, 1986] and the geographic distribution of earthquakes largely guides the definition of sources [Electric Power Research Institute, 1986]. Methods of seismicity smoothing have recently been introduced to avoid arbitrary decisions regarding placement of area-source boundaries [Frankel et al., 1995, 1996, 2000] and to better represent the fractal geometry of distributed seismicity as a self-organized critical-state process [Woo, 1996].

8.3.2 Earthquake Recurrence Frequency Determining the earthquake recurrence frequency of the defined seismic sources is an important explicit task in PSHA, whereas it is either implicit or is disregarded in deterministic seismic hazard analysis. Earthquake recurrence frequency is based largely on statistical analyses of the historical record of earthquakes for all but the most tectonically active areas of the world where detailed paleoseismic studies of active faults have been performed. Paleoseismology is the geological study of prehistoric earthquakes [McCalpin, 1996; Yeats et al., 1997] and aids the analysis of large-earthquake occurrence frequency. Earthquake frequency estimates in PSHA typically assume independence of earthquake events, or Poisson arrival times. However, time-dependent treatments of earthquake recurrence estimates are the basis for © 2003 by CRC Press LLC



8-5

FIGURE 8.2 Elements of PSHA shown in relation to constructing a uniform hazard spectrum. (From EERI, Earthquake Spectra, 5, 675–699, 1989. With permission.)

earthquake forecasting in areas, such as the San Francisco Bay area, where a good historical and paleoseismic record of past earthquakes is available.

8.3.3 Ground Motion Attenuation Empirical ground motion attenuation relationships are widely used to establish the amplitude of earthquake ground motion at a site of interest (see Chapter 5). In engineering applications, the ground motion parameters of interest are typically peak ground acceleration (PGA), response spectral acceleration (PSA), response spectral velocity (PSV), and spectral displacement (SD). Proper implementation of most modern ground motion attenuation relationships requires that the seismic sources are characterized by the details of a fault-rupture model including depth to the top and bottom of the earthquake rupture zone, fault dip, and the style of fault slip (i.e., strike-slip, normal, or reverse). These faultrupture parameters are a product of the tectonic environment of the region in which the analysis is being performed.



8-6


45°N 44°N 43°N 42°N 41°N 40°N 39°N 38°N 37°N 36°N 35°N 34°N

0

33°N

150 300 Kilometers

32°N 18°E 20°E 22°E 24°E 26°E 28°E 30°E 32°E 34°E 36°E 38°E 40°E 42°E 44°E 46°E 48°E 50°E 52°E

FIGURE 8.3 Seismic source zones overlaid on major faults and tectonic features, for Turkey. (From Erdik, M. et al., 1999, Assessment of Earthquake Hazards in Turkey and Neighboring Regions, contribution to Global Seismic Hazard Assessment Program, available at http://seismo.ethz.ch/gshap/turkey/papergshap71.htm.)

8.3.4 Ground Motion Probability The estimation of the probability of exceeding some amplitude of shaking at a site in some period of interest requires that a probability distribution of the ground motion amplitudes be assumed. The Poisson model serves as a reasonable assumption in most engineering applications except in rare cases where a single earthquake source may dominate the hazard at a site and the earthquake occurrence model for the source can be considered time-dependent, or non-Poissonian [Cornell and Winterstein, 1988]. Poisson models have traditionally been used throughout seismic hazard assessment. However, timedependent earthquake occurrence estimates have been used for earthquake forecasting in the San Francisco Bay area of California [Working Group on California Earthquake Probabilities, 1999] as well as elsewhere in California [Working Group on California Earthquake Probabilities, 1995]. Time-dependent probability models are discussed later in this chapter.

8.4 Definition of Seismic Sources The fundamental assumptions of a defined earthquake source is that (1) earthquake occurrence is uniformly distributed for given magnitude within the source, and (2) earthquake occurrence is only considered between a minimum earthquake magnitude of engineering interest (Mmin) and a maximum magnitude (Mmax) that is representative of the entire source [Reiter, 1990]. The seismic sources are shown as map representations of lines (fault sources), and area source zones that are defined on the basis of a number of different types of geological, geophysical, and seismological data (Figure 8.3). These data are summarized in Table 8.1 along with their indicated usefulness in the definition of types of seismic sources. The defined geographic distribution of seismic sources and the specification of all source characteristics required for the seismic hazard analysis is termed the seismotectonic model. The seismotectonic model provides a complete description of earthquake occurrence in time and space to an outer distance of an engineering interest, and to a depth sufficient to encompass the seismogenic thickness of brittle crust beneath the site. Depending on the seismotectonic regime and the application for the results, the maximum distance and depth considered may be several hundred kilometers and a hundred kilometers, respectively. The entire model is summarized in an input file format appropriate to the PSHA computer code being used. © 2003 by CRC Press LLC


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TABLE 8.1

General Data Types and Their Applications in Identifying and Characterizing Seismic Source Zones Zone Type Faults Data Type

Area Sources

Location

Activity

Length

Dip

X X X X

X X X X X X X X X

X X X

X

Depth

Style

Area

X X X X

X X

Depth

Geological/Remote Sensing Detailed mapping Geomorphic data Quaternary surface rupture Fault trenching data Geochronology Paleoliquefaction data Borehole data Aerial photography Low sun-angle photography Satellite imagery Regional structure Balanced cross section

X X X X X X X

X X

X X X X X

X

X X

X X

X

X X X X X

X

X X X

X X X

X

X

X

X X X

X X

Geophysical Regional potential field data Local potential field data High resolution reflection data Standard reflection data Deep crustal reflection data Tectonic geodetic/strain data Regional stress data

X X X X X X

X X X

X

X X

X

X

X

Seismological Reflected crustal phase data Historical earthquake data Teleseismic earthquake data Regional network seismicity data Local network seismicity data Focal mechanism data

X X X X

X X

X X

X X X

X X

X X X

X X

X

8.4.1 Area Sources Area seismic sources define regions of the Earth’s crust that are assumed to have uniform seismicity characteristics that are distinct from neighboring zones, and are exclusive of active faults that are individually defined. The central and eastern United States (CEUS) region is often cited as a leading example of a region where seismic hazard is defined through the use of area seismic source zones [Thenhaus, 1983; Reiter, 1990; Coppersmith, 1991; Coppersmith et al., 1993]. This region is located interior to the North American tectonic plate where earthquake occurrence is much less frequent than in the western United States, the historical and instrumental seismicity generally does not correlate well with geologic structures observable at the surface, evidence of prehistoric earthquakes that is preserved in the geologic record is difficult to find, and strain-rates of crustal deformation are exceedingly low. With the exception of a few areas, such as the New Madrid Seismic Zone, the result of these characteristics is a seismotectonic environment in which the identification of geologic structures that are responsible for earthquakes is ambiguous and not unique. Interpretations of the regional distribution of seismicity largely guide the definition of area seismic sources in this region [Thenhaus, 1983; EPRI, 1986]. Analogous regions of the world are areas that are located large distances from active plate boundary zones (Figure 8.4). Such regions are referred to as “stable continental interior regions” [Johnston et al., 1994]. Stable continental interiors, as the name implies, are some of the least active areas worldwide with regard to earthquake © 2003 by CRC Press LLC


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Active Volcanoes, Plate Tectonics, and the “Ring of Fire” Eurasian Plate

North American Plate CASCADE RANGE San Andreas Fault

Aleutian Trench

“Ring of Fire”

Mid-Atlantic Ridge

Hawaiian "Hot Spot"

Eurasian Plate

Arabian Plate

Cocos Plate

Java Trench

East Pacific Rise

Nazca Plate

Indo- Australian Plate

South American Plate

African Plate

Pacific Plate

USGS

Antarctic Plate

FIGURE 8.4 Plate tectonic setting of the world (from the U.S. Geological Survey). Primary tectonic plates are labeled by name. Heavy black lines indicate plate boundaries. “Ring of Fire” is a colloquialism referring to the earthquakes and volcanoes that occur along the northern boundary of the Pacific tectonic plate, extending from Japan through North America.

activity and are generally comprised of areas of very old continental crust in which the most active geologic process operating today is that of erosion. An alternative to defining uncertain area source boundaries within regions of low seismicity is that of seismicity smoothing. Woo [1996] formalized a kernel-estimation method of seismicity smoothing, noting that the practice of seismic source zonation “should not be merely routine when applied to areas where such correlations [between geological structure and seismicity] are tenuous.” Woo [1996] argued that use of “Euclidean zones” (standard area sources) unrealistically impose a uniform spatial distribution of epicenters in PSHA that conflicts with the clustering habit and inter-event correlation of recorded seismicity [Kagan and Knopoff, 1980; Korvin, 1992]. Woo goes on to say that the power-law of the Gutenberg–Richter relationship can be explained by the theory of self-organized criticality where, over geologic time periods, regional build-up of crustal stress is marginally balanced by the stress released during earthquakes. Some of this stress is manifested in aseismic deformation and folding. However, the regional fault network is self-organized to the extent that earthquakes occur as a critical chain reaction. As Woo [1996] notes, “if the process were supercritical, it would run away, but if the process were subcritical, it would terminate rapidly.” Noteworthy in this regard was the documented regional increase in seismicity throughout the western United States following the magnitude 7.3 Landers, California earthquake [Hill et al., 1993]. This was the first time that such a large regional influence has been scientifically documented from the occurrence of a single earthquake. Frankel et al. [1996, 1998, 2000; http://earthquakes.usgs.gov/hazards/] applied seismicity smoothing in recent updates of the U.S. national seismic hazard maps that have been produced over the last 24 years by the U.S. Geological Survey under the auspices of the National Earthquake Hazards Reduction Program (NEHRP). This model separates the CEUS into two broad areas of different estimated maximum potential earthquakes. The mid-continent region of the central United States is defined as an area in which the maximum earthquake is judged to be magnitude MW 6.5. The region of the Appalachian Mountains eastward, and the Gulf Coast area of the southern United States, are areas of rifted continental crust © 2003 by CRC Press LLC


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CEUS maximum-magnitude zones

50¡

240¡

250¡

260¡

270¡

290¡

280¡

50¡

6.5

40¡

40¡ 7.5 7.5 6.5

30¡

30¡

7.2 7.5

290¡

240¡

250¡

260¡

270¡

280¡

FIGURE 8.5 Maximum magnitude zones for the central and eastern U.S. used by Frankel et al., 1996. Magnitudes are in terms of the moment magnitude (MW) scale.

(areas of past episodes of extension and faulting) and defined as areas capable of sustaining earthquakes as large as MW 7.5 (Figure 8.5). Earthquake frequency throughout these broad regions was determined on a 0.1° grid of points using the common Gutenberg–Richter relationship of occurrence frequencies (see Chapter 4): log N (m) = a − bm

(8.5)

where N(m) = the number of earthquake events equal to or greater than magnitude m occurring on a seismic source per unit time, and a and b are regional constants (10a = the total number of earthquakes with magnitude > 0, and b is the rate of seismicity; b is typically 1 ± 0.3). The a-value of this relationship was determined for the regional grid of points that have been smoothed over a distance of 50 km using a Gaussian smoothing function [Frankel, 1995; Frankel et al., 1996]. Thus, area sources of this model are only used to characterize regions of uniform maximum magnitude, not uniform earthquake frequency. While seismicity smoothing frees the PSHA analyst of subjective judgment in locating area source boundaries, subjective judgment is not eliminated by these methodologies, and is still required in choosing reasonable smoothing parameters and inter-event correlation distances based on the available seismicity data [Frankel and Safak, 1998]. These choices have a large impact on the estimated ground motion amplitudes [Perkins and Algermissen, 1987].

8.4.2 Fault Sources Line sources are defined in PSHA ground motion analyses as map-view representations of three-dimensional fault planes for the purpose of explicit representation of faults that are considered capable of earthquake rupture. By far, these types of sources are primarily defined in active tectonic regions that are generally located in proximity to the boundaries of the world’s tectonic plates (Figure 8.4). However, strain from plate–boundary tectonic processes are transmitted large distances through the Earth’s crust. Earthquake faults can, therefore, be located large distances from these plate boundaries, albeit at greatly diminished rates of activity and geographic concentration. Faults exhibit a wide range of offset styles that depend on the prevailing tectonic stress regime, be it compression or extension, and the threedimensional geometry (i.e., strike and dip) of the individual fault within that stress regime (see Chapter 4). Many modern ground motion attenuation relationships (see Chapter 5) are specific to the © 2003 by CRC Press LLC


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style of faulting and require specification of the three-dimensional geometry of the defined fault through the Earth’s crust so that source-to-site distances are accurately calculated. The definition of earthquake faults need not be restricted to faults that are observable at the surface. Blind-faults (faults that do not break the surface), such as ruptured in the 1983 Coalinga and 1994 Northridge, California earthquakes [Wentworth and Zoback, 1990], can and should be included in a PSHA seismotectonic model, with appropriate specification of the depth to the top and bottom of the earthquake rupture zone.

8.5 Earthquake Frequency Assessments There are two fundamental approaches to assess earthquake recurrence frequency of the defined seismic sources in PSHA. These are historical and geological frequency assessments. Historical frequency assessments are based on statistical analyses of the historical catalog of earthquakes that have occurred within a region. Geological frequency assessments are generally based either on a prehistoric record of earthquake occurrence on faults (termed paleoseismicity ), which is compiled through detailed field geologic investigations, or on physical estimates of seismic moment either on individual faults or distributed throughout broad regions. Moment-based recurrence frequency estimates require some knowledge of the average long-term rate at which faults are slipping, or the rate at which tectonic deformation is occurring over a region.

8.5.1 Historical Frequency Assessments Historical catalogs of earthquakes are heterogeneous; that is, the data typically: • Are nonuniform with respect to time periods of complete reporting for earthquakes of various magnitudes • Are nonuniform with respect to magnitude measures used to quantify earthquake size • Contain a nonuniform mix of mainshock and aftershock earthquake events • Contain duplicate earthquake entries • May contain man-made events (such as blasts) that are not a product of the natural tectonic environment of a region Significant scrutiny (“clean-up”) of these catalogs is therefore required prior to performing statistical analyses to determine representative estimates of earthquake recurrence frequency. This is not to denigrate the value of historic earthquake catalogs — without such catalogs, the earthquake record would only extend back to a few decades ago. With historic catalogs, the record extends back hundreds, in some cases thousands, of years. Recent diligent efforts to research historic earthquakes are a significant contribution to PSHA [see, for example, Lee et al., 1988; Downes, 1995; Stucchi, 1993; Usami, 1981; Ambraseys and Finkel, n.d.; and Ambraseys and Melville, 1982]. An initial project earthquake catalog typically contains subcatalogs from various international and local seismological reporting agencies, resulting in duplicate earthquake entries. Prioritization and ranking of the various data contributed to the catalog are required to select the most reliable entries in terms of earthquake location, time of occurrence, and magnitude. Conversion of multiple magnitude measures to a single, representative magnitude for all earthquakes in a catalog is performed using empirical correlation relationships either available in seismological research literature (see Chapter 4) or developed directly from the various magnitude measures in the catalog itself, providing that sufficient data are available for obtaining statistical regression conversion relationships. Dependent events are removed from the catalog based on magnitude–time–distance parameters appropriate for characterizing aftershock earthquake sequences [see, for example, Reasenberg and Jones, 1989]. Removal of dependent events assures that the Poisson assumption of the PSHA is not violated in terms of earthquake recurrence. © 2003 by CRC Press LLC


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1.0 Intensity IV V VI VII VIII

V

VI

0.1

σλ =

λ / λ

MMI VI complete this range only

VII

Slope - T1/2

VIII

0.01 5

10

Time (Years)

100

FIGURE 8.6 Completeness time plots in terms of earthquake epicenter intensity following the method of Stepp [1973]. Each symbol refers to a different earthquake intensity class.

Most commonly, the statistical procedures proposed by Stepp [1972] are used to assess completeness times of the reported magnitudes, which assume the earthquake sequence in a catalog can be modeled as a Poisson distribution. If k1, k2, k3 … kn are the number of events per unit time interval, then: λ=

1 n

∑

n i =1

ki

(8.6)

and its variance is σ2 = λ/n, where n equals the number of unit time intervals. If unit time is one year, σλ = λ1/2/T1/2 as the standard deviation of the estimate of the mean where T is the sample length in years. This test, then, is for stationarity of observational quality. If data for a magnitude interval are plotted as log (σλ) vs. log (T), then the portion of the line with slope T–1/2 can be considered homogeneous (Figure 8.6) and used with data for other magnitude ranges (but for different observational periods) similarly tested for homogeneity to develop estimates of recurrence frequency. Over large regions, Gutenberg and Richter [1954] found that the average recurrence frequency of earthquakes follows an exponential distribution related to magnitude (Equation 8.5). In its cumulative form, the Gutenberg–Richter relation of recurrence frequencies is unbounded at the upper magnitude. In PSHA, this relationship imposes the unrealistic assumption that the maximum potential earthquake for any region under consideration is unbounded and unrelated to the seismotectonic setting. The © 2003 by CRC Press LLC


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truncated exponential recurrence relationship [Cornell and Vanmarcke, 1969] is therefore commonly used in practice:

( )

N (m) = N m

0

( (

))

( (

exp −β m − m0 − exp −β mu − m0

( (

1 − exp −β m − m u

0

))

))

for m ≤ mu

(8.7)

where m0 is an arbitrary reference magnitude; mu is an upper-bound magnitude where n(m) = 0 for m > mu; and β = b · ln10. In this form, earthquake frequency approaches zero for some chosen maximum earthquake of a region. Other magnitude-frequency relations are discussed in Chapter 4.

8.5.2 Geologic Earthquake Frequency Assessments Characterizing earthquake recurrence frequency on individual faults, as opposed to regionally distributed area sources, is a more challenging proposition. Many earthquake faults have recurrence frequencies for significant earthquakes of hundreds to thousands of years. It is largely fortuitous, then, if even one large-earthquake interoccurrence interval is represented in the historical record. This lack of empirical earthquake data precludes robust assessments of earthquake frequency by statistical treatments of historical earthquake data. Other means are required for determining earthquake frequency on seismically active faults. Significant efforts have been made in the past 25 years to characterize the rate at which faults slip in many seismically active regions of the world [McCalpin, 1996]. Fault slip-rate can be related to earthquake occurrence frequency through the use of seismic moment [Molnar, 1979; Anderson, 1979]. Seismic moment, Mo , is the most physically meaningful way to describe the size of an earthquake in terms of static fault parameters. It is defined as: Mo = µ Af D

(8.8)

where m is the rigidity or shear modulus of the fault, usually taken to be 3 × 1011 dyne/cm2; Af is the rupture area on the fault plane undergoing slip during the earthquake; and D is the average displacement over the slip surface. The seismic moment is translated to earthquake magnitude according to an expression of the form:

( )

log M o M = c M

(8.9)

Based on both theoretical considerations and empirical observations, c and d are rationalized as 1.5 and 16.1, respectively [Molnar, 1979; Anderson, 1979]. Actually, to be consistent with the definition of moment magnitude, d should be set equal to 16.05 [Kanamori, 1978; Hanks and Kanamori, 1979]. The total seismic moment rate is the rate of seismic energy release along a fault. According to Brune [1968], the slip rate of a fault can be related to the seismic moment rate M 0T as follows: M oT = µA f S

(8.10)

where S is the average slip rate (per unit time) along the fault. The seismic moment rate, therefore, provides an important link between geologic and seismicity data. While the Gutenberg–Richter relationship describes the regional occurrence frequency of earthquakes, it has been found to be nonrepresentative of large earthquake occurrence on individual faults [Schwartz and Coppersmith, 1984; Wesnousky, 1994]. Physically, this can be attributed to the breakdown of the power law of the Gutenberg–Richter relationship between large and small earthquakes because they are not self-similar processes [Scholz, 1990]. Geologic investigations of faults of the San Andreas system of western California and of the Wasatch fault in central Utah have indicated that surface-rupturing © 2003 by CRC Press LLC


8-13

Annual Number of Earthquakes, N (m)


FIGURE 8.7 Comparison of the exponential (solid line) and characteristic recurrence (dashed line) frequency curves. (From Youngs, R.R. and Coppersmith, K.J., Bull. Seismol. Soc. Am., 75, 939–964, 1985.)

10 1 –1

10 10

–2

10

–3

10

–4

10

–5

4

5 6 7 Magnitude, m

8

earthquakes tend to occur within a relatively narrow range of magnitudes at an increased frequency over that which would be estimated from the Gutenberg–Richter relationship. These have been termed characteristic earthquakes. The characteristic recurrence frequency distribution reconciles the exponential rate of small- and moderate-magnitude earthquakes with the larger characteristic earthquakes on individual faults (Figure 8.7). The summed rate of earthquakes over many faults in a region reverts to the truncated exponential distribution [Youngs and Coppersmith, 1985] and is therefore consistent with the regional empirical Gutenberg–Richter relationship. The characteristic recurrence frequency distribution can be separated into a noncharacteristic Gutenberg–Richter relationship for small and moderate earthquakes, and a characteristic frequency part for large earthquake occurrence. The cumulative rate of noncharacteristic, exponentially distributed earthquakes, Ne , is estimated from the seismic moment and seismic moment rate as follows: − β m −0.25 1−e ( u )

N e= M oT Mo e

− β ( mu −0.25)

(

−c/2 b  b10 − c / 2 b10 1 − 10 +  c −b c 

) 

(8.11)

 

The cumulative rate of characteristic earthquakes, Nc , is related to the cumulative rate of noncharacteristic earthquakes by the expression: Nc =

− β m −m −1.5 β Ne e ( u 0 )

(

− β m −m −0.5 2 1−e ( u 0 )

)

(8.12)

Similar to the truncated exponential recurrence model, frequency estimates from the characteristic recurrence model approach zero at the defined maximum magnitude for the source. Figure 8.7 compares the truncated exponential and characteristic frequency distributions. If a fault can be considered truly characteristic, then only a single earthquake of specified magnitude is expected to occur on the fault. Such a model was used by Frankel et al. [1996, 2000] and the Working Group on California Earthquake Probabilities [1995, 1999] for large faults in California that have been well characterized paleoseismically. In this case, the frequency of the characteristic event, which is assumed to rupture an entire fault segment or series of segments, is given by the expression: N char =


M 0T M 0 ( M char )

(8.13)


8-14


where Mchar is the magnitude of the characteristic event. This is referred to as the characteristic earthquake or maximum-magnitude model. This expression becomes somewhat more complex if the characteristic event is assumed to have a truncated Gaussian magnitude distribution (to account for inherent randomness in the magnitude of the event) as was assumed by the Working Group on California Earthquake Probabilities [1999]. To conserve the mean seismic moment rate, N char must be reduced when the truncated Gaussian distribution is used. This reduction is a function of both the standard deviation and the truncation limit. The Working Group on California Earthquake Probabilities [1999] used a standard deviation of 0.12 and a truncation limit of ±2 standard deviations. In this case, N char would have to be multiplied by 0.94 to conserve the mean seismic moment rate. The cumulative truncated Gaussian magnitude distribution is given by the equation:

N char

m  M + zσ  νchar Fchar  f M (m) dm − f M (m) dm 0 0   =   M + zσ   f M (m) dm − 1 2     0

∫

∫

(8.14)

∫

where N char is the annual number of events with magnitude greater than or equal to m, νchar is the mean rate of characteristic events on the fault (equal to the inverse of the recurrence time), F char is the reduction factor needed to conserve the mean seismic moment rate [see Field et al., 1999], M is the characteristic magnitude on the fault (referred to as Mchar above), z is the truncation limit, σ is the standard deviation, and fM(m) is the Gaussian (normal) probability density function, given by: f M (m) =

1 σM

 1  m − M  2 exp −    2π  2  σ M  

(8.15)

The above integrals are widely available in statistics books. In the case of the application by the Working Group on California Earthquake Probabilities [1999], F char = 0.94, σM = 0.12, and z = 2. The truncated exponential distribution can also be characterized in terms of seismic moment rate so that it can be used in conjunction with slip rate. This distribution is given by Equation 8.14, in which N 0 is given by the expression [Shedlock et al., 1980; Campbell, 1983]: N 0 = N 0′

10 − b(m0 −m0′ ) − 10 − b(mu −m0′ ) 1 − 10 − b(mu −m0′ )

(8.16)

where N 0′ =

M 0T (c − b)

[ b[1 − 10 − b(m −m′ ) ] u

0

]

M 0 (mu )10 − b(mu −m0′ ) − M 0 (m0′ )

−1

(8.17)

and m0′ ≤ m0 is the magnitude corresponding to a physical lower limit below which earthquakes are not expected to occur or do not contribute to the observed slip on the fault, M0( m0′ ) is the seismic moment of this lower limit magnitude, and M0(m u) is the seismic moment of the upper bound magnitude m u. The physical lower limit magnitude should not be confused with the lower-bound magnitude m 0 , the lower limit of engineering significance. If there is no physical limit to the smallest earthquake that can occur on a fault, or if mu >> m0′ , then Equation 8.17 can be simplified considerably, resulting in the relationship [Campbell, 1983]: N 0′ =


M 0T (c − b)10bmu bM 0 (mu )

for mu >> m0′

(8.18)



8-15

which can be used with the truncated exponential distribution above or as an estimate of the a-value in the Gutenberg–Richter relationship given in Equation 8.5. Petersen et al. [1996] used an incremental version of the above relationship to estimate the a-value for characteristic faults in California.

8.5.3 Conservation of Seismic Moment on Segmented Faults The maximum magnitude and characteristic earthquake recurrence models are conceptually linked to the idea that large fault zones rupture in a segmented manner and rarely break their entire length in a single earthquake. The segmented nature of the mechanics of faulting was revealed through intense paleoseismic investigations of the San Andreas and Wasatch fault zones in the western United States [Schwartz and Coppersmith, 1984]. Relatively small displacements observed in natural exposures or excavations of the fault zones were not laterally continuous. Larger displacements, however, were continuous over longer lengths and crossed structural discontinuities within the fault zone. The logical confinement of ruptures between identifiable structural discontinuities, or rupture barriers, within fault zones led to the concept of segmented fault rupture [King and Nabelek, 1985; Schwartz, 1988]. This concept has proven very useful in explaining the extent of recent earthquake ruptures [e.g., Crone et al., 1985], in defining paleoseismic ruptures [e.g., Machette et al., 1992], and in relating the development of geologic structure to repeated earthquake rupture of fault zones [Cowie and Scholz, 1992]. Although fault segmentation has proven a very useful tool in earthquake hazards assessment, it is important to recognize that segment boundaries do not repeatedly arrest all earthquake ruptures and that their position is not necessarily constant in geologic time and space [Wheeler and Krystinik, 1992]. Nonetheless, a basic tenet of fault segmentation is that, in a relative sense, smaller earthquakes tend to be confined to single segment ruptures, whereas larger earthquakes tend to be characterized by multisegment ruptures. Specific lengths of segment ruptures depend on the tectonic environment of the region and the style of faulting that is present. Repeated faulting of all styles, over geologic time, will produce recognizable geologic structures at segment boundaries. Detailed documentation of fault slip rates along faults of the San Andreas system in southern California has shown that slip rate is not constant along all segments of a single fault zone [Working Group on California Earthquake Probabilities, 1995, 1999]. Slip rate typically varies among the various segments and could be due to any number of physical changes that may occur along the fault. A difficulty in PSHA, therefore, is accounting for the varying slip-rate values between different segments of individual faults. The various slip rates could be completely accommodated in the PSHA by a series of fault sources specific to each segment with each segment’s earthquake rate governed by the segment slip rate. This would be an unrealistic model, however, both in terms of the resulting distribution of probabilistic ground motion and the representation of large historical earthquake ruptures that have been documented to rupture more than one segment on some faults. The Working Group on California Earthquake Probabilities [1995, 1999] developed a “cascade” model of earthquake recurrence frequency to satisfactorily account for varying slip rates and fault depths on a single fault zone in a PSHA. The 1995 cascade model assumes that large earthquakes break multiple, contiguous segments of a fault at a frequency that is governed by the lowest-slipping segment. Once the moment rate (Equation 8.17) of the slowest-slipping segment is depleted in the production of these large earthquakes, it drops from any further considerations regarding multisegment ruptures and the slip rates of the remaining segments are reduced by the rate of the slowest-slipping segment. A new set of multisegment ruptures are thereby defined, and the procedure repeats until only single-segment ruptures of the highest-slipping segments are left to rupture in single earthquakes at a rate that is determined from the residual slip when all multisegment ruptures have been exhausted. This novel modeling approach maintains the slip-rate and seismic-moment budget on each defined fault segment. In the 1999 model, each possible cascade on a fault zone was assigned a relative weight by a panel of experts and the final weights adjusted to achieve a moment-balanced model.



8-16


8.5.4 Time-Dependent Probability Modeling


T1

T1

T2

T2

u

u

CUM. COSEISMIC SLIP

FIGURE 8.8 Three types of earthquake occurrence models. Upper row of figures shows stress patterns of increase and decrease through multiple earthquake cycles. Lower row of figures shows corresponding patterns of fault slip through the earthquake cycles. (a) Perfectly periodic model of constant stress increase to a certain level (T1), and constant stress drop back to a certain level during the earthquake (T2). (b) Time-predictable model illustrating stress buildup to a certain level and nonuniform stress drops. (c) Slip-predictable model showing nonuniform stress buildups and stressdrops to a certain level. (From Scholz, D.H., 1990, The Mechanics of Earthquake Faulting, Cambridge University Press, Cambridge. With permission.)

STRESS

Use of the previously described magnitude-frequency models in most seismic hazard applications assumes that the occurrence of an earthquake is independent of all other earthquakes, both spatially and temporally. That is, that earthquake occurrence follows a Poisson process, which can be characterized by a mean annual rate and a variance equal to this mean rate. These applications are therefore time-independent. Time-dependent occurrence models, on the other hand, assume that the probability of a future earthquake increases with the elapsed time since the last earthquake. Faults that are early in their seismic cycle are less likely to have an earthquake than the Poisson model would predict and faults late in their seismic cycle are more likely to have an earthquake. Such models are called renewal models. The consequences of time-dependent probability on seismic hazard have been investigated only to a limited extent in the literature [Cramer et al., 2000], but it has found widespread use in engineering practice and in loss modeling. It has also found professional acceptance in assessing short-term probabilities of large earthquakes on the San Andreas and related faults in California [Working Group on California Earthquake Probabilities, 1988, 1990, 1995, 1999], which has greatly impacted hazard mitigation policy in the San Francisco and Los Angeles areas. Following the great 1906 San Francisco earthquake, Reid [1910] proposed the elastic rebound theory in which earthquakes occur whenever stress builds to a certain level on a fault (Figure 8.8). The earthquake relieves this stored stress and the earthquake cycle begins anew. With the assumption of constant stress increase, the recurrence time in this model is perfectly periodic. Based on a long earthquake history in the vicinity of Kyoto, Japan and measured coastal uplifts during earthquakes, Shimazaki and Nakata [1980] proposed two other alternative forms of recurrence. The first is a time-predictable model that predicts earthquakes will occur when stress accumulation on the fault reaches a critical level, but that the stress drop and magnitude of the earthquakes vary among the seismic cycles (Figure 8.8). Thus, the time to the next earthquake can be predicted from the slip in the previous earthquake assuming a constant fault-slip rate. The second is a slip-predictable model in which earthquake failure on the fault resets the stress on the fault to some constant level irrespective of the earthquake’s magnitude (Figure 8.8). Thus, slip in the next earthquake can be predicted from the time since the previous earthquake. The motivation for time-dependent probability models arose from the identification by seismologists of “seismic gaps” along segments of major plate boundaries of the circum-Pacific region [see for example, Sykes, 1971]. Seismic gaps were identified as unbroken sections of major plate boundaries that were bounded on each end by ruptures from previous earthquakes. The implication from such observations was that the unbroken sections had an increased likelihood of rupturing in a future earthquake than those sections that had previously ruptured. Nishenko [1991] formalized the concept for 96 circumPacific plate boundary segments in terms of a conditional probability that a large earthquake would occur in future time windows of 5, 10, and 20 years, given that one had occurred at some known time in the past. A primary issue in such earthquake forecasts is the reliable quantification of large (characteristic) earthquake recurrence intervals. In that these large earthquakes are rare events in themselves, there is

(a)

t

u

(b) TIME

t

(c)

t


8-17


insufficient available data on any individual rupture segment from which to obtain a robust statistical distribution of recurrence times. Nishenko and Buland [1987] found that normalized earthquake recurrence intervals for large earthquakes in the circum-Pacific region follow a lognormal distribution with a virtually constant intrinsic standard deviation of σD = 0.205 for historic recurrence data and 0.215 for combined historic and geologic recurrence data, when a normalizing function T/Tave was used. In this formulation, T is the recurrence interval of an individual earthquake sequence, and Tave is the observed average recurrence interval for the sequence. This distribution has since become a primary element of the renewal-type time-dependent earthquake models used by the Working Group on California Earthquake Probabilities [1988, 1990, 1995, 1999]. A finite value for the average intrinsic standard deviation (usually taken to be between 0.21 and 0.5) is a significant element of the model, because it introduces a degree of aperiodicity in the occurrence of characteristic earthquakes. The physical reality of a finite value for the intrinsic standard deviation is also significant because it may present a barrier to precise earthquake prediction since physical reasons for this value are currently unknown [Scholz, 1990]. In part, it might be due to stress interactions from other earthquakes in the region, as discussed later in this chapter. The probability that a large earthquake will occur on a fault at time τ in an interval (T, T + ∆T), assuming a probability density function for recurrence time fT(t), can be given by the integral: P (T ≤ τ ≤ T + ∆T ) =

∫

T + ∆T

T

fT (t ) dt

(8.19)

If the elapsed time since the previous earthquake on the fault Te is known, the conditional probability that the earthquake will occur in the next ∆T years is given by the ratio:

∫ )

(

P Te ≤ τ ≤ Te + ∆T τ > Te =

Te + ∆T

Te

∫

∞

T

fT (t ) dt

fT (t ) dt

(8.20)

It has been common to assume a lognormal probability density function for recurrence time [Nishenko and Buland, 1987; Working Group on California Earthquake Probabilities, 1988, 1990, 1995; Cramer et al., 2000], which is given by the equation: fT (t ) =

1 t σ lnT

2   1  t Tˆ    exp −    2  σ lnT   2

(8.21)

where σlnT is the standard deviation of the logarithm of recurrence time and Tˆ is the median recurrence time, related to the mean by the expression: Tˆ = T exp

(

1 2

σ ln2 T

)

The standard deviation is composed of two parts, an intrinsic standard deviation σi and a parametric standard deviation σp , where σ lnT = σ i2 + σ 2p The intrinsic standard deviation represents aleatory or random variability, whereas the parametric standard deviation represents epistemic or modeling uncertainty. The latter standard deviation accounts for uncertainty in the median estimate of the recurrence interval, which comes from deriving it from events with uncertainty dates, such as paleoseismic estimates. Epistemic uncertainty can also be included by



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Monte Carlo simulation, rather than including it in σlnT [Working Group on California Earthquake Probabilities, 1995, 1999]. While the lognormal distribution has been the most common distribution used to describe the variability in recurrence intervals, several other distributions have been proposed and used. Most notable are the Weibul and time-predictable distributions [Cornell and Winterstein, 1988] and the Brownian passage time distribution [Working Group on California Earthquake Probabilities, 1999]. Other nonPoissonian distributions are reviewed by Cornell and Winterstein [1988]. Faults are not only affected by earthquakes that occur on them, but also by earthquakes that occur on nearby faults, through stress transfer [Stein, 1999]. The occurrence of a large earthquake modifies shear and normal stresses on other faults in the region, although these stress changes are small, being on the order of several bars or less. Considering that stress drops in earthquakes are on the order of 50 to 100 bars, the changes related to stress transfer are only a small fraction of the stress drops involved in fault rupture. Nonetheless, the frequency of earthquakes has been observed to increase in areas of increased stress transfer and decrease in areas of decreased stress transfer. For example, stress changes following the MW 6.9 Hyogo-ken Nanbu, Kobe, Japan earthquake is believed to have produced a tenfold probability decrease of a large earthquake in the next 30 years on the western segment of the Arima-Takatsuki Line (the fault that terminated the Kobe rupture on the north), where stress decreased [Toda et al., 1998]. On the other hand, it was estimated that there was a fivefold increase in probability on the eastern segment of the Arima-Takatsuki Line, where stress was increased (Figure 8.9). Incorporating such stress changes augments the physical bases of time-dependent earthquake probability estimates. The permanent probability gain caused by a stress increase is amplified by a transient gain that decays with time [Stein, 1999]. The opposite occurs for a stress decrease. The transient gain is an effect of rateand state-dependent friction [Dietrich, 1994], which describes behavior seen in laboratory experiments and in natural seismic phenomena, such as earthquake sequences, clustering, and aftershocks. The transient gain can be significant, but will decrease exponentially after the earthquake, according to Omori’s law, until it reaches the level of the static stress change. The rate increase can be converted to a probability gain using Equation 8.2. The seismicity rate equation is given by [Dietrich, 1994; Stein, 1999]: R (t ) =

  − ∆σ f exp   Aσ n 

r    −t   − 1 exp  t  + 1    a

(8.22)

where R(t) is the seismicity rate as a function of time t, following a Coulomb stress change ∆σf , A is a constitutive parameter, σn is the total normal stress, ta is the aftershock duration (equal to ∆σ/ τ˙ , where τ˙ is the stressing rate on the fault), and r is the seismicity rate before the stress perturbation. To evaluate this equation, the Coulomb stress change is calculated and r, ta , and τ˙ are estimated from observations, allowing Aσn to be inferred. Using such a model, Parsons et al. [2000] estimated a 62 ± 15% probability of an earthquake capable of causing strong shaking in Istanbul in the next 30 years as a result of the 1999 MW 7.4 Izmit, Turkey earthquake. This can be compared to a probability of 49 ± 15% using only the renewal model. The Poisson model results in a 30-year probability of 20 ± 10%. The probability during the next decade is estimated to be 32 ± 12% compared to a renewal rate of 20 ± 9%. Large earthquakes can also have a significant quiescent affect on seismicity, called a stress shadow. Harris and Simpson [1998] evaluated the observed suppression of MW 6 earthquakes in the San Francisco Bay area after the 1906 MW 7.8 San Francisco earthquake, and found a set of stress and rate-and-state parameters that were consistent with the observed rate change. Applying these parameters to the Hayward fault, they found that the probability of a MW 6.8 earthquake during the period 2000 to 2030, such as occurred in 1868, is 15 to 25% lower if the effect of the 1906 stress shadow is included. Stress transfer following the great 1906 San Francisco earthquake is one of the models considered by the Working Group on California Earthquake Probabilities [1999] in their time-dependent probability estimates for the © 2003 by CRC Press LLC


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M ≥1.0 Aftershocks

Coulomb Stress Change (bars)

for Optimally Oriented Faults -0.5

0.0

0.5 for Major Strike-Slip Faults

FIGURE 8.9 Illustration of stress transfer following the 1995 Hyogo-ken Nanbu (Kobe), Japan earthquake and aftershocks greater than magnitude 2.0. Star indicates the epicenter of the.earthquake located on the northeast trend of the fault rupture. The Arima-Takatsuki Tectonic Line trends east-northeast at the northern end of the fault rupture. 63% of the aftershocks were found to occur where Culomb stress increased on optimally oriented faults by greater than 0.1 bar. (From Toda, S. et al., J. Geophys. Res., 103, 24,543–24,565, 1985. Also http://quake.usgs.gov/research/ deformation/modeling/ papers/kobe/fig6.jpg/.)

San Francisco Bay area. Figure 8.10 illustrates the regional, as well as fault-segment-specific, conditional probabilities of MW 6.7 earthquakes in the San Francisco Bay region made by the Working Group for a 30-year time window from 2000 to 2030. The Working Group estimated this probability to be 70 ± 10% with individual fault segments contributing anywhere from 4 to 32% of this overall probability. Also new in these assessments is the incorporation of a probability (i.e., 9%) that a future earthquake may occur off the major faults in the regions that were considered in the study.

8.6 Maximum Magnitude Assessments Assessment of the maximum magnitude earthquake for the defined seismic sources is an important, fundamental task in PSHA. For PSHAs addressing low-probability hazard (i.e., long return-period hazard), the maximum magnitude earthquakes may dominate the ground motion assessments [Bender, 1984]. In probabilistic analyses, the maximum earthquake is defined as the earthquake that is assessed as physically capable of occurring within, or on, a defined seismic source in the contemporary tectonic © 2003 by CRC Press LLC


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SAN FRANCISCO BAY REGION EARTHQUAKE PROBABILITY

70% odds (±10%) for one or more magnitude 6.7 or greater earthquakes from 2000 to 2030. This result incorporates 9% odds of quakes not on shown faults.

Expanding urban areas

21%

New odds of magnitude 6.7 or greater quakes before 2030 on the indicated fault

18%

Odds for faults that were not previously included in probability studies

Increasing quake odds along fault segments Individual fault probabilities are uncertain by 5 to 10%

FIGURE 8.10 Time-dependent earthquake probabilities in the San Francisco Bay area, California for a time window from 2000–2030. (From the Working Group on California Earthquake Probabilities, 1999, U.S. Geological Survey Open-File Rep. 99-517, http://Geopubs.wr.usgs.gov/fact sheet/fs152–99.)

stress regime. Another term defining such an event is maximum credible earthquake [California Division of Mines and Geology, 1975]. A number of diverse methods have been used to define such earthquakes, each dependent on the purpose of the hazard assessment, the amount and kinds of seismological and geological data that lend themselves to such assessment, and the variety of seismotectonic settings in which PSHAs have been performed [dePolo and Slemmons, 1990]. The assessment of maximum earthquake magnitude is possible mainly because empirical data indicate a correlation between earthquake magnitude and fault parameters of rupture length, rupture area, and displacement [Wells and Coppersmith, 1994; see Chapter 4]. However, the use of several techniques can result in more reliable estimates than any single technique by itself [Coppersmith, 1991]. Maximum magnitude assessments in PSHA are broadly divisible into those that characterize area sources and those that are specific to individual earthquake faults.

8.6.1 Area Source Determinations Area sources are generally employed due to the lack of recognizable earthquake faults and seismically active geologic structure. Empirical correlation equations between fault rupture parameters and earthquake size, therefore, have limited application to these source types. Maximum magnitudes for these sources are typically assessed from an extrapolation of the historical seismicity of the region, from




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compelling worldwide analogs of the regional tectonic setting, from regional paleoseismologic data and interpretations (if available), or simply from the judgments of experts. Lacking clear geological guides from which to estimate maximum earthquakes in regions of low seismicity, methods of estimating maximum magnitudes from historical earthquake data have been commonly used. Since large earthquakes in these regions have very long recurrence times, it is generally assumed that the largest historical earthquake is the minimum value for a maximum earthquake estimate. Nuttli [1979], for example, evaluated the largest earthquake of the 1811–1812 New Madrid earthquake sequence in the New Madrid Seismic Zone as mb 7.4 and expressed confidence that the sum of the energy of the three principal shocks of the sequence defines the maximum earthquake for this seismic source (mb 7.5). Elsewhere in the central United States region, magnitude increments of between 0.5 and 1.0 unit above the historically observed maximum earthquake were judged to approximate earthquakes with recurrence intervals of around 10,000 years in application to nuclear facility sites. Nuttli [1981] later extended this approach for normalized areas of 100,000 km2 and a time period of 1000 years in application to seismic zones of the central United States. Justification was based on the fact that these parameters provided maximum magnitude estimates in general agreement with the historical maximum earthquakes of both the New Madrid and Charleston seismic zones, which are considered to be essentially the maximum earthquakes in these zones. Such techniques assume that the addition of magnitude increments to historical maximum observations accounts, to some extent, for the relative shortness of the historical reporting period. For a b-value of 1.0 in the Gutenberg–Richter recurrence relationship (see Chapter 4), the addition of 1.0 magnitude unit to the historical maximum observation is equivalent to multiplying the length of the observation period by a factor 10. Justification is then required for expecting the maximum magnitude event within this period of time. A primary issue with this technique is the correct characterization of the form of recurrence–frequency relationship. Minor changes in the Gutenberg–Richter b-value imply greatly differing time periods of catalog compensation, and other forms of recurrence–frequency relationships may also be appropriate [Wesnousky et al., 1983; Wesnousky, 1994]. The technique of using worldwide tectonic analogs for assessing maximum magnitudes is premised on the acquisition of more complete data by substituting space for time. In many regions, the historical period of earthquake reporting is far too short to have probably sampled the largest possible earthquake. However, even if the occurrence of maximum earthquakes is random in time and space, the likelihood of having observed a maximum earthquake is greater over a collection of similar regions worldwide. This was the basis for a far-reaching study by the Electric Power Research Institute [Johnston et al., 1994] of stable continental interior earthquakes worldwide. From a regionalization of the world into areas of similar geologic and tectonic histories and a detailed examination of the historical earthquakes in each, this study was able to identify associations of maximum earthquakes with specific classes of continental crust. Very old continental crust that had not been disturbed by regional tectonism over the last billion years exhibited lower magnitude earthquakes than continental crust that had been disturbed over the last 0.5 billion years. Such analogies can provide strong arguments for maximum magnitude assessments in regions of sparse seismicity. Paleoseismologic data, such as paleoliquefaction, can be an insightful tool in assessing the maximum magnitudes of low-seismicity regions. Unlike tectonic analogs that substitute space for time, paleoseismological data extend the record of earthquakes into prehistoric time. Munson et al. [1992, 1994] documented widespread liquefaction features throughout southern Illinois and Indiana dating from a single earthquake 6100 ± 200 years ago. A second strong earthquake was documented as occurring 12,000 years ago. Historical earthquakes in this region up to magnitude 5.5 have no reports of accompanying liquefaction, and the prehistoric earthquakes therefore appear to be considerably larger than the historic earthquakes. Obermeier et al. [1993] evaluated the earthquake that occurred 6100 years ago as a magnitude 7.5 earthquake based on the physical dimensions and properties of the liquefaction features. Thus, although the source of the prehistoric earthquakes remains unknown, assessments of the seismic hazard in this region must assess significantly higher maximum magnitudes than have been observed historically. A similar example can be cited for the Pacific northwest region of the United States where no large © 2003 by CRC Press LLC


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earthquake has affected coastal Oregon and Washington historically. Yet, regional paleoseismological evidence suggests sudden, regional submergence of coastal marshes along the Oregon and Washington coasts [Atwater, 1987; 1992]. These phenomena have been ascribed to prehistoric great earthquakes (moment magnitude of 8 ~ 9) and their associated tsunamis that occurred 300 years ago, and earlier, along the Cascadia subduction zone. Recently, evidence from tsunami observations in Japan permitted precise dating of the last earthquake at 1700 and its magnitude at ~9 [Satake et al., 1996].

8.6.2 Individual Fault Determinations Guidelines for establishing maximum magnitudes for individual faults are significantly better than for establishing maximum magnitudes for area seismic sources. Estimates of maximum magnitudes on faults are typically computed from empirical correlation relationships between earthquake magnitude and rupture dimensions [e.g., Wells and Coppersmith, 1994]. The most common characteristic that is correlated with earthquake magnitude is fault rupture length. Extensive study has been made of this correlation over the past 30 years [Bonilla and Buchanan, 1970; Mark and Bonilla, 1977; Bonilla, 1980; Wells and Coppersmith, 1994; among many others; see Chapter 4] and the database of worldwide earthquake surface ruptures has grown rapidly [e.g., Wells and Coppersmith, 1994]. In addition, the formal statistical treatment of the data has improved over the years. Modern correlation relationships: 1. 2. 3. 4.

Quantify the scatter in the data in terms of the standard deviation Are sensitive to earthquake magnitude type Provide unique definition of fault-type categories Minimize the error in prediction by providing separate regression relationships for the various independent variables

Wells and Coppersmith’s [1994] relationships, presented in Chapter 4, are based on data from 244 historical continental earthquakes worldwide that produced surface rupture and had focal depths shallower than 40 km and magnitudes greater than 4.5. Two primary sources of uncertainty exist in employing magnitude-rupture length correlation equations in the assessment of earthquake magnitudes. One is the variability of the regression equation itself, which has been described in Wells and Coppersmith’s [1994] assessments in terms of the standard deviations of the regressions and which can be considered in the application of the relationships. The other is the uncertainty of establishing future rupture lengths. While the empirical correlation relationships provide a relatively complete assessment of past earthquake ruptures related to earthquake magnitude, their forward application in predicting future earthquake magnitude on a fault is ambiguous owing to the need to define the length of future fault ruptures. In applications of a few decades ago, rather arbitrary fractional lengths of known earthquake faults were used to determine maximum magnitudes, premised on the empirical observation that faults seldom rupture their entire lengths in single earthquakes, and commonly ruptured in less than half of their entire length [Albee and Smith, 1966]. However, the concept of fault segmentation also has proven to be a useful tool in the definition of future potential lengths of fault rupture. For example, in the cascade model of determining earthquake recurrence frequencies on singular faults with segment-specific slip rates, the magnitude of each earthquake cascade, whether a multi- or single-segment rupture, is defined by the individual cascade rupture dimension.

8.6.3 Mixed Source Determinations The previous discussions of earthquake recurrence frequency and maximum magnitude assessment in PSHA were organized around area and fault source determinations for simplicity of presentation. However, it is common practice to define a mixed-source type in which one or more earthquake faults are defined within the boundaries of a regional area source. Such mixed-source definitions require particular care in specifying earthquake frequencies and maximum magnitudes to avoid double counting of earthquake occurrences. The simplest manner of handling such sources is to define two separate sets of © 2003 by CRC Press LLC



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minimum and maximum magnitudes, one for the area source and one for the fault sources, respectively. Such a treatment typically defines the area source as a region of background seismicity in which smalland moderate-magnitude earthquakes are modeled as random events up to a maximum magnitude of about 6.5, with a recurrence frequency statistically determined from the catalog of earthquakes in the region. Above this magnitude, the larger earthquakes can be modeled in various ways as occurring on the defined earthquake faults with a recurrence frequency defined either from an extrapolation of the historical data, available paleoseismic data, or some combination of both. Maximum magnitudes may then be based on the physical parameters of the faults, as previously described. The magnitude break in area source/fault source modeling techniques for the mixed-source type is often rationalized around the threshold magnitude of surface faulting in the tectonic province of the site. In the Basin and Range province of the western United States, this threshold magnitude is around 6.75 [Bucknam and Anderson, 1979]. Care should be taken to evaluate the implied seismicity and seismic moment rates for mixed-source types to assure that the summed seismicity parameters are reasonable within the constraints of available seismotectonic data. This is of particular importance if the modeled magnitude range of the defined area source overlaps with those of the defined fault sources. Unrealistic regional magnitude-frequency relations could easily result from such a treatment of seismic sources.

8.7 Ground Motion Attenuation Relationships The ground motion attenuation relationships provide the means of estimating a strong-motion parameter of interest from parameters of the earthquake, such as magnitude, source-to-site distance, faulting mechanism, local site conditions, etc. [see Chapter 5]. This relationship is a particularly important element in PSHA for three reasons: 1. It dictates the detailed requirements of the seismic source definition. 2. It dictates the ground motion parameters that may be estimated. 3. It is a major contributor to uncertainty in the PSHA results [McGuire and Shedlock, 1981; Bender, 1984]. A wide variety of empirical ground motion attenuation relationships is available for application in PSHA [Campbell, 1985; see also Chapter 5] and research has shown ground motion attenuation to be regionally dependent. In large part, the choice of an appropriate relationship is governed by the regional tectonic setting of the site of interest, whether it is located within a stable continental region or an active tectonic region, or whether the site is in proximity to a subduction zone tectonic environment.

8.7.1 Impact on Seismic Source Definition A fundamental aspect of applying attenuation relationships within the PSHA methodology is the distance measure on which the chosen relationship is based. Two broad categories exist: • Those based on a measure of an earthquake’s distance from the site, whether measured as an epicentral or hypocentral distance • Those based on a distance from the earthquake fault rupture Epicentral distance is measured as an earthquake’s horizontal distance to a site irrespective of earthquake depth. Hypocentral distance is measured as the slant distance to the site, accounting for both the horizontal and vertical distances from the earthquake to the site. Such types of attenuation relationships do not require the specification of fault planes in the definition of seismic sources. Area source definitions completely satisfy the application requirements of these attenuation relationships and point-source models of earthquake rupture suffice in the PSHA model. If such relationships are used with explicit linear or planar fault sources, the rupture dimensions of earthquakes on these sources must be constrained to infinitely small rupture areas that approximate points. Otherwise, the distance measure may be applied inappropriately and the ground motion hazard may very likely be overestimated. © 2003 by CRC Press LLC


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Application of hypocentral distance measures requires that at least a top and bottom depth of the area source be defined in order to constrain the depths of the modeled earthquakes. Typically, these depth parameters are defined on the bases of either regional or local seismological network data and are a measure of the thickness of brittle crust in a region. Generally, this is referred to as the thickness of the seismogenic layer. In active tectonic regions, such as the western United States, the seismogenic layer generally ranges between 10 and 20 km deep, depending on the locality. In the stable continental region of the eastern United States, the seismogenic layer may range up to 40 km deep in some localities. Most modern attenuation relationships for active tectonic regions are based on various distance measures from the fault rupture zone (see Chapter 5). These relationships allow the specification of the top and bottom of seismogenic faulting (as in the seismogenic layer), can accommodate specific definitions of fault-dip (i.e., the inclination of the fault from horizontal), and require specification of the style of faulting for each defined source. A significant aspect of empirical attenuation relationships is the large scatter in the ground motion data on which the relationships are based, which results in large standard errors about the mean relationship. Campbell [1997] was able to significantly reduce the standard deviation of his relationships by segregating the strong motion database according to fault-rupture style (among other non-fault parameters, such as soil type) prior to regression analysis. His relationships, as well as others, therefore require explicit definition of fault-rupture style, consisting of normal or strikeslip, and reverse faulting. As attenuation relationships have evolved into these more precise definitions of the earthquake source, their application has challenged the PSHA analyst with more precise definitions of seismic sources.

8.7.2 Reference Site Class In addition to defining the earthquake source, application of ground motion attenuation relationships is specific to a soil or rock type on which the PSHA ground motion estimate is to be made. These ground types are referred to as the site class, and are defined in broad categories such as hard rock, soft rock, firm soil, and soft soil. In some cases, such as Campbell [1997], the site classes are unambiguously defined by soil shear-wave velocities. More commonly, the site classes are only qualitatively defined soil types. The choice of site class is important in PSHA since soil tends to amplify long-period motion and deamplify short-period motion over that of rock. Such site effects are embodied in the various site classes of modern spectral attenuation relationships (see Chapter 5). The site class that is chosen for application in PSHA, referred to as the reference site class, may depend on a number of factors, not the least of which is the purpose of the PSHA. Site-specific engineering PSHA evaluations are often performed to obtain a more precise measure of ground motion amplitude than can be found in regional hazard maps contained in building code documents. If seismic engineering for the site is to follow code procedures, then the site class for the PSHA must be consistent with the reference site class on which the codified procedures are based. If dynamic site response analyses are to be performed in order to produce synthetic time histories, either at the ground surface or at various depths (e.g., for pile design), then the reference site class for the PSHA depends on the geotechnical data that are available, the depth to which the geotechnical data extend, and the depth of bedrock at the site. The reference site class in such case may be either soil or rock.

8.8 Accounting for Uncertainties Development of a seismotectonic model and the many required input parameters to PSHA admits to a wide range of interpretations and uncertainties. Median probabilistic seismic hazard models consist of a single, best-estimate set of defined sources that are characterized by a single set of best-estimate seismicity and fault-rupture parameters [Bernreuter et al., 1989]. Development of such models is generally made with cognizance of diverse alternative choices, but individual modeling and parameter selections are made relative to the purpose of the hazard estimate and with respect to the representative nature of the individual selections. For example, the Algermissen et al. [1982] PSHA model for the United States © 2003 by CRC Press LLC



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was premised on a single set of seismic sources and input parameters but only following consideration of diverse views presented in a series of workshops held prior to developing the PSHA models [Thenhaus, 1983]. The Frankel et al. [1996] national PSHA model was similarly constructed following a series of regional workshops across the United States to sample professional opinion on PSHA input, but also contained a limited logic-tree approach to more explicitly represent critical uncertainties in the national seismic hazard estimates. Fully probabilistic seismic hazard models may employ a number of alternative seismic source interpretations with probability distributions defined for the various seismicity and fault-rupture parameters for each source of each model. Models similar to the fully probabilistic one are generally required to establish a mean seismic hazard result [Bernreuter et al., 1989]. In application to the seismic hazard of nuclear power plants in the eastern United States, Bernreuter et al. [1989] solicited 11 distinct PSHA models from individual experts with each model weighted by its creator as to credibility. Feedback was given to each of the experts on the ground motion consequences of their model so that each expert was comfortable with the results. However, little interaction among the experts was promoted. In an alternative approach, the Electric Power Research Institute [EPRI, 1986] performed a very structured PSHA that promoted much interaction and data exchange among experts of six Tectonic Evaluation Committees (TEC), each of which was composed of at least one geologist, geophysicist, and seismologist. Defined seismic sources by each TEC were thoroughly documented within a probabilistic framework as to their physical characteristics that may promote the generation of earthquakes and as to their spatial association with the cataloged earthquakes in the region. The result of this thorough probabilistic treatment was six highly detailed regional seismotectonic models of the eastern United States from which complete probabilistic descriptions of ground motion at the nuclear sites could be obtained. The EPRI [1986] PSHA stands as probably the most comprehensive PSHA performed to date. It should be pointed out that the Bernreuter et al. [1989] and EPRI [1986] PSHAs were designed to address very low levels of risk associated with projects in the nuclear industry. Such comprehensive investigations were developed to address annual risk levels at the power plant sites of 10–4 and lower. Most PSHA applications address common buildings and industrial facilities where annual levels of risk of 10–2 to 10–3 are generally acceptable as an industry or code standard. PSHA methodologies are therefore scaled back from those of the nuclear industry for appropriateness to the project objectives and for cost effectiveness. There are two types of variability that can be included in PSHA. These are aleatory and epistemic variabilities [SSHAC, 1997]. Aleatory variability is uncertainty in the data used in an analysis and generally accounts for randomness associated with the prediction of a parameter from a specific model, assuming that the model is correct. Specification of the standard deviation (σ) of a mean ground motion attenuation relationship is a representation of aleatory variability. Epistemic variability, or modeling uncertainty, accounts for incomplete knowledge in the predictive models and the variability in the interpretations of the data used to develop the models. Aleatory variability is included directly in the PSHA calculations by means of mathematical integration. Epistemic uncertainty, on the other hand, is included in the PSHA by explicitly including alternative hypotheses and models. This uncertainty can be accounted for through the evaluation of multiple individual seismotectonic models or through the formulation of a logic tree that includes multiple alternative hypotheses in a single model. The logic tree allows a formal characterization of uncertainty in the analysis by explicitly including alternative interpretations, models, and parameters that are weighted in the analysis according to their probability of being correct. Logic tree models may be exhaustively evaluated, or adequately sampled through Monte Carlo simulation, which is computationally a more efficient procedure. An example of a logic tree seismotectonic model is shown in Figure 8.11. Each alternative hypothesis, indicated by a branch of the logic tree, is given a subjective weight corresponding to its assessed likelihood of being correct. The proposed alternative hypotheses account for uncertainty in earthquake source zonation, maximum magnitude, earthquake recurrence rate, location and segmentation of seismogenic faults, style of faulting, distribution of seismicity between faults and area sources, and ground motion attenuation relationships. © 2003 by CRC Press LLC


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Seismic Segmentation Segmentation Segments Attenuation Fault Model Relationship Recurrence Sources Model

Status of Total Fault Activity Length

Dip

Maximum Recurrence Recurrence Magnitude Data Rate

Unnamed Unsegmented 0.2

Oquirrh Mtns

Campbell

Model A

Wasatch

0.4

0.333

East Coshe

Exponential 0.3

West Valley

Cominston

65°

5000 0.04

Ogden

0.5

.3333 0.28

SLC Provo

Segmented

Active

37 km

1.0

1.0 45°

Nephi

0.8

0.5

Levon

Hansel Valley

Model B

Sadigh

Bear Lake

0.6

Backgnd

0.333

N/A

Characteristic 0.7

N/A

Active 1.0

N/A

N/A

7.0 0.15 7.25 0.7 7.5 0.15 6.0 0.3 6.25 0.5 6.5 0.2

Fault 1.0

2500 0.48 2000 0.16

Segment 1.0 N/A

1667 0.04 8.5 0.333 9.3 0.334 9.8 0.333

Joyer-Fumal 0.333

FIGURE 8.11 Example logic tree characterization for seismic sources. (From Youngs, R.R. et al., 1987, “Probabilistic Analysis of Earthquake Ground Shaking along the Wasatch Front, Utah,” in P.L. Gori and W.W. Hays, Eds., Assessment of Regional Earthquake Hazards and Risk along the Wasatch Fault, Utah, U.S. Geological Survey Open File Rep. 87-585, pp. M1-M110.)

8.9 Typical Engineering Products of PSHA The fundamental engineering product of PSHA is an amplitude of some ground motion parameter that is associated with a particular return period. This probabilistic format of relating ground motion amplitude to a specific return period is now commonplace in a number of seismic design codes and recommended practices, including those of the National Earthquake Hazards Reduction Program (NEHRP), the International Building Code (IBC), the National Fire Protection Association (NFPA), the American Petroleum Institute (API), and the International Standards Organization (ISO), among others. Probabilistic results can be presented in a number of formats. Perhaps the most widely recognized product is that of a ground motion hazard map, such as produced by the U.S. Geological Survey under the National Earthquake Hazards Reduction Program for the United States (Figure 8.12) and one of the world that was recently produced under the auspices of the Global Seismic Hazard Assessment Program (GSHAP) [Giardini, 1999; Figure 8.13]. Such maps illustrate the regional differences in ground motion amplitude (typically peak ground acceleration, or PGA) at a constant return period (i.e., a constant probability of exceedance). These maps allow the rapid comparison of the seismic hazard for regions and the identification of the most hazardous regions, on a uniform basis. A common goal of hazard models is to rapidly estimate a hazard curve for a particular engineering site of interest. The hazard curve is a plot showing the change in ground motion amplitude relative to return period (Figure 8.14). Ground motion amplitude always increases with increasing return period in Poisson hazard models and, for a single fault, will asymptotically approach the mean ground motion amplitude of the maximum magnitude earthquake at the given source-to-site distance when attenuation variability is not included in the estimate. Another common product in engineering PSHA is the constant-probability, or uniform hazard, response spectrum (Figure 8.15). These curves illustrate ground motion amplitudes over a number of oscillator periods of engineering interest at a constant return period. Comparison of such curves at a constant return period, but for various site classes, illustrates the modification of ground motion amplitudes by various types of soil and rock. Soils tend to deamplify short-period motion, but amplify longperiod motion. Rock sites have the inverse effect. The probabilistic response spectrum is generally smooth © 2003 by CRC Press LLC

0068_C08_fm Page 27 Wednesday, August 14, 2002 7:11 AM

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Peak Acceleration (%g) with 10% Probability of Exceedance in 50 Years

50°

-120

°

site: NEHRP B-C boundary -110°

-100°

-90°

-80°

-70°

50°

40°

40°

30°

30°

Nov. 1996 -120

180 100 80 60 40 30 25 20 15 10 9 8 7 6 5 4 3 2 1 0

-70°

°

-110°

-100°

-90°

-80°

U.S. Geological Survey National Seismic Hazard Mapping Project

FIGURE 8.12 Four hundred seventy-five-year return period ground motion hazard map of the conterminous United States. (From Frankel, A., 1996, U.S. Geological Survey Open-File Rep. 96–532. With permission.)

FIGURE 8.13 Four hundred seventy-five-year return period ground motion hazard map of the world. (From Giardini, D. Ann. Geofis., 42, 1999. http://www.gfz-potsdam.de/pb5/pb53/project/gshap/final_result.html.)



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Peak Ground Acceleration - Site Class=C - Soft Rock

Return Period (years)

10 4

10 3

10 2 Mean 5th% 16th% 50th% 84th% 95th%

10 1 0.0

0.1

0.2

0.3

0.4

Horizontal Acceleration (g)

FIGURE 8.14 Example of a peak ground acceleration (PGA) hazard curve on a soft rock site class for a logic-tree seismotectonic model in a low seismicity region of Eurasia. Mean estimate and confidence intervals are shown by different line types in the legend of the figure.

and broader in shape than the response spectrum obtained from an actual earthquake recording, since the probabilistic spectrum is the result of the aggregated ground motion contributions from all magnitudes and distances of significance to a site, weighted by their frequency of occurrence. Median hazard models result in a single estimate of the uniform hazard spectrum (UHS). More fully probabilistic PSHA models can represent the spread of UHS results accounting for uncertainty (e.g., through a logic tree) and are often presented by percentile levels (Figure 8.16). Such a complete description of the seismic hazard allows explicit representation of various levels of conservatism that may be applied in seismic engineering design.

8.10 PSHA Disaggregation The PSHA methodology aggregates ground motion contributions from earthquake magnitudes and distances of significance to a site of engineering interest and, as such, the PSHA results are not representative of a single earthquake. However, engineering models and computer codes generally require empirical or synthetic earthquake acceleration time series as input to dynamic analyses. Specific magnitudes and distances are also often required in slope stability and liquefaction analyses. An issue, then, is the selection of representative earthquake time acceleration series given a probabilistic uniform hazard response spectrum. A procedure called disaggregation (or deaggregation) has been developed to examine the spatial and magnitude dependence of PSHA hazard results. Considerable attention has recently been focused on PSHA disaggregation in recent research literature [e.g., Stepp et al., 1993; Cramer et al., 1996; Chapman, 1995; McGuire, 1995; Bazzurro and Cornell, 1999; Harmsen et al., 1999]. © 2003 by CRC Press LLC


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5%-Damped Horizontal Acceleration (g)

1

0.1

Hard Rock Soft Rock Firm Soil Soft Soil 0.01 0.001

0.01

0.1

1

10

Period (sec)

FIGURE 8.15 Example median uniform hazard response spectra (UHS) for a moderate seismicity site for various site classes.

The PSHA results are disaggregated to determine the magnitudes and distances that contribute to the calculated exceedance frequencies (i.e., the hazard) at a given return period and at a structural period of engineering interest (typically, the fundamental period of a structure). In this process, the hazard for a given return period and at a specified ground motion period is partitioned into selected magnitude and distance bins and the relative contribution to the hazard of each bin is calculated by dividing the bin exceedance frequency by the total exceedance frequency of all bins. The bins with the largest relative contributions — the modes — identify those earthquakes that contribute the most to the total hazard. If there are no clear modes, the controlling or design earthquakes are typically defined by the mean magnitude and mean distance. These results are displayed as a histogram giving the percent contribution to the specified hazard of those earthquakes that are capable of causing ground motions equal to or greater than that corresponding to this hazard as a function of magnitude and distance. This histogram will be different for spectral accelerations of varying structural periods because of the difference in the way these spectral values scale with magnitude and distance. The relative frequencies specified by these histograms can be used to develop mean estimates of magnitude and distance, or to identify the modal contributions to the site hazard, in order to define a set of controlling or design earthquakes corresponding to specified structural periods and return periods. These design earthquakes can then be used as bases to select or construct input time histories for use in a dynamic site-response analysis or for groundfailure evaluation. Figures 8.17 and 8.18 illustrate disaggregation plots. Figure 8.17 is unimodal and the mode of the distribution is relatively clear from the plot. Figure 8.18, however, illustrates a relatively strong bimodal contribution to PSHA hazard at the specific return period and structural period at which the disaggregation was performed. In such cases, two or more design earthquakes might need to be specified in order to fully represent the spectral content of ground motion expected at the site. Note that using a mean magnitude and distance for this bimodal distribution would result in a large magnitude earthquake that has no physical association with a known active fault.



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FIGURE 8.16 Example uniform hazard response spectrum for a single site class showing confidence limits obtained from a fully probabilistic application of the PSHA methodology. Note that because of lognormal distributions in many parameters used in PSHA, the mean estimate is always higher than median estimate.

The expected (median) ground motion amplitude corresponding to the disaggregated mean or modal magnitude and distance can be calculated by substituting these values into the attenuation relationships that were used in the PSHA. The difference between the logarithm of the ground motion value corresponding to the PSHA hazard at the return period of interest and the logarithm of the ground motion value for the disaggregated mean magnitude and distance, divided by the logarithmic standard error of estimate of the attenuation relationship, is referred to as ε (epsilon) [McGuire, 1995]. ε is the number of standard deviations that the probabilistically derived ground motion amplitude deviates from the median ground motion amplitude for an event defined by the mean magnitude and distance. An ε of 1 indicates that the probabilistic value of ground motion corresponds to the one-standard-deviation value of the deterministic ground motion. The larger the absolute value of ε, the greater the contribution of ground-shaking variability to the calculated hazard. Very large absolute values of ε should be avoided, since they indicate that the hazard is potentially being overly dominated by variability in the attenuation relationship.

8.10.1 Scaling Empirical Earthquake Spectra As previously mentioned, a common application of the design earthquake parameters resulting from a PSHA disaggregation is the identification of suitable earthquake records to be used in dynamic engineering testing and design. The defined magnitude and distance parameters from the disaggregation serves as a guide in the selection of three-component (two horizontal and one vertical) empirical earthquake time series from appropriate recording stations of historical earthquakes. The design earthquake parameters are only a general guide, however, with other factors such as site class, earthquake mechanism (i.e., style of slip), and representative spectral shape also having a bearing on the record selection. All of these parameters cannot usually be completely satisfied in the record search, and prioritization of the search © 2003 by CRC Press LLC


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Percent Contribution to Exceedance

10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0

8.00

7.00

6.00

5.00

145

135

125

115

km)

105

nce (

95

Dista

85

75

65

55

45

35

15

25

5

0.0

e

ud

it gn Ma

FIGURE 8.17 PSHA disaggregation plot showing a typical unimodal distribution of earthquake magnitude and distance to ground motion exceedance frequency. The mode of this distribution is a magnitude 6.5 to 7.0 earthquake occurring at a distance of 5 to 10 km from the site.

criteria is required. Typically, the spectral amplitudes of the identified suitable records do not match the UHS (i.e., the target spectrum) within the period band of engineering interest, and scaling of the empirical records is required. The scaling is commonly performed on some average of the spectra of the two horizontal components of motion. There are a number of averaging methods that can be applied, including a simple mean, a geometric mean, and the square root of the sum of squares (SRSS), among others. The geometric mean is defined with respect to the two horizontal components as (H1*H2)1/2 and may be preferred as it is the averaging method consistent with that applied in empirical ground motion attenuation relationships that are used to establish the UHS. Once the mean spectrum of the two horizontal components of motion is established, it can be scaled to a best-fit criterion to the target spectrum within the period band of engineering interest (Figure 8.19). The best-fit criterion is defined as a fit where 50% of the empirical spectral amplitudes are both above and below the target spectrum within the engineering period band of interest. The scale factor to achieve the best-fit spectrum may then be applied to each horizontal component time series to obtain empirical motions that are representative of expected earthquake ground motions at the site for a return period of interest. If dynamic response analyses are to be performed on the soil column at the site, the above procedure can be performed for a reference site class representative of the input soil layer for the empirical time series.

8.11 PSHA Case Study This section presents an illustrative case study of a simple, median, peak ground acceleration (PGA) hazard assessment along the proposed offshore Oman India pipeline route. The proposed Oman India pipeline traverses approximately 1135 km of the northern Arabian Sea floor and adjacent continental shelves at water depths of over 3 km on its route from Ra’s al Jifan, Oman, to Rapar Gadhwali, India (Figure 8.20). Ground-shaking hazard was quantified in terms of PGA for return periods of 200, 500, and 1000 years using the PSHA computer program Seisrisk III [Bender and Perkins, 1987]. © 2003 by CRC Press LLC


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Percent Contribution to Exceedance

6.0

5.0

4.0

3.0

2.0

1.0

8.00

7.00

6.00

5.00

145

135

)

125

(km

115

ce

105

tan

95

Dis

85

75

65

55

45

35

25

15

5

0.0

e

ud

it gn a M

FIGURE 8.18 PSHA disaggregation plot showing a bimodal distribution of earthquake magnitude and distance to ground motion exceedance frequency. The primary mode of this distribution is a magnitude 6.5 to 7.0 earthquake at 80 to 85 km from the site. The secondary mode is a magnitude 6.5 to 7.0 earthquake at 5 to 10 km from the site. This distribution is for a site near the eastern coast of Honshu, Japan that is in close proximity to a shallow active fault (secondary mode), although the Japan Trench subduction zone is the strongest contributor to the hazard (primary mode).

This summary is excerpted from the original publication [Campbell et al., 1996] and the reader is referred there for further discussions and a full citation of references on which the work is based. This PSHA was performed in 1995. On January 26, 2001, the MW 7.9, Bhuj (Gujarat, India) earthquake struck the Kutch region of northwestern India in the vicinity of the western terminus of the planned pipeline. This region was identified in the PSHA as one of high hazard. Thus, the case study serves as an example of the utility of PSHA in the engineering and planning of future development. The case study further illustrates that generally conservative results are obtained from time-independent, stationary models of seismicity if parameter estimates are made carefully and estimates of maximum magnitude earthquakes are realistic and not merely based on the maximum earthquake observed in a short reporting period [see McGuire and Barnhard, 1981]. © 2003 by CRC Press LLC


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5%-Damped Horizontal Acceleration (g)

1

0.1

0.01

200 Yr. UHS H1 H2 Mean

0.001 0.01

0.1

1

10

Period (sec)

FIGURE 8.19 Example scaled empirical earthquake spectra to a target, 200-year UHS. Solid bold line is the 200year return period target UHS. Heavy dashed line indicates the geometric mean of the two horizontal components. Light line styles are the H1 and H2 components. The geometric mean of the empirical spectra has been scaled to a best-fit criterion within the period band of 0.6 ± 0.5 seconds.

55°

60°

65°

70°

75°

PAKISTAN IRAN

MAGNITUDE id

ge

25°

y

R

Rapar Gadhwali

ur

ra

OMAN

M

Ra'as al Jifan

INDIA

ne

e

Oman - India

Owen

Fra ctu

re

Zo

20°

lin

pe

Pi

ARABIAN 0

8 to 8.2

(2)

7 to 7.9

(12)

6 to 6.9 (40) 5 to 5.9 (223) 4 to 4.9 (876) 3 to 3.9 (47) all others (89)

SEA 250

500

Kilometers

FIGURE 8.20 Location map of the Oman India pipeline route shown in relation to the regional distribution of earthquakes. © 2003 by CRC Press LLC


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20°

30°

40°

50°

60°

70°

80°

90°

40° 40°

30° 30°

20° 20°

10° 10°

0° 40°

50°

60°

70°

80°

FIGURE 8.21 Plate tectonic setting of the region surrounding the northern Arabian Sea showing regional tectonic features. (After Jacob, K.H. and R.L. Quittmeyer, Geodynamics of Pakistan, Geological Survey of Pakistan, pp. 305–317, 1979. With permission.)

8.11.1 Tectonic Setting Within the Arabian Sea basin, the Owen Fracture Zone and the Murray Ridge are two distinct structural geologic provinces of a transform plate boundary that accommodates slow, right-lateral differential motion between the Arabian and Indian plates (Figure 8.21). The northern tectonic boundaries of the Arabian and Indian plates are in continental collisional contact with the Eurasian plate, giving rise to the complex compressional tectonics of the Zagros and Himalayan Mountains. However, only in the Gulf of Oman is subduction currently occurring (i.e., where the ocean floor of the Arabian Sea is being thrust beneath the overriding Eurasian plate). Rupture along the contact between these two plates results in great thrust earthquakes, as demonstrated by an MS 8.2 earthquake and accompanying tsunami that occurred off the coast of Pakistan in 1945 (Figure 8.20).

8.11.2 Regional Seismicity The seismicity of the Arabian Sea and surrounding areas is dominated by earthquakes along the major tectonic plate boundaries (Figures 8.20 and 8.21). The primary sources of earthquake data used for the study were the Catalog of Middle East Earthquakes and the Catalog of Earthquakes for Peninsular India, 1839–1900. The Middle East catalog contains more than 22,000 earthquakes that occurred from 1900 to 1983. These catalogs were supplemented with several historic earthquake accounts of India. Seismicity between 1983 and 1992 was taken from the Preliminary Determination of Epicenters (PDE), published monthly by the U.S. Geological Survey. The regional earthquake catalogs were aggregated into a single catalog by removing duplicate entries through an automated winnowing procedure. The aggregated earthquake catalog used surface-wave magnitude (MS) to quantify earthquake size. MS was converted to moment magnitude (MW), the © 2003 by CRC Press LLC



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magnitude measure used in the strong-motion attenuation relationships described later, using relationships between magnitude measures given in Khattri et al. [1984], Hanks and Kanamori [1979], and Ekstrom and Dziewonski [1988]. The aggregated earthquake catalog was culled of aftershocks and the remaining earthquakes were analyzed for completeness by determining the time period over which events of various magnitudes were found to be completely reported. The analysis indicated that earthquakes of various magnitudes are completely reported for the following periods: MW 5.0 ± 0.2 for the past 20 years; MW 5.4 ± 0.2 for the last 30 years; MW 5.8 ± 0.2 for the last 60 years; and MW 6.0 for the last 80 years. Complete reporting times for larger earthquakes range from about 100 years for MW 6.2 to about 300 years, or the total period of the historic catalog, for great earthquakes (MW ≥ 8.0).

8.11.3 Great Earthquakes On June 16, 1819, a great (MS ≈ 8) earthquake occurred in the Rann of Kutch, India near the eastern terminus of the pipeline route. This earthquake was not on a plate boundary but, rather, was an intraplate earthquake similar to those that occurred in New Madrid, Missouri in 1811 and 1812. The Kutch earthquake was accompanied by surface rupture along a zone measuring 32 km by 16 km. The Kutch and New Madrid earthquakes are two examples of only a few historic intraplate earthquakes that have ruptured the ground surface. The Kutch earthquake caused damage over an extensive area. In the town of Bhuj nearly 7000 houses were “overthrown” with a reported 1140 casualties. The recent MW 7.9 Gujuarat earthquake that occurred on January 26, 2001 also devastated the city of Bhuj as well as the larger region of Gujuarat State in northwestern India [EERI, 2001]. Another great (MS 8.2) earthquake ruptured the plate interface zone of the Makran Subduction Zone on November 27, 1945. Historic accounts indicate a rumbling sound accompanied the earthquake at Karachi, Pakistan, but only a few windows were reported broken. A tsunami followed the earthquake and was most severe on the Makran coast, northwest of Karachi, where a telegraph office was reportedly washed to sea and a number of buildings were damaged. In the suburbs of Bombay, India, boats were reportedly smashed at their moorings. Two new islands had appeared in the Arabian Sea about 180 miles west of Karachi after the earthquake.

8.11.4 Earthquake Source Characterization The earthquake source characterization of the northern Arabian Sea and surrounding areas consisted of defining earthquake source zones and earthquake recurrence relationships that accurately modeled the occurrence of earthquakes in space and time within the study area. This model was developed to be consistent with the contemporary understanding of the tectonics and seismicity of the region as documented in the technical literature. The earthquake source zones are shown in Figure 8.22. Earthquake recurrence was modeled using the Gutenberg–Richter relationship, Equation 8.5. Earthquakes were modeled between a minimum magnitude of 5.0 and the magnitude of the largest earthquake judged capable of occurring within each of the earthquake source zones.

8.12 The Owen Fracture Zone–Murray Ridge Complex The tectonic model of the Owen Fracture Zone–Murray Ridge Complex (Figure 8.22) consists of linear representations of young faults that have been identified in a number of offshore seismic reflection and geophysical studies. South of latitude 20°N, the Owen Fracture Zone was modeled as a series of linear faults along the eastern side of a series of narrow, discontinuous ridges and troughs, consistent with interpretations of faulting in seismic reflection profiles. There are significant structural differences in the Owen Fracture Zone north of about 29°20'N. At this latitude, the narrow, linear trend of the southern and central segments of the Owen Fracture Zone merges with the broader structure of the Qalhat Seamount. © 2003 by CRC Press LLC


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55°

60°

65°

70° Chama n

PAKISTAN IRAN

25°

ZN 4

Omach-Nai

ZN 5

Makran Subduction Zone

y

R

id

Rapar Gadhwali

ur (Qalhat Seamount)

e

in

Oman - India

l pe

Pi

Zo

lt

re Fra ctu

ARABIAN

ZN 6

SEA

ZN 1

Owen

Fa u Si

qu

alr ah

Central

South

INDIA

M

North

ne

Ra'as al Jifan

20°

ZN 3

ra

OMAN

ZN 2 ge

North South (Dalrymple Trough)

75°

FIGURE 8.22 Seismic sources used in assessing probabilistic peak ground acceleration (PGA) hazard along the Oman India pipeline. Faults are shown as bold lines. Area sources are ruled. Vertical ruled area of the Makron Subduction Zone interface thrust fault dips northward beneath Zone 5.

At the northern end of the Owen Fracture Zone, a low basement ridge defines a southwestern extension of the Qalhat Seamount, some 60 km northwest of the main plate boundary. Geophysical data suggest that this western margin of the Qalhat Seamount could be fault-bounded. Because this seamount is an integral part of the transform plate boundary, we modeled bounding faults along both the eastern and western flanks of this feature. Short, east-trending cross-faults were modeled between the east and west flanking faults, consistent with interpretations of geophysical data. Bathymetric and geophysical data indicate that most of the ridges and intervening troughs associated with the Murray Ridge are fault-bounded. Although the overall structure of the Murray Ridge is a bathymetric high, it is split by deep, fault-controlled troughs that are floored by very recent sediments. The Dalrymple Trough is a prime example of one of these troughs. The present floor of the Dalrymple Trough has down-dropped 800 m below the adjacent Arabian Sea floor. Based on these interpretations, we modeled all linear bathymetric ridges and intervening trough with bounding faults.

8.12.1 Maximum Magnitude Burr and Soloman [1978] provide a comprehensive account of the source parameters of all large earthquakes that had occurred on oceanic transforms up to the mid-1970s. Of the 36 earthquakes studied, 35 had M ≤ 7. The largest earthquakes that have occurred in the vicinity of the Owen Fracture Zone–Murray Ridge Complex are three MS 5.9 events that occurred from 1933 to 1935. Since 1964, the largest reported earthquake on this zone was MS 5.7. We adopted a maximum magnitude of 6.8 for all segments of the oceanic plate boundary  a value only slightly smaller than that observed in association with oceanic transform earthquakes. Because a slip-rate model used to determine earthquake frequencies uses maximum magnitude as one of its parameters, an upper bound of 6.8 rather than 7.0 was chosen to give frequencies for moderate earthquakes that are consistent with those observed since 1964. A larger maximum magnitude allows too much of the seismic moment release along the transform boundary to be taken up by infrequent, large earthquakes, resulting in unreasonably long repeat times for magnitude 5 to 6 earthquakes.




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8.12.2 Earthquake Recurrence Frequencies A moment-based frequency model was used to estimate earthquake recurrence rates from tectonic slip rate, Mmax , b-value, crustal shear rigidity, and the seismogenic area of the fault. We used a slip rate of 1.75 mm/year for this analysis, which is the average rate determined from worldwide models of rigid plate interactions. Earthquake recurrence rates were calculated for each structural segment along the length of the oceanic transform plate boundary using the length of each structural segment, a crustal thickness of 8 km, and a shear rigidity of 3 ×1011 dyne/cm typical of crustal rock. A b-value of 0.9 was determined from a maximum likelihood fit of 39 earthquakes of M ≥ 4.8 that have occurred on, or in the vicinity of, the oceanic transform boundary. Except for the northern (Qalhat Seamount) segment of the Owen Fracture Zone, the calculated recurrence rates were distributed equally among all modeled faults that define each structural segment of the transform boundary. The recurrence rate for the eastern and western flanking faults of the northern Qalhat Seamount segment was distributed in such a way as to give twice as much seismicity to the easternbounding fault. This was done to account for both the greater degree of fault offset and the higher historic rate of earthquakes along the eastern margin of this portion of the plate boundary (Figure 8.20). A comparison of the earthquake recurrence rates determined from the assumed slip rate and the maximum likelihood fit of the 39 earthquakes that have been observed along the entire length of the Owen Frature Zone–Murray Ridge Complex indicates that the estimated annual frequency of earthquakes of 4.8 ≤ M ≤ 6.2 given by both procedures agrees to within ±10%.

8.13 Makran Subduction Zone The Makran Subduction Zone megathrust boundary between the Arabian and Eurasian plates dips gently northward beneath the coasts of Iran and Pakistan from its origin at a sediment-filled trench off the Makran continental slope [Jacob and Quittmeyer, 1979] (Figure 8.22). Earthquakes located approximately 400 km north of the trench at a depth of about 60 km have focal mechanisms indicative of extensional stresses in the subducting slab of Arabian Sea floor. Normal-faulting earthquakes in this “slab-bend” region of the subducting plate is a common feature of subduction zones throughout the world. They represent a transition region within the subducting slab from compression trenchward of this zone to extension in the deeper part of the slab, where it is being consumed within the Earth’s mantle. This region marks the maximum possible extent of the seismogenic portion of the plate interface beneath Pakistan and Iran. A cross-sectional plot of seismicity across the Makran region was used to identify the top of the downgoing slab as it penetrates the Earth’s mantle. This cross section indicates that the seismogenic portion of the plate interface extends some 200 to 300 km north from the oceanic trench offshore southern Pakistan and southeastern Iran to a depth of approximately 30 km. Based on this observation, we modeled the megathrust interface of the Makran Subduction Zone as a 250-km-wide, shallow (~7°) planar fault. Based on tectonic considerations, the Makran Subduction Zone was estimated to be approximately 1000 km long, representing that portion of the Arabian–Eurasian convergence zone between the Ornach-Nal fault on the east and the “Oman line” on the west. The convergence rate between the Arabian and Eurasian plates across the Makran Subduction Zone has been estimated to be about 5 cm/year from regional and worldwide geodynamic models of plate interactions. This convergence rate reflects the total deformation rate between the two plates, which is manifested in the subduction of the Arabian plate beneath the Eurasia plate. Some of this convergence is very likely accommodated aseismically along the interface, and in folding of the overriding southern edge of the Eurasian plate in the Makran Mountains of southern Pakistan and southeastern Iran. Geologic studies that might indicate how this overall convergence rate is partitioned between seismic and aseismic compressional deformation processes have not yet been performed.



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8.13.1 Maximum Magnitude The largest known earthquake on the Makran Subduction Zone was an MS 8.2 earthquake in 1945. However, there is no reason to believe that the entire plate interface cannot rupture in a single “megathrust” earthquake. Based on this hypothesis, we assigned a maximum magnitude of 9.2 to this zone, consistent with both empirical rupture area–magnitude relationships and the magnitude of the great 1964 Prince William Sound, Alaska earthquake that ruptured a similar length.

8.13.2 Earthquake Recurrence Frequencies Using seismic moment-based relationships between convergence rate, crustal shear rigidity, and the cross-sectional area of the converging plates, we estimated the recurrence rate of earthquakes for various magnitudes that would be expected to occur on the Makran Subduction Zone assuming that all 5 cm/year of the estimated convergence rate was released in earthquakes. The resulting recurrence rates were found to be significantly larger than those observed historically. Probable reasons for this inconsistency are that some of the convergence is released by earthquakes occurring within the overriding Eurasian plate and some is accommodated through aseismic deformation. Because of this inconsistency, we adopted area-normalized earthquake recurrence rates that were developed from the historical occurrence of earthquakes in this zone [Khattri et al., 1984]. These rates, which were defined in MS , were adjusted to correspond to MW using common empirical relationships between these two magnitudes’ measures. Khattri et al.’s [1984] recurrence frequencies were normalized to a 40-year time period, not the 1-year time period that is usually used to develop earthquake recurrence relationships. For consistency with other recurrence relationships developed in this study, we converted these rates to an annual rate. We partitioned these recurrence frequencies into two parts. Earthquakes of 7.6 ≤ M ≤ 9.2 were assumed to occur on the plate interface. Earthquakes of M < 7.6 were assumed to occur within the shallow crust of the overriding Eurasian plate. This partitioning results in an average recurrence interval of 200 years for earthquakes of similar size to the 1945 earthquake, an interval that is consistent with the observation that only one event of this size has occurred on this zone in 300 years for which the earthquake catalog is considered to be complete in this region. Using a range of magnitudes to model the occurrence of earthquakes on the plate interface was consistent with other seismological investigations that suggested the plate interface is a segmented thrust fault.

8.14 Southwestern India and Southern Pakistan The Ornach-Nal and Chaman faults accommodate left-lateral movement between the Eurasian and Indian plates in southern Pakistan (Figure 8.22). Earthquakes of M ≥ 6.4 on these faults were modeled as linear ruptures. Throughout a broader zone, mostly east of the Ornach-Nal and Chaman faults (ZN 4, Figure 8.22), earthquakes smaller than 6.4 were modeled as point sources uniformly distributed throughout the zone. The area source encompasses a region of diffuse seismicity related to a broader zone of deformation within southern Pakistan. Shallow earthquakes of M ≤ 7.6 occurring within the Eurasian plate were placed in a broad source zone in southern Pakistan and southeastern Iran that encompasses the Makran Mountains (ZN 5, Figure 8.22). The Makran Mountains form the leading edge of crustal deformation along the southern boundary of the Eurasian plate above the Makran Subduction Zone. Crustal faults of this zone characteristically trend east–west and have both thrust and strike-slip components of slip. Compressional deformation and seismicity are widespread and are not limited to a few major faults. We have modeled earthquakes of M ≥ 6.4 within this zone as linear ruptures on a series of uniformly spaced faults that follow the predominant east–west strike of the structural trend of the region. Smaller earthquakes are modeled as point sources distributed uniformly throughout the zone.




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We adopted the earthquake source zones proposed by Khattri et al. [1984] for our source zones in western India (ZN 1 to 3, Figure 8.22). These zones were developed based on the association of clusters of historic earthquake occurrences with ancient tectonic trends of the Indian subcontinent  a common technique used throughout the world for developing seismic source zones in intraplate environments. Earthquakes of M < 6.4 were modeled as point sources uniformly distributed within the source zones. Larger-magnitude earthquakes in the Kutch and West Coast of India source zones (ZN 1 and 2) were modeled as linear ruptures on faults representing the major tectonic trends in these regions. In the Kutch zone, these modeled faults strike east-west following the Kutch Rift-Delhi Trend. Notably, the January 26, 2001 Bhuj (Gujarat, India) earthquake exhibited east-west-trending surface rupture along this same trend. In Zone 1 (Figure 8.22), we modeled a single north-trending fault to coincide with the Panvel Flexure-West Coast fault zone.

8.14.1 Maximum Magnitude The maximum magnitude associated with shallow seismicity in the Makran Mountains (ZN 5, Figure 8.22) was estimated to be about 7.6 (earthquakes larger than this were constrained to occur on the plate interface of the Makran Subduction Zone). This is about one-half magnitude higher than the largest observed crustal earthquake in this zone. It is, however, generally consistent with calculated maximum magnitudes for faults with lengths of up to 120 km that have been mapped in the Pakistani portion of this zone. Khattri and others [1984] assigned a maximum magnitude of 8 to both the Kutch and West Coast of India source zones (ZN 1 and 2, Figure 8.22) based on the historic occurrence of the 1819 Kutch earthquake (MS ~ 8) and the presence of Quaternary deformation along the older Panvel Flexure tectonic trends in the West Coast of India zone. They assigned a relatively small maximum magnitude of 6 to the Arravali source zone (ZN 3, Figure 8.22), consistent with its relatively small source dimensions and historical seismicity. We adopted these maximum magnitudes for this study.

8.14.2 Earthquake Recurrence Frequencies We adopted the area-normalized earthquake recurrence frequencies given in Khattri et al. [1984] for all of the source zones in this region (ZN 1 to 5, Figure 8.22). These rates were annualized and adjusted to MW as discussed previously for the Makran Subduction Zone. Earthquake recurrence rates for M ≥ 6.4 earthquakes in the Kutch and West Coast of India source zones (ZN 1 and 2) were uniformly distributed among the modeled faults in these zones in proportion to their total fault lengths.

8.15 Southeastern Arabian Peninsula and Northern Arabian Sea The Arabian Sea basin and eastern Arabian Peninsula were placed in a broad background zone of diffuse seismicity (ZN 6, Figure 8.22). This zone is characterized by the infrequent occurrence of small to moderate earthquakes. The total area of comparable background seismicity is quite large, extending beyond the study area westward across the entire Arabian Peninsula to the Red Sea Rift and the Lavant Transform plate boundaries. Earthquakes of M ≥ 6.4 within the study area were constrained to two faults on the Omani continental shelf that have been identified as being potentially active from offshore boreholes and geophysical investigations. We included the Siquirah fault (Figure 8.22) based on an interpretation of reflection profiles that suggests that it is a profound structural feature of the southeast Omani outer-continental shelf. The fault displaces sea-bottom reflectors, indicating recent movement, although no earthquake epicenters plot near the fault (Figure 8.20). The northward extend of the Siquirah fault was based on the interpretation that the entire coastline and linear continental slope of eastern Oman is possibly the result of strike-slip faulting. The lack of epicenters in the vicinity of the Siquirah fault might only indicate a recurrence interval of significant earthquakes that is longer than the historic period of observation. © 2003 by CRC Press LLC


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A second, shorter fault located east of the Siquirah fault (Figure 8.22) and near the base of the Oman continental slope bounds a narrow linear basement ridge. The ridge forms the eastern structural boundary of a sedimentary trough between the continental shelf and floor of the Oman basin. Consistent with our interpretation of similar features within the Murray Ridge, we modeled this basement ridge as being fault-bounded. We refer to this fault as the Oman Basin fault.

8.15.1 Maximum Magnitude We assigned a maximum magnitude of 6.4 to the background zone (ZN 6, Figure 8.22). This value is three quarters of a magnitude higher than that observed historically. We believe that the higher maximum magnitude unit was warranted because of the large degree of uncertainty associated with the extremely low level of seismicity in this region. We adopted a maximum magnitude of 7.6 for the Siquirah fault based on empirical rupture length–magnitude relationships and the assumption that one half of the total length of the fault could rupture in a single event. Similarly, we assigned a maximum magnitude of 7.2 to the much shorter Owen Basin fault based on the assumption that the entire length of that fault could rupture in a single event.

8.15.2 Earthquake Recurrence Frequencies Since only five historic earthquakes have occurred in this region, it was not possible to develop earthquake recurrence frequencies using a formal statistical procedure. Instead, we adopted the b-value that was determined from the maximum likelihood fit of 39 earthquakes that occurred within the Owen Fracture Zone–Murray Ridge Complex. We estimated the earthquake recurrence rate in this zone from the observation that three MS 4.1 to 5.0 earthquakes had occurred in this region within the last 22 years. Lacking available geologic or geodynamic data for the Siquirah and Owen Basin faults, we simply used the recurrence relationship developed for the background zone to model the cumulative occurrence of M ≥ 6.4 earthquakes on these faults. Based on this model, the calculated cumulative recurrence interval for earthquakes of M ≥ 6.4 is 400 years. This estimate is consistent with the lack of observed earthquakes along this portion of the Omani continental shelf within the last few hundred years.

8.16 Ground Motion Models PGA was estimated from attenuation relationships of the form: log(PGA) = b 1+ b 2M – b 3logR – b 4R + ε

(8.23)

where PGA is the mean horizontal component of peak ground acceleration (g), M is earthquake magnitude (MW), R is distance from the earthquake source to the site (km), ε is a random error term with a mean of zero and a standard deviation equal to the standard error of estimate of log (PGA), and b1 through b4 are parameters dependent on the tectonic environment. The attenuation relationships adopted for this study were chosen to represent as closely as possible the earthquake and propagation characteristics of the major tectonic environments encountered in the Arabian Sea and surrounding regions. Separate relationships were used to model the stable oceanic and continental interior regions of the Arabian and Indian plates; the oceanic and continental transform boundaries between the Eurasian, Arabian, and Indian plates; and the megathrust interface of the Makran Subduction Zone.

8.16.1 Stable Continental Interior Earthquakes Stable continental interior regions, such as the Arabian Peninsula (Oman) and the Indian subcontinent (southwestern India), are composed of very old, Precambrian crust, often referred to as stable continental interiors. These regions are known to occasionally produce earthquakes that have relatively high stress © 2003 by CRC Press LLC



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drops and relatively low anelastic attenuation. The best studied of these regions is the stable continental interior of eastern North America. Since these regions are characterized by relatively infrequent earthquakes, there are an insufficient number of strong-motion recordings with which to develop reliable empirical attenuation relationships. As a result, attenuation relationships developed for these regions have been based on intensity data (usually characterized in terms of the Modified Mercalli Intensity [MMI] scale) or, more recently, on simple seismological models of the earthquake source and propagation medium. One of the most recent and best-documented theoretical attenuation relationships for stable continental regions is that developed by the Electric Power Research Institute [EPRI, 1993] for eastern North America. Because of its thorough review and sound seismologic basis, this model was selected to represent the attenuation of PGA in the stable continental-interior regions of Oman and India. The model was developed to represent the attenuation characteristics of sites on hard rock using a median stress drop of 120 bars and an anelastic attenuation parameter (Q) consistent with observed earthquakes in eastern North America. The standard error of estimate (σln PGA) associated with the EPRI attenuation relationship, averaged over magnitude and distance, was estimated to be 0.7 for the near-source distances of most concern in this study.

8.16.2 Stable Oceanic Interior Earthquakes There are no attenuation relationships available for stable oceanic interior regions. However, the oceanic lithosphere is known to be an extremely efficient waveguide for high-frequency seismic energy. For example, the anelastic attenuation of high-frequency waves in the Ngendei region of the Southwest Pacific has been found to be consistent with Q of 450 for that part of the lithosphere above the Moho (6.65 km below mudline) and Q of 1000 for that part of the lithosphere below this depth. These values are consistent with Q observed in the stable continental-interior regions of eastern North America [EPRI, 1993]. Based on this similarity, the EPRI attenuation relationship was used to model the attenuation of PGA from earthquakes occurring in the intraplate regions of the Arabian Sea.

8.16.3 Transform Plate Boundary Earthquakes Transform plate boundary earthquakes, such as those typical of the strike-slip San Andreas fault system in western California, have lower average stress drops than intraplate earthquakes [EPRI, 1993]. However, unlike California, plate boundary earthquakes associated with the Owen Fracture Zone–Murray Ridge Complex and the Ornach-Nal and Chaman faults occur on a transform boundary between intraplate regions of low anelastic attenuation, similar to the craton of eastern North America. Therefore, the source characteristics of these plate-boundary earthquakes are expected to be similar to those in other plate boundary environments (e.g., the San Andreas fault system); whereas, the attenuation characteristics of these earthquakes are expected to be typical of the attenuation characteristics of an intraplate environment. The majority of strong-motion recordings from plate-boundary earthquakes are from California, where anelastic attenuation is much greater than in stable continental interiors. Therefore, attenuation relationships from these regions are not applicable for this region. Instead, we modified the EPRI attenuation relationship to predict the attenuation of PGA from plate-boundary earthquakes in the northern Arabian Sea and southern Pakistan regions. EPRI [1993] gives stress drops for earthquakes in interplate and intraplate tectonic environments that have been calculated from strong-motion and standard seismograph recordings. These calculations indicate a median stress drop of 120 bars for intraplate regions. On the other hand, the data for interplate strike-slip and normal faulting earthquakes, typical of the plate-boundary earthquakes in the northern Arabian Sea and southern Pakistan regions, were found to be consistent with a median stress drop of about 85 bars. Research has indicated PGA ∝ ∆σ0.8. Therefore, PGA predicted by the EPRI attenuation relationship was reduced by 25% for plate boundary earthquakes in the northern Arabian Sea and southern Pakistan regions. © 2003 by CRC Press LLC


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8.16.4 Subduction Zone Earthquakes Subduction-zone earthquakes, similar to those associated with the Makran Subduction Zone, have been found to have significantly different attenuation characteristics from either shallow crustal interplate or intraplate earthquakes. Therefore, it is important to model these earthquakes with an attenuation relationship appropriate for this tectonic environment. The attenuation relationship selected for this purpose was one developed from rock recordings of large subduction-zone earthquakes throughout the world. The standard error of estimate (σln PGA) associated with this relationship for the larger earthquakes of interest in this study is 0.55.

8.17 Soil Amplification Factors Estimates of PGA from the attenuation relationships described above are for hard rock. Therefore, it is necessary to multiply these estimates by an appropriate site amplification factor in order to account for the existing predominant soil conditions at mudline along the pipeline route. This adjustment was done using the amplitude-dependent amplification factors given in Borcherdt [1993]. The classification of the existing soils along the pipeline route was based on preliminary geotechnical and seismic data collected along the pipeline route. The soil amplification factors for each of the soil classifications given by Borcherdt [1993] were normalized to hard rock and the amplitude of PGA for the existing soil conditions are obtained by multiplying the estimate of PGA on hard rock by these normalized factors. The maximum value of PGA on soft soils was limited to 0.45 g based on site-response studies of Holocene Bay Mud in the San Francisco Bay area. If shear strains large enough to cause significant cyclic degradation (e.g., liquefaction) are induced in these deposits, then actual values of PGA for these soft soils may be further limited to values on the order of 0.2 to 0.25 g. Of course, for such large strains, ground failure will become an important issue.

8.18 Results Values of PGA on hard rock were calculated at 130 locations along the pipeline route for return periods of 200, 500, and 1000 years (Figure 8.23). However, much of the pipeline route is characterized by soft pelagic and detrital deposits that are subject to submarine turbidite flows if disturbed by strong ground shaking from earthquakes. A map showing 500-year values of PGA on hard rock and on the existing soil conditions at mudline (in parentheses) at selected locations along the pipeline route and Indus Canyon is given in Figure 8.24. The existing soil conditions at all of the selected sites were classified as soft soil. For all return periods, the highest values of PGA were obtained at the intersection of the pipeline route with the Owen Fracture Zone, where calculated values on hard rock (soft soil) were 0.35 g (0.40 g), 0.56 g (0.45 g), and 0.77 g (0.45 g) for return periods of 200, 500, and 1000 years, respectively. Intermediate values of PGA were calculated for the eastern pipeline terminus at the India coast and at the crossing of the southwest extension of the Qalhat Seamount, located approximately 60 km west of the Owen Fracture Zone, where values on hard rock (soft soil) ranging between 0.17 g (0.32 g) and 0.31 g (0.40 g) were calculated for a 200-year return period and values ranging between 0.45 g (0.45 g) and 0.57 g (0.45 g) were obtained for a 1000-year return period. The lowest values of PGA were calculated for the Arabian Sea Abyssal Plain, east of the Owen Fracture Zone, where estimates for hard rock (soft soil) ranged from 0.03 g (0.08) for a 200-year return period to 0.09 g (0.22 g) for a 1000-year return period.

8.19 Conclusions The computed ground-shaking hazard along the Oman India pipeline was found to be relatively high in the vicinity of the Owen Fracture Zone–Murray Ridge Complex and at the India coast in the Kutch region. These values are high enough to potentially trigger geologic hazards such as liquefaction, slope © 2003 by CRC Press LLC


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0.80 OMAN

0.70

Owen Fracture Zone

INDIA 200-yr

0.60

PGA (g)

Kutch Zone

SWExtension, Qalhat Seamount

0.50

500-yr 1,000-yr

0.40 Siquirah Fault

0.30 0.20

Indus Fan Crossing

0.10

68.56

68.18

67.79

67.37

66.93

66.43

65.88

65.23

64.64

64.02

63.40

62.78

62.16

61.63

61.26

60.73

60.22

59.72

0.00

Longitude (deg. E)

FIGURE 8.23 Longitudinal profile of PGA on hard rock along the pipeline route for three return periods.

60°

65°

IRAN

70°

PAKISTAN

25°

Rapar Gadhwali

OMAN

0.11 (0.25)

Ra'as al Jifan

INDIA

20°

0.10 (0.23)

Pi

pe

lin

e

0.07 (0.18) Oman - India 0.30 (0.39)

0.56 (0.45)

0.08 (0.20)

0.44 (0.45)

0.05 (0.13)

ARABIAN

SEA

FIGURE 8.24 Calculated PGA on hard rock and soft soil (in parentheses) with a return period of 500 years at selected locations along the pipeline route and at the Indus Canyon.

instability, and turbidity flows in areas that are susceptible to these hazards. Notably, liquefaction and ground failures were widespread throughout Western Gujuarat State in the 2001 Bhuj earthquake. Although the computed ground-shaking hazard elsewhere along the pipeline route was found to be relatively low, estimates of PGA are high enough offshore to also potentially trigger geologic hazards in areas that are highly susceptible to these hazards (e.g., unstable channel slopes).

8.20 PSHA Computer Codes There are a number of PSHA computer codes that are available to the analyst. A few are distributed free, or at low cost [McGuire, 1976, 1978; Bender and Perkins, 1987; U.S. Geological Survey (http://geohazards.cr.usgs.gov/eq/html/hazsoft.html)]. An excellent source for software is the National Information © 2003 by CRC Press LLC


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Service for Earthquake Engineering at the University of California, Berkeley (http://nisee.berkelye.edu/ software_and_data/eng_soft/index.html). Some codes are not necessarily user-friendly as they are primarily products of scientific/engineering research efforts and are not created for easy use with an end-user in mind. Several commercially available codes are available and are user-friendly in terms of the data input interface and overall ease of use. They also offer a wide variety of output enhancements in addition to the basic PSHA results. Prior to selection of a specific computer code for use in engineering applications, an analyst should have a clear understanding of his or her specific needs. Some codes are specific to area source modeling, while others are specific to the requirements of fault modeling. Some codes are appropriate for creating grids of PSHA values suitable for contouring in ground motion maps, while others are better adapted for site-specific analyses. Commercial codes often come with a variety of databases and built-in models, including ground motion attenuation relationships and seismotectonic models specific to certain regions, and generally have the flexibility of modeling both area and fault sources, as well as mixed sources. There is likely to be a suitable code available for any practical application required by the PSHA analyst.

Defining Terms Aleatory — Uncertainty in the data used in an analysis; generally accounts for randomness associated with the prediction of a parameter from a specific model, assuming that the model is correct. Specification of the standard deviation (σ) of a mean ground motion attenuation relationship is a representation of aleatory variability. Characteristic earthquake — Surface-rupturing earthquakes occurring on a known tectonic structure, within a relatively narrow range of magnitudes at an increased frequency over that which would be estimated from the Gutenberg–Richter relationship. Epistemic — Modeling uncertainty; accounts for incomplete knowledge in the predictive models and the variability in the interpretations of the data used to develop the models. Intensity — A metric of the effect, or the strength, of an earthquake hazard at a specific location, commonly measured on qualitative scales such as MMI, MSK, and JMA (see Chapter 4). Paleoseismicity — Prehistoric earthquakes — since there is no human record, these earthquakes are identified (i.e., location, magnitude, etc.) via geologic trenching and other evidence. Return period — The reciprocal of the annual probability of occurrence — earthquake probabilities of occurrence are commonly stated in terms of a return period, which misleads some people since they infer the earthquake occurs on a regular cycle equal to the return period. Seismic hazard — The likelihood or probability of experiencing a specified intensity of any damaging phenomenon, at a specific site, or over a region. Seismotectonic model — An analytical model combining models of earthquake sources, occurrence, and attenuation.

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Giardini, D., Ed., 1999, “The Global Seismic Hazard Assessment Program (GSHAP) 1992–1999,” Ann. Geofis., 42(6), 957–1230. Gutenberg, B. and C.F. Richter, 1954, Seismicity of the Earth, 2nd ed., Princeton University Press, Princeton, NJ. Hanks, T.C. and H. Kanamori, 1979, “A Moment-Magnitude Scale,” J. Geophys. Res., 84, 2348–2350. Harmsen, S., D. Perkins, and A. Frankel, 1999, “Disaggregation of Probabilistic Ground Motions in the Central and Eastern United States,” Bull. Seismol. Soc. Am., 89, 1–13. Harris, R.A. and R.W. Simpson, 1998, “Suppression of Large Earthquakes by Stress Shadows: A Comparison of Coulomb and Rate-and-State,” J. Geophys. Res., 103, 24,439–24,451. Hill, D.P., P.A. Reasenberg, A. Michael, et al., 1993, “Seismicity Remotely Triggered by the Magnitude 7.3 Landers, California, Earthquake,” Science, 260, 1617–1623. Jacob, K.H. and R.L. Quittmeryer, 1979, “The Makran Region of Pakistan and Iran: Trench-Arc System and Active Plate Subduction,” in A. Farah and K.A. DeJong, Eds., Geodynamics of Pakistan, Geological Survey of Pakistan, pp. 305–317. Johnston, A.C., K.J. Coppersmith, L.R. Kanter, and C.A. Cornell, 1994, The Earthquakes of Stable Continent Interiors, Vol. 1, Assessment of Large Earthquake Potential, Electric Power Research Institute, Palo Alto, CA. Kagan, Y.Y. and L. Knopoff, 1980, “Spatial Distribution of Earthquakes: The Two Point Correlation Function,” Geophys. J. R. Astron. Soc., 62, 303–320. Kanamori, H., 1978, “Quantification of Earthquakes,” Nature, 271, 411–414. Khattri, K.N., A.M. Rogers, S.T. Algermissen, and D.M. Perkins, 1984, “A Seismic Hazard Map of India and Adjacent Areas,” Tectonophysics, 108, 93–134. King, G. and J. Nabelek, 1985, “Role of Fault Bends in the Initiation and Termination of Earthquake Ruptures,” Science, 228, 984–987. Korvin, G., 1992, Fractal Models of the Earth, Elsevier, Amsterdam. Lee, W.H.K. et al., 1988, Historical Seismograms and Earthquakes of the World, Academic Press, New York. Machette, M.N., S.F. Personius, and A.R. Nelson, 1992, “Paleoseismology of the Wasatch Fault Zone: A Summary of Recent Investigations, Interpretations, and Conclusions,” in P.L. Gori and W.W. Hays, Eds., Assessment of Regional Earthquake Hazards and Risk along the Wasatch Front, Utah, U.S. Geological Survey Prof. Paper. 1500-A-J, pp. A1-A71. Mark, R.K. and M.G. Bonilla, 1977, Regression Analysis of Earthquake Magnitude and Surface Fault Length Using the 1970 Data of Bonilla and Buchanan, U.S. Geological Survey Open-File Rep. 78-1007. McCalpin, J.P., Ed., 1996, Paleoseismology, Vol. 62 in the International Geophysics Series, Academic Press, New York. McGuire, R.K., 1976, Fortran Computer Program for Seismic Risk Analysis, U.S. Geological Survey OpenFile Rep. 76-67. McGuire, R.K., 1978, FRISK: Computer Program for Seismic Risk Analysis Using Faults as Earthquake Sources, U.S. Geological Survey Open-File Rep. 78-1007. McGuire, R.K., 1993, The Practice of Earthquake Hazard Assessment, IDNDR Monograph, International Association of Seismology and Physics of the Earth’s Interior/European Seismological Commission, University of Colorado Department of Physics, Boulder, CO. McGuire, R.K., 1995, “PSHA and Design Earthquakes: Closing the Loop,” Bull. Seismol. Soc. Am., 85, 1275–1284. McGuire, R.K. and T.P. Barnhard, 1981, “Effects of Temporal Variations in Seismicity on Seismic Hazard,” Bull. Seismol. Soc. Am., 71, 321–334. McGuire, R.K. and K.M. Shedlock, 1981, “Statistical Uncertainties in Seismic Hazard Evaluations in the United States,” Bull. Seismol. Soc. Am., 71, 1287–1308. Molnar, P., 1979, “Earthquake Recurrence Intervals and Plate Tectonics,” Bull. Seismol. Soc. Am., 69, 115–134.



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Munson, P.J., C.A. Munson, N.K. Bleuer, and M.D. Labitzke, 1992, “Distribution and Dating of Prehistoric Earthquake Liquefaction in the Wabash Valley of the Central U.S.,” Bull. Seismol. Soc. Am., 63, 337–342. Munson, P.J., C.A. Munson, and N.K. Bleuer, 1994, Late Pleistocene and Holocene Earthquake-Induced Liquefaction in the Wabash Valley of Southern Indiana, U.S. Geological Survey Open-File Rep. 94-176, pp. 553–557. Nishenko, S.P., 1991, “Circum-Pacific Seismic Potential: 1989–1999,” Pure Appl. Geophys., 135, 169–259. Nishenko, S.P. and R. Buland, 1987, “A Generic Recurrence Interval Distribution for Earthquake Forecasting,” Bull. Seismol. Soc. Am., 77, 1382–1399. Nuttli, O.W., 1979, “Seismicity of the Central United States,” in Geology in the Siting of Nuclear Power Plants, A.W. Hathaway and C.R. McClure, Jr., Eds., Reviews in Engineering Geology, Vol. 4, pp. 67–94. Nuttli, O.W., 1981, “On the Problem of Maximum Magnitude of Earthquakes,” in W.W. Hays, Ed., Evaluation of Regional Seismic Hazards and Risk, U.S. Geological Survey Open-File Rep. 81-437. Obermeier, S.F., J.R. Martin, A.D. Frankel, T.L. Youd, P.J. Munson, C.A. Munson, and E.C. Pond, 1993, Liquefaction Evidence for One or More Strong Holocene Earthquakes in the Wabash Valley of Southern Indiana and Illinois, with a Preliminary Estimate of Magnitude, U.S. Geological Survey Prof. Paper 1536. Parsons, T., S. Toda, R.S. Stein, A. Barka, and J.H. Dietrich, 2000, “Heightened Odds of Large Earthquakes Near Istanbul: An Interaction-Based Probability Calculation,” Science, 288, 661–665. Perkins, D.M. and S.T. Algermissen, 1987, “Seismic Hazards Maps for the U.S.: Present Use and Prospects,” in K.H. Jacob, Ed., Proceedings from the Symposium on Seismic Hazards, Ground Motions, Soil Liquefaction and Engineering Practice in Eastern North America, Technical Report NCEER-87–0025, pp. 16–25. Petersen, M.D. et al., 1996, Probabilistic Seismic Hazard Assessment for the State of California, U.S. Geological Survey Open-File Rep. 96-706. Reasenberg, P.A. and L.M. Jones, 1989, “Earthquake Hazard after a Mainshock in California,” Science, 243, 1173–1176. Reid, H.F., 1910, “The Mechanics of the Earthquake,” in The California Earthquake of April 18, 1906, Report to the State Earthquake Investigation Commission, Publication No. 87, Vol. II, Carnegie Institution of Washington, D.C. Reiter, L., 1990, Earthquake Hazard Analysis: Issues and Insights, Columbia University Press, New York. Satake, K., K. Shimazaki, Y. Tsuji, and K. Ueda, 1996, “Time and Size of Giant Earthquake in Cascadia Inferred from Japanese Tsunami Records of January 1700,” Nature, 379, 246–249. Scholz, D.H., 1990, The Mechanics of Earthquake Faulting, Cambridge University Press, Cambridge. Schwartz, D.P., 1988, “Geologic Characterization of Seismic Sources: Moving into the 1990s,” in Engineering and Soil Dynamics II: Recent Advances in Ground Motion Evaluation, J.L. v.Thun, Ed., Geotechnical Special Publication No. 20, American Society of Civil Engineering, New York. Schwartz, D.P. and K.J. Coppersmith, 1984, “Fault Behavior and Characteristic Earthquakes: Examples from the Wasatch and San Andreas Fault Zones,” J. Geophys. Res., 89, 5681–5698. Shedlock, K.M., R.K. McGuire, and D.G. Herd, 1980, Earthquake Recurrence in the San Francisco Bay Region, California, from Fault Slip and Seismic Moment, U.S. Geological Survey Open-File Rep. 80-999. Shimazaki, K. and T. Nakata, 1980, “Time-Predictable Recurrence Model for Large Earthquakes,” Geophys. Res. Lett., 7, 279–282. SSHAC (Senior Seismic Hazard Assessment Committee), 1997, “Recommendations for PSHA: Guidance on Uncertainty and Use of Experts,” Report NUREG/CR-6372, U.S. Nuclear Regulatory Commission, Washington, D.C. Stein, R.S., 1999, “Role of Stress Transfer in Earthquake Occurrence,” Nature, 402, 605–609. Stepp, J.C., 1972, “Analysis of Completeness of the Earthquake Sample in the Puget Sound Area and Its Effects on Statistical Estimates of Earthquake Hazard,” Proceedings of the First Microzonation Conference, Seattle, WA, pp. 897–909. © 2003 by CRC Press LLC



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Stepp, J.C., 1973, “Analysis of Completeness of the Earthquake Sample in the Puget Sound Area,” in S.T. Harding, Ed., “Contributions to Seismic Zoning,” Technical Report ERL 267-ESL 30, pp. 16–28, National Oceanic and Atmospheric Administration, Washington, D.C. Stepp, J.C., W.J. Silva, R.K. McGuire, and R.W. Sewell, 1993, “Determination of Earthquake Design Loads for a High Level Nuclear Waste Repository Facility,” in Proceedings of the Natural Phenomena Hazards Mitigation Conference, Vol. 2, pp. 651–657, October 19–22, Atlanta, GA. Stucchi, M., Ed., 1993, Historical Investigations of European Earthquakes, CNR – Istituto di Ricerca sul Rischio Sismico, Milano. Sykes, L.R., 1971, “Aftershock Zones of Great Earthquakes, Seismicity Gaps, and Earthquake Prediction for Alaska and the Aleutians,” J. Geophys. Res., 76, 8021–8041. Thenhaus, P.C., 1983, “Summary of Workshops Concerning Regional Seismic Source Zones of Parts of the Conterminous United States, Convened 1979–1980, Golden, Colorado,” U.S. Geol. Surv. Circular 898. Thenhaus, P.C., 1986, “Seismic Source Zones in Probabilistic Estimation of the Earthquake Ground Motion Hazard: A Classification with Key Issues,” Proceedings of Conference 34: Workshop on Probablistic Earthquake Hazards Assessments, pp. 53–71. Toda, S., R.S. Stein, P.A. Reasonberg, and J.H. Dietrich, 1998, “Stress Transferred by the Mw = 6.5 Kobe, Japan, Shock: Effects on Aftershocks and Earthquake Probabilities,” J. Geophys. Res., 103, 24,543–24,565. Usami, T., 1981, Nihon Higai Jishin Soran (List of Damaging Japanese Earthquakes), University of Tokyo Press (in Japanese). Wells, D.L. and K.J. Coppersmith, 1994, “New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement,” Bull. Seismol. Soc. Am., 84, 974–1002. Wentworth, C.M. and M.D. Zoback, 1990, “Structure of the Coalinga Area and Thrust Origin of the Earthquake,” in M.J. Rymer and W.L. Ellsworth, Eds., The Coalinga, California, Earthquake of May 2, 1983, U.S. Geological Survey Prof. Paper 1487, pp. 41–68. Wesnousky, S.G., 1994, “The Gutenberg–Richter or Characteristic Earthquake Distribution, Which Is it?,” Bull. Seismol. Soc. Am., 84, 1940–1959. Wesnousky, S.G., C. Scholz, K. Shimazaki, and T. Matsuda, 1983, “Earthquake Frequency Distribution and the Mechanics of Faulting,” J. Geophys. Res., 87, 6829–6852. Wheeler, R.L. and K.B. Krystinik, 1992, “Persistent and Nonpersistent Segmentation of the Wasatch Fault Zone, Utah: Statistical Analysis for Evaluation of Seismic Hazard,” in P.L. Gori and W.W. Hays, Eds., Assessment of Regional Earthquake Hazards and Risk along the Wasach Front, Utah, U.S. Geological Survey Prof. Paper. 1500-A-J, pp. B1–B47. Woo, G., 1996, “Kernel Estimation Methods for Seismic Hazard Area Source Modeling,” Bull. Seismol. Soc. Am., 86, 353–362. Working Group on California Earthquake Probabilities, 1988, Probabilities of Large Earthquakes Occurring in California on the San Andres Fault, U.S. Geological Survey Open-File Rep. 88-398. Working Group on California Earthquake Probabilities, 1990, “Probabilities of Large Earthquakes in the San Francisco Bay Region, California,” U.S. Geol. Surv. Circular 1053. Working Group on California Earthquake Probabilities, 1995, “Seismic Hazards in Southern California: Probable Earthquakes, 1994 to 2024,” Bull. Seismol. Soc. Am., 85, 379–439. Working Group on California Earthquake Probabilities, 1999, Earthquake Probabilities in the San Francisco Bay Region: 2000 to 2030 — A Summary of Findings, U.S. Geological Survey Open-File Rep. 99-517. Yeats, R.S., K. Sieh, and C.R. Allen, 1997, The Geology of Earthquakes, Oxford University Press, New York. Youngs, R.R. and K.J. Coppersmith, 1985, “Implications of Fault Slip Rates and Earthquake Recurrence Models to Probabilistic Seismic Hazard Estimates,” Bull. Seismol. Soc. Am., 75, 939–964.



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Youngs, R.R., Swan, F.H., Powers, M.S., Schwartz, D.P., and Green, R.K., 1987, “Probabilistic Analysis of Earthquake Ground Shaking along the Wasatch Front, Utah,” in P.L. Gori and W.W. Hays, Eds., Assessment of Regional Earthquake Hazards and Risk along the Wasatch Fault, Utah, U.S. Geological Survey Open File Report 87-585, pp. M1-M110.

Further Reading There is an extensive literature on seismic hazard analysis. Reiter’s book [1990] is a good introduction, as is Cornell’s classic paper [Cornell, 1968], which started the field, and Cornell and Vanmarcke [1969]. McGuire has made a number of contributions over the years [1995; many others] which are very instructive. McGuire [1993] is an excellent compendium of international seismic hazard assessment practice, as is the more recent GSHAP project and papers, available on-line at [http://seismo.ethz.ch/ gshap/]. McCalpin’s [1996] book is an excellent summary of the state of the art in the relatively new field of paleoseismology. Yeats et al.’s [1997] book provides an excellent overview of geology related to earthquakes and synopses of worldwide seismotectonic settings. Sholz’s [1990] book is highly instructive in the theory of fault rupture mechanics and earthquake generation, and provides an insightful synopsis of hazard analysis and earthquake prediction.



9

Tsunami and Seiche 9.1 9.2 9.3 9.4 9.5

Introduction Tsunamis vs. Wind Waves Tectonic Tsunami Sources Initial Waves Generated by Submarine Landslides Exact Solutions of the Shallow-Water (SW) Equations Basic Equations and Solutions of the 1+1 or Two-Dimensional Equations · Linear 1+1 Theory · Exact Solutions of the LSW Boundary Value Problem · Nonlinear 1+1 Theory · The Solitary Wave Solutions · The Evolution of Solitary Waves · The Maximum Run-Up of Solitary Waves · The Validity of the Solitary Wave Solutions · The N-Wave Results · Evolution and Run-Up of N-Waves · 1+1 Wave Run-Up on Composite Beaches · Example of Calculation of the Run-Up of Solitary Waves on a Continental Shelf with a Beach · Example of Calculation of the Run-Up of Solitary Waves on a Composite Beach Fronted by a Seawall

9.6

Numerical Solutions for Calculating Tsunami Inundation The Splitting Technique · Boundary Conditions for Fixed Boundaries · The Finite-Difference Scheme · The Moving Boundary Condition · Verification of the Model

9.7

Harbor and Basin Oscillations Introduction · Calculating Basin Oscillations · Forced Oscillations in Basins of Simple Planform · The Sloshing of the Los Angeles Reservoir: a Case Study · Introduction to Harbor Resonance · Harbor Resonance for Harbors of Simple Geometry · Example of Analytical Harbor Resonance Computation · Numerical Modeling of Harbor Resonance

9.8

Tsunami Forces Forces on Piles · Impact Forces on Seawalls · Example of Impact Force Computation · Practical Design Considerations

9.9

Costas Synolakis University of Southern California Los Angeles, CA

Producing Inundation Maps The California Experience · Existing Analyses of Tsunami Hazards in California · Developing Inundation Maps for the State of California

Acknowledgments References

9.1 Introduction Tsunamis are long waves of small steepness generated by impulsive geophysical events of the seafloor and of the coastline, such as earthquakes and submarine or aerial landslides. Volcanic eruptions and asteroid impacts are less common but more spectacular triggers of tsunamis. The determination of the terminal



9-2


effects of tsunamis as they strike shorelines and coastal structures is one of the quintessential problems in earthquake engineering. Tsunamis are notorious for exporting “death and destruction at distant coastlines,” for tsunamis sometimes travel across the world’s oceans without dissipating sufficient energy to render them harmless. In the past 10 years, 12 major tsunamis have struck coastlines around the Pacific Rim, causing more than 3000 deaths and an estimated U.S. $1 billion (2001 dollars) in damage. Fortuitously, these tsunamis have either struck less developed coastlines or developed coastlines at low season with few or no visitors along the coast. Within the contiguous 48 states of the United States, the most significant historic tsunami has been the 1964 Alaskan tsunami, which killed nine people in Crescent City, California and caused more than U.S. $30 million (1964 dollars) in damage. Before the 1995 Kobe, Japan and the 1999 Izmit, Turkey earthquakes, it had been estimated that tsunamis cause between 5 and 15% of the earthquake damage worldwide. Table 9.1 lists the major tsunamis of the past 100 years. The term tsunami, also known as seismic sea wave or tidal wave, comes from the Japanese term meaning harbor wave. In Japan, historical documentation of tsunamis goes back almost 1000 years and suggests that they attack Japan’s shores, on average, about once every decade. Since ancient times, harbors have been centers of commercial activity, and when even relatively small tsunamis enter a harbor they can trigger substantial harbor oscillations by bouncing off the harbor’s embankments and combining together to form larger waves. Alaska’s 1964 infamous Good Friday earthquake triggered large tsunamis that entered harbors throughout the region, including at Anchorage, Valdez, and Seward, and caused catastrophic destruction. Not only can these harbor waves reach substantial heights in a harbor, with amplification factors of 6 not entirely uncommon, but often the water motions persist for many hours. Most likely, in early Japan, harbors were where most people witnessed and recognized these giant waves as something out of the ordinary — thus seismic sea waves became known as great harbor waves. In Spanish, the word for tsunami is maremoto, meaning a trembling sea. Tidal wave is an exact translation from the Greek name for tsunami, well known to the ancient Greeks. The eruption of a volcano on Thera, around 1680 B.C., triggered a large tsunami that had until recently been considered the cause for the destruction of Minoan civilization on the island of Crete, about 60 miles south of Thera (see Figure 9.1). The disappearance of the Minoans was the event that created the myth of Atlantis described in Plato’s Timaeus (320 B.C.). Modern estimates from models such as shown in Figure 9.1 [Yalciner et al., 2002] suggest waves with run-up of 12 m close to Cnossos, Crete. It is now well established from different sources that the Minoan palaces were not abandoned until about 200 years after the eruption, so the tsunamis from Thera were one of the many fatal blows that the Minoans suffered before ultimately succumbing to the Dorians, who migrated from central Europe and the mainland of Greece. Although the initial manifestation of a tsunami more often than not resembles a fast ebbing tide, the term tidal wave is less commonly used, to avoid the association with tides, not only incorrect with regard to its origin (nothing to do with the tides), but also inappropriate in its descriptive character.

9.2 Tsunamis vs. Wind Waves Tsunamis are created by sudden movements or disturbances of the seafloor, submarine explosions, or impacts of large objects, such as landslides from the coastline or asteroids, or landslides that occur in or flow into the sea, also known as subaqueous slumps. These events trigger a series of fast-moving, long waves of initial low amplitude that radiate outward in a manner resembling the waves radiating when a pebble is dropped in the ocean. In contrast, most of the waves observed on beaches are generated by wind dragging or disturbing the surface of the sea. Tsunamis are generated by disturbing the seafloor, wind waves by disturbing the ocean surface. Another mechanism for triggering tsunamis is shaking of a closed basin, such as a reservoir, lake, or harbor. These tsunamis are also referred to as sloshing waves or seiches and sometimes they can be observed several hours after large earthquakes even at large distances. The 1755 Great Lisbon earthquake triggered sloshing at Loch Lomond in Scotland that persisted for several hours and caused the shoreline to advance repeatedly to elevations up to 1 m from the still water line. © 2003 by CRC Press LLC

Year

Date

Coordinates

Location

M

hmax

No. of Deaths

1891 1892 1894 1894 1894 1896 1897 1897 1899 1899 1902 1904 1906 1906 1906 1907 1907 1908 1913 1913 1914 1915 1915 1916 1917 1918 1918 1918 1918

29-Nov 16-May 22-Mar 27-Apr 10-Jul 15-June 15-Aug 21-Sep 10-Sep 30-Sep 26-Feb 25-Jun 31-Jan 17-Aug 17-Aug 14-Jan 23-Oct 28-Dec 22-Feb 11-Oct 12-Jan 26-May 7-Aug 1-Jan 1-May 15-Aug 7-Sep 11-Oct 8-Nov

48.1N 123.4W 14N 143.3E 42.3N 145.1E 38.7N 23E 40N 29E 39.6N 144.2E 38N 143.7E 6N 122E 60N 140W 3S 128.5E 14N 91W 52N 159E 1N 81.5W 51N 179E 33S 179E 77W 18N 38N 16E 15.5E 38N 41.75S 171.5E 7S 148E 31.1N 130.4E 2S 137E 38.5N 20.7E 4S 154E 16S 177W 5.5N 123E 45.5N 151.5E 18.5N 67.5W 44.6N 151.5E

Seattle, Washington Marianas Islands and Guam Nemuro, Japan Lokris, Greece Istanbul, Turkey Sanriku, Japan Tohoku District, Japan Sulu Sea, Philippines Yakutat Bay, Alaska Banda Sea, (Ambon) Indonesia El Salvador Near Petropavlosk, Kamchatka Equador–Colombia Aleutian Islands, Alaska Valparaiso, Central Chile Jamaica Calabria, Italy Messina, Italy Tasman Sea, New Zealand Near east end of New Guinea Sakurajima, Japan North coast of New Guinea Ionian Islands (near Ithaki) New Britain, Papua New Guinea Kermadec Islands–Fiji S. Mindanao, Philippine Islands Kuril Islands (near Ostrov Urup) Puerto Rico S. Kuril Islands

— 7.50 7.90 7.00 >7.00 7.60 7.70 8.70 8.60 7.80 — 8.10 8.60 8.30 8.60 6.50 5.90 7.2/7.5 6.80 7.90 6.2/7.1 7.90 6.70 7.75 8.00 8.30 — 7.50 7.80

2.1 4 4 3 >6 3 3.6 7 16/60 12/60 5 2 5 — 3.6/S 2.4 — 13 1.5 0.1 3 2.8 0.8/1.5 2.8 12 12 12.1 6 2

— — 1 — — 27,122 — 13 — 3,620 185 — 500–1,500 — — — — — — — 55 — — — — 6 47 42 —

9-3



Tsunamis in the Last 100 Years

Tsunami and Seiche

TABLE 9.1

Year

4-Dec 30-Apr 6-May 11-Nov 3-Feb 1-Sep 16-Sep 7-Mar 11 and 12 Sept 4-Nov 28-Dec 16-17 June 7-Mar 26-May 18-Nov 3-Oct 3-Jun 18-Jun 22-Jun 3-Mar 27-Oct 28 and 29 May 19-May 23-May 26-27-Dec 24-May 2-Aug 5-Dec 24-Aug 7-Dec


Coordinates 26S 71W 21.5S 172.5E 5S 154E 28.5S 70W 53N 161E 35.6N 139E 11.5S 160E 35.7N 135E 44.5N 34.5E 34.5N 121.5W 54N 161E 16.3N 98W 51N 170W 51N 131W 44.5N 56.3W 10.5S 161.7E 19.5N 104W 19.5N 103.5W 19N 104.5W 39.2N 144.7E 58.6N 137.1W 42S 152.2E 1S 120E 36.7N 141.4E 39.8N 37.5E 10.5W 77E 44.1N 139.5E 8.5N 83W 15S 76W 33.7N 136E

Location Copiapo, Chile North of Vava’u, Tonga Bismarck Sea, New Guinea Atacuma, Chile East Kamchatka Kwanto, Japan Near Rennel, Solomon Islands SW Honshu Island, Japan Near Crimea, Black Sea Pt. Arguello-Lompoc, California Near Petropavlovska, Kamchatka Acapulco, Mexico Near Umnak, E. Aleutian Islands Queen Charlotte Islands, Canada Grand Banks, Newfoundland, Canada Guadalcanal, Solomon Islands Jalisco, Mexico Jalisco, Mexico Jalisco, Mexico Sanriku Coast, Japan Lituya Bay, Alaska Blanche Bay, New Britian Sulawesi, Indonesia Ibaraki, Japan Erzincan, Turkey Lima, Callao, Peru Northern part of Sea of Japan Panama–Costa Rica Near Lima, Peru Japan (Kumanonoda)

M 7.80 8.30 7.70 8.30 8.30 8.00 7.10 7.50 6.50 7.30 7.30 8.10 8.10 7.00 7.40 7.90 8.10 7.80 6.90 8.30 LS — 7.60 7.10 8.00 8.40 7.00 7.50 8.1/8.6 8.00

hmax 5 2.5 2.5/5.6 9 8 12–13 — 11.2/1.5/1.1 1 1.5–2 0.1/2 8/2.5 0.2/1 1.5 4.6 10/7.5 2.8/0.75 0.1/2 10/6 28–30 ≈150 5.9/≈2 3/2.3 0.8/1.5 15 2 3.5 0.22 2 10/7

No. of Deaths — — — >100 3 2,144 — 3,017/325 — — — — — — 51 50 — — 10 >3,000 — 500 17/8 — — 250 10/7 — — 9,984


1918 1919 1919 1922 1923 1923 1926 1927 1927 1927 1927 1928 1929 1929 1929 1931 1932 1932 1932 1933 1936 1937 1938 1938 1939 1940 1940 1941 1942 1944

Date


9-4

TABLE 9.1 (CONTINUED) Tsunamis in the Last 100 Years

14.1N 62.4E*2/25.4N 63E*3 52.75N 163.5W 49.8N 124.5W 19.3N 68.9W 33N 135.6E 35.5N 27.2E 21S 174W 18N 121E 19.2N 156.1W 42.2N 143.8E 9.5W 127E 52.8N 159.5E 38.1N 20.6E 18.2S 178.3E 34.3S 80.6W 3.4S 80.6W 36.2N 1.6E 36.7N 25.8E 51.3N 175.8W 58.6N 137.1W

Arabian Sea Aleutian Islands, Alaska E. Vancouver Island, British Columbia Dominican Republic Nankaido, Honshu, Japan Sea of Crete Tonga Island Philippine Islands Kona, Hawaii Tocachi-Oki, Japan East of Mindanao, Philippines Paramushir Island, Kuril Islands Kefallonia and Zakynthos, Ionian Islands Suva, Fiji Boso-Oki, Japan Peru–Ecuador Orleansville, Algeria Amorgos, South Aegian Sea Central Aleutian Islands Lituya Bay, Alaska

44.3N 148.5E 53.4N 159.8E 11.78S 80W 30.0N 10E 38.3S 72.6W 18.5S 168.3E 17.2N 99.6W 24.4N 122.1E 40.5N 29E 44.9N 149.6E

Iturap, USSR Kamchatka, USSR Ancon, Peru Agadir, Morocco The Great Chilean Earthquake S. Vanuatu (near Efate) S. Mexico (Acapulco) E. Taiwan–Ryukyu Islands Near Cinarcik, Marmara Sea S. Kuril Islands

8.30 7.40 7.30 8.10 8.10 7.10 7.80 7.20 6.90 8.10 7.20 8.20 7.20 6.75 7.50 7.30 6.75 7.50 7.9–8.3 — — 8.10 7.70 7.80 — 8.60 7 7.2 7.3 6.30 8.1

15.2 30–35 30 4.6 6.6 1.2 0.1/2 2 3.6 6.5 — 18–20 — 3 3 1/18/0.5 — 25 15–16 30 520 5 2 5.7 — 25 1.5 — 0.2 1 5

— 165/17 1 >100 1,997/1,405 — — 16/15 — 28/5/600/33 — — — 5/8 1 7 — — 2 — 0/5 — — — — 534/1,260/4/5 — 30 15 — —

9-5



1958 1959 1961 1960 1960 1961 1962 1963 1963 1963

27-Nov 1-Apr 23-Jun 4-Aug 21-Dec 9-Feb 8-Sep 29-Dec 21-Aug 4-Mar 19-Mar 4-Nov 11-Aug 14-Sep 26-Nov 12-Dec 9-Sep 9-Jul 9-Mar 9 July at 20:00 10 July in morning 6-Nov 4-May 13-Jan 29-Feb 22-May 23-Jul 19-May 13-Feb 18-Sep 13-Oct

Tsunami and Seiche

1945 1946 1946 1946 1946 1948 1948 1949 1951 1952 1952 1952 1953 1953 1953 1953 1954 1956 1957 1958

Date

Coordinates

1963 1964 1965 1965 1965 1966 1966 1966 1967 1967 1967 1968 1968 1968 1968 1969 1969 1970 1970 1971 1971 1973 1973 1973 1974 1974 1974 1975 1975

20-Oct 28-Mar 24-Jan 4-Feb 6-Jul 17-Oct 28-Dec 31-Dec 11-Apr 12-Apr 3-Sep 1-Apr 16-May 3-Sep 14-Aug 11-Aug 22-Nov 31-May 1-Nov 14-Jul 26-Jul 28-Feb 17-Jun 24-Jun 31-Jan 1-Feb 3-Oct 10-Jun 29-Nov

44.5N 150.3E 61.1N 147.5W 2.4S 126E 51.3N 178.6E 38.4N 22.3E 10.7S 78.8W 25.5S 70.6W 11.8S 166.8E 3.4S 119.1E 5.5N 97.3E 10.6S 79.8W 32.3N 132.5E 40.7N 143.6E 41.7N 32.6E 0.2N 119.8E 42.7N 147.6E 57.7N 163.6E 9.2S 78.8W 4.9S 145.5E 5.5S 153.9E 4.9S 153.2E 50.5N 156.6E 43N 146E 43.3N 146.4E 7.4S 155.6E 7.4S 155.6E 12.3S 77.8W 42.8N 148.2E 19.3N 155W


Location S. Kuril Islands The Great Alaskan Earthquake Ceram Island, Indonesia W. Aleutian Islands North Corinth Gulf, Greece Offshore Chimbote, N. Peru Taltal, N. Chile N. New Hebrides Islands (Vanuatu) Makassar Strait, Indonesia Malay Peninsula Offshore Chimbote, N. Peru Seikaido, Japan N. Honshu, Japan (near Tohoku) Amasra, Turkey N. Celebes, Banda Sea, Indonesia SE Hokkaido, Kuril Islands Bering Strait, Alaska Offshore Chimbote, N. Peru Bismarck Sea, New Guinea Bismarck Sea, New Guinea Bismarck Sea, New Guinea Kamchatka, Kuril Islands Kuril Islands and Hokkaido, Japan Kuril Islands and Hokkaido, Japan Solomon Islands Solomon Islands Callao, Peru Kuril Islands and Hokkaido, Japan S. Hilo, Hawaii

M

hmax

No. of Deaths

6.7/7.2 8.5 7.6 8.2 6.9 8 7.8 8.1 5.5 7.5 7 7.5 7.9–8 6.60 7.7–7.8 7.8 7.3 7.6/6.6 7 7.8–7.9 7.7–7.9 7.2–7.5 7.4 7.5 7 7.4 8.1 6.8–7.0 7.2

15 70/67.1 4 10 20/3 3 1 2 3 2 2 2.4–3 5 3 10 2.6/5 15 1.8 3 3 10/3.4 1.5 4.5/1.5 4.6 4.6 4.5 1.58 4.9/5.5 8/14.3

— 123/115 71 — — 125 3 — 58/13 14 — 1 52 — 200/392 — — — 3 2 — — — — — — — — 2/16


Year

0068_C09_fm Page 6 Wednesday, August 14, 2002 1:35 PM

9-6


6.3N 124E 11S 118.4E 8.5S 123.5E 1.7S 135.9E 1.6N 79.3W 46.2N 122.2W 36.2N 1.35E 40.4N 139.1E 17.8N 101.6W 6.2S 149.1E

1990 1990 1992 1992 1992 1993 1994 1994 1994 1995 1995 1995 1996 1996 1996 1997 1998 1998 1999

25-Mar 4-Apr 25-Apr 2-Sep 12-Dec 12-Jul 15-Feb 2-Jun 3-Nov 14-May 15-Jun 9-Oct 1-Jan 17-Feb 21-Feb 21-Apr 17-Jul 6-Aug 17-Aug

9.9N 84.8W 40.4N 124.3W 11.76N 87.4W 8.5S 121.9E 42.8N 139.2E 5S 104.3E 10.5S 112.8E 59.5N 135.3W 8.3S 125.1E 38.4N 22.3E 18.9N 104.1W 0.7N 119.9E 0.9S 137E 9.6S 79.6W 12.6S 166.7E 2.9S 141.9E 25.1N 95.1E 40.7N 30E

Moro Gulf, Philippines Sunda Islands Lomblen Island, Indonesia W. Irian, Indonesia Colombia–Ecuador Mount Saint Helens, Washington El Asnam, Algeria Noshiro, Japan Acapulco, Mexico Whiterman Ra, New Britain, Papua New Guinea Puntarenas, Costa Rica Mindanao, Philippines Cape Mendocino, N. California Offshore Nicaragua Flores, Indonesia Japan Sea (offshore W. Hokkaido) Southern Sumatra, Indonesia East Java, Indonesia Skagway, Alaska Timor, Indonesia Aigiou, Greece Manzanillo, Mexico Sulawesi, Indonesia Irian Jaya, Indonesia Chimbote, Peru Santa Cruz Island, Vanuatu Aitape, Papua New Guinea Burma–India Kocaeli, Turkey

7.8 8 — 8.1 7.7 5.1 7.7 7.7 7.6 7.7 7 — 7.1 7.2–7.4 7.5 7.6 7 7.2 LS 6.9 6.3 7.3–7.6 7.6 8.1 6.6/7.5 7.9 7.1 7.2 7.8

5 15 10 2 5 225 — 14.5 1.2 0.1

8,000/4,000 189 539–540 100/15 500/600 57 — 103–104 — —

1 2.5 1.8 10 26 30.6–31.7 — 12 12 4 2 5–11 5/3.43 7.7 ≈5 0.2 15 — 2.9

— — — 168–170 2,080 330 7 ≈200 1 11 — 1 9/24 127/108 12/2 100/0 2,182/3,000 2 3–11

9-7



16-Aug 19-Aug 18-Jul 12-Sep 12-Dec 18-May 10-Oct 26-May 21-Sep 16-Oct

Tsunami and Seiche

1976 1977 1979 1979 1979 1980 1980 1983 1985 1987

Year

Date

Coordinates

1999 2000 2000 2001

26-Nov 26-Jan 4-May 23-Jun

16.4N 168.2E 5.1N 120.2E 1.1S 123.6E 16.2S 73.6W

Location Pentacost Island, Vanuatu Islands Tawi-Tawi, Philippines Sulawesi, Indonesia Camana, Peru

M

hmax

7.3 0 7.5 8.4

5/6 20 5/6 4

No. of Deaths 3/5 0 0 23



Note: LS = Land Slide. When multiple entries are provided they should be taken as indicative of the range of values along the target coastline, or that sources disagree on the correct value. Sometimes values refer to estimates of the wave height, otherwise to estimates of the maximum run-up or estimates of overland flow depths. Other than tsunamis in the last half of the twentieth century which have been properly surveyed, all other height estimates should be interpreted with extreme caution, for tsunami run-up varies substantially over the coast for any given event. The use of the table is only for indicating tsunami incidence around the world. Source: Data are from Soloviev and Go’s Catalogue of Tsunamis, the National Geophysical Database Center, the Novosibirsk Tsunami Laboratory of the Siberian Science Computing Center, and from Camfield [1980].


9-8



Tsunami and Seiche

9-9

FIGURE 9.1 The tsunami that started it all. Initial wave from the 1680 B.C. eruption of the Thera volcano in the Aegean. The tsunami has been blamed for destroying the Minoan civilization in Crete, but computations suggest that the wave disrupted but did not destroy the Minoans. Shown as Color Figure 9.1.

Both wind waves and tsunamis are characterized by a wavelength, the horizontal distance between crests or peaks; a period, the time it takes successive peaks to pass a fixed point; and a height, the vertical distance from the wave trough to its crest. Wind waves tend to have a wavelength up to 200 m (666 ft) and periods of about 0.5 to 30 sec [Prager, 1999]. In contrast, tectonic tsunamis near the source typically have a wavelength of hundreds of kilometers and periods of tens of minutes. Wind waves vary in height from tiny ripples on the sea surface to the rare rogue waves imaged in the motion picture, The Perfect Storm. © 2003 by CRC Press LLC


9-10


Tsunamis, on the other hand, race across the open ocean as a series of long, low-crested waves, usually less than 1 m high. Their steepness is so small that a ship out at sea may not feel a tsunami pass beneath the hull [Prager, 1999]. In general, waves are considered deep-water waves if their wavelength L is relatively small compared to the water depth d through which they travel. Wind waves do not “feel” the seafloor until within tens of meters from the coastline, depending on the slope of the beach. In the open ocean, where depths average about 4 km (2.5 mi), most wind waves are deep-water waves, i.e., with a short wavelength relative to depth, d/L > 1.5. In contrast, shallow-water (SW) waves are those with a long wavelength relative to depth, d/L < 20. The depth and nature of the seafloor strongly influence how SW waves propagate or travel. Because tsunamis have such long wavelengths, even when traveling through very deep water, they are considered SW waves [Prager, 1999]. In wind-generated waves, the orbital motion of the water particles decreases with depth from the water surface. As energy is transferred through the motion of the water particles, the energy of wind waves traveling through deep water is concentrated near the surface. By contrast, the energy imparted to the water during tsunami formation sets the entire water column in motion. Orbital velocities do not decrease significantly with depth, and although the wave height at the surface is relatively small, the energy contained throughout the entire water column is substantial. Furthermore, the rate at which water waves lose energy is inversely proportional to their wavelength. So tsunamis not only contain a lot of energy, and move at high speeds, but they can also travel great distances with little energy loss. The speed or wave velocity or celerity c is calculated by dividing the wavelength L by its period T. The speed of deep-water waves does not depend on the depth, and the waves are dispersive, as each component frequency of a complex spectrum propagates at its own frequency-dependent speed. It is for this reason that complex sea states generated by storms far offshore manifest themselves in groups of waves of approximately similar period when they strike the coast. SW waves travel at a speed c = gd where d is the local depth, hence all frequencies in the spectrum of a tsunami travel at the same velocity. It is for this reason that tsunamis do not alter their shape substantially as they propagate over fairly constant depth. In typical ocean depths of 4 km, a tsunami travels at a speed of nearly 200 m/sec, or almost 700 km/h (437 mph) — the speed of jet aircraft. When tsunamis enter shallower water they slow down; at a depth of 30 m, an SW wave travels at only 59 km/h (36 mph). As they move toward the coast, tsunamis pass through varying depths and over complex seafloor topography. Changes in the depth and seafloor cause them to continuously evolve and change shape. A tsunami generated from an earthquake off Peru may look entirely different along the Peruvian coastline as compared to when it enters a bay in California, and still different when it strikes a beach in Hawaii. Both tsunamis and wind waves behave similarly as they approach a coastline; they refract and shoal. Shoaling is the process in which the wave front steepens and the wave height increases. The front of the wave enters shallower water and moves more slowly than the tail of the wave, since the depth is smaller, hence the steepness at the front. If the wave is sufficiently steep and the continental shelf long, it eventually breaks, as the wave in essence trips over itself. However, when refracting, the crest lengths of tsunamis often cause unexpected wave patterns in refraction compared to wind waves. During the 1992 Flores, Indonesia event, the tsunami struck Babi Island about 6 mi off Flores and concentrated its energy on the fishing villages built on the lee side of the island, which was sheltered from wind waves (see Figure 9.2). The tsunamis appear to have hit the island, traveled around its shoreline as a trapped wave, and inundated the backside [Yeh et al., 1992], as also described in Section 9.6. When tsunamis start advancing up on dry land, they can snap trees, destroy engineered structures, and carry boats far inland. During the 1994 Mindoro, Philippines event a 2-m tsunami carried a 6000-ton power-generating barge moored at the delta of the Baryan River 1 mi inland and left it there. When the water level recovered, there was not sufficient freeboard to tow the barge back to the delta [Imamura et al., 1995]. Not all tsunamis break at the shoreline; some just swiftly submerge the shore and generate swirling currents. Most tsunamis manifest themselves on the coastline as a leading depression wave, a particular kind of what are referred to in mathematics as N-waves or dipole waves. Numerous anecdotal stories relate how © 2003 by CRC Press LLC


Tsunami and Seiche

9-11

FIGURE 9.2 A view of Babi Island, off Flores, Indonesia (top of photo). The village on the back side of Babi was completely destroyed by the tsunami, which wrapped around the island, killing hundreds.

people set out to collect fish left stranded and flapping by a great retreat of the sea. In fact the great tsunami of All Saints Day, November 1, 1755, which destroyed Lisbon, Portugal and led the two French philosophers Voltaire and Rousseau to argue whether optimism had a place in human life (see Chapter 1), was preceded by a leading depression wave. So was the April Fool’s Day 1946 tsunami which, after destroying the Scotch Cap Lighthouse at Unimak Island, Alaska, killing five people (Figure 9.3), 2300 mi away and 5 h later hit Hilo, Hawaii, killing 159 people [Dudley and Lee, 1988]. So was the 1992 Nicaraguan tsunami and, conspicuously, all tsunamis of the past 10 years surveyed by the International Tsunami Survey Team (ITST) had at least several reports of leading depression N-waves. Tsunamis can also cause sediment erosion or sediment deposition, or they can rip apart coral reefs that lie in their path. Coastal regions that are low lying or are located between steep cliffs or bodies of water are particularly vulnerable to tsunami damage. The September 1, 1992 Nicaraguan tsunami deposited a vast sediment blanket over many lowlands along the affected areas. On June 3, 1994, an earthquake occurred in the Java trench in the Indian Ocean. The magnitude 7.2 quake triggered a large tsunami that struck the coast of southeast Java and rolled on to hit southwest Bali. Some 200 people were killed, 400 injured, and 1000 left homeless. Post-tsunami surveys found clues, such as trees with sand-encrusted bark and leaves, that indicated that run-up reached some 5 m in west Bali and up to 14 m in southeast Java. Several beaches were completely washed away, while rivers effectively blocked evacuation routes. Eyewitnesses near G-camp in Southeast Java, a surfing locale of renown, reported that within a 20-m section of a nearby coral reef, about a meter’s worth of surface growth had been shaved off [Synolakis et al., 1995], see Figure 9.4. The ITST found large pieces of the reef on a nearby beach. Some of the © 2003 by CRC Press LLC


9-12


FIGURE 9.3 Scotch Cap, Unimak, Alaska. The lighthouse in the inset stood where the marker indicates. The wave rose 42 m past the structure on the headlands. The lighthouse was completely destroyed and five people perished.

eroded sand from the shore was deposited in broad offshore bars. The same tsunami was documented along the northwestern Australian coast. In one area a surge of water, some 3–4 m (10–13.3 ft) high, carried fish, crayfish, and rocks nearly 300 m (1000 ft) inland. The 1998 Papua New Guinea tsunami deposited a sediment layer that in some areas was 1 m (3.3 ft) high. Up until recently, earthquake-induced seafloor deformation was believed to be the primary cause of most tsunamis, even though numerous major landslides and associated waves were triggered in fjords and lakes of southern Alaska by the great 1964 Alaska earthquake (see summary and references in Plafker et al., 1967). It is now suspected that landslides play a much greater role in tsunami generation than previously believed. Landslide-generated tsunamis differ from the classic long waves, in that they are steeper and disperse rapidly, particularly in shallow water. There are several important differences between tsunamis triggered by mass movements and by earthquakes, also called tectonic tsunamis. Tectonic tsunamis tend to have longer wavelengths, longer periods, and a larger source area than those generated by mass movements of earth. However, whereas there is little question that the timing of the seafloor deformation is not important to first order in calculating tsunami evolution, there is also little question that the timing of mass movements is more important in the wave evolution; very slow movements will not generate large waves. Nonetheless, the characteristic time cannot be determined very accurately. When a potential tsunami-triggering earthquake occurs, sufficient information is often available to predict whether or not a massive wave will be created. However, mass movements often occur and trigger tsunamis unexpectedly and sometimes aseismically. The 1994 Skagway, Alaska tsunami was triggered by sediment instabilities at extreme low tides, without any detectable associated seismic event. Figure 9.5A shows the slabs that failed in retrograde fashion from C to B to A and triggered the tsunami. Figures 9.5B and C © 2003 by CRC Press LLC


Tsunami and Seiche

9-13

FIGURE 9.4 The aftermath of the 1994 East Java tsunami. There had been no damage from the earthquake and it had been hardly felt. Shown as Color Figure 9.4.

show stills from an animation of the tsunami as it attacks the nearby dock of the Pacific Arctic Railway Company. Notice how the dock is destroyed as the wave advances from north to south [Synolakis et al., 2002a]. Although still controversial, the 1998 Papua New Guinea tsunami that killed more than 2100 people, with waves ranging up to 12 m, was triggered by a submarine slump. Figure 9.6A shows a graphic of the wave as it attacks Sissano Lagoon on the north coast of Papua New Guinea. The aftermath is shown in Figure 9.6B. This event was documented extensively [Synolakis et al., 2002b] in Science, August 17, 2001, and the New York Times, April 23, 2002. There are at least four characteristics of mass movements that determine whether or not a tsunami will form, its length, width, thickness, and the inclination of the slope that fails and triggers the landslide. The effects on the generated waves of the geomechanical characteristics of the material that slides remain controversial, primarily due to lack of validated constitutive models and lack of knowledge as to the effect of the timing of the seafloor motions. None of these characteristics can yet be accurately predicted and the relevant information on geometric slide characteristics typically comes only after the event. The potential for tsunami-triggering mass movements often can only be assessed in the context of the surrounding geology, and this typically requires a multidisciplinary approach to modeling and bathymetric cruises. In some cases, information on submarine landslides can be obtained from the resultant breaks in underwater cables. The timing of communications cable breaks and the subsequent loss of communications can be used to document undersea mass movements and actually record the timing of the event. Observers during undersea debris flows have also reported seeing muddy seawater rolling toward the surface. In the absence of such information, it is nearly impossible to determine the exact timing.

9.3 Tectonic Tsunami Sources Although landslides, volcanoes, and asteroid impacts can all trigger tsunamis, by far the most common cause is submarine earthquakes. Even if the seafloor motion itself does not trigger tsunamis, the shaking may trigger coseismic landslides. Recent speculation suggests that up to one third of the tsunamis in the © 2003 by CRC Press LLC


9-14


(A)

(B)

FIGURE 9.5 (A) The three slabs that slid during the 1994 Skagway, Alaska disaster, triggering the wave shown in (B) and (C).



9-15

Tsunami and Seiche

(C)

FIGURE 9.5 (CONTINUED)

past 10 years may have been cogenerated by quake-induced landslides. Not all earthquakes generate tsunamis. Looking at earthquake catalogs, one can deduce that in the past 30 years, there have been approximately one magnitude 8 or higher earthquake and about ten magnitude 7 submarine earthquakes per year, yet only 20 of them have reportedly created tsunamis. The pattern and extent of vertical ground deformation from an earthquake uniquely determines whether or not a tsunami is formed. Earthquake fault geometries constitute a ternary family featuring three fundamental end members: strike-slip, thrust, and normal faults. Strike-slip or transform faults involve horizontal motion of the Earth’s crust, while thrust and normal faults entail vertical motion. Submarine thrust or normal faults produce tsunamis as the seafloor lifts up or drops down, and either pushes the water up or pulls it down — triggering wave motion on the ocean surface. On the other hand, strike-slip motions, generally, do not generate sufficient vertical displacement on the seafloor, yet they may generate tsunamis through coseismic events. Most faults combine both strike-slip and thrust motions, but primarily only faults that have predominantly vertical displacement and create sufficiently large seafloor deformations appear to trigger tsunamis. Generally, the larger the magnitude of an earthquake, the larger the area that is deformed, as shown in Table 9.2. The deformed area usually contains an area of uplift and subsidence, whereas quite frequently there is more than one dipole shape of the wave. The deformation area refers to the horizontal extent of deformation, while slip length is a measure of vertical change. Strong earthquakes not only deform larger areas, but they do so by a greater amount of slip, thus producing disproportionally larger tsunamis than smaller events. In addition to an earthquake’s magnitude, the deeper the hypocenter or focus of an earthquake, the smaller the vertical deformation of the Earth’s surface. A deeper hypocenter allows the seismic energy to spread over a larger volume so that less energy reaches the ground surface. Earthquakes deeper than about 30 km (18.75 mi) rarely cause sufficient deformation to generate tsunamis. However, truly great megathrust earthquakes that occur deeper than 30 km, such as the 1960 Chilean event, can occasionally trigger tsunamis. To understand the process, refer to Figure 9.7, which shows a typical subduction zone © 2003 by CRC Press LLC


9-16


(A)

(B)

FIGURE 9.6 (A) The aftermath of the Papua New Guinea disaster. Only the stilts from the houses remain. The bucket on the tree in the picture is a watermark that is used to indicate the flow depth during the tsunami. (B) Initial and final profiles of the Papua New Guinea wave. Part (A) shown as color Figure 9.6. © 2003 by CRC Press LLC


9-17

Tsunami and Seiche

TABLE 9.2

Estimates of Fault Parameters for Tsunamigenic Earthquakes

Mw

W (km)

L (km)

D (m)

S (m)

L/V (sec)

7 8 9 9.5

30 80 240 250

70 200 60 1000

0.6 2.7 9.0 27.0

0.16 0.70 2.30 7.00

23 70 200 330

Note: L, W, and D are the fault width, length, and displacement at the dislocation also known as fault slip, respectively, and V is the rupture velocity. S is the corresponding vertical seafloor displacement. Data from Synolakis et al. (1997a).

(Deep Water Tsunami) Vertical Displacement

Uz

No Coastal Movement

X Z

Ocean Rupture

Continental Shelf Coastline Interplate Thrust

X

FIGURE 9.7 Definition sketch of subduction zone generation of tsunamis.

event and the leading depression N-wave tsunami generated on the ocean surface. If the rupture is closer to shore then the subsidence takes place primarily onshore and the initial tsunami may manifest itself as a leading elevation wave. An earthquake whose epicenter lies inland will only generate a tsunami if it produces sufficient vertical deformation offshore on the seafloor. Therefore, only very strong inland thrust earthquakes, as compared to even moderate offshore earthquakes, are potential tsunami generators (unless of course they trigger a massive landslide into the sea). For example, the 1994 Northridge earthquake that shook Los Angeles violently resulted in vertical ground deformations of up to 2 m (6 ft), but did not produce a tsunami. Had the fault ruptured with the same ferocity about 60 km (40 mi) west offshore, it would have probably created a substantial tsunami inside Santa Monica Bay. The first piece of information required for modeling tsunamis is the size and distribution of seafloor deformation following an earthquake, and the amount of energy released. The amount of seafloor deformation can either be measured or predicted by another model. The most accurate means of determining seafloor deformation is to actually measure it by comparing the underwater topography (bathymetry) of the seafloor post-quake to pre-quake data. Unfortunately, this cannot be done quickly and is often impossible, as bathymetry at sufficiently high resolution rarely exists for most coastline areas of the United States and the world. Given the difficulties in actually determining the seafloor deformation that triggers a tsunami, earthquake engineers usually rely on predictions provided by seismologic models, referred to as source models. The input for a tsunami inundation model comes from an earthquake model. These computer simulations are based on models of elastic deformation on half-spaces and are applicable for all earthquakes whether submarine or not. In a sense, for each earthquake, seismologists estimate what the surface deformation would be in a material with the same elastic properties as the Earth’s interior, given an internal displacement of the size inferred from seismic records. Each earthquake event is modeled using what is referred to as the Harvard fault plane solution or CMT. The Harvard solution uses seismologic recordings, at different stations around the world and solves © 2003 by CRC Press LLC


9-18


FIGURE 9.8 The estimated energy as a function of the seismic moment. The anomalous events 42, 24, and 36 are tsunami earthquakes, particularly efficient in generating tsunamis. (From Newman, A.V. and Okal, E.A. 1998. “Teleseismic Estimates of Radiated Seismic Energy: The E/M0 Discriminant for Tsunami Earthquakes,” J. Geophys. Res., 103, 26885-26898.)

the classic inverse problem in geophysics to determine the rupture characteristics of the source and its location. The CMT reveals, fairly accurately, the moment magnitude of the earthquake. If the seismic moment is M0 , then: M0 = µDA

(9.1)

where µ ≈ 5 − 7 × 10 dyn/cm is the rigidity, D is the slip, and Α is the area of the fault. D and Α both increase with the moment, as shown in Table 9.2 [Liu and Synolakis, 2003]. Α is estimated from the aftershock distribution and is usually assumed rectangular. Other earthquake characteristics important for estimating the patterns of ground deformation, such as the strike, dip, and slip angles, are also inverted from the CMT algorithm. A measure of the barrier interval (the heterogeneity of the fault plane) over the rupture velocity V is defined as the rise time, and this is quite an elusive parameter to determine accurately. Tsunami models use the energy released, the size of the deformed area, the mean displacement at the surface l < D, and the dip δ, strike φ, and slip λ angles, to infer a seafloor displacement pattern, using what are known as Okada’s [1985] formulas. These closed form solutions are based on Mansinha and Smylie [1971] and, straightforward as they may be, they are too long to be repeated here. Then, tsunami models assume that water motion occurs instantaneously; therefore, the initial tsunami wave is assumed to be of the same shape as the seafloor displacement. Whatever mass of fluid is displaced by the seafloor moving up or down causes an equivalent displacement of the water surface in the same direction. The instantaneous assumption is based on the fact that tsunamis propagate at speeds up to 220 m/sec (733 fps), while seismic waves cause rupture to propagate at typical speeds of 2 to 3 km/sec (1.25 to 1.9 mph). Certain earthquakes are quite efficient in generating tsunamis and may produce large tsunamis at moment magnitudes lower than otherwise expected. These anomalous events include tsunami earthquakes (Kanamori, 1972). Figure 9.8 suggests a method for uniquely identifying tsunami earthquakes as 11


2


Tsunami and Seiche

9-19

those with a deficiency of up to two orders of magnitude in the ratio of the estimated seismic energy EE to the seismic moment M0. The energy EE is estimated from the high frequencies in the P-wave part of the signal, while M0 is estimated from the longer frequencies in the surface wave part of the signal. This EE/M0 measure will eventually be part of TREMORS, a quick and potent algorithm used to estimate source characteristics based on a single broad band instrument. TREMORS is now in use in the tsunami warning centers in several countries. Once the initial wave conditions are established, tsunami models estimate the evolution of the tsunami from its source to the target coastline, based on the underlying seafloor bathymetry. When the simulated wave arrives at the coastline, tsunami models become inundation models and calculate the evolution of the tsunami as it moves inland. Tsunami models are really the synthesis of earthquake, wave, and flood inundation models. It should be stressed that the solutions used for tectonic tsunamis are most often based on idealized elastic dislocation theory applicable to a uniform half-space [Mansinha and Smylie, 1971]. In reality, nonuniform slip distributions arising from barriers (or asperities) can cause local ground displacements that can be up to two or three times the values predicted by the Okada [1985] formulas. Recent anecdotal evidence also suggests that sediment lenses within tens of meters from the ground surface can amplify the ground displacement up to a factor of two. Until more evolved ground deformation models predict the vertical displacement more accurately, caution is needed in interpreting results derived from initial conditions based on Okada [1985].

9.4 Initial Waves Generated by Submarine Landslides Modeling tsunamis generated by submarine landslides is not as well understood as waves generated by seismic displacements. Coseismic deformation of the seafloor occurs very rapidly relative to the propagation speeds of SW waves, allowing for simple specification of initial conditions by transferring the terminal deformation to the free surface. The idea that submarine landslides might generate long waves is not new. Gutenberg [1939] suggested that “submarine landslides are to be considered at least as one of the chief causes, if not indeed the major cause of tsunamis.” He supported his statements by referring to the work of Montessus de Ballore, who himself referred to earlier work by Verbeck. Gutenberg [1939] wrote that the large waves that drowned many people in Chile in Ceram in 1899 were probably triggered by coseismic landslides. He also referred to a report by Milne in the 1898 meeting of the British Association for the Advancement of Sciences. Milne suggested that tsunamis on Japan’s east coast were the result of submarine slides on the Tusacarora slope. Gutenberg finally refers to Forster’s 1890 work, which attributed underwater cable breaks in Greece to coseismic submarine slides. Recent work has also highlighted the possibility of substantial tsunamis generated by submarine slides and slumps. Hasegawa and Kanamori [1987] studied the 1929 Grand Banks “earthquake” and tsunami. Eissler and Kanamori [1987] studied the 1975 Kalapana earthquake and tsunami on the Island of Hawaii. While there is still continuing debate on the exact causative mechanism of the 1946 Aleutian tsunami [Kanamori, 1985; Okal, 1992; Pelayo and Wiens, 1992; Fryer et al., 2001; Okal et al., 2002a, 2002b), the working assumption is that the near-source damage was due to a submarine slump. Compared with the understanding of earthquake-induced initial tsunami waves, the understanding of landslide initial waves is marginal. A few empirical and computational methods exist to generate oneor two-dimensional surface waveforms generated by underwater mass movements. Wiegel [1955] discusses impulsively generated water waves, described as “the sudden movement of a submerged body for a short interval of time,” which “may be considered representative of a submarine landslide.” He states that the energy in the wave generated by a submerged falling block is on the order of 1% of the initial potential energy of the block. Wiegel’s [1955] study considered both vertically falling blocks and blocks sliding down an inclined plane. His data suggest that wave height increases with increasing slope, submerged weight, and decreasing depth of submergence. He also reported that wave period increases with decreasing slope. © 2003 by CRC Press LLC


9-20


water level

Ds D0 Slide Scar h

FIGURE 9.9 Definition sketch for landslide waves.

Based on the work of Striem and Miloh [1975], Murty [1979] used the energy released by a moving block sliding from its initial position to its final position, tranferred that energy into a solitary wave and calculated the height of the wave. This approach was also used by McCulloch [1985] when discussing the tsunami hazard associated with landslides offshore of southern California. The formulation used by Murty equates the potential energy of a sliding mass with the energy contained in an initial wave, assumed to be a solitary wave. Murty’s equation takes the form: H=

[

]

( 2/3) 1/ 2 1 8 (3) µlh ( γ − 1) ( Do − Ds ) D

(9.2)

where H is the predicted wave height; Do, Ds , h, and l are defined in Figure 9.9; and µ is an empirical parameter to represent the energy transfer from the sliding mass to the water wave it generates. γ is the specific gravity and it is the ratio of the density of the slide to the local water density. Murty (1979) used an energy transfer of µ = 1% from the sliding mass into wave generation based on the experiments performed by Wiegel. McCulloch assumed values of D = Do = 700 m, Ds = 600 m, l = 2500 m, h = 50 m, µ = 0.01, and γ = 1.6 as representative of typical landslide parameters offshore of Southern California. The calculated wave using these values is 14 m, in accordance with values estimated by other methods. Due to an arithmetic error, McCulloch had calculated it as 0.14 m, leading to an underestimation of the tsunami hazards off Southern California [Borrero, 2002]. In principle, Murty’s formula should work well only when the run of the slide Do − D is known. In most cases, wave generation takes place almost immediately, and the energy transfer is far less efficient as the slide proceeds into deeper water. If Do is significantly larger than Ds , the formula overpredicts the wave height. Heinrich [1992] used a two-dimensional finite difference solution of the Navier–Stokes equations to model wave generation from landslides. He validated his use of the numerical scheme by comparing it to laboratory data and found generally good agreement. His simulations modeled a right triangular block sliding down a 45˚ incline and showed the largest discrepancy with model experiments just after initiation of movement of the sliding mass — where turbulence is greatest. Similar results have been obtained by Raichlen and Synolakis [2002] where flow separation is seen to occur. Jiang and LeBlond [1992] have proposed a model for wave generation where the “landslide is treated as the laminar flow of an incompressible viscous fluid.” They modeled their deforming slide as a parabola perched on an inclined plane. When released under gravity, the slide mass was allowed to freely deform moving down the incline. The solution was based on the two-layer 2 + 1-dimensional SW equations. For one particular case, with an initial slide 686 m (2286 ft) long and 24 m (80 ft) thick on a 4˚ slope, the waves traveling seaward had a maximum crest amplitude of 5 m with a shoreward propagating trough



9-21

Tsunami and Seiche

∆X

Z max Z min

X min Xg

D

T b

θ

FIGURE 9.10 Definition sketch for landslide-generated waves by moving bodies.

of the same magnitude. Jiang and LeBlond [1992] noted that the maximum depended on the density of the slide, with less dense slides transferring more energy than more dense slides, and calculated an energy transfer rate of µ = 15%. Watts [1997, 1998] also studied waves generated by underwater landslides. He presented scaling equations for slide-generated waves based on laboratory experiments. Watts’ analysis is the basis for the initial wave shapes used in this study and will be discussed in some detail here. Pelinovsky and Poplavsky [1996] and later Watts [1997] presented the force balance on a submerged solid block sliding along a plane inclined at angle θ, as shown in Figure 9.10, as: 1 ds  ds  ≈ (mb – mo ) g (sin θ – Cn cos θ) – Cd ρoωl cos θ sin θ   (mb + Cmmo ) dt 2  dt  2 2

2

(9.3)

where s mb mo ρ0 ω l Cm , Cn, Cd

= = = = = = =

the instantaneous position of the center of mass the mass of the sliding block the mass of the displaced fluid the density of water the width of the block the length of the block along the incline coefficients of added mass, Coulombic friction, and fluid dynamic drag, respectively

Pelinofsky and Poplavsky [1996] argued that terminal velocity is reached when the block is no longer accelerating, hence d 2S/dt2 = 0, and derived that the terminal velocity ut is given by:  2 gL  ut =   ( γ − 1) (sin θ − Cn cos θ)  Cd  © 2003 by CRC Press LLC

(9.4)


9-22


and

ao =

(γ − 1) g sin θ (γ + 1)

(9.5)

Setting Cm = 1, Cn = 0, and using experimentally derived values for the term Cd sin θ cos θ, Watts [1998] and Borrero [2002] derive, for a semielliptical sliding body, that: ut = 0.5 gbπ ( γ − 1) sin θ

(9.6)

where ao and ut are the initial acceleration and terminal velocities of the slides, respectively; b = l cos θ is the length parallel to the upper surface of the sliding block; and γ is the specific gravity of the block. These expressions are the basis for a curve fit based on Watts [1997, 1998], which describes a characteristic two-dimensional tsunami amplitude of a sliding ellipse down an inclined plane. This equation, as described in Watts and Borrero [2001], is: T   b η2d ≈ so 0.0506 sin1.25 θ − 0.0328 sin 2.25 θ      b   d

(

)

1.25

(9.7)

where T is the thickness of the ellipse, d is the depth over the ellipse, b is the length of the ellipse along the inclined plane, and so is a characteristic “run” defined as ut2/a0. For rotational slumps, one additional parameter is needed, the radius of curvature R. Then: T   b η2d ≈ soδφ0.39 0.1308 sin0.22 θ −      b   d

(

)

1.25

 b    R

0.63

(9.8)

Watts and Borrero (2001) report that this empirical formula is valid for T < 9.2L, L < R < 2L, d > 0.06L, θ < 30°, and ∆φ < 0.53. In the method of Watts, these equations describe a characteristic tsunami amplitude, not a particular wave height at any fixed point in space. To describe the wave shape explicitly, the value of η2d described above is used in expressions derived from alleged curve fits of laboratory and numerical data [Watts, 1997, 1998, 2000]. Values for the location of the maximum depression Zmin, the distance between the crest of the elevation wave and the trough of the depression wave ∆x, and the height of the maximum elevation wave Zmax and Zmin are given by Borrero (2002) as:

(

X min = 0.95 X g + 0.4338 so cos θ


)

(9.9)

∆X = 0.5 t o gd = 0.5 λ

(9.10)

Z min = 2.1 η2d

(9.11)

 0.2 d  Z max = 0.64 η2d  0.8 + b sin θ  

(9.12)


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Tsunami and Seiche

These four equations describe the longitudinal wave shape. For the direction transverse to the slide motion, the width w of the landslide is used and a sech2 profile is fitted, and the following expression is derived for the three-dimensional waveform generated by a submarine landslide: η( x, y ) =

ω  3y  sech 2    w + λ λ +w

2 2   ( X − Xmin )   X − Xmin − ∆X   −  1.2 Zmin −   Zmax λ      λ + Z maxe −1.2 Z mine     

(9.13)

Bohannon and Gardner [2002] use a modification of Murty’s formula. They suggest the energy contained in one cycle of a sinusoidal wave of height a and wavelength is given by ε = µρgwλa2, where again µ is the energy transfer coefficient of Murty. They assume the sliding mass to have volume equal to LTw, and derive the initial wave height for a mass dropping a distance ∆z as: H=

µ ( γ − 1) LT∆ z λ

(9.14)

In as yet unpublished work Synolakis and Uslu [2003] argue that Murty’s and Bohannon and Gardner’s formulations both need an arbitrary specification of the drop of the slide, and assume a value of the energy transfer coefficient. Generally, if one uses as the drop of the slide the entire height between the location of the slide and the nearest flat seafloor, the formulas predict unrealistic initial wave heights. Clearly, the energy transfer coefficient depends on the instantaneous depth. As the slide goes into deeper water, the transfer is less efficient. Based on analytical results, Synolakis and Uslu (2003) assume that the initial wave is generated within a horizontal motion of no longer than half the slide length. They propose that the energy transfer is similar to that of a wave maker for the first tens of seconds of motion, and 1/3 1/3 d g ( g a0 ) , where again that the initial wave is generated within a time t 0 = (1 / 4)  λ − 1 ao =   g sin θ  λ + 1 They calculated the net energy in an isosceles N-wave with height H and sech-like transverse shape as ε=

3/ 2 2 3 πρgw (dH ) = (1 2) ρg LTw∆ z 5

with ∆ z = (1 2) aot 02 sinθ. Therefore, 1/3

 L2T 2   ao  H = 0.139      d  g

2/9

(9.15)

Note that in the Synolakis and Uslu (2003) analysis, the height of the depression wave is equal to the height of the elevation wave, and does not rely on any assumptions on the transfer coeffiecient µ or any fitted empirical factors. The results computed using the four different landslide wave formulas are presented in Table 9.3. Given the present state of the art, it is clear that further progress will have to await validation of these formulas with numerical and laboratory experiments, currently under way, see Synolakis and Raichlen [2002].


d = Ds (m) Munson–Nygren (New England) East Breaks Gulf of Mexico Seward (Alaska) Papua New Guinea Palos Verdes, CA

Skagway, Alaska

a b c d

45000 200000 70000 70000 150 150 3000 4500 5000 4000 4000 480 480 3000 610

Thickness h (m)

β (o)

Watts ηm

250 35 20 20 30 30 450 600 50 70 70 20 10 150 24

4 4 4 4 4 4 8.95 8.95 5 7.1 4.6 30 30 3 5.1

46 12 86 9 0.6 0.2 17 42 8 12 8 2 2 11 1.4

169 133 47 61 1.9 2.4 66 98 12 14 14 3 1.4 16 3

Murty b (µ = 1%) 174 35 68 11 5 3 64 143 13 27 27 2 0.7 87 6

Refers to Equation 9.14. Refers to Equation 9.2. Refers to Equation 9.15. Estimates derived using ∆z in the right-most column, which is calculated as in the Synolakis and Uslu formula (Equation 9.15).


Synus with ∆z c (µ = 100%)

Modified Murty with ∆z d (µ = 1%)

Modified Bohannon with ∆z d (µ = 100%)

∆z

38 28 20 11 0.6 0.5 20 34 6 9 6 4 3 6 1.4

17 12 8 5 0.3 0.2 8 12 1.4 3 2.3 1.2 0.5 3 0.5

26 14 5 8 1.0 1.2 35 43 5 8 6 8 5 5 1.7

8 8 1 5 0 1 18 14 2 3 2 11 5 1 1


Santa Barbara, CA Kitimat, British Columbia

1900 1900 200 1350 80 160 1600 1250 350 350 350 200 100 300 119

L (m)

Bohannon & Gardner a (µ = 1%)


9-24

TABLE 9.3


9-25

Tsunami and Seiche

9.5 Exact Solutions of the Shallow-Water (SW) Equations To calculate tsunami currents, forces, and run-up on coastal structures and inundation of coastlines one must calculate the evolution of the tsunami wave from the source region to its target. The evolution of waves on beaches is one of the classic problems of coastal engineering. Most practical engineering problems involve directional waveforms with frequency spectra ranging from short to extremely long waves, called infragravity waves, and a number of numerical methods now exist for evaluating their interaction with the coastline. In the last 10 years consensus is emerging that certain terminal effects, such as coastal flooding and inundation, are mainly affected by the infragravity waves. These waves can be described by a certain class of equations known as the shallow-water wave equations (SW), which are also the standard model for tsunamis or tidal waves. The SW equations are approximations of the Navier–Stokes equations (N-S), which describe most incompressible flows. While N-S equation solvers now exist, interest in the SW equations has been rekindled in the last two decades because comparisons with both large-scale laboratory data and field data have demonstrated a remarkable and surprising capability to model complex evolution phenomena, and in particular the maximum run-up. The maximum run-up is arguably the single most important parameter in the design of coastal structures such as seawalls and dikes and for evaluating the inundation potential of tsunamis. Exact solutions of the SW equations are useful in two respects: one for assessing directly the effects of different bathymetric and topographic features and of geometric parameters in the preliminary design of structures, and also for validating the complex numerical models used for final design, which often involve ad hoc assumptions. While elegant 2+1 solutions exist [Kanoglu and Synolakis, 1998], this section only presents certain common 1+1 propagation problems, such as sinusoidal, solitary, and N-waves. The waves evolve over constant depth and then over plane beaches and composite beaches. Even though most results derived for idealized waveforms often used tsunami engineering to describe the leading wave of a tsunami, the generalization to realistic spectral distributions is trivial with the closed-form integrals provided. It should be underscored again that exact solutions are very helpful in validating numerical solutions of the SW equations, and no modeling of any real tsunami should ever be undertaken with any code before comparing its predictions with the benchmark solutions described here. The SW equations describe the evolution of the water surface elevation and of the depth-averaged water particle velocity of waves with wavelengths large compared with the depth of propagation. The equations assume that the pressure distribution is hydrostatic everywhere, i.e., there is no variation with depth of any of the flow variables other than the hydrostatic pressure. One general form of the SW equations is: ht + (uh)x + (vh) y

=0

ut + uux + vu y + ghx = gdx

(9.16)

vt + uv x + vvy + ghy = gd y where h(x,y) is the undisturbed water depth, u and v are the depth-averaged water particle velocities in the cross-shore x and longshore y directions, respectively, η(x,y,t) is the wave amplitude measured with respect to the undisturbed water surface, and g is the acceleration of gravity. These equations are referred to as the 2+1 equations for the independent variables are the two space propagation directions x,y and the time t. The three equations (9.16) are coupled and nonlinear and they can be derived directly from the Navier–Stokes equations, if the viscous effects and vertical accelerations are neglected, or from a Hamiltonian approach [Liu, 1995]. A consequence of the approximations involved is that these equations are nondispersive, i.e., all waves propagate at a speed c = gh( x , y ) that only depends on the depth h(x,y). Note that the coriolis effect can be trivially added in Equation 9.16, when needed.



9-26


t*= t*max

* t=0 H

y*

R

x* d

L

X*= X*1

INITIAL SHORELINE POSITION X*= 0

β X*= X*0

FIGURE 9.11 Definition sketch for shallow-water wave theory.

9.5.1 Basic Equations and Solutions of the 1+1 or Two-Dimensional Equations The so-called canonical problem of the SW equations is the calculation of a long wave climbing up a sloping beach coupled to a constant depth region. This topography consists of a plane sloping beach of angle β, as shown in Figure 9.11. The origin of the coordinate system is at the initial position of the shoreline and x˜ increases seaward. Dimensionless variables are introduced as follows: ˜ = ηd, u˜ = u gd , and t˜ = d g x˜ = xd, h˜0 = h0d, η

(9.17)

where η u h0 d

= = = =

the amplitude the depth-averaged horizontal velocity the undisturbed water depth the depth of the constant-depth region

The topography is described by h0(x) = x tan β when x ≤ cot β and h0(x) = 1 when x > cot β. Even though in engineering practice dimensionless variables are not preferred, here they have distinct advantages as everything scales simply with an offshore characteristic depth. Note that with this normalization (nondimensionalization) the dimensionless frequency ω is equal to the dimensionless wave number k. To see ˜ = ck ˜˜, and ω ˜ =ω ˜ g d , while k˜ = k d . For this reason, in analytical this, note that in dimensional terms, ω solutions ω and k are sometimes used interchangeably. In numerical solutions, dimensional variables are most often used. Consider a tsunami evolution problem described by the 1+1 nonlinear form of the SW (NSW) equations (9.16): ht + (uh)x

=0

ut + uux + ηx = 0

(9.18)

with h(x,t) = η(x,t) + h0(x). By examination, it is clear that nonlinear effects are small when the surface ηx and velocity gradients ux are small; however, the propagation distances in x over which these nonlinear effects manifest themselves to affect the results or how they are affected is not clear a priori.

9.5.2 Linear 1+1 Theory The NSW system (Equation 9.18) can be linearized by retaining the first-order terms only, resulting in the following set of equations. First, let h0(x,t) = h0(x). Then the NSW equations reduce to the linear set: © 2003 by CRC Press LLC


9-27

Tsunami and Seiche

ηt + (uh0 )x = 0 ut + ηx

=0

(9.19)

It is easy to eliminate u(x,t) and derive the following u(x,t)-independent equation in terms of η(x,t): ηtt − ( ηx h0 )x = 0

(9.20)

an equation referred to as the LSW equation. For constant depth h0(x,t) = d0, Equation 9.19 takes the form: ηtt − ηxx = 0

(9.21)

This is the classic one-dimensional wave equation, with solutions that can be written either as combinations of sine and cosine functions or of exponentials. The exponential functions are particularly useful as eigenfuctions in this problem, and thus one can write the entire solution for the amplitude η(x,t) = Ai e –iω(x+t) + Ar e iω(x–t) when h0(x) = 1. Ai is the amplitude of the incident wave and Ar is the amplitude of the reflected wave. Note the difference in sign in the arguments of the exponentials. The phase ω(x + t) indicates a wave moving towards the negative x direction, i.e., towards the beach, while the phase ω(x – t) indicates a wave moving in the positive x direction, i.e., offshore. (Recall that dimensionless variables are used, and since in this non-dimensionalization the dimensionless c = 1, and then ω = k.) When the depth is linearly and monotonically decreasing to zero, h0(x) = x tan β, i.e., for a sloping beach, Equation 9.20 becomes: ηtt − tan β ( xηx )x = 0

(9.22)

with the following finite-at-the-shoreline solution:

(

)

η( x , t ) = B (ω, β) J 0 2ω x cot β e − iωt −φ when h0 ( x ) = x tan β

(9.23)

J0 is the Bessel function of the first kind. Bessel functions are built into symbolic manipulator programs such as MATHEMATICA or MATLAB and exist in most FORTRAN subroutine libraries such as IMSL. Tables of Bessel functions can be found in Abramowitz and Stegun [1964]. B(ω,β) is referred to as the amplification factor, not to be confused with the arbitrary fudge factor sometimes used to match tsunami field data with numerical predictions from threshold-type models that interrupt the computation at the 10-m contour to avoid inundation calculations, the latter only euphemistically also called the amplification factor. Titov and Synolakis [1997] discuss these models and their limitations. These basic solutions can be combined to derive solutions specific to topographies that are combinations of a constant depth and a sloping beach. To this end, Keller and Keller (1964) presented a steadystate solution for the canonical model of Figure 9.11, simply by deriving interface conditions at x = cot β to match the inner and outer beach solutions, (x < cot β) and (x > cot β), respectively. The resulting equations allow simple algebraic solutions for the two unknowns, i.e., the amplitude of the reflected wave Ar and the shape of the transmitted wave ηt in terms of the incident wave height Ai. For an incident wave, Ai cos (kx − ωt), written for convenience as Ai cos[ω(x − t)] since ω = k, then the wave transmitted to the beach and the reflected wave moving offshore are given by: ηt ( x , t ) = 2 Ai B(ω, β) cos (ωx − ωt − 2 ω cot β + φ) © 2003 by CRC Press LLC

(9.24)


9-28


where  J (2ω cot β)  φ (ω, β) = arctan  1   J 0 (2 ω cot β) 

(9.25)

and J 02 (2 ω cot β) + J12 (2 ω cot β)

(9.26)

ηr ( x , t ) = Ai cos (ωx − ωt − 2 ω cot β + 2 φ)

(9.27)

B (ω, β) = 1 and

Note that the reflected tsunami amplitude is equal to the incident amplitude, but there is a phase shift φ that is both frequency ω and beach slope β dependent. Any combination of sinusoidal waves approaching the beach will reflect with a combined amplitude that will in general be different from the combined incident amplitude of the combination. This property cannot be underscored strongly enough, as many coastal engineers consider the reflected amplitude of spectra of long waves as equal to the incident amplitude, just relying on the monochromatic wave results. This is not true, and can lead to erroneous results when calculating run-up.

9.5.3 Exact Solutions of the LSW Boundary Value Problem Since the governing equation (9.20) is linear and homogeneous, then, as Stoker (1947) pointed out, standing wave solutions can be used to obtain traveling wave solutions by linear superposition. This is an important detail, often ignored; many have relied on numerical solutions to solve the problem above, which is easily solvable by old-fashioned integration. At least for the canonical problems and other simple topographies and for well-defined tsunami spectra, a numerical solution of the field equation is unnecessary. When a boundary condition for the wave amplitude η(x0,t) is specified, the solution follows directly from the Fourier transform of the equation. For example, when the incident wave at the constant depth region is known at some x = x1, and can be described by a Fourier integral of the form: η( x1 , t ) =

∫

∞

−∞

Φ (ω ) e − iωt

(9.28)

then the transmitted wave to the sloping beach is given by: η( x, t ) = 2

∫

∞

−∞

Φ (ω )

(

)

J 0 2ω x cot β e

− iω ( x0 +t )

J 0 (2ω cot β) − iJ1 (2 ω cot β)

dω

(9.29)

with the understanding that for all physical problems of engineering interest, one takes the real part of the integral. In other words, the real part is: η( x, t ) = 2

∫

∞

−∞

Φ (ω )

(

)

J 0 2ω x cot β cos (ωX 0 + ωt + φ) J (2 ω cot β) + J12 (2 ω cot β) 2 0

dω

(9.30)

This solution is only valid when x ≥ 0; when x < 0, Equation 9.20 does not reduce to Bessel’s equation. To obtain details of the wave motion in this case, one must solve the NSW (Equation 9.18). Notice that



9-29

Tsunami and Seiche

the integral (Equation 9.30) can be evaluated with standard numerical methods. However, the advantage of this form is that it allows calculation of the solution for many physically realistic tsunami waveforms simply by plugging in the Φ(ω) of the incoming wave, hopefully known at some offshore location x1.

9.5.4 Nonlinear 1+1 Theory To solve the nonlinear set (Equation 9.18) for the sloping beach case, h0(x) = x tan β, Carrier and Greenspan [1958] introduced the hodograph transformation, u = ψ σ , into Equation 9.18, and they σ derived the following equation:

(σψ )

σ σ

= σψ λλ

(9.31)

Notice the similarity with the linear form of the SW equation, (ηx h0)x = ηtt. Also, notice the conservation of difficulty. Instead of having to solve the coupled nonlinear set (Equation 9.18), one now has to solve a linear equation, but the transformation equations that relate the transformed variables with the physical variables: u=

ψσ σ

(9.32)

 σ2 ψ λ u2  x = cotβ  − +  4 2  16

(9.33)

ψ λ t = cotβ  σ −   σ 2

(9.34)

η=

ψ λ u2 − 4 2

(9.35)

are nonlinear, coupled, and implicit. Yet, a redeeming feature is that in the hodograph plane, i.e., in the (σ,λ) space the shoreline is always at σ = 0. This allows for direct analytical solutions and for much simpler numerical solutions, without the complications of the moving shoreline boundary. In general, it is quite difficult to specify initial or boundary data for the nonlinear problem in the physical space coordinates (x,t) without making restrictive assumptions; a boundary condition requires specification of the solution at (x0, ∀t), and an initial condition specification at (t0, ∀x), but, in practice, the wave approaching the beach is only known offshore for (x0 ≥ cot β, t < t0), where t0 is the time at which the wave reaches the x location X0. Even when boundary or initial conditions are available in the space, the process of deriving the equivalent conditions in the space is not trivial. These difficulties have restricted the use of this transformation to problems that can be reduced directly to those solved by Carrier and Greenspan [1958]. Synolakis [1986] revived the Carrier and Greenspan formalism by developing a method to specify a boundary condition including reflection. He used the solution of the equivalent linear problem, as given by the transform integral (Equation 9.30), at the seaward boundary of the beach, i.e., at x = x0 = cot β corresponding to σ = σ0 = 4. Then, Equation 9.35 implies that η(X 0 , t) = 1/4 ψλ (4, λ). Assuming that ψ(σ0, λ) → 0 as λ → ±∞, then Synolakis [1987] showed that the Carrier and Greenspan potential is given by:  λ − iκx0  1− 

 2 Φ(κ ) J 0 (σ κx 0 2) e 16i dκ ψ ( σ, λ ) = − x 0 −∞ κ J 0 (2 κx 0 ) − iJ1 (2 κx 0 )

∫


∞

(9.36)


9-30


where the substitution κ = 2/x0 k˜ was used for simplification. Recall also that with the normalization used x0 = cot β. An astonishing feature of the NSW is that the predictions for the maximum run-up are identical to those of the LSW, when identical boundary conditions are specified at x = cot β. The maximum run-up according to LSW is the maximum value attained by the wave amplitude at the initial position of the shoreline, while the maximum run-up is given by the maximum value of the amplitude at the evolving shoreline η(xs,λ), where xs is the x coordinate of the shoreline tip and corresponds to σ = 0. Carrier [1966] and Synolakis [1987] have shown that the linear and nonlinear theory produce mathematically identical predictions. Carrier and Greenspan’s transformation of coordinates suggests a criterion for validity of the exact nonlinear theory solutions, based on the regularization of the Jacobian of the transformation from the (x, t) space to the (σ, λ) space. After some algebra, this criterion translates into:

(

J = c t σ2 − t λ

2

)

(9.37)

and for monochromatic waves: 2 Ai ω 2 cot 2 β ≤ 1

(9.38)

This criterion is often referred to as the breaking criterion and indicates whether solutions become multivalued, in analogy to physical wave breaking. As Meyer [1988] pointed out, it is only a criterion of validity of the Carrier and Greenspan transformation.

9.5.5 The Solitary Wave Solutions Solitary waves have long been used as a model for the leading wave of tsunamis. Solitary waves were first described by Scott-Russel [1833] as the great waves of translation, and consist of a single elevation wave. While capturing some of the basic physics of tsunamis, they do not model the physical manifestation of tsunamis in nature, which are invariably N-wave-like, with a leading depression wave followed by an elevation wave. A solitary wave centered offshore at x = x1 at t = 0 has the following surface profile: η( x ,0) = H sech 2 γ ( x − x1 )

(9.39)

where γ = 3H 4 . The function Φ(k) associated with this profile is derived in Synolakis [1986] and it is given by: 2 Φ (k ) = ω cosech (αω ) e iωx1 3

(9.40)

where α = π/(2γ). In the context of water-wave theory, the solitary wave (Equation 9.39) is an exact solution of the Korteweg–de Vries (KdV) equation, therefore a KdV solitary wave propagates over constant depth with no change in shape. The KdV theory is both dispersive and nonlinear, and solitary waves are the only waves with this unique property of unchanging shape. However, Equation 9.39 can be used as an initial condition for other wave theories, without, of course, the a priori expectation that the SW model will preserve the classic soliton properties, which include their ability to go through each other (interact in mathematical lingo) without any change in shape through nonlinear interactions. This having been said, since the LSW is nondispersive and linear, and hence all waves propagate over constant depth with no change in shape, in the range of wave steepness and amplitudes relevant for tsunamis, it is now well established that, at least for the 1+1 problem far from the shoreline, the LSW theory, which also preserves the wave shape for propagation over constant depth, is quite adequate [Liu et al., 1991], and useful when the engineering problem has simple geometry. © 2003 by CRC Press LLC


9-31

Tsunami and Seiche

9.9.6 The Evolution of Solitary Waves The derivation of the amplitude evolution for solitary waves is not as straightforward as often assumed. The wave is not of the form convenient for Green’s [1832] or Lamb’s [1932] style of evolution analysis, because the amplification factor (Equation 9.26) depends on the frequency ω, and there is a ω-dependent phase shift. It is therefore not obvious that linear superposition will produce a similar amplitude variation given this frequency-dependent phase shift. To describe the evolution of a solitary wave up a plane beach, Synolakis [1986, 1987] substituted Equation 9.40 into Equation 9.30 to obtain: η( x, t ) =

4 3

∫

∞

−∞

ω cosech (αω )

(

)

J 0 2 ω xx 0 e

− iω ( x0 − x1 +t )

J 0 (2 x 0ω ) − iJ1 (2x˜0ω )

dω

(9.41)

where, as earlier, α = π 3H . As per Synolakis [1988, 1989], this integral can be evaluated directly through contour integration. In the region where the wave evolves as it is climbing up a sloping beach, x is large, and Equation 9.41 becomes: η( x, t ) =

4π 2  x0    3α 2  x 

1/ 4

∞

∑ (−1)

ne − ( π/α ) θ′n

n+1

(9.42)

n=1

θ′ = X 0 − X1 − t − 2 xx 0 The maximum of the power series is 1/4 ; therefore, the maximum local value of the wave amplitude ηmax is given explicitly by: ηmax  x 0  =   x H

1/ 4

1 =   h0 

1/ 4

(9.43)

This is an amplitude variation similar to Green’s law. The region over which Equation 9.43 applies is the region of gradual shoaling; the region of rapid shoaling is often identified with the Boussinesq result, i.e., ηmax ∼ h. The fact that both evolution laws may coexist was first identified by Shuto [1972]. Synolakis and Skjelbreia [1993] also present results that show that Green’s law-type evolution is valid over a wide range of slopes and for finite-amplitude waves, at least in the region of gradual shoaling. Figure 9.12 shows profiles of an H/d = 0.02 solitary wave climbing up a 1:19:85 beach and compares laboratory data with the analytical NSW predictions of Synolakis [1986, 1987].

9.5.7 The Maximum Run-Up of Solitary Waves The results of the previous section can now be readily applied to derive a result for the maximum runup of a solitary wave climbing up a sloping beach. Writing R(t) = η(0,t), i.e., R(t) is the free-surface elevation at the initial shoreline; in the LSW theory, the shoreline does not move beyond x = 0. The maximum value of R(t) is the maximum run-up R, arguably the most important parameter in the longwave run-up problem, and it is the maximum vertical excursion of the shoreline at the time instant of maximum run-up. According to Synolakis [1986], from Equation 9.41, it can be deduced that: R(t ) = 8 H

∞

∑ I (4γx n) + I (4γx n) n=1


(−1)n+1ne −2γ ( x −x −t ) n 1

0

0

1

0

0

(9.44)


9-32


0.04 (a) 0.02

η 0

0.02

2

0

2

4

6

8

10

12

14

16

18

20

0.04

η

(b) 0.02

0 0.02 2

0

2

4

6

8

10

12

14

16

18

20

0.04 (c) 0.02

η 0

0.02

2

0

2

4

6

8

10

12

14

16

18

20

0.04 (d) 0.02

η 0 0.02 2

0

2

4

6

8

10

12

14

16

18

20

χ 0.08 (e)

0.06

η

0.04 0.02 0 0.02

2

0

2

4

6

8

10

12

14

16

18

20

0.08 (f)

0.06

η

0.04 0.02 0 0.02

2

0

2

4

6

8

10

12

14

16

18

20

FIGURE 9.12 The climb of a H/d = 0.02 solitary wave up a 1:19.85 sloping beach. Normalized free surface profiles shown at different times.



9-33

Tsunami and Seiche

0.10 (g)

0.08 0.06

η

0.04 0.02 0 0.02

2

0

2

4

6

8

10

12

14

16

18

20

0.10 (h)

0.08 0.06

η

0.04 0.02 0 0.02

2

0

2

4

6

8

10

12

14

16

18

20

0.06 (i)

0.04

η

0.02 0 0.02 0.04

2

0

2

4

6

8

10

12

14

16

18

20

0.06 (k)

0.04

η

0.02 0 0.02 0.04

2

0

2

4

6

8

10

12

14

16

18

20

FIGURE 9.12 (CONTINUED)

The series can be simplified further by using the asymptotic form for large arguments of the modified Bessel functions. The resulting series is of the form

∑

∞

n=1

(−1)n+1n3/2χn

Its maximum value occurs at χ = 0.481 = e−0.732. This value defines the time tmax, when the wave reaches its maximum run-up. At tmax the maximum of the series smax = 0.15173. Defining as R the maximum value of R(t), and evaluating the term: 8 π 3 s max , then the following expression results for the maximum run-up: 5

R = 2.831 cotβ H 4

(9.45)

This result is formally correct when H >> 0.288 tan β — the assumption implied when using the asymptotic form of the Bessel functions. Equation 9.45 was first derived by Synolakis [1987] and has since been referred to as the run-up law. As will be apparent in later sections, this methodology to find the maximum run-up is quite powerful and it will allow calculation of the run-up of other waveforms such as N- or dipole waves, not to mention the run-up of waves evolving over piecewise linear bathymetries. © 2003 by CRC Press LLC


9-34


THE MAXIMUM RUNUP OF SOLITARY WAVES CLIMBING UP A 19.85 BEACH

1 6 5 4 3

R/d

2

nonbreaking waves breaking waves asymptotic solution

0.1 6 5 4 3 2

0.01 0.001

2

3

4 5 6

0.01

2

3

4 5 6

0.1

2

3

4 5 6

1

H/d

FIGURE 9.13 Normalized solitary wave run-up on a 1:19.85 beach as a function of the normalized off-shore height.

Recent results suggest that the dependence of the run-up on the slope and on the offshore wave height in two-dimensional problems of idealized conditions is often quite similar to this one-dimensional power law. Maximum run-up data for breaking and nonbreaking solitary waves of different heights and propagating over a wide range of depths on a 1:20 laboratory beach are presented in Figure 9.13. The parameter H in the ordinate represents the maximum normalized wave height measured at a distance L from the toe of the beach, where L is one measure of the horizontal extent of the wave. Here L = (1/γ ) arccosh ( 1 / 0.05 ), where again γ = 3H / 4 . In essence this is the distance offshore from the toe of the beach to the crest of the wave, so that the wave height over the toe is 5% of the maximum wave height. Since Synolakis [1987], this measure is the standard referencing distance for specifying the height of a solitary wave at the toe of a sloping beach [Kobayashi et al., 1987; Briggs et al., 1993, 1994, 1995]. Thus, heights of longer solitary waves are defined from measurements further from the beach than those of shorter waves, assuring that all waves propagated through the same relative distance L between the measurement location and the toe of the beach. Figure 9.13 shows two distinct run-up regimes for breaking and nonbreaking waves. Breaking on the laboratory beach occurs first during the backwash when H > 0.044; breaking during run-up occurs when H > 0.055. The existence of these two different run-up regimes in single-wave run-up had never been observed before the original publication of Figure 9.13. One possible explanation is that most experimental investigations have dealt primarily with breaking solitary waves and, even when nonbreaking wave data were generated, they were grouped together with breaking wave data for the purpose of deriving empirical relationships. The asymptotic result (Equation 9.45) is valid for waves that do not break during run-up, suggesting that it is appropriate to use the qualifier “nonbreaking” for waves that do not break during run-up but may or may not break during rundown. The real usefulness of any asymptotic result is how well it identifies the scaling, i.e., if it can identify how the solution depends on the problem parameters; numerical solutions will invariably produce more accurate specific predictions, but they can rarely provide useful information about the problem scaling. To check if the run-up law (Equation 9.45) provides the correct scaling, Synolakis [1986, 1987] examined the classic laboratory data set of Hall and Watts [1953]. That study includes both breaking and nonbreaking wave data without identifying them as such, clearly because there was no realization of the differences. The empirical run-up relationships derived by Hall and Watts (1953) are not directly applicable when © 2003 by CRC Press LLC


9-35

Tsunami and Seiche

THE MAXIMUM RUNUP OF NONBREAKING WAVES CLIMBING DIFFERENT BEACHES

10

1

1:30 1:20 1:11.43 1:5.671 1:3.732 1:2.747 1:2.144 1:1 runup law

R/d

4

2

0.1 8 6 4

2

–0.01 2

0.01

4

6

8

2

4

6 8

0.1

2

4

6

1

8

10

5.4

2.831 cot β (H/d)

FIGURE 9.14 Normalized wave run-up on a single beach as a function of the run-up law.

determining the run-up of nonbreaking waves. To perform an a posteriori identification of those data, the breaking criterion H < 0.49 (cotβ)–10/9 was used; this criterion is discussed in the next section. Figure 9.14 presents all the nonbreaking solitary wave data from that and from two other studies. The asymptotic result does seem to model the existing laboratory data satisfactorily. Most importantly, it does seem to collapse all the nonbreaking Hall and Watts data into the same curve; not identifying the correct scaling led Hall and Watts to report their data in plots of R vs. H, individually for different beach slopes.

9.5.8 The Validity of the Solitary Wave Solutions Any change of variables is valid if the Jacobian remains regular; any solutions of the type shown in Equation 9.41 are valid for functions Φ(k) such that the Jacobian is never equal to zero, i.e., when Equation 9.37 is regular. The Jacobian becomes singular when the solution is multivalued, i.e., when the surface slope ∂η/∂x becomes infinite. In the (x,t) space, this point is often interpreted as the point of wave breaking. After elementary manipulations and asymptotic expansions as σ → 0, the Jacobian becomes: 1  J → cot 2 β 4  uλ −   2

(


)

2


9-36


The limiting H when uλ − 1 goes through zero is: 2 H < 0.8183 (cotβ)

−

10 9

(9.46)

This is a weaker restriction than that derived by Gjevik and Pedersen [1981], who determined that solitary-like waves do not break if H < 0.479(cotβ)–10/9. However, there are two basic differences between the two results. The Gjevik–Pedersen criterion suggests a limiting H for solitary wave breaking during the backwash. Equation 9.46 indicates when a wave first breaks during run-up. It is not surprising, therefore, that the former is a stronger criterion, since long waves that do not break during run-up may break during rundown. Also, the Gjevik–Pedersen result was derived by using the sinusoidal wave whose one cycle best fits the Boussinesq profile (Equation 9.39), while Equation 9.46 is based on the actual KdV profile. Equation 9.46 still remains — 10 years after it was derived — the only analytic criterion for determining the breaking of solitary waves on plane beaches. In terms of real tsunamis, Equation 9.46 provides an upper limit for checking whether the tsunami will break on any given beach or seawall. Tsunamis are N-waves that tend to be steeper than solitary waves and thus break at smaller heights.

9.5.9 The N-Wave Results Most tsunami eyewitness accounts suggest that tsunamis are N-wave-like, i.e., they are dipolar, which means they appear as a combination of a depression and an elevation wave, and frequently as a series of N-waves, sometimes known as double-N-waves [Tadepalli and Synolakis, 1994]. Up until recently, the solitary wave model was used exclusively to evaluate the run-up of tsunamis. The N-wave model was motivated by observations from earthquakes in Nicaragua (September 1, 1993); Flores, Indonesia (December 12, 1992); Okushiri, Japan (July 7, 1993); East Java, Indonesia (June 6, 1994); Kuril Islands, Russia (October 4, 1994); Mindoro, Philippines (November 14, 1994); Manzanillo, Mexico (October 9, 1995); Chimbote, Peru (March 3, 1996); Papua New Guinea (July 17, 1998); Vanuatu (November 26, 1999); and Caminade, Peru (June 20, 2001), all of which produced tsunami waves that caused nearby shorelines to first recede before advancing. The most specific description was during the October 9, 1995 Manzanillo, Mexico earthquake. One eyewitness saw the shoreline retreat beyond a rock outcrop, which was normally submerged in over 5 m depth and at a distance of about 400 m from the shoreline, suggesting a leading depression wave. A photograph of Manzanillo bay emptying, taken by the same eyewitness, is shown in Figure 9.15A. Figure 9.15B shows the 2 m (6.6 ft) tsunami climbing up the central square in La Manzanilla. Modeling tsunamis with solitary waves cannot possibly explain these observations, because a solitary wave is a leading elevation wave. Therefore, and to reflect the fact that tsunamigenic faulting in subduction zones is associated with both vertical uplift and subsidence of the sea bottom, Tadepalli and Synolakis [1994] conjectured that all tsunami waves at generation have an N-wave or dipole shape. Tadepalli and Synolakis [1994, 1996] proposed a general function as a unified model for near-shore, far-field, and landslide tsunamis, as follows:

[

]

η( x ,0) = ( x − x 2 ) ε Hsech 2 γ ( x − x1 )

(9.47)

Here γ = 3 H p0 4 , L = X1 – X2, p0 is a steepness parameter, and ε < 1 is a scaling parameter defining the crest amplitude, introduced only for reference to ensure that the wave height of the wave in Equation 9.47 is H. Note that X1 and X2 are analogous to Xmin and Xmin + ∆X in Figure 9.10. ε can be chosen to fit desired field-inferred surface profiles. H and the wavelength of the profile inferred from Equation 9.47 are vertical and horizontal measures of ground deformation, respectively. When a wave propagates with the trough first it is referred to as a leading depression N-wave or LDN. When the crest arrives first, it is a leading elevation wave or LEN. When the crest and trough heights are equal, these



9-37

Tsunami and Seiche

N-waves are referred to as isosceles; the latter can be described by Equation 9.47 by setting L = 0, or more directly with: η ( x , 0) =

[

]

[

]

3 3H sech 2 γ ( x − x1 ) tanh γ ( x − x1 ) 2

(9.48)

with γ=

3 2

3 H 4

The basic premise of the N-wave model is that the leading waves of tsunamis at generation are always N-wave-like. When tsunamis are generated near shore — typical distances from near-shore subduction zones to target coastline are of the order of 100 to 300 km — then the tsunami invariably manifests itself with a leading N-wave (refer to Figure 9.7). Even when generated far-field, the leading wave manifestation at the shoreline is always N-wave-like, because of the leading wave height and steepness, typically both of O(10–3) to O(10–4). Landslide tsunamis are always N-wave-like at generation, but are much steeper than corresponding tectonic tsunamis of the same height; hence, they disperse rapidly and are hardly detectable far-field. While the SW equations are useful when specifying initial conditions on the free surface, when considering the effects of an evolving seafloor, the derivation of the SW equations changes, and a forcing term appears on the right-hand side of the equations of conservation of momentum. The forced LSW takes the form: ηtt − ηxx = h0tt

(9.49)

Consider the following seafloor motion, which literally rips the seafloor by propagating an uplift and a subsidence in the positive x direction at constant speed equal to the speed of the generated tsunami waves:

[

]

h0 ( x , t ) = − (2ε H γ ) tanh γ ( x − t )

(9.50)

h0(x,t) is measured from horizontal data. Most submarine earthquakes are bipolar or multipolar, with regions of sudden uplift and subsidence. The ground deformation stops quickly after the rupture and does not propagate indefinitely as the definition of Equation 9.50 suggests. Also, in most cases of tectonic tsunamis, the seafloor motion is much faster than the speed of the tsunami waves; hence, the deformation can be considered instantaneous. Nonetheless, Equation 9.50 is sufficient to motivate the shape of the initial profile (Equation 9.47), which is one particular and exact solution of the nonhomogeneous problem (Equation 9.49). An earlier misconception in tsunami engineering had been that most tsunamis were solitary waves. This was based on a mathematical theory known as inverse scattering, which predicted that all waveforms with positive net volume would evolve into series of waves with at least one soliton at infinity. This had been a particularly useful theory because it allowed engineers in principle to ignore the evolution details, then difficult to calculate anyway. From estimates of the initial wave, engineers would calculate the height of the leading solitary wave that would involve far-field, taken to be infinity, and thus estimate the impact of the tsunami at distant shores. While mathematically sound, in the context of tsunami engineering the theory was abandoned when Tadepalli and Synolakis [1996] showed that LDN waves with initial heights of 0.0001 were practically unchanged after propagating over 2000 depths, suggesting that the wave propagation is essentially linear and nondispersive, i.e., no leading solitons emerge in the range of wave heights and steepness and propagation distances of geophysical interest. The fact that LDN waves are stable over transoceanic propagation distances explains why the waves that struck Hawaii after the Alaskan 1946 and Chilean 1960 events may have been LDN waves, as reported by eyewitnesses. © 2003 by CRC Press LLC


9-38


FIGURE 9.15A Tenacatita Bay during the leading depression N-wave of the 1995 Manzanillo tsunami. Shown as Color Figure 9.15A.

9.5.10 Evolution and Run-Up of N-Waves Tadepalli and Synolakis [1996] show that N-waves evolve according to Green’s law (Equation 9.43), whether leading depression or leading elevation. Introducing φ = θ + 2X0, and performing tedious contour integrations, the maximum run-up of the generalized N-wave (Equation 9.47) is found, for LDN waves, to be: 5

R=4

1

3 πεQ ( L, γ ) cot β H 4 p04 .

(9.51)

This is valid for large 4x0γ, and for H < Hbr for LDN waves. This expression is valid for a wide range of L and it can be rewritten in terms of the maximum run-up of the Boussinesq solitary profile Rsol as 1 R = 3.3 εp 04 QRsol. It is reassuring that this expression is asymptotically close to the run-up law for solitary waves (Equation 9.45); in the asymptotic limit solitary waves profiles are almost identical to the N-waves (e.g., L = 30 and ε = 0.032). Another type of N-wave of this class exists, with leading elevation and depression waves of the same height and at a constant separation distance. Tadepalli and Synolakis [1996] refer to this wave as an isosceles N-wave with a surface profile given by Equation 9.48. This wave profile is an LDN and has a maximum wave amplitude H. Using contour integration to evaluate the maximum of RT = η(9,t), one can find that: 1

R Nwave = 3.86 (cot β) 2 H 5/ 4

(9.52)

Comparing the run-up of a solitary wave (Equation 9.45) with the run-up of an isosceles N-wave, RNwave = 1.364Rsol. Because of the symmetry of the profile, this is also the minimum rundown of an isosceles leading depression N-wave. Tadepalli and Synolakis [1996] show that the normalized maximum run-up of nonbreaking isosceles LEN is smaller than the run-up of isosceles LDN, and that both are higher than the run-up of a solitary wave with the same wave height; the latter is known as the N-wave effect. Comparing the time of maximum run-up for a solitary wave to that of an N-wave, one finds that:

(t max )solitary wave − (t max )N−wave = 0.γ201 = 0.232 H s


(9.53)


9-39

Tsunami and Seiche

FIGURE 9.15B The 1995 Manzanillo tsunami advancing on la Manzanilla. By the time the bottom photo was taken, the wave had already advanced about 100 m. Eyewitnesses reported that the wave advanced as fast as people could run. Shown as Color Figure 9.15B.

Interestingly, a nonbreaking isosceles LEN reaches the shoreline earlier than a solitary wave of the same offshore wave height, and the time lag is larger for the smaller waves. The maximum run-up of LEN isosceles waves is given by: 1

5

R = 3.041 p04 cot β H 4

(9.54)

and the maximum run-up of isosceles LDN is given by: 1

5

R = 5.48 p04 cot β H 4 © 2003 by CRC Press LLC

(9.55)


9-40


Nic. Profile N–wave

1 0.5

η

(m) 0 –0.5 1 0

20

40

60 x (km)

80

100

120

FIGURE 9.16 Comparison of the initial wave of the 1992 Nicaraguan profile as calculated using MOST and fitted with a leading depression N-wave.

The earlier stipulations regarding the interpretation of the Jacobian regularization condition not withstanding, Tadepalli and Synolakis [1996] also derived the breaking criteria for isosceles N-waves. The limiting values for the applicability of this theory for isosceles LENs and H– for isosceles LDNs are: H + = 0.1660 (cot β)

−10/9

, and H − = 0.1623 (cot β)

−10/9

(9.56)

Note that LDN and LEN waves break earlier than the equivalent solitary waves of the same offshore height. The two-dimensional character of the generation region limits the direct application of the N-wave and solitary wave models. However, N-wave theory does provide a conceptual framework for analysis and for explaining certain field observations qualitatively. In this regard, it is intriguing to perform simple calculations using the model to model the Nicaraguan topography. One segment of the Pacific coastline of Nicaragua is a 73-km (45-mi) long, almost uniform plane beach slope of cot β = 33.18, fronted by a 200-m (666-ft) deep continental shelf. This simplicity has allowed the use of two-dimensional numerical shoreline models coupled with three-dimensional offshore propagation models to calculate the run-up and inundation. Figure 9.16 shows a comparison between the numerically generated surface profile for the Nicaraguan tsunami with an N-wave, at the time when the wave reaches the toe of the beach, as calculated by Titov and Synolakis [1993]. The measured-average and numerically computed maximum run-up values were 6 ± 2 m (20 ± 6.6 ft), while the run-up laws predict 3.5 m (11.6 ft), a satisfactory result given the uncertainties in initial conditions and topographic resolution.

9.5.11 1+1 Wave Run-Up on Composite Beaches The methodology developed in the previous sections for wave run-up on a sloping beach can be generalized to study tsunami run-up over more generalized topography. A common practical problem is the determination of the run-up of a tsunami propagating over fairly complicated bathymetry before reaching the shoreline, such as a constant depth region fronting a steep continental shelf, which then slopes gently to the coastline, or a beach and then a seawall. Shaw [1974] studied several problems of this nature, while Goring [1978] studied wave transmission over a slope between two constant depth regions. Neu and Shaw [1987] examined the filtering action of a submerged seamount, a trench slope-shelf system and the effect of a continental slope-shelf system. All these studies used sinusoidal waves, and despite the physical interest of the problem, no analytical results appropriate for asymptotic analysis existed until Kanoglu [1996]. Most topographies of engineering interest can be approximated by piecewise linear segments allowing the use of LSW to determine approximate analytical results for the wave run-up of more complicated waveforms, in closed form. To motivate the problem, consider the continental slope and shelf topography studied by Neu and Shaw [1987], shown in Figure 9.17, which is also a definition sketch for this section.



9-41

Tsunami and Seiche

X 3

2

1

∇ h1 m1 h3

h2 m2 2

x1 x2

FIGURE 9.17 Definition sketch for wave run-up on a composite beach.

There are three regions, and two possible choices for the characteristic length scale for normalization of the variables. Here the depth h2 of the constant depth region three is used for non-dimensionalization. By inspection, the solution for the wave height η(x,t) in the three regions is given by:

(

)

η( x , t ) = BJ 0 2 ω h1 / m1 e − iωt when 0 < x < x1

(9.57)

  2ω h2   2ω h2   − iωt η ( x , t ) =  K1 J 0  when x1 < x < x 2  + K 2Y0   e  m2   m2   

(9.58)

and

{

η( x , t ) = η( x , t ) = Aie

− iωx / h3

+ Ar e

iωx / h3

}e

− iωt

when x 2 < x

(9.59)

Only the incident wave height Ai is known a priori. To determine B, K1, K2 , and Ar, matching conditions for the amplitude and surface slope at the two interface points x1 and x2 are used, and this results in a system of four equations in four unknowns, written in matrix form as:   2ω h  1 J0     m2     2 ω h1    J1    m2      J 2 ω h2   0  m2      2ω h  2  J1   m   2  

 2 ω h1  Y0    m2   2 ω h1  Y1    m2   2 ω h2  Y0    m2   2 ω h2  Y1    m2 

0

0 iωx2

−e

h3

iωx2

ie

h3

 2ω h1   J0    m1     2ω h1   J1    m1     0     0  

 0  K1       0  K iωx2 2   =  − A  Ar  e h3  i    − iωx2  h3  B   e

(9.60)

In a similar fashion one can build equivalent matrices for any reasonable piecewise linear topography. © 2003 by CRC Press LLC


9-42


In most engineering applications, the problem would be considered solved and numerical matrix inversion would provide solutions for the four unknowns. However, with numerical solutions it is not simple to visualize the parameter dependence of R on the individual slopes m1 and m2 and on the transition depth h1. Alternatively, the problem can be solved in analogy to geometric optics. When solving for the magnification of an optical system, individual refracting surfaces are represented by 2 × 2 matrices. Gerrard and Bunch [1987] developed a methodology for explicit evaluation of the focal length of an optical system with n refractive surfaces. Kanoglu [1996] and Kanoglu and Synolakis [1998] developed a formulation to determine the amplification of a tsunami evolving piecewise linear topography by representing the wave evolution over each segment by 2 × 2 matrices, as follows. Kanoglu (1996) associated each constant depth region of depth hr with the matrix:  − iω x p hr  Dpr =  e iω x p −  hr ie

  iω x p  h  −ie r  iω x p hr

e

(9.61)

He associated each linearly varying depth region with positive slope mr with the matrix:

( (

J 2ω h / m p r 0 S pr+ =   J 2ω h / m p r  1

) )

( (

) )

Y0 2 ω hp / mr   Y1 2 ω hp / mr  

(9.62)

and each linearly varying depth region with negative slope (negative mr) with:

( (

) )

 J 2ω h / | m | p r 0 S pr− =  − J 2 ω h / | m | p r  1

( (

) )

Y0 2 ω hp / | mr |   −Y1 2 ω hp / | mr |  

(9.63)

The superscripts in the expressions for the Spr matrices are used to emphasize the differences between positively and negatively sloping regions; in the nomenclature henceforth they will be dropped, with the understanding that either Equation 9.62 or Equation 9.63 will be used, depending on the sign of mr . Notice also, that in Equations 9.61, 9.62, and 9.63 the first subscript p identifies the transition point and the second subscript r identifies region, i.e., if a region has two transition points, there are two associated 2 × 2 matrices. In any piecewise linear topography the shoreward and seaward matrices are special and are henceforth denoted by P11 and R. If the topographic feature of interest has n linear segments, then there are another (n − 2) intermediate segments. The associated matrices are either Spr or Dpr . For brevity they are both denoted as Qpr . If Kn = [Ai , Ar] is the incident wave vector, the transmitted wave vector towards the shore is K1 = [B,0] and it is given by:   n− 2 P11K1 =  Q j ( j +1) Q(−j1+1) ( j +1)  R(n−1) n K n   j =1

∏

(9.64)

Here again R(n–1)n is the most seaward matrix. This product allows direct and explicit calculation of the transmitted wave amplitude B and of the reflected wave amplitude Ar , because it only involves the inversion of a product of 2 × 2 matrices, which ultimately is a 2 × 2 matrix. Each topographic segment adds one Q matrix and one inverse matrix to the product, except in the left and the right boundaries, where the only unknowns are the amplification factor and the reflected wave height. © 2003 by CRC Press LLC


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Tsunami and Seiche

9.5.12 Example of Calculation of the Run-Up of Solitary Waves on a Continental Shelf with a Beach Noting again that the governing equation is linear and homogeneous, solutions can be superposed, once the amplification factor B closest to the initial shoreline is known. For the topography of Figure 9.17, the amplification factor is determined from Equation 9.64, which in this case reduces to: B (ω, h1 , h2 , m1 , m2 ) = −

− 2m2 1 e πω h1 ϕ (ω ) + iχ (ω )

iω x2 h2

(9.65)

where ϕ(ω, h1, h2, m1, m2) + iχ(ω, h1, h2, m1, m2) is a complex function defined by:  2 ω h1  J0    m1  ϕ c (ω ) + iχ c (ω ) =  2 ω h1  J1   m1 

+

 2 ω h1  Y0    m2   2 ω h1  Y1    m2 

  2ω h   2 ω h2  2 J 0   − iJ 1   m2   m 2 

 2 ω h1  J0    m1 

 2 ω h1  J0   m2 

 2 ω h1  J1   m1 

 2 ω h1  J1   m2 

     (9.66)

  2ω h   2 ω h2  2 Y 0   − iY1  m2   m2  

    

Using the tools developed earlier, it is easy to find the amplitude at the shoreline for a solitary wave evolving over the topography of Figure 9.17, as: R (t ) = η(0, t ) = −

4 m2 3 π h1

cosech (αω ) iω ( xs − x2 −t ) e dω −∞ ϕ (ω ) + iχ (ω )

∫

∞

(9.67)

Conjecturing that ϕ + iχ does not have any poles in the upper half plane, and calculating the Laurent expansion, and again using asymptotic expansions, Kanoglu and Synolakis [1998] found that:

R (t ) =

3π

8

m1

∞

H

5/ 4

∑ (−1)

n+1 3/ 2

n e

−

 h1 nπ  − (1/m2 )  θ+ 2  α   m1

(

 h1 −1  

)

(9.68)

n=1

Its maximum run-up is given by: R = 2.831 m1 H 5/ 4

(9.69)

Realizing that m1 = cot β, observe that it is identical to the run-up of solitary waves on single plane beaches (Equation 9.45). This implies that, at least for those solitary waves for which the asymptotic analysis is appropriate, the run-up depends only on the slope of the shoreward segment, and the effect of the seaward sloping segment is negligible. Similar results can be found for the run-up for any reasonable combination of n positively sloping segments. To better understand this result, refer to Figure 9.18, which shows the variation of the maximum run-up with the depth at the transition point between the two segments of the composite beach of Figure 9.17; the shoreward slope is kept constant and the seaward beach varies from 1:10 to 1:100. The figure also shows predictions from the numerical solution of the NSW of Titov and Synolakis (1995). © 2003 by CRC Press LLC


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m 1 = 1/10, Analytical solution m = 2 Analytical solution m = 2

1/1, 1/1,

1/20, 1/100

1/50,

1/100

0.100

(a) 0.080

R 0.060

H = 0.01

0.040 0.020 0.0

0.2

0.4

0.6

0.8

0.005

1.0

(b)

0.004

R H = 0.001

0.003

0.002 0.0

0.2

0.4

0.6

0.8

1.0

h1

FIGURE 9.18 Solitary wave run-up on a composite beach; comparison of analytical and numerical predictions.

Observe that, if the transition point is at one and a half offshore depths or deeper, i.e., h1 > 0.5, then the shoreward segment dominates the run-up, and the effect of the seaward segment is negligible, as predicted by Equation 9.69. As h1 → 0, the shoreward segment vanishes and the seaward segment dominates. Notice also that, as expected, as H increases the effect of the second region on maximum run-up also increases; smaller waves, being longer, do not feel the transition as much as shorter but higher waves. More extensive results can be found in Kanoglu (1996) for shoreward slopes of 1:10 to 1:20.

9.5.13 Example of Calculation of the Run-Up of Solitary Waves on a Composite Beach Fronted by a Seawall The results of the previous sections suggest that the run-up of most nonbreaking waves is dominated by the slope closest to the shoreline. Consider here another example to check this assertion with a more complex topography, consisting of three segments and a vertical wall. Laboratory data exist for this topography from a U.S. Army Corps of Engineers, Coastal Engineering Research Center experiment of wave run-up on a physical model of Revere Beach, Massachusetts. This beach profile and the laboratory are discussed in greater detail in Yeh et al. [1996]. The profile of the model is shown in Figure 9.19. It consists of three piecewise linear slopes of slopes 1:53, 1:150, and 1:13 from seaward to shoreward. At the shoreline there is a vertical wall. In the laboratory experiments to evaluate the overtopping of the seawall, the wavemaker was located at 23.22 m and tests were done at two depths, 18.6 and 21.3 cm. Proceeding as earlier, Equation 9.64 can be rewritten directly as: −1 −1 P11K = Q12Q22 Q23Q33 D34 A4


(9.70)


9-45

Tsunami and Seiche

23.2m 15m

1 2 3

4.4m

4

5

2.9m

6

7

0.9m

8

9

10

WAVE GAGES

d=21.8 cm

d=18.8 cm 1/13 1/150 VERTICAL WALL

1/53 WAVE MAKER

FIGURE 9.19 Drawing of the laboratory set-up for the Revere Beach experiments showing locations of measurements. The seawall is on the right.

and now the amplification factor B can be evaluated easily. The amplitude at the shoreline is: R (t ) = η(0, t ) = − ( 4 3)

m1 π h0

cosech (αω ) e ( s ϕ (ω ) + iχ (ω ) −∞

∫

iω x − x3 −t )

∞

dω

(9.71)

Again, ϕ(ω) + iχ(ω) is a complicated but determinable expression from Equation 9.70 in terms of Bessel functions of zero and first order, quite easily using tools such as MATHEMATICA or MATLAB. Kanoglu and Synolakis [1998] conjectured again that ϕ(z) + iχ(z) is an entire function in the upper half plane, and derived the Laurent expansion and its asymptotic form as: R(t ) = 8 h0−1/4 H

∞

∑ (−1)

n+1

nχ n

(9.72)

n=1

where

χ=e

−

 1 π  x − x − 2t  α s 3  m1

(

)

h0 − h1 +

1 m2

(

) m11 (

h1 − h2 +

 h2 −1  

)

This is a power series of the form ∑(–1)n+1 nχn and its maximum is equal to 1/4 . Therefore, the maximum run-up for solitary waves propagating up Revere Beach is given by the run-up law: R = 2 h0−1/ 4 H

(9.73)

The run-up law above suggests that the maximum run-up only depends on the depth at the seawall fronting the beach, and it does not depend on any of the three slopes in front of the seawall. The result can be generalized for N-waves, by substituting the correct transform Φ(ω) in Equation 9.72. Figure 9.20 presents comparisons of the predictions of Equation 9.73 with the laboratory experiments of Briggs et al. [1993], where appropriate, i.e., up to the limiting H where the waves broke in their physical manifestation. The run-up law (Equation 9.73) predicts the nonbreaking data surprisingly well. Note that no Jacobian regularization conditions as yet exist for wave evolution on composite beaches, and the Kanoglu–Synolakis theory should be applied with caution. © 2003 by CRC Press LLC


9-46


1

Theory, R = 2 h –1/4 H w

0.1

R

0.01

0.01

d = 18.8 cm

Experiment Theory

d = 21.8 cm

Experiment Theory

0.1

1

H FIGURE 9.20 Wave run-up on Revere Beach. Comparison of analytical predictions and laboratory measurements.

9.6 Numerical Solutions for Calculating Tsunami Inundation Although analytical solutions are useful for first-order analysis and for determining upper limits for tsunami inundation for preliminary design, in most applications a numerical solution of the 2+1 evolution of the tsunami from generation to the shoreline is undertaken. Depending on the sophistication of the model, numerical solutions are capable of predicting coastal inundation, even for extreme events such as the 1993 Hokkaido-Nansei-Oki tsunami [Titov and Synolakis, 1997, 1998]. Although the existing numerical solutions cannot resolve the specific pattern of the breaking front, in those cases when tsunamis break, high-end numerical models adequately predict the overall wave behavior and give reliable predictions of run-up values over a wide range of wave parameters. Numerical solutions for wave inundation are notoriously unstable, as shoreline motions involve small water depths and large velocities. Whereas several models had been developed and published in the 1960s and 1970s attempting to calculate the shoreline one-plus-one or two-plus-one evolution of tsunamis generated by submarine earthquakes or mass movements, none was validated either by comparison with laboratory experiments or with field data. As early as 1990, in a U.S. National Science Foundation workshop in Catalina, California, the problem of understanding the 2+1 near-shore evolution and associated shoreline motions was identified as a priority, and the development of comprehensive largescale laboratory data described as essential for further progress [Liu et al., 1991]. To this end, a series of laboratory tests were undertaken by Briggs et al. [1993, 1994, 1995] in a large wave basin at the U.S. Army Corps of Engineers Coastal Engineering Research Center (CERC) in Vicksburg, Mississippi. The CERC water tank is 25 m wide, 30 m (100 ft) long, and 60 cm (2 ft) deep. Waves were realistically created in the tank by a horizontal wave generator with 60 different paddles, each 45 cm (0.5 ft) wide and moving independently. The tank and one of the models are shown in Figures 9.21A and 9.21B. These experiments provided run-up observations for validating numerical models and supplemented comparisons with analytical results, as per the previous section. By serendipity, several large tsunamis have occurred since 1992, in Nicaragua, Indonesia, Japan, Russia, Mexico, Peru, and Papua



Tsunami and Seiche

9-47

FIGURE 9.21A The 30-m wave basin at the Coastal Engineering Research Center, showing the directional spectrum generator and the conical island used in the experiments by Briggs et al. [1993, 1994].

FIGURE 9.21B Top view of a solitary wave attacking the conical island in the Coastal Engineering Research Center basin during the 1994 experiments. The wave is approaching from the top. Note the enhanced run-up on the back of the island, known as the Babi Island effect.

New Guinea, which provided additional field data for model validation. The two 1992 tsunamis identified serious deficiencies in the older modeling efforts, which used models that do not calculate run-up motions, as their predictions involved errors of factors of five to ten, when compared with field run-up observations. These older models would stop the wave evolution calculations at some threshold offshore depth, sometimes at the initial shoreline or even at the 5-m (16.7-ft) or 10-m (33.3-ft) depth contour to avoid the shoreline evolution computation. In essence, the early models treated the ocean as if it had vertical walls near the coastline, and predicted the height of the tsunamis as they hit these seawalls. Even casual observation of wind waves hitting a seawall or evolving on a natural beach would point out that this is unsatisfactory, as wave height can change dramatically when it comes ashore. The deficiencies of threshold models triggered rapid development of 2+1 numerical inundation models, i.e., models that include shoreline motions in the tsunami evolution calculations. Comparisons between field data and model predictions are referred to as model validation or verification and are a crucial part of any scientific modeling effort. Without comparison to real-world data there is no basis to accept the predictive capability of any model. To underline this process, the National Science Foundation of the United States organized a follow-up workshop to the 1990 Catalina workshop in Friday Harbor in 1995, as described in Yeh et al. [1996]. The three organizers provided modelers with well-described © 2003 by CRC Press LLC


9-48


initial conditions for four benchmark problems, one of which was the seafloor deformation of the Hokkaido-Nansei-Oki tsunami of 1993. The modelers prepared predictions of the associated water motions and of the inundation computations and presented their results in the workshop. It was then that the actual laboratory or field data were shown to assess the relative effectiveness of different numerical models. A conspicuous characteristic of almost all models presented was their gradual evolution from threshold 1+1 propagation models to 1+1 inundation models, to threshold 2+1 models to 2+1 inundation models. This evolution, often extending over a 10-year period, allowed modelers to identify modeling nuances and artifacts and the community at large to understand what is important to first order. The Hokkaido-Nansei-Oki tsunami of 1993 that struck Okushiri island with extreme run-up heights of 30 m (100 ft) and currents of the order of 10 to18 m/sec (33.3 to 60 fps) was a disaster, but provided fortuitous high quality data. High-resolution seafloor bathymetry existed before the event and when coupled with bathymetric surveys following the event allowed meaningful identification of the seafloor deformation. The only two models that were proven capable of modeling the entire range of available data from the laboratory scale to the Hokkaido-Nansei-Oki event were those by Imamura et al. [1996], TUNAMI-N2, and Titov and Synolakis [1996, 1998], VTCS-3. Both are copyrighted by the developers. The latter has become the standard model of the National Oceanic and Atmospheric Administration for coastal inundation and is now known as MOST (Method of Splitting Tsunami). One conclusion of the successes of these modeling efforts has been that — at least for this event — the details of the timing of seafloor deformation may not be as important as some believed, and that what ultimately matters is the differences between initial and final water depth. Since publication of the successful modeling of the Hokkaido-Nansei-Oki tsunami, there is renewed focus on better understanding of the initial conditions [Titov and Synolakis, 1997]. Both TUNAMI-N2 and MOST use finite-difference (FD) algorithms to solve the NSW equation set (Equation 9.16). Whereas solution methods for coupled hyperbolic partial differential equations (PDEs) exist in some computational packages of MATLAB and MATHEMATICA, the substantial and nonstandard difficulty is with the prediction of tsunami inundation in what is referred to as the run-up computation. The tsunami wave evolution over dry land involves the interaction of three phases of matter [Liu et al., 1991]. In FD type numerical solutions, this involves introducing additional grid points as the tsunami front evolves on the beach and runs up, the removal of these grid points as the wave runs down, and the repetition of this cycle as the next tsunami wave in the tsunami train approaches the beach. Whereas it has been argued that finite-element (FE) algorithms are more naturally suited for this type of problem, in practice, FE methods have been proven cumbersome and less flexible than FD solutions. TUNAMI-N2 and MOST differ in two ways. TUNAMI-N2 uses a fixed computational grid, involves a friction factor and, although it lets the wave advance past the initial shoreline, its maximum run-up prediction is based on the maximum wave height at the shoreline. MOST uses a variable computational grid, no friction factors, and its run-up prediction is based on the elevation of the last wet grid point the wave encounters as it climbs up on the beach. The methodology of MOST will be described briefly here. MOST does not include bottom friction terms in the model. Although the bottom friction does affect the dynamic of the run-up process in the surf zone, there are several reasons for not using the friction terms in an FD model. The commonly used bottom friction model for SW approximation is the Chésy formula with different types of roughness coefficient [Packwood and Peregrine, 1981; Kobayashi and Greenwald, 1987; Liu et al., 1995]. This formula is an empirical relationship developed from steady channel flows and, possibly, it does not reflect the dynamic of the rapid run-up process adequately. Also, there is no consensus on a proper form of the roughness coefficient in the formula. A number of studies have been devoted to the designing of a proper roughness coefficient instead of the commonly used Manning’s coefficient [Fujima and Shuto, 1989]. However, several studies suggest that an unsteady flow during run-up is not very sensitive to changes in the roughness coefficient value [Packwood and Peregrine, 1981; Kobayashi and Greenwald, 1987; Zelt, 1991]. Any numerical algorithm of moving boundary for the wave run-up induces a numerical friction near the tip of the climbing wave, and this complicates the situation with the proper choice of the friction coefficient for a numerical model. The roughness coefficient at the present stage of the science appears to be a fairly arbitrary parameter, adjusted to fit any given © 2003 by CRC Press LLC


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Tsunami and Seiche

experimental data set, but is very difficult to be determined a priori. In principle, this reduces dramatically the prediction ability of a numerical model. In practice, the choice of coefficient in TUNAMI-N2 has been well calibrated through its repeated use for prediction of past tsunami events, but then again its friction factor is applicable only to the numerical procedure in TUNAMI-N2. Since in any engineering problem the interest is the evaluation of the maximum run-up level for design purposes, and friction can only reduce it, it is recommended that if a computation is otherwise stable, no friction factor be used. A variety of boundary and initial conditions can be specified for these equations. To solve the problem of tsunami generation due to bottom displacement, one specifies the following initial conditions: d ( x , y , t ) = d0 ( x , y , t ), t ≤ t 0 , and d ( x , y , t ) = d0 ( x , y , t ), t > t 0

(9.74)

Usually, t0 is assumed to be small, so that the seafloor movement is an almost instantaneous vertical displacement, which can be directly translated into an initial condition, so that η(x,y,t = 0) = d(x,y,t0). This is an excellent approximation for tectonic tsunamis where the rupture velocity is substantially larger than the local tsunami speed over the deformation area. For landslide-generated tsunamis when the slide evolves at speeds of the same order as the local water-wave velocity, then one must solve the forced equivalent of the NSW (Equation 9.16), as for example in Equation 9.49. To avoid the additional complication of introducing an evolving seafloor in TUNAMI-N2 or MOST, the standard practice is to obtain an initial condition for the landslide tsunami from some other approximate model and to transfer this initial condition to the two codes.

9.6.1 The Splitting Technique For arbitrary topography and bottom displacements MOST uses an FD algorithm based on the splitting method, also known as the method of fractional steps of Yanenko [1971]. This method reduces the numerical solution of the two-dimensional (2+1) problem into consecutive solution of two locally onedimensional problems. This is achieved by splitting the governing system of Equation 9.16 into a pair of 1+1 systems, each containing only one space variable, as follows: ht + (uh)x = 0  ut + uuz + ghx = gdx  vt + uv x = 0

ht + (vh) = 0 y  vt + vv y + ghy = gd y  ut + vu y = 0

(9.75)

The two systems of Equation 9.75 can then be solved sequentially at each time step using standard numerical methods. MOST uses an explicit FD scheme, although most often implicit numerical schemes are preferred when using the splitting method with elliptic and parabolic equations. Splitting gives a substantial reduction of the number of operations compared with implicit schemes applied directly to two-dimensional elliptic or parabolic equations. The NSW equations (Equation 9.16) form a hyperbolic quasi-linear system and explicit methods have proven most efficient. The main advantage is the potential of solving the characteristic form of the two 1+1 equations, which helps establish a well-posed boundary value problem (BVP) for the numerical method. The characteristic form of equations also allows for an efficient FD realization [Titov and Synolakis, 1995]. Each of the systems in Equation 9.75 is a hyperbolic quasi-linear system with all real and different eigenvalues and can be written in characteristic form as follows: pt + λ1 px = gdx qt + λ 2qx = gdx v ′ + λ 3v ′ = 0


(9.76)


9-50


where p = u + 2 gh q = u − 2 gh

(9.77)

v′ = v are the Riemann invariants of this system, and λ1 = u + gh λ 2 = u − gh

(9.78)

λ3 = u are the eigenvalues. We use an explicit FD method to solve Equation 9.75 along the x and y coordinates sequentially, every time step. The first two equations in Equation 9.75 constitute a one-dimensional NSW problem. At every time step, MOST solves a one-dimensional NSW propagation problem along each coordinate plus one more equation describing a nonlinear momentum flux in the direction normal to this coordinate. In summary, the overall procedure utilizing the splitting technique for the system (Equation 9.75) transformed into Equation 9.76. Suppose values un, vń, hn for time instant t are given. The algorithm of computing values un+1, vń+1, hn+1 for time t + dt consists of the following steps: 1. The primitive variables un, vn, hn are converted into the Riemann invariants pn, qn, vń using the transformation in Equation 9.76. 2. pn+1/2, qn+1/2, vń+1/2 are computed by solving numerically Equation 9.77 along the x coordinate. 3. pn+1/2, qn+1/2, vń+1/2 are than converted back to the primitive variables un+1/2, vn+1/2, hn+1/2. 4. Steps 1 through 3 above are repeated for un+1/2, vń+1/2, hn+1/2 along the y coordinate to compute the values un+1, vń+1, hn+1. Note that Riemann invariants are different here, because u and v interchange with each other in Equation 9.78.

9.6.2 Boundary Conditions for Fixed Boundaries The splitting method requires solving the two 1+1 systems of Equation 9.75 every time step. Boundary conditions are established for each 1+1 problem using characteristic analysis, as follows. Equation 9.76 is a hyperbolic quasi-linear system with real and distinct eigenvalues (Equation 9.78), with three families of characteristic lines with slopes λ1, λ2, and λ3. λ1 > 0, λ2 < 0 everywhere the Froude number (u / gd ) is less than 1, while λ3 can be either positive or negative. A well-posed boundary value problem requires the number of boundary conditions for Riemann invariants to be equal to the number of outgoing characteristic lines for this boundary. Therefore, one or two boundary conditions are necessary on each boundary depending on the sign of λ3 on that boundary. The boundary conditions for a totally reflective left boundary are: p = −q v′ = 0

(9.79)

while the reflective conditions for the right boundary are: q = −p v′ = 0


(9.80)


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Tsunami and Seiche

Gustafsson and Kreiss [1979] used this characteristic approach to develop absorbing boundary conditions for time-dependent problems. A totally absorbing boundary allows waves to go through (absorb) but it does not allow any waves to reflect back into the computation region. In characteristic terms, the invariants on outgoing characteristics do not carry any disturbances back into the computational area. For the right boundary, the requirement of no wave motion on that characteristic implies that u = 0, v = 0, η = 0, therefore q = –2 gd , v′ = 0. In addition, MOST assumes that the water depth is constant outside the area of computation and equal to the depth at the right boundary dn, hence q is constant on that boundary. Therefore, appropriate conditions are: q = −2 gdn v′ = 0

(9.81)

while for the left boundary: p = 2 gdn v′ = 0

(9.82)

The run-up computations require a moving boundary condition to be used for the tip of the climbing tsunami wave. Titov and Synolakis [1995] developed a moving boundary condition for 1+1 NSW equations. The same basic approach can be used for the run-up boundary condition and will be discussed briefly in the next section.

9.6.3 The Finite-Difference Scheme We use the following explicit finite-difference scheme for each equation in the system shown in Equation 9.78.  n  ∆  n n ∆t pin 1 n n + λ ( ∆ + ∆ x ) pi − 2∆tλ i ∆ x  x  λ i pi  = ∆t ∆xi −1 + ∆xi  i − x  ∆xi    ∆   g  ( ∆ − x + ∆ x ) din − 2∆tλni ∆ x  x  din  ∆xi −1 + ∆xi   ∆ xi   

(9.83)

where fi n = f ( x i , t n ) ∆t fin = f ( xi , t n + ∆t ) − f ( xi , t n ) ∆ x f i n = f ( x i + ∆x , t n ) − f ( x i , t n ) ∆ − x fin = f ( xi , t n ) − f ( xi + ∆x , t n ) Note that this scheme allows for the spatial grid with a variable space step ∆xi . The condition of stability for the scheme is the Courant–Friedrichs–Lewy (CFL) criterion: ∆t ≤ min i

which always has to be satisfied. © 2003 by CRC Press LLC

∆x i ui + ghi

(9.84)


9-52


FIGURE 9.22 Definition diagram for shoreline calculations.

The FD scheme (Equation 9.83) is used for the computation of the unknown variables p, q, and v´ in the interior grid points of the computational area. However, these equations cannot be used to compute boundary values. At those points, the boundary conditions determine only two among the three invariants. The other value on the boundary (the value of the Riemann invariant on the incoming characteristic) is computed by MOST by the upwind FD scheme: pbn+1 = pbn −

[ (

∆t n λ ∆ pn − g ∆ − x dbn ∆x b 1 − x b

) (

)]

(9.85)

where pb, db are the values of the variables on the boundary. During shoaling the wavelength of the tsunami becomes shorter. Therefore, calculations using a uniform grid throughout the computational domain suffer either loss of accuracy in the near-shore field or loss of efficiency through the use of a very fine grid. Neither approach produces consistent resolution. MOST uses a variable in each direction grid to keep consistent resolution [Titov and Synolakis, 1995], as in cylindrical two-dimensional domains, where the depth is changing predominantly along one direction. To model tsunami wave propagation in areas with complex bottom profiles containing complicated shoreline patterns and islands, an additional nested grid is often needed for the near-shore computations, when computer resources do not allow for large grids. The nested grid has finer grid spacing for an efficient computation of the shorter waves in the near-shore area.

9.6.4 The Moving Boundary Condition Calculation of the evolution on the dry bed involves moving boundary conditions. The Froude number may be greater than one near the shoreline point, implying that all characteristic families have the same inclination in this region. Hence, it is impossible to use the direct relationships between the Riemann invariants near the shoreline. MOST uses approximations of the boundary values from previous space nodes, as shown in the definition sketch in Figure 9.22. The shoreline algorithm uses a time-dependent space step ∆x(t) of the last node of the computational area. The objective is to maintain the shoreline boundary point, represented consecutively by (A), (B), or (C) on Figure 9.22 on the surface of the beach during the computation. The length of the last space step ∆x(t) is adjusted every time step, so that the shoreline point (A) is at the intersection of the beach with © 2003 by CRC Press LLC


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Tsunami and Seiche

3000

amplitude (cm)

2500 2000 1500 1000 500 0 2000

4000

6000

8000

distance from north to south (m)

FIGURE 9.23 Comparison of MOST predictions with field measurements during the 1993 Hokkaido-Nansei-Oki tsunami. The heavy line, solid circles, and open circles are MOST predictions at 50, 150, and 450 m resolution, respectively. Vertical bars are threshold model-type predictions with calculations stopping at the 10-m contour. Stars are the field measurements.

the horizontal projection of the last “wet” point, for example, the n − 1 node in Figure 9.22. The value of the velocity on the shoreline node is equal to the velocity on the previous “wet” point. Additional grid points are introduced as needed, as follows. Referring to Figure 9.22, at the time interval between times t and ∆t, there are n grid points, n − 1 fixed grid points, and the instantaneous shoreline, points (A) or (B) in the computation. At time t + 2∆t, when the shoreline point (C) reaches beyond the next fixed grid point (the nth fixed node of the constant dry bed grid), this nth fixed point is introduced between the shoreline point (C) and the previous internal fixed node n − 1 and η(D) = η(C). Now, there are n + 1 grid points in the computational area and the process is repeated. During rundown, the number of dry grid points is reduced sequentially in an analogous manner.

9.6.5 Verification of the Model As an example of validating codes for use in tsunami engineering, Figure 9.23 shows the comparison among the computed values and with field measurements from the 1993 Hokaido-Nansei-Oki tsunami, at Okushiri Island, Japan. The model is seen to predict even extreme run-up values of 30 m (100 ft) adequately. This was an extremely difficult tsunami because there was overland flow over Aonae cape, as shown in Figure 9.24.

9.7 Harbor and Basin Oscillations 9.7.1 Introduction to Basin Oscillations The sloshing of basins, reservoirs, dams, and harbors is a classical problem of hydrodynamics. This sloshing occurs when a closed or open basin is excited either by ground motion or offshore waves, or by impulsive atmospheric disturbances, such as barometric fronts or pressure waves from volcanic eruptions. The resulting waves are also known as seiches.11 1Seiche is a word believed to originate from the Latin siccus, which means dry or exposed [Wilson, 1972], but it seems now to be out of favor in the English scientific literature.



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FIGURE 9.24 Computed results using MOST of the tsunami running over Aonae Cape during the 1993 HakkaidoNansei-Oki tsunami.

As these waves approach the boundaries of the basin, they reflect; when the boundaries are vertical, the reflection process is almost perfect, and the reflected waves have the same frequency as the incident ones with no phase shifts. As the excitation continues, interference sets up standing waves, which tend to grow; most of these waves are long and dissipation is often not important to first order. When the basin is closed, or when the harbor entrance is small, the resulting waves may grow, as there is no or little wave energy radiated offshore, respectively. The latter has led to the formulation of the classical “harbor paradox,” where closing the entrance of a harbor sometimes leads to amplification of the waves, contrary to lay intuition, which would have led one to expect that the narrower the entrance, the smaller the wave motion inside the harbor. Both from the engineering and the analytical points of view the problem is intriguing. Most large water bodies, but also harbors, have adjacent communities and/or constructed marine facilities. Largeamplitude wave motions within these water bodies can be rather disruptive, not to mention outright catastrophic, since the inundation associated with such large water motions can be extensive, and have been reported to last for several hours. It is well known that oscillations in Lake Erie excited by barometric pressure disturbances can last for more than a week beyond the forcing. There have been numerous anecdotal reports in the literary literature over the past 2000 years of unexplained and rapid rises in water level; often these unusual phenomena were associated with astronomical cycles, but as the understanding of tides grew, these associations proved inadequate. In Japan, where historic records exist for almost 1000 years, these motions were often associated with tsunamis. Tsunami is the Japanese word for what is referred to in English as a tidal wave. Interestingly, the exact transliteration of the word tsunami means harbor wave, a reflection perhaps of the fact that these waves were first observed in harbors. In more modern times, it is believed that the rhythmic oscillations occurring at the narrow end of Lac Léman off Geneva were first mentioned in a chronicle by Schulthaiss in 1549 and recorded in 1730 by deDuiller [Wilson, 1972]. The first scientific study was initiated by Forel through his observations of the oscillations of the same lake, in 1869. Forel noticed that the amplitude of the oscillation increases towards © 2003 by CRC Press LLC


Tsunami and Seiche

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the western end of the lake, and that the oscillations may occur at all times of the year, and seem only to be affected by the “state of the atmosphere.” Chrystal [1905], in his seminal study of lake seiching, refers to Forel as the Faraday of seiching; Faraday first described capillary (surface-tension controlled) waves generated in small closed basins under continuous vertical excitations. Chrystal [1905] published a comprehensive study of basin seiching, including numerous observations. He quoted a description of seiching from the Scots Magazine of 1755 because, as he wrote, the “source is not easily accessible to everyone.” He correlated this phenomenon with the great Lisbon earthquake of 1755. Indeed, this description may still not be easily accessible, so it is provided below. On the 1st of November last, Loch Lomond, all of the sudden, and without the least gust of wind, rose against its banks with great rapidity, and immediately retiring, in about five minutes subsided as low, in appearance, as ever it used to be in the greatest drought of summer. In about five minutes after, it returned again, as high and with great rapidity as before. The agitation continued in the same manner from half an hour past nine till fifteen minutes after ten in the morning; the waters taking five minutes to subside and as many to rise again. From ten to eleven the agitation was not too great; and every rise is somewhat less than the immediately preceding one; by taking the same time, viz. five minutes to flow and five minutes to ebb, as before. About eleven the agitation ceased. The height of the waters was measured immediately after and was found to be 2 feet 6 inches (76cm) perpendicular. The same day, at the same hour, Loch Lung and Loch Keatrin were agitated in much the same manner; and we were informed from Inverness, that the agitation in Loch Ness was so violent as to threaten destruction to some houses built on the sides of it. The Great Lisbon earthquake occurred on the morning of November 1, 1755; Chrystal observed that both Loch Ness and Loch Lomond lie along an almost straight line with the center of the disturbance in Lisbon. Interestingly, the same event generated a rather large and destructive tsunami; our current understanding suggests that this earthquake was at least a magnitude 8 and was tsunamigenic, and a comparatively large portion of its energy was in the long wave part of the spectrum. These long waves do not attenuate rapidly, explaining perhaps why they had sufficient energy to excite the lakes in Scotland. More recently, the Great Alaskan earthquake of March 27, 1964 produced anecdotal reports of sloshing in different reservoirs operated by the Army Corps of Engineers, and coastal seiches along the coastlines of Texas and Louisiana [Korgen, 1995]. The observations of seiches in the nineteenth century led to the formulation of simple mathematical models based on the linear theory of long wave evolution. Some of the greatest names in hydrodynamics, including Green, Rayleigh, Stokes, and Lamb, have provided simple analytical results for simple geometries. In summary, all formulations to date either assume lakes with orthogonal cross sections or fairly long canal-shaped lakes, and with simple depth variation in the longitudinal direction, either uniformly sloping or constant or convex or concave parabolic, or with cylindrical symmetry. All these formulations allow for simple one-dimensional equations of motion, either in one rectilinear coordinate or in the radial direction. For simplicity with assigning the boundary condition, all studies have assumed that the lake walls are vertical beyond the initial shoreline, i.e., that there is a vertical boundary wall along the shoreline; this allows the imposition of no fluid motion past the boundary, an assumption which is perhaps adequate when the shoreline motions are small, but clearly not so, when the basin has gently sloping boundaries, which may produce large horizontal excursions. It is interesting that difficulties encountered in most of the nineteenth- and twentieth-century studies in matching the results for any other than the fundamental period — not to mention with the wave height — with observations, these difficulties led Chrystal [1905] to ask, “Is this an accident due to the position at which the limnograph2 was placed, or are these seiches unstable owing to irregularities of the lake bottom near one or more of the corresponding nodes?” 2

Limnograph is the name given to a tide-gage instrument, that is, an instrument that measures the water level variation, when deployed inside a lake. Typically these instruments only respond to slow variations such as tidal changes. © 2003 by CRC Press LLC


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It is perhaps worthwhile to speculate that these difficulties in interpretation may be due to the excitation of transverse modes in different lakes and basins. When the forcing source is an atmospheric disturbance and usually coming from the same direction, then the periods of oscillations observed in any given lake may be consistent from year to year, yet if they occur in the transverse direction they may not be accessible with the simple longitudinal-mode theories proposed earlier. Unless the direction of excitation is very close to the longitudinal direction, both transverse and longitudinal modes may be excited and any expectation of predicting the amplitude of the oscillation with a one-dimensional theory may not be well placed for closed basins, appropriate as it may be for harbors, where the excitation is often one dimensional. Sloping boundaries may dramatically complicate the interpretation; even the theory of long waves evolution and run-up over infinitely wide ocean beaches was only fully developed in the last 30 years, with consistent numerical results becoming available only in the last 10 years. These results suggest that the wave height off the beach may be dramatically underestimated if there is no shoreline-evolution computation, such as when imposing a vertical wall-type boundary condition, as in the early studies.

9.7.2

Calculating Basin Oscillations

In basin oscillation studies it is customary and appropriate to integrate the basic Navier–Stokes equations over the depth, but it is preferred to express the resulting LSW equations in terms of the volume flow rate per unit time per unit width of vertical cross section: qx =

∫ ud A, and q =∫ vd A y

A

(9.86)

A

where A is the cross-sectional area of the basin at the particular plane of integration. It is customary and not unrealistic for long waves to assume that the vertical accelerations of the free surface are small in comparison with the acceleration terms ∂u/∂t and ∂v/∂t. Convective terms of the form u(∂u/ ∂x) are also neglected in comparison to ∂u/∂t, similarly in the y direction. With all other restrictions above, the equation of conservation of mass can be written as: ∂qx ∂q y ∂η + + =0 ∂x ∂y ∂t

(9.87)

while Newton’s law becomes, in terms of qx , qy :

∂qx ∂t

+ g (h + η)

∂η = ∂x

τ xz

z=η z = −h (h + η) ∂patm − ρ ρ ∂x

(9.88)

and

∂q y ∂t

+ g (h + η)

∂η = ∂y

τ yz

z=η z = −h (h + η) ∂patm − ρ ρ ∂y

(9.89)

Now, it is convenient to approximate the bottom shear stress τxz | z=–h = Kqx where K is a bottom friction factor, and similarly τyz | z=–h = Kqy . At the free water surface, z = η, the shear stress can be incorporated in a forcing term of the form: Fx ( x , y , t ) = © 2003 by CRC Press LLC

τ xz z = − η (h + η) ∂patm – ρ ρ ∂x

(9.90)


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After substitution, what results is a set of three coupled equations: ∂qx ∂q y ∂η + + =0 ∂x ∂y ∂t

(9.91)

∂qx ∂η + Kqx + g (h + η) = Fx ( x , y , t ) ∂t ∂x

(9.92)

∂q y ∂t

+ Kq y + g (h + η)

∂η = Fy ( x , y , t ) ∂y

(9.93)

for the unknowns qx , qy , and η.

9.7.3

Forced Oscillations in Basins of Simple Planform

For calculating oscillations in narrow closed basins, where there is no y (width) dependence, qx can be trivially eliminated among the equations, resulting in the following: ∂F ∂2η ∂η ∂   +K −g =− x (h + η) ∂η ∂t 2 ∂t ∂x  ∂x  ∂x

(9.94)

and, in a long rectangular basin of uniform depth h = d, length L >> width and with vertical boundaries, the equation becomes: ∂F ∂2η ∂η 2 ∂ 2 η +K −c =− x 2 2 ∂t ∂t ∂x ∂x

(9.95)

an equation in the canonical form of a forced one-degree dynamic system, which can be solved by separation of variables. An equivalent equation can be trivially derived for the volume flow rate. c = gd is the wave velocity. The standard boundary condition is of the form qx(0,t) = qx(L,t) = 0, i.e., there is no flow at the two boundaries, which is equivalent to imposing a vertical wall at the shoreline. Then, the solution for the free oscillations (Fx(x,t) = 0) is the following: η( x , t ) = ae − Kt / 2 cos kx cos ( γt + )

(9.96)

qx (t ) = (aγ k ) e − Kt / 2 sin kx sin ( γt + )

(9.97)

and

The amplitude a and the phase difference ε are, of course, to be determined from initial conditions. Also, k = nπ/L, n = 1, 2, 3, … and γ = ω 1 − K ω 2 ; since ω = kc, then: ω = (nπ L) gd

(9.98)

Therefore, the periods of free oscillation — when damping is negligible — are: Tn =


2L n gd

(9.99)


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The fundamental mode is when n = 1. Equation 9.99 apparently was first proposed by Merian [1828] and bears his name. As explained, the assumption is that the basin is one dimensional, with constant – depth and width. There have been attempts to account for variable depth by using the average depth d over the longitudinal axis, or the so-called deBoys approximation: Tn =

2 n

∫

L

0

dx

(9.100)

gh ( x )

to calculate the periods of oscillation, but neither of the two is known to produce satisfactory results; their effectiveness will be checked later, and another analytical method for obtaining the natural frequencies will be discussed. An interesting result regarding atmospheric excitation is given by Wilson [1972]. When Equation 9.95 is forced by a Gaussian-distributed pressure pulse of length l, and the equation solved using a Fourier series, the excitation produces resonance when the ratio of the length of the pulse to the basin length is l/L = 8/9. A number of other one-dimensional solutions for variable depth are presented in Lamb [1932] and summarized in Defant [1961]. By scrupulously choosing the depth variation h(x) in Equation 9.94, the latter may take the form of Bessel’s or Legendre’s equation. Then the natural frequencies can be calculated readily. Unfortunately, solutions only exist for basins with uniformly varying depths or with hyperbolic depth profiles. Even for the one-dimensional case of a trapezoidal bottom variation, no solution exists, and authors revert to numerical procedures [Gardarsson, 1997]. When bottom friction is negligible, the 2+1 LSW is:

g

∂ ∂ (hη) 1 ∂ 2 η ∂ ∂ (hη) +g = ∂y ∂y ∂x ∂x c ∂t 2

(9.101)

subject to the condition of no flux, h∂η/∂n = 0 at the boundaries. h(x,y) is the local depth, which may vary inside the basin. Equation 9.101 is valid for inviscid, incompressible, irrotational flows with long waves of small amplitude. For two-dimensional reservoirs, when the width W is of the same order as the length L, an analytic solution exists only for a basin of uniform depth h = d. Then, Equation 9.101 becomes:  ∂2η ∂2η  ∂2η = c2  2 + 2  2 ∂t ∂y   ∂x

(9.102)

∂η ∂η ∂η ∂η x = 0, y , t ) = x = a, y , t ) = x , y = 0, t ) = ( ( ( (x =, y = b, t ) = 0 ∂x ∂x ∂y ∂y

(9.103)

with c = gd subject to

and initial conditions for η(x,y,t = 0) and ∂n/∂t(x,y,t = 0) specified by any well-behaved functions. Using standard separation of variables methods of engineering mathematics, it is trivial to show that the natural frequencies of Equation 9.102 are given by: ω nm = π g d n 2 (d a) + m 2 (d b) 2

2

(9.104)

for any initial conditions. The two lowest-frequency modes are the ones for n = 1, m = 0 and n = 0, m = 1 also sometimes referred to as fundamental modes, while n = m = 1 is the first coupled mode. The solution for η(x,y,t) in generic form is given by the eigenfunction expansion: © 2003 by CRC Press LLC


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η( x, y, t ) =

∞

∞

∑ ∑(A

nm

n=0 m=0

cos ω nmt + Bnm sin ω nmt ) cos

nπx mπy cos a b

(9.105)

with the understanding that both n and m cannot be simultaneously zero. Anm and Bnm are determined from the two initial conditions, by expanding η(x,y,t = 0) and ∂n/∂t(x,y,t = 0) in Fourier series in terms of the cosine eigenfunctions. If the width b of the basin is much smaller than the length, and it can be formally shown then the lengthwise motions dominate and the periods of motion are given by: T=

2a n gd

(9.106)

Raichlen [1966] notes that Equation 9.106 estimates the first mode of Loch Earn, Scotland, with a = 6.2 mi (10 km), d = 200 ft (61 m) as T = 13.65 min, with an observed period of 14.5 min. For Lake Baikal in Siberia, with a = 413 mi (660 km), d = 2230 ft (675 m), Raichlen calculated T = 4.52 h, with an observed period of T = 4.64 h. However, for Lac Léman in Geneva, Switzerland, with a = 43.5 mi (70 km) and d = 525 ft (159 m), T = 59 min, while the observed period is 83.5 min, a difference attributed to the complexity of the shape of the lake. While these formulas can be applied to calculate adequate first estimates of the natural frequencies of basins excited by strong ground motions, such as the Los Angeles Reservoir (LAR) during the 1994 Northridge earthquake, they cannot be used directly for harbors, which are in essence basins with openings.

9.7.4

The Sloshing of the Los Angeles Reservoir: A Case Study

The MW = 6.7 Northridge earthquake occurred on January 17, 1994 at 4:30 a.m. PST, with an epicenter about 1 mi south-southwest of Northridge, California at a focal depth of 12 mi [Hall et al., 1994]. Numerous national and international reconnaissance teams performed field surveys immediately following the earthquake and at least three preliminary reports have been published [EQE, 1994]. These preliminary reports did not refer to any run-up observations around any of the LA area dams or reservoirs. On January 18, 1994, the day following the event, the Los Angeles Times reported that a 30 ft (9 m) wave had overtopped the Los Angeles dam (LAD), but that there had been no structural damage. The LAR is located about 6 mi from the epicenter of the earthquake, inside the Van Norman complex of the Department of Water and Power (DWP). This site suffered substantial damage in the 1971 San Fernando earthquake, and the LAR was built to replace the Lower San Fernando dam; that older dam is now used as a debris basin. Lateral spreading, liquefaction, and ground settlement were observed in the entire area referred to as the Van Norman complex. Based on the intensity contour maps of Trifunac et al. [1994], peak horizontal and vertical accelerations were in excess of 0.60 and 0.80 g, respectively. Hall et al. [1994] reported that the dam settled 9 cm (3.54 in.), while DWP claims that the dam moved horizontally 7.5 cm (3 in.); both numbers are consistent with fairly impressive ground shaking. The LAR is trapezoidal-shaped in plan view; at the rim the trapezoid has 790 m (2600 ft) height and 1130 m (3700 ft) and 710 m (2325 ft) bases. The southeastern part of the reservoir is referred to as the Los Angeles Dam or LAD. The dam is 25 m (83 ft) high and it is built on bedrock. At the time of the earthquake, the water surface is believed to have been 7 m (23 ft) below the crest of the dam, which is at an elevation of 360 m (1200 ft) above sea level. The reservoir was rapidly emptied to check for cracks, starting the day after the event. The slope of the embankments ranges from 3.5 horizontal to 1 vertical, to 3:1. The area was surveyed on January 18, 1994 by two groups of faculty and students of Civil Engineering from the University of Southern California; the group headed by Synolakis surveyed the hydrodynamic © 2003 by CRC Press LLC


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aspects and, in particular, attempted to evaluate the 30-ft (9-m) high wave of the newspaper reports. They were unable to find eyewitnesses or the origin of the report. However, during a walk-around inspection of the embankments of the LAD, they located conspicuous chalk marks that bore no relationship to any of the visible cracks. East of the water-intake tower, they found a line of debris of fragments of bird nests. On closer inspection, it was noticed that underneath the catwalk there were numerous remains of bird nests. They speculated that during the ground shaking, parts of the bird nests fell in the reservoir and they were carried by the sloshing waves up the embankment. The fact that this debris line existed only east of the catwalk could provide a clue as to the predominant direction of sloshing in the reservoir. On the east side of the reservoir there is a narrow section with a crest 3.3 m (10 ft) lower than the rest of the reservoir. This section is an overflow and it leads to a storm channel; there were unconfirmed reports that there was some overtopping in this section, but the team learned of them long after the field survey took place. The measured data suggest that the sloshing may have reached 3.3 m (15 ft) vertical height above the still water level of January 17, 1994, the date of the earthquake. If this observation is correct, then the northeastern embankment (whose crest is lower) might have overtopped had the water level been higher at the time of the earthquake. Observations of significant run-up heights of this order are rare. The conventional paradigm suggests that dams over 22 m (75 ft) high do not overtop, unless there is a landslide or other impulsive catastrophic occurrence, although perhaps this dictum represents more wishful thinking than sound engineering judgment. While it may never be possible to reconstruct what happened in the LAR, Ruscher [1998] attempted to determine if the run-up distances measured on the embankment of the LAD were compatible with the sloshing expected from the ground motion measured at the site. The only method available then to address these questions for this particular study was a series of laboratory shaking tests using a scale model; inundation models have yet to be tested for shaking reservoirs with sloping boundaries where run-up is important. The laboratory experiments revealed sharply resonant water-surface motions highly dependent on the excitation parameters and on the water depth. Four distinct modes of sloshing were observed. In the laboratory, these modes are realized for fixed depths and amplitudes of excitation by varying the frequency. The different regimes of sloshing are shown in Figure 9.25A, while the resonance results are shown in Figure 9.25B. Note that Ruscher [1998] was able to find the correct scaling for the dimensionless frequency, maximum wave height, and maximum run-up. Let v*, η*, and R* refer to the dimensional frequency, wave height, and run-up, respectively. L is the longitudinal length of the reservoir, from rim to rim, S the displacement at the base, and d the undisturbed depth. Figure 9.25B suggests that the correct dimensionless variables are:

v =v*

Ld η* L R* L , η= , and R = g S d S d

(9.107)

These dimensionless variables allow extrapolation from the model results to the prototype. Note that the scaling may be forcing-direction dependent, in which case L changes.

9.7.5

Introduction to Harbor Resonance

In his classic introduction to the chapter on Harbor Resonance (HR) in Ippen’s Estuary and Coastal Hydrodynamics [1966], Fred Raichlen wrote: It has been found that the maximum wave amplitude at locations within a harbor can be greatly affected by a resonance phenomenon. For certain incident wave periods a particular harbor can act as an amplifier, thereby magnifying the oscillations within the harbor above those which one would expect. This phenomenon of resonant oscillations in harbors has been termed by various investigators as seiche, surging, or range action. © 2003 by CRC Press LLC


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Harbor oscillations occur when incident storm waves contain frequencies at directions of incidence that cause the harbor to amplify their amplitudes at select locations. Harbor and basin oscillations can also be excited by incident tsunamis. Except for large ports, most harbors have natural frequencies that are longer than most storm waves and shorter than most tsunami waves; however, the possibility needs to be carefully evaluated because the exposure is great. Even if harbor oscillation does not result in casualties, the loss of use of harbor facilities even for a few days can result in substantial monetary losses, as one can extrapolate from the losses in Kobe (1995). The 1964 Alaskan tsunami caused an estimated U.S. $1 million damage to the Port of Long Beach. Notably, most of the damage was in the Cerritos channel and was due to the tsunami-induced currents, not to overtopping. More recently the 1999 Marmara earthquake caused a small tsunami and possibly harbor oscillations that caused an oil tanker to break off its moorings, triggering a refinery fire that burned for days. It is for this reason that the Federal Emergency Management Agency (FEMA) is currently (2002) developing standards and guidelines for ports and marine terminals for tsunami attack. The engineering problem of interest is to determine whether oscillations will be triggered, given an incident tsunami wave. The problem is not as straightforward as would appear, for tsunamis are highly transient waves, and occasionally it is difficult to identify frequencies that are sustained long enough to cause oscillations. Typically HR is evaluated numerically using complex numerical codes such as MIKE21 or CGWAVE or the proprietary code of Lee [1969]. All HR codes calculate the amplification of individual sinusoids at given incident directions everywhere inside the harbor. In this case, the directional spectrum of the incident tsunami is determined and frequencies close to the known natural frequencies of the harbor are identified and then input in the HR codes to determine amplification factors at specific locations inside the harbor. One disadvantage is that nonlinear coupling between frequencies is not considered, as the importance of the coupling has not yet been established. Long wave codes such as MOST or TUNAMI-N2 have been used to calculate HR as well, but their relative advantages compared to traditional HR codes have not yet been described. Numerically this is not a simple undertaking, since HR codes have to be run for several hours to follow the wave as it reflects and re-reflects back and forth inside the harbor. Numerical errors mount, particularly if the harbor has sloping boundaries, or outside the harbor at the boundaries of the computation, and occasionally numerical overflows appear. Here, first, certain simple analytic results will be presented suitable for first-order analysis to determine if more in-depth studies are necessary.

9.7.6

Harbor Resonance for Harbors of Simple Geometry

Raichlen [1966] describes the classic problem of a rectangular harbor of constant depth with an opening α, width 2w, length l, and depth d. The harbor is open to an infinite sea and the problem of interest is to determine the wavelength of the incident wave that will produce resonance. The coordinate system is as shown in Figure 9.26, and it is centered at the mouth entrance. The engineering problem is formulated as a forced, single-degree-of-freedom damped oscillator. The objective is not only to determine the resonant frequency but also the amplification of waves incident at the resonant frequency inside the harbor. In the classic theory of harbor resonance, a harbor of simple geometry is assumed to act as a damper oscillator. In dynamics, a damped oscillator is described by an equation of motion of the form d2y/dt2 + 2ζωdy/dt + ω2y = F(t). It is customary in dynamics to define Q = 1/2ζ. Q is the dissipation factor and it is a measure of the damping of the system and, in a simple system, it is independent of the frequency. It is also known as the Q-factor and it is infinite for a system with no dissipation. For one-degree-offreedom systems, critical damping occurs when Q = 1/2 and a system is underdamped when Q > 1. In analogy with dynamics, we define the power amplification factor R , a parameter that represents the ratio of the amplitude of the wave at some reference location inside the harbor to the incident wave amplitude, by:

R2 =


1

(1 − ω ω r )

2

+

2 1 ω ωr ) 2 ( Q

(9.108)


9-62


Resonance mode

Corner mode

Uniform mode

Ripples mode

FIGURE 9.25A The four modes of oscillation of the Los Angeles Reservoir.

where ω is the frequency of the incident wave and ωr is the resonant frequency of the harbor. In structural dynamics, the square of the denominator of Equation 9.108 is also known as the normalized impedance and sometimes denoted by Z = 1 – (ω/ω – r)2 + i(1/Q) (ω/ωr), so that R2 = 1/|Z|2. Miles and Munk [1961] note that harbors are complicated multi-degree-of-freedom systems; hence, Equation 9.108 is not applicable, except near resonance, which is what is of interest anyway. At resonance R = Q. In real harbors, Q varies between 2 and 10. Raichlen [1966] notes that a good approximation of Equation 9.108 is:  R r2 ω ≈ 1 + 4 Q 2 1 −  2 2 R  ωr 

(9.109)

when ω is very close to the resonant frequency ωr . A harbor dissipates energy both internally and through radiative losses at the harbor opening. Since the problem is linear, individual values of Q can be calculated and then their inverses added. Miles and Munk [1961] estimate the internal losses for a standing wave of amplitude a over depth h and conclude that the internal dissipation is negligible compared with the radiative losses. Hence, they continue on to estimate Q based on radiative losses only, by writing the mean potential and kinetic energies radiated from the mouth of the harbor as E = (1/4) ρg|η|2 per unit area. Then, the radiated energy over the harbor entrance is given by: dE = dt

∫

π/ 2

− π/ 2

2

ρgc η rdθ

(9.110)

while the energy within the harbor perimeter is: E=


1 2

∫

harborarea

2

ρg η d S

(9.111)


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10

M1

M2

M3

M4

η1

5 0 .5

-10 -15 0.00

0.05

0.10

ν

0.15

0.20

0.25

0.00

0.05

0.10

ν

0.15

0.20

0.25

0.00

0.05

0.10

ν

0.15

0.20

0.25

10

η2

5 0 .5

-10 -15

25 20

R

15 10 5 0

d=20mm, S=4mm; d=20mm, S=8mm; d=20mm, S=16mm;

d=30mm, S=9mm; d=40mm, S=8mm;

FIGURE 9.25B Normalized heights at the center (top), corner (middle), and maximum run-up on the Los Angeles Reservoir as a function of the normalized frequency.

When the harbor has an opening of width α, with kα 0.3, where S is now the distance from the circumference of the pile to the wall. No data have been reported for S/2R > 2, so it is unlikely that ground effects are important when the pile is more than two diameters away from the wall. Again, these results have been obtained for submerged piles under steady conditions, so their extrapolation to tsunami calculations should be with caution. Calculating the x − y current distributions and magnitudes and their time variation is possible using the SW equations described in Section 9.5. However, harbor resonance effects, breakwaters, and seawalls with characteristic sizes smaller than the grid spacing are transparent to the numerical computations. For example, a typical grid size ∆x, ∆y ≈ 100 m (333 ft) will miss all coastal structures smaller than 100 m, unless the grid is positioned appropriately. This is not as simple as it sounds, for numerical grids © 2003 by CRC Press LLC


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are calculated so as to model the hydrodynamic evolution correctly by attempting to maintain a constant number of grid points per wavelength, as the wavelength changes. Sophisticated higher-order simulation methods for calculating currents and forces are now under development but they have so far only been used to calibrate parameters through laboratory experiments. Their computational complexity only permits their use close to the structure, with initialization from flow variables such as velocities and wave heights obtained from SW models. Generally, wave forces can be thought of as having two parts, an inertial component and another due to the dynamic effects of the moving flow. When the structure is not fully submerged, generally, the forces are calculated in the manner of classic analyses of drag forces in fluids. When there is impact on a seawall and a structure that causes full reflection of the wave, then the forces are calculated using impact force theory.

9.8.2

Impact Forces on Seawalls

Impact forces are calculated by different methods, depending on whether or not the breaking wave is forming a surge or a bore. Impact forces on the vertical front face of a structure have traditionally been estimated using the classic formula of Cross [1967]. In his classic work, he quotes from the account by Eaton et al. [1961] of the attack of the 1960 tsunami on Hilo. At first there was only the sound, a dull rumble like a distant train, that came from the darkness far out towards the mouth of the bay … As our eyes searched for the source of the ominous noise, a pale wall of tumbling water, the broken crest of the third wave was caught in the dim light thrown across the water by the lights of Hilo. Cross [1967] proposed that the force on a seawall b wide is given by  1 Fwall (t ) =   ρgbη2 ( x = X w , t ) + C f (t ) ρbη( x = X w , t ) C 2  2 where ηw = η(x = Xw, t) is the water surface elevation on the wall located at some x = Xw , b is the width of the wall, C is the surge or bore velocity, and Cf = (1 + tan1.2θ) is a computed force coefficient. tanθ is the slope of the front face of the bore as it impacts the wall (see Figure 9.29). For practical applications, Cross suggested calculating η(x = Xw, t) as if the wall were not there, i.e., the bore would pass through the wall relatively unchanged. Therefore, Cf (t) could be a function of time, since the front slope of the wave may change as the wave evolves. Writing the depth at the seawall as hw , Ramsden and Raichlen [1990] wrote Cross’ equation as: Fwall (t )

2

η   C   1   ηw  + C (t ) w = (1 2) ρgbH  2   H  f  H   gH 

(9.131)

In Cross’ original formulation, Cf ≈ 1 for a gentle surge with θ = 0 and ranges to Cf ≈ 4.5 for θ = 70°, for a very steep bore. In other words, the impact force depends on the local depth at the seawall hw, the bore height H and the slope of the front face of the bore tanθ. As it turns out, the bore celerity depends exclusively on H/h. Figure 9.30 shows the variation of the bore slope, and normalized run-up as a function of the bore strength H/h.

9.8.3

Example of Impact Force Computation

One example of calculation of tsunami forces on seawalls is the case study performed by Ramsden [1993], who used the description by Eaton et al. [1961] of the May 23, 1960 tsunami impact on Hilo, Hawaii. Recall that the May 23, 1960 megathrust earthquake was the largest seismic event recorded in the past © 2003 by CRC Press LLC


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g

(a)

η(x,t)

θ(x,t)

z w

C(x) x u

SWL

h

dη/dx 1 H (b)

R(t) SWL h 3

FIGURE 9.29 Definition sketch for the forces on seawalls from bores. (After Ramsden, 1993.)

century, yet it did not generate the largest tsunami. The impact of the 1960 tsunami was dramatically different from that of the April 1, 1946 Aleutian tsunami, which was the largest tsunami of the past century in terms of height, underscoring how important source- and site-specific studies are for tsunami hazard assessment. Eaton writes that the two tide gages in Hilo harbor were “put out of action” by the leading depression wave before the highest wave, which was the third in the tsunami train, struck Hilo. Eaton and other observers from the United States Geological Survey situated themselves on the north end of Wailuku bridge and they measured wave heights with tape measures at “various reference points on the northernmost pier.” Their results are shown in the record in Figure 9.31, which is perhaps the only record available of a tsunami wave train with the signature of a bore. Eaton et al. [1961] wrote that the tsunami hit Hilo at 12:07 a.m. Hawaiian time (10:07 GMT) and the initial disturbance was reported as a leading elevation wave. The wave had traveled from Chile over 6600 mi (10,560 km) in about 15 h, for an average speed of 442 mph (707 km/h). The estimated arrival time had been 20 min earlier than observed, and Eaton speculated that part of the difference may be attributed to the slow propagation times over extreme shallow water near the bridge. It is also possible that a long leading depression wave of smaller height may have arrived but gone unnoticed because of its size. The crest of the first wave appears on the record as an elevation wave of height of about 1.2 m followed by a depression wave cresting at about −0.9 m. The second elevation wave crested 33 min later followed by −2.1 m depression 10 min later. The third elevation wave was a bore of approximate wave height of 6.1 m and crested about 20 min after the second wave. There were four other smaller waves measured behind the bore for the following 45 min. The entire phenomenon lasted for about 2 h after the first arrival. (In what follows, the calculations will be presented only in SI units.) The estimated time for the travel of the bore over the 2100 m separating the tip of the breakwater to the shoreline was about 2.5 min, giving an estimated speed of 12.7 m/sec. The local beach slope was estimated at tanβ = 0.015 or about 1:67. Assuming that the beach slope is fairly uniform, Ramsden [1993] then proceeded to calculate the force on a tall 3-m deep seawall at the shoreline from the Hw = 6.1-m high 1960 Hilo bore as follows (refer to the definition sketch shown in Figure 9.29). © 2003 by CRC Press LLC


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Tsunami and Seiche

3.00 Experimental:

a)

Theoretical:

1.00

solitary waves undular bores turbulent bores: S=0.0 turbulent bores: S=0.02 Tanaka (1986)

IIdη/dxII

120° sharp crested wave 0.50 0.30

0.10

undular bores

strong turbulent bores

range of dry bed surge data

0.05 10 Theoretical: Su and Mirie (1980) moving hydraulic jump reflection Stoker (1957)

b) 7

R/2H

5

undular bores

strong turbulent bores

3

1 3 c)

Rg/c

2

1

range of dry bed surge data

0.7 0.5 strong turbulent bores

0.3 undular bores 0.1 0.1

0.3

0.5

1

3

5

10

30

H/k FIGURE 9.30 Experimental and theoretical maximum water surface slopes (a); run-up normalized by twice the incident wave height (b); and run-up normalized by twice the velocity head due to the wave celerity (c).



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14 12 10 8 6 4 2 0

Approx. mean Lower low water

-2 -4 -6

0h00m 10h00m

MAY 23

0h30m

1h00m 11h00m HOURS

1h30m

2h00m (Hawaiian Time) 12h00m (G.C.T.)

FIGURE 9.31 Measurements of the 1960 tsunami arriving at Hilo, Hawaii, from measurements made at the Wailuku River bridge (height in feet). (After Eckart et al., 1961.)

Given that the bore followed a −2.1-m depression wave, the estimated local depth hw at the tip of the seawall as the bore impinged was hw = 0.9 m, since the total depth was 3 m. The depth h where the estimate of H = 6.1 m was made has to be estimated so that the effective bore strength H/h can be calculated; recall what is known is only the depth at the seawall hw . Finding H/h is, in general, an iterative procedure and one uses Figure 9.30A. First, find the distance 3L from the seawall where the slope is calculated. Anticipating that this is a strong bore, first guess an effective frontal slope for the bore of dη/dx = 0.3. This implies that the effective horizontal length scale of the bore face L = H/(dη/dx) = 6.1 m/ 0.3 = 20.3 m. Therefore, the depth h is given by h = hw + 3L tanβ = 1.8 m. Therefore, given that H = 6.1 m then H/h = 3.4, and according to Figure 9.30A, the guess of dη/dx = 0.3 is adequate. Using Figure 9.32, the F/Fi ≈ 3.1, using the top of the envelope of data values in the figure. Then Fi = (1/2)ρg(2H + hw)2 ≈ 842 × 103 Nt/m, therefore F = (F/Fi) × Fi.= 2.6 × 106 Nt/m. Using Figure 9.30B, it is estimated that the expected run-up on the seawall is R/2H = 2.6; therefore, the expected run-up had the wall been that high is R = 32 m. The overturning moment can be estimated from Figure 9.33. For H/h = 3.4, the top of the data envelope suggests an M/Mi = 6.6; therefore, M = 23.1 × 106 Nt/m. If one uses the Cross [1967] equation with the maximum run-up as the maximum height on the wall of R = 32 m, then F = (1/2)ρgR2 + ρCfRc2, per unit width of the seawall. Given that dη/dx = tanθ = 0.3, then Cf = 1 + (tanθ)2 = 1.09. Using the estimate of c = g (H + hw ) = 8.25 m/sec, then F = 5.0 × 106 Nt + 2.4 × 106 Nt = 7.4 × 106 Nt/m. However if one uses the local speed of the bore C as obtained from Figure 9.34, then c/ gh = 3.3 for H/h = 3.4. Then F = (1/2) ρg (H + hw)2 + 2ρCf Hg (hw + H) = 240 × 103 + 3.3 × 836 × 103 Nt/m = 3 × 106 Nt/m. Also, note that if one used the height of the bore H and the depth ahead of the bore hw instead of the effective H/h, then H/hw = 6.8, and then F/Fi = 4.9, giving a force of 4.1 × 106 Nt/m, which is 57% higher than the force calculated from using the effective H/h. Clearly, extreme care is warranted in using the appropriate H/h in the force calculations. Ramsden [1993] points out that when b/H ≈ 1, then three-dimensional effects take over. Threedimensional effects are expected to reduce the overall force. On the other hand, when b 120, Cd = 2.0. The reason is that the larger the width of the structure, the larger the drag, not only because the frontal area increases, but also because of suction pressures smaller than hydrostatic on the back face. The wider the object, the smaller the back pressure. For velocities V > 10 fps, CCM recommends:  1 Fdyn =   Cd ρV 2dsb  2

(9.140)

Debris loads are a significant hazard during tsunami attack. During the 1946 Alaskan tsunami, in the area most affected on Unimak and Senak Island, the tsunami carried logs from a nearby lumber plant and deposited them to elevations up to 42 m (140 ft). The debris line from tsunami-borne logs is still visible along the southern coastlines of Unimak and Senak. Logs and driftwood are omnipresent along the Pacific Northwest as well. In the densely populated beaches of Southern California parking lots front the first row of houses. Contrary to intuition, it does not take a large wave to float a vehicle and carry it inland. During the 1995 Manzanillo, Mexico tsunami, a 3-m (10-ft) tsunami carried recreational vehicles more than 100 m (333 ft) inland. Waterborne debris can become battering rams when they hit structures. At high speeds, large pieces of driftwood can resemble incoming missiles, at least as far as the initial impact to a wooden structure is concerned. Calculating debris impact loads involves guesswork as to the size of the object being carried by the flow and whether it is dragging along the beach face or the ocean floor. The CCM recommends for the impact load Fi, Fi = wV ( gt )

(9.141)

where w is the weight of the object impacting the structure, V is its velocity, and t is the duration of impact. As per the CCM, in the absence of any specific information as to the size of debris, consider w = 1000 lb, with V = gds for tsunamis. Clearly, large objects such as vehicles are not carried at the same speed as the tsunami current, so Equation 9.141 provides again a conservative estimate. In terms of the duration time t the CCM recommends a range of 0.7 to 1.1 sec for wood walls, 0.5 to 1.0 for wood piles, 0.2 to 0.4 for reinforced concrete walls, 0.3 to 0.6 for concrete piles, and 0.3 to 0.6 for reinforced concrete piles and concrete masonry walls and pipes. The values differ because of the differences in stiffness among the different materials. Heavier structures on shorter piles are stiffer, so it would be reasonable to use the low values in the ranges and use the upper values for lighter structures on longer piles.



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9.9 Producing Inundation Maps 9.9.1 The California Experience Inundation maps provide emergency managers in coastal communities necessary tools to plan and mitigate tsunami disasters. Inundation maps are not only useful in assessing the population and facilities at risk, but are also helpful in planning for emergency response. The preparation of inundation maps involves the assessment of the local geologic hazards, their interpretation in terms of tsunami initial conditions, and the calculation of the resulting potential coastal inundation. Inundation maps are now under preparation for most coastal areas of the Pacific states of the United States, most coastal areas of Japan, and several other vulnerable areas around the world. This section presents, as a case study, the preparation of tsunami inundation maps in California. Even using these state-of-the-art inundation prediction tools, California presents unique challenges in assessing tsunami hazards. First, there is an extremely short historic record of tsunamis in the state. Whereas in some areas in the Pacific 1000-year-long records exist, in California there are none known before the nineteenth century. Several tsunamis have been reported since 1800, but in most cases the information is not sufficient for reasonable inferences of the inundation. Second, most of the geologic work in the state has concentrated on identifying the risks associated with on-shore faults. Even at the time of writing (May 2002), there is scant and mostly unpublished information on offshore faults or landslide and slump scars suggestive of past submarine mass failures. Third, earlier estimates of tsunami hazards relied almost entirely on far-field sources and used pre-1980s inundation mapping technology. This created the impression among policy planners and the general public that the tsunami hazard was small. Fourth, near-shore seismic events may trigger tsunamis arriving within less than 20 min from generation, allowing little time for evacuation. Fifth, the coastal population density is the highest among the five Pacific states, and a tsunami arriving on the southern California beaches on a summer Sunday afternoon with tens of thousands of people on the beach poses nontrivial risks whose mitigation needs to be carefully planned for.

9.9.2

Existing Analyses of Tsunami Hazards in California

The most comprehensive calculation of tsunami hazards for California is the work of Houston and Garcia [1974] and of Houston [1980], both of which focused on the hazard in Southern California from farfield events. McCulloch [1985] also focused on the hazards in the Los Angeles region primarily from farfield events, but also considered several local events. Satake and Sommerville [1992] analyzed the Lompoc 1927 earthquake and the associated local hazards. In a seminal review, McCarthy et al. [1993] analyzed the historic records of tsunamis in California and predicted qualitatively the hazard over the entire State. Synolakis et al. [1997b] reviewed pre-1997 studies and observed that the earlier run-up estimates did not include inundation calculations. When performed with the new generation of inundation models, runup estimates were occasionally up to 100% higher than the earlier calculations suggested, depending on the near-shore topography. Borrero et al. [1999, 2001] studied near-shore tectonic, landslide, and slump sources in East Santa Barbara channel and produced run-up estimates ranging from 2 to 13 m. Locat et al. [2002] provide estimates for the leading wave heights for landslide-generated waves off Palos Verdes ranging from 10 to 40 m, depending on the initiation depth. The bathymetry off Palos Verdes is shown in Figure 9.35, with features suggestive even to non-marine geologists of landslide scarps. The current state of understanding is reviewed in Borrero [2002] and in Synolakis et al. [2002c]. Houston and Garcia [1974] used a combination FD solution and analytic solution of the LSW to calculate tsunami propagation, except in the Santa Monica and San Diego Bays, where they used an FE solution to resolve possible local resonance effects. They argued that the only reliable data for defining source characteristics at that time were from the 1964 Alaskan and the 1960 Chilean earthquakes. Based on these data, they approximated the initial ground deformation by a hypothetical uplift mass of ellipsoidal shape, about 600 mi long, with an aspect ratio of 1:5 and maximum vertical uplift of 8 to 10 m.



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FIGURE 9.35 The bathymetry in Santa Monica and San Pedro Bays. (After Bohannon and Gardner, 2002.) TABLE 9.4 Revised Predictions for Tsunami Hazards in Southern California Location

R100

R500

POLA/POLB Port Huaneme Santa Barbara

8 ft 11 ft 15 ft

15.0 ft 21.0 ft 33.0 ft

They then divided the Aleutian trench into segments and calculated the wave evolution from each segment, and repeated the procedure for tsunamis from the Peru-Chile trench to derive 100-year (R100) and 500-year (R500) tsunami run-up heights. Borrero [2002] and Synolakis et al. [2002c] have argued that the 100-year hazard in California is dominated by distant events, hence the Houston and Garcia analysis is probably adequate. Given the recent results on offshore landslide hazards, they argued that the 500-year hazard is dominated by local events and revised Houston and Garcia’s estimates. An example of the revised estimates is given in Table 9.4. McCulloch’s [1985] study was a seminal work on tsunami hazard potential in Southern California. McCulloch relied on Houston’s results for far-field tsunamis and then used seismological data to make predictions for near-shore events. McCulloch relied on several empirical formulas developed in Japan. These formulas had been extensively used before 1992; since then, high quality run-up data from the 1992 to 2001 events for many areas around the Pacific suggest that these formulas may only be applicable in Japan and that they can substantially underpredict the run-up elsewhere. McCulloch used the Japanese data to argue that a local seafloor earthquake having a magnitude 7.5 and a hypocentral depth of 4 km (2.5 mi) to 14 km (8.75 mi) could produce a tsunami accompanied by a run-up height of 4 m (13 ft) to 6 m (20 ft). In 1985, a 6-m tsunami may have appeared a marginal hazard, even though the tsunami height in the 1964 Alaskan tsunami in Crescent City, which killed 11 people, was about 6.2 m (20.6 ft), while the run-up height was 3.8 m (12.6 ft). The 1992 to 2001 postevent field surveys have shown that even a 4-m tsunami can cause extensive damage and flooding in flat coastlines, such as those in Santa Monica Bay or in Orange and San Diego Counties. Perhaps the most serious implication of McCulloch’s assessments is his conclusion that landslidegenerated waves would be small. As noted earlier, McCulloch’s calculation had an arithmetic error and his 0.014 m value should have been 14 m, consistent with newer estimates. Locat et al. [2002] provide estimates for the same slide ranging from 10 to 40 m. Homa Lee (private communication, 10/19/01) has suggested that a slide in this location may have happened in the past 500 years. McCarthy et al. [1993] performed a systematic analysis of all historic and possible tsunami hazards in California and they qualitatively calculated the tsunami hazard in California as high along the coast from Crescent City to Cape Mendocino, moderate south of the Cape to north of Monterey, high south of © 2003 by CRC Press LLC


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runup (m)

20 15 10 5 0

runup (m)

Monterey to Palos Verdes, and moderate south of Palos Verdes to San Diego. Synolakis et al. [1997b] revisited the McCarthy et al. estimates and identified the need for modeling from near-shore events. As an example, they considered a hypothetical fault rupture along the San Clemente fault. They found that results using the older pre-1980 methodology were as much as 50% lower than results using current inundation models. Borrero et al. [2001] studied tsunamis in East Santa Barbara Channel using the state-of-the-art inundation code used by NOAA-PMEL and known as MOST. They considered tsunamis generated from coseismic displacements from thrust faults underlying the Santa Barbara Channel. They also considered tsunamis generated by slope failures along the walls of the Santa Barbara Channel. Their results include predictions from the Gaviota mud flow [Edwards et al. 1993] and from the recently mapped Goleta slide [Greene et al., 2000]. Borrero et al. [2001] and Synolakis et al. [2002c] used a variety of publicly available maps and sources to develop a 250 m ≈ 9 arcsec computational grid including the Scripps Institute of Oceanography 3 arcsec grid of near-shore bathymetry. Examples of their work and of run-up distributions along the coast of Santa Barbara County are shown in Figure 9.36. Interestingly, their results are consistent with earlier reports of 9-m (30-ft) run-up for the 1812 tsunami [McCulloch, 1985] — revised “by reference to other earlier unpublished reports as 3–4 m (10–13.3 ft).” Unpublished results suggest that there is sedimentologic evidence also to associate the landslide with the 1812 event. Borrero et al.

20 15 10 5 0

Goleta slide, case 1

Goleta slide, case 2 -18m

60

Goleta case 1 50

-18m +6m

40

Goleta case 2

200m

400m +6m

30

200m

20

Santa Cruz Island

600m

10

1000m

0 0

20

40

60 Kilometers

FIGURE 9.36 Run-up estimates for two different locations of the Goleta slide.


80


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runup (m)


25 20 15 10 5 0 Los Angeles Harbor

Kilometers

40

-12m

30

+4m

20

10 wave gauge locations contours of initial surface

0 0

10

20

Kilometers

30

40 0

10

20

runup (m)

FIGURE 9.37 Run-up estimates from tsunamis triggered by the Palos Verdes debris avalanche.

[2001] found that purely tectonic sources could generate tsunamis with ≈ 2-m (6.7-ft) run-up, while combination of tectonic sources and submarine mass movements could generate extreme run-up of ≈ 20 m (66.67 ft) in one location. For the latter, they observed narrow run-up peaks and warned that, “A wave of this size anywhere along the populated shores of southern California would be devastating, and further mapping work is urgently needed to quantify this possibility.” Borrero [2002] also estimated the economic losses associated with a tsunami in San Pedro Bay, as shown in Figure 9.37. His results are shown in Figure 9.38, which also compares the relative economic impact from a tsunami and from flooding from a dam break.

9.9.4

Developing Inundation Maps for the State of California

In 1996, the Tsunami Hazard Mitigation Federal/State Working Group prepared a report to the United States Congress recommending the preparation of inundation maps for five states: Alaska, California, Hawaii, Oregon, and Washington. The report led to mobilization of significant federal resources for tsunami hazards mitigation, and to the establishment of the U.S. National Tsunami Hazard Mitigation Program (NTHMP), which provides resources in all five states for mitigating tsunami hazards. The NTHMP was the focus of a program review during the International Tsunami Symposium held on August 5 to 7, 2001 in Seattle, Washington [NOAA, 2001]. As early as 1997, the California’s Coastal Region Administrator of the Governor’s Office of Emergency Services (OES), through a series of workshops and publications, informed local governments and © 2003 by CRC Press LLC


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FIGURE 9.38 Socioeconomic impact from a possible rupture of the Palos Verdes debris avalanche and of a dam break around Long Beach, California.

emergency agencies of the plans to address tsunami hazards and presented the NTHMP. OES solicited input as to the levels of hazards to be represented on the maps, as the short length of the historic record did not permit a comprehensive probabilistic hazard assessment. It was then decided that the maps would include realistic worst-case scenarios to be identified further in the mapping process. In 1998, as funding became available for the state, OES contracted to the Tsunami Research Program of the University of Southern California the development of the first generation of inundation maps for the state. The State of California has the most densely populated coastlines of the five states in the NTHMP. The state had to utilize the same limited resources as the other four but assess offshore tsunami hazards over a much longer coastline. A comprehensive tsunami hazard evaluation involves both the probabilistic hazard assessment of different far-field and near-field, on-shore and offshore sources and the hydrodynamic computation of the tsunami evolution from the source to the target coastline. Given the level of funding, this was not feasible, and this presented another challenge for California. Given the quantitative agreement between model results and measurements for the 1964 tsunami of the work of Houston and Garcia [1974], it was decided to focus on near-shore tsunami hazards, which had not been modeled before 1999. If inundation predictions from near-shore events proved smaller than twice the far-field tsunami results of Houston and Garcia, then far-field sources would have to be considered as well. Early results suggested that for the areas studied, near-shore sources produced higher inundation heights that were twice the 100-year values of Houston and Garcia, hence only near-shore sources were considered. The State of California was also faced with the decision of choosing its mapping priorities. By considering the geographic distribution of population centers, the state opted to perform modeling of the Santa Barbara and San Francisco coastlines in year one, of Los Angeles and San Diego in year two, and of Monterey Bay in year three. The next decision was the resolution of the numerical grids to be used © 2003 by CRC Press LLC


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in developing the maps. The technology existed for high-resolution maps with grids of sizes as small as 5 m (16.7 ft) square, but this would result in a relatively small spatial coverage with large computational grids and painful computations. It was decided to produce maps at 125 m (417 ft) resolution, based on Titov and Synolakis [1997], who had argued that dense grids may improve numerical accuracy but do not improve the realism if the available bathymetric/topographic sets are not of similar resolution. In the State of California, the best available sets varied in resolution between 50 m (167 ft) and 150 m (500 ft). Also, given the uncertainties in locating and understanding source mechanisms, results with higher resolution would be misleading. The next question was whether to provide emergency planners with inundation results at different levels of risk. For example, one suggestion was to include low- and high-risk lines on the inundation maps. Another suggestion was to provide separate lines for near-field and far-field events. On discussing these issues with emergency preparedness professionals across the state, it was felt that a single line representing a worst-case scenario was preferable, for it simplified the preparedness response of city officials and it better informed the general public. Further, without a probabilistic hazard assessment it was difficult to rank the relative risk from different scenarios. Lines identifying risk zones for near-field and far-field events could also prove cumbersome and confusing for the public. It was therefore decided to consider, for every locale in the region under consideration, the worst-case near-shore event that was plausible based on the available historic earthquake and tsunami information. The inundation mapping effort first identified offshore faults and offshore landslide and slump hazards. Difficulties encountered included the lack of detailed high-resolution marine surveys over all target coastlines. With the exception of marine surveys undertaken by the U.S. Geological Survey off Santa Monica Bay and of the Monterey Bay Aquarium Marine Institute (MBARI) off Santa Barbara and Monterey Bay, high-resolution surveys are not available for other parts of the state, if indeed they do exist at all. Hence, and given that on-shore earthquakes can trigger submarine landslides, in regions where marine geology data did not exist, steep submarine soft sediment slopes were considered as possible sources. Offshore faults and slide-prone areas were then used to develop initial tsunami waves as discussed in Borrero et al. [2001], and then the inundation model MOST was used to obtain inundation heights and penetration distances along the target coastline. The inundation predictions for any given event are highly bathymetry and topography dependent and vary substantially along the coast. Since the location of the source is seldom accurately known, the source was moved around within the range of uncertainty. Along California’s flat coastlines, this relocation of the tsunami sources resulted in relocation of the maximum along the coast. When asked, emergency planners preferred to have a single value for each region identifying the maximum elevation that tsunami waves from the different local offshore sources would attain. This practice would simplify the communication of the risk to the public and it would provide information that was easy to remember and implement in regional emergency preparedness. For example, a region could plan for tsunami evacuation areas above a certain minimum elevation across its jurisdiction. Hence, in the development of the maps, sources were relocated along the coast and the highest inundation value among different runs identified. Interestingly, in the areas studied there were no areas that consistently experienced higher run-up than adjacent locales. Synolakis et al. [2002c] found that most low-lying coastal areas could experience high run-up, if the source was relocated in an appropriate direction, within the uncertainties of defining the source. Thus, the inundation maps for California do not represent the inundation from any particular event or characteristic earthquake, but the locus of maximum penetration distances from relocating worst-case scenario events. Once draft versions of the maps became available, OES presented them in regional meetings with emergency preparedness officers and other interested parties such as the State Lands, Seismic Safety and Coastal Commissions. Further input was solicited, and an emergency response manual [OES, 2002] with guidelines for mitigation was produced. OES also produced a video for school use and distributed numerous copies of other commercial video programs describing tsunami hazards. The development of the state’s inundation maps was featured in four Discovery channel television documentaries and in numerous national and local news stories. One representative map for South San Francisco is shown in Figure 9.39. © 2003 by CRC Press LLC


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FIGURE 9.39 Example of a California inundation map for South San Francisco.

Since many engineers are occasionally asked to make recommendations on using inundation maps, it is appropriate to end with some of the guidelines from OES’s [2000] Local Planning Guidance on Tsunami Response: • The development of a tsunami plan requires a multidisciplinary approach and should involve local specialists (emergency responders, planners, engineers, utilities and community based organizations). The city or county administrative office should appoint a tsunami plan working group and designate a chairperson, usually the emergency services manager. • One of the most critical elements of a tsunami plan is the evacuation and traffic control plan. A distant-source tsunami may allow several hours to evacuate. A near-source tsunami may require immediate self-evacuation through areas damaged by the earthquake. Each jurisdiction should analyze how much time an evacuation would require and build that into the decision-making procedure. • Inundation projections and resulting planning maps are to be used for emergency planning purposes only. They are not based on a specific earthquake and tsunami. Areas actually inundated © 2003 by CRC Press LLC


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by a specific tsunami can vary from those predicted. The inundation maps are not a prediction of the performance in an earthquake or tsunami of any structure within or outside the projected inundation area. • Elements to consider in developing an evacuation plan are 1. Locate optimum evacuation routes. The primary objective is to move up and inland away from the coast. Finally, for further information on tsunamis, the author recommends the following URLs: http://www.pmel.noaa.gov/ http://www.pmel.noaa.gov/tsunami/home.html http://www.usc.edu/dept/tsunamis http://www.geophys.washington.edu/tsunami/ http://www.wsspc.org/tsunami/tsunami.html http://geopubs.wr.usgs.gov/open-file/of99–360/ http://www.civil.tohoku.ac.jp/english/tunami/node1.html http://walrus.wr.usgs.gov/staff/egeist/egeist.html http://www.earth.northwestern.edu/research/okal/ http://yalciner.klare.metu.edu.tr/ http://www.tsunami.org/ http://www.mbari.org/data/mapping/SBBasin/basin.htm http://omzg.sscc.ru/tsulab http://tsun.sscc.ru/htdbpac

Acknowledgments The author acknowledges the work of his former Ph.D. students, Drs. Utku Kanoglu, Vasily Titov, Cristophe Ruscher, Jose Borrero, and Srinivas Tadepalli, and his current students, Irina Hoffman, Diego Arcas, Matt Swensson, and Burak Uslu. They are all magnificent. The intellectual contributions of Professors Raichlen, Okal, Liu, Yeh, and Yalciner and of NOAA-PMEL Director Dr. Eddie Bernard and Frank Gonzalez are gratefully acknowledged here. I am equally grateful to Rich Eisner and Dick McCarthy and to my colleagues at the LA County Emergency Preparedness Commission for all their ideas, enthusiasm, and encouragement. Without the generous support of the Earthquake Hazard Mitigation Program of the National Science Foundation and of its project manager, Dr. Cliff Astill, we would still be estimating tsunami hazards with slide rules. Charles Scawthorn and Joanne Blake provided invaluable editing assistance. Finally, the author acknowledges Chris Gaudiot, whose support in the benwillian saga made it all possible.

References Abe, K. and Ishil, H. 1980. “Propagation of Tsunami on Linear Slope between Two Flat Regions. II. Reflection and Transmission,” J. Phys. Earth, 28, 543–552. Abramowitz, M. and Stegun, I.A. 1964. Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics Series 55, U.S. Department of Commerce, Washington, D.C. Berkhoff, J.C.W. 1972. “Computation of Combined Refraction-Diffraction,” Proc. 13th Coastal Engineering Conference, Vancouver, vol. 1, pp. 471–490, American Society of Civil Engineers, New York. Berrard, A. and Burch, J.M. 1987. Introduction to Matrix Methods in Optics, University Microfilms International, John Wiley & Sons, New York. Bohannon, R.G. and Gardner, J.V. 2002. “Submarine Landslides of San Pedro Sea Valley, Southwest Los Angeles Basin,” in Prediction of Underwater Landslide Hazards, in preparation. Borrero, J., Ortiz, M., Titov, V., and Synolakis, C. 1997. “Field Survey of Mexican Tsunami Produces New Data, Unusual Photos,” Eos Trans. Am. Geophys. Union, 78, 85, 87–88. © 2003 by CRC Press LLC


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Borrero, J.C., Dolan, J.F., and Synolakis, C.E. 2001. “Tsunamis within the Eastern Santa Barbara Channel,” Geophys. Res. Lett., 28(4), 643–646. Briggs, M.J., Synolakis, C.E., Harkins, G.S., and Hughes, S.A. 1993. “Large Scale Three-Dimensional Laboratory Measurements of Tsunami Inundation,” Pure Appl. Geophys. Briggs, M.J., Synolakis, C.E., Harkins, G.S., and Green, D. 1994. “Laboratory Experiments of Tsunami Runup on a Circular Island,” Pure Appl. Geophys., 144, 569–593. Briggs, M.J., Synolakis, C.E., Harkins, G.S. et al. 1995. “Laboratory Experiments of Tsunami Runup on a Circular Island,” Pure Appl. Geophys., 144 (3–4), 569–593. Carrier, G.F. 1966. “Gravity Waves of Water of Variable Depth,” J. Fluid Mech., 24, 641–659. Carrier, G.F. and Greenspan, H.P. 1958. “Water Waves of Finite Amplitude on a Sloping Beach,” J. Fluid Mech., 17, 97–110. Chrystal, G. 1905. “On the Hydrodynamical Theory of Seiches,” Trans. R. Soc. Edinburgh, 41 (Part III), 599–649. Cross, R.H. 1967. “Tsunami Surge Forces,” J. Waterways Harbor Division, 93 (4), 201–231. Dean, R.G. and Harleman, D.R.F. 1966. “Interaction of Structures and Waves,” in Coastline and Estuarine Hydrodynamics, Ippen, A.T., Ed., McGraw Hill, New York, 341–402. Demirbilek, Z., 1994. “Comparison between REFDIFS and CERC Shoal Laboratory Study,” unpublished report, Waterways Experimental Station, Vicksburg, MS, p. 53. Demirbilek, Z. and Pachang, V. 1998. “CGWAVE: A Coastal Surface Water Wave Model of the Mild Slope Equation.” Demirbilek, Z., Xu, B., and Pachang, V. 1996. “Wave-Current Interaction at Inlets,” in Proc. 25th International Coastal Engineering Conference, 1219–1232. Eaton, J.P., Richter, D.H., and Ault, W.U. 1961. “The Tsunami of May 23, 1960 on the Island of Hawaii,” Bull. Seismol. Soc. Am., 51 (2), 135–157. Edwards, B.D., Lee, H.J., and Field, M.E. 1995. “Seismically Induced Mudflow in the Santa Barbara Basin, California,” in Submarine Landslides: Selected Studies in the U.S. Exclusive Economic Zone, Schwab, W.C., Lee, H.J., and Twichell, D.C., Eds., U.S. Geological Survey Bulletin, pp. 167–175. Eissler, H.K. and Kanamori, H. 1987. “A Single-Force Model for the 1975 Kalapana, Hawaii, Earthquake,” J. Geophys. Res. Solid Earth, 92 (6), 4827–4836. Fryer, G.J., Watts, P., and Pratson, L.F. 2001. “Source of the Tsunami of 1 April 1946: A Landslide in the Upper Aleutian Forearc,” Unpublished manuscript. Fujima, K. and Shuto, N. 1990. “Formulation of Friction Laws for Long Waves on a Smooth Dry Bed,” Coastal Eng., 33 (1), 25–47. Gardarsson, S.M. 1997. “Shallow-Water Sloshing,” Ph.D. thesis, University of Washington, Seattle. Gerard, A. and Burch, J.M. 1987. Introduction to Matrix Methods in Optics, University Microfilms International, John Wiley & Sons, New York. Gjevik, B. and Pedersen, G. 1981. Run-Up of Long Waves on an Inclined Plane, Preprint Series, Institute of Mathematics, University of Oslo, Norway. Goring, D.G. 1978. Tsunamis: the Propagation of Long Waves onto a Shelf, Report No. Kh-R-38, W.M. Keck Laboratory of Hydraulics and Water Resources, Division of Engineering and Applied Science, California Institute of Technology, Pasadena. Green, G. 1837. Cambridge Philosophical Transactions, Vol. 6, p. 457. Green, H.G., Maher, N., and Paull, C.K. 2000. “Landslide Hazards off of Santa Barbara California (Abstr.),” American Geophysical Union Fall Meeting.` Gusiakov, V.K. 2001. “Basic Pacific Tsunami Catalogs and Database, 47 BC–2000 AD,” in Proc. International Tsunami Symposium, August 7–10, Seattle, WA, pp. 263–272. Gustafsson, B. and Kreiss, H.-O. (1979). “Boundary Conditions for Time Dependent Problems with an Artificial Boundary,” J. Comp. Phys., 30, 333–351. Gutenberg, B. 1939. “Tsunamis and Earthquakes,” Bull. Seismol. Soc. Am., 29(4), 517–526. Hall, J.V. and Watts, J.W. 1953. “Laboratory Investigation of the Vertical Rise of Solitary Waves on Impermeable Slopes,” Tech. Memo 33, Beach Erosion Board, U.S. Army Corps of Engineers. © 2003 by CRC Press LLC


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Hasegawa, H.S. and Kanamori, H. 1987. “Source Mechanism of the Magnitude 7.2 Grand Banks Earthquake of November 1929: Double Couple or Submarine Landslide?” Bull. Seismol. Soc. Am., 77(6), 1984–2004. Heinrich, P. 1992. “Nonlinear Water Waves Generated by Submarine and Aerial Landslides,” J. Waterway Port Coastal Ocean Eng., 118 (3), 249–266. Houston, J.R. 1980. “Type 19 Flood Insurance Study,” Waterways Experiment Station Rep. H-80-18, U.S. Army Corps of Engineers. Houston, J.R. and Garcia, A.W. 1974. “Type 16 Flood Insurance Study,” Waterways Experiment Station Rep. H-74-3, U.S. Army Corps of Engineers. Imamura, F., Synolakis, C.E., Gica, E., Titov, V., Listanco, E., and Lee, H.J. 1995. “Field Survey of the 1994 Mindoro Island, Philippines Tsunami,” Pure Appl. Geophys., 144 (3–4), 875–890. Imamura, F., Subandono, D., Watson, G., Moore, A., Takahashi, T., Matsutomi, H., and Hidayatt, R. 1996. “Irian Jaya Earthquake and Tsunami Cause Serious Damage,” Eos Trans. Am. Geophys. Union Ippen, A.T. (Ed.). 1996. Coastline and Estuarine Hydrodynamics, McGraw-Hill, New York. Jiang, L. and LeBlond, P.H. 1992. “The Coupling of a Submarine Slide and the Surface Waves which it Generates,” J. Geophys. Res. Oceans, 97 (C8), 12731–12744. Kanamori, H. 1985. “Non-Double-Couple Seismic Source (Abstr.),” Proceedings of the 23rd General Assembly, International Association of Seismological Physics Earth International, Tokyo, p. 425. Kanamori, H. 1972. “Mechanisms of Tsunami Earthquakes,” Phys. Earth Planet Int., 6, 346–359. Kanamori, H. and Anderson, D.L. 1975. “Theoretical Basis of Some Empirical Relations in Seismology,” Bull. Seismol. Soc. Am., 65 (5), 1073–1095. Kanoglu, U. 1996. “The Runup of Long Waves around Piecewise Linear Bathymetries,” Ph.D. thesis, University of Southern California, Los Angeles. Kanoglu, U. and Synolakis, C.E. 1988. “Long Wave Runup on Piecewise Linear Topographies,” J. Fluid Mechanics, 374, 1–28. Keller, J.B. and Keller, H.B. 1964. “Water Wave Runup on a Beach,” ONR Rep. Contract NONR-3828(00), Department of the Navy, Washington, D.C. Kobayashi, N. and Greenwald, J.H. 1987. “Wave Reflection and Runup on Rough Slopes,” J. Waterways Ports Coastal Eng., 113, 282–298. Korgen, B.J. 1995. “Seiches,” Am. Sci., 83, 330–341. Lamb, H. 1932. Hydrodynamics, 6th ed., Dover, New York. Lee., J.J. 1969. “Wave Induced Oscillations in Harbors of Arbitrary Shape,” Ph.D. thesis, California Institute of Technology, Pasadena. Lee, J.J., Lai, C.P., and Li, Y. 1998. “Application of Computer Modeling for Harbor Resonance Studies of Long Beach Los Angeles Harbor Basins,” Proc. 26th ICCE, Copenhagen, Denmark, American Society of Civil Engineers, New York. LeMehaute, B. and Wilson, B.W. 1962. “Harbor Paradox,” J. Waterways Harbors Division, (May), 173–195. Liu, P.L.-F. and Synolakis, C.E. 2003. Tsunami Hydrodynamics, World Scientific, London, in preparation. Liu, P.L.-F., Synolakis, C.E., and Yeh, H.H. 1991. “Report on the International Workshop on Long Wave Runup,” J. Fluid Mech., 229, 675–688. Liu, P. L.-F., Cho, Y.-S, Briggs, M.J., Kanoglu, U., and Synolakis, C.E. 1995. “Runup of Solitary Waves on a Circular Island,” J. Fluid Mech., 320, 259–285. Locat, J., Locat, P., and Lee, H.J. 2001. “Numerical Analysis of the Mobility of the Palos Verdes Debris Avalanche, California, and its Implications for the Generation of Tsunamis,” Unpublished manuscript. Mansinha, L. and Smylie, D.E. 1971. “The Displacement Fields of Inclined Faults,” Bull. Seismol. Soc. Am., 61, 1433–1440. McCarthy, R.J., Bernard, E.N., and Legg, M.R. 1993. “The Cape Mendocino Earthquake: A Local Tsunami Wakeup Call?” in Proc. Eighth Symposium on Coastal and Ocean Management, New Orleans, pp. 2812–2828.



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McCulloch, D.S. 1985. “Evaluating Tsunami Potential,” in Evaluating Earthquake Hazards in the Los Angeles Region: An Earth Science Perspective, U.S. Geological Survey Professional Paper 1360, pp. 375–414. Mei, C.C. 1989. The Applied Dynamics of Ocean Surface Waves, World Scientific, London. Merian, J.R. 1828. Über die Bewegung tropfbarer Flüssigkeiten in Gefassen, Basle, see Von der Muhll, Math. Ann. 27, 575. Meyer, R.E. 1988. “On the Shore Singularity of Water Wave Theory,” Physical Fluids, 29, 3142–3183. Miles, J. and Munk, W. 1961. “Harbor Paradox,” J. Waterways Harbors, WW3, 111–130. Newman, A.V. and Okal, E.A. 1998. “Teleseismic Estimates of Radiated Seismic Energy: The E/M0 Discriminant for Tsunami Earthquakes,” J. Geophys. Res., 103, 26885–26898. Okada, Y. 1985. “Surface Deformation Due to Shear and Tensile Faults in a Half-Space,” Bull. Seismol. Soc. Am., 75 (4), 1135–1154. Okal, E.A. 1992. “Use of the Mantle Magnitude Mm for Reassesment of the Seismic Moment of Historical Earthquakes. I. Shallow Events,” Pure Appl. Geophys., 139, 17–57. Okal, E.A., Fryer, G.J., Borrero, J.C., and Ruscher, C. 2002a. ”The Landslide and Local Tsunami of 13 September 1999 on Fatu Hiva (Marquesas Islands; French Polynesia),” Bull. Soc. Geol. France, in press. Okal, E.A., Synolakis, C.E., Fryer, G.J., Heinrich, P., Borrero, J.C., Ruscher, C., Arcas, D.R., Guille, G., and Rousseau, D. 2002b. “A Field Survey of the 1946 Aleutian Tsunami in the Far Field,” Bull. Seismol. Soc. Am., in press. Pelayo, A.M. and Wiens, D.A. 1990. “The November 20, 1960 Peru Tsunami Earthuake: Source Mechanism of a Slow Event,” Geophys. Res. Lett., 17(6), 661–664. Pelinovsky, E., Yuliadi, D., Prasetya, G., and Hidayat, R. 1997. “The 1996 Sulawesi Tsunami,” Natural Hazards, 16 (1), 29–38. Prager, E.J. 1999. Furious Earth, McGraw-Hill, New York. Raichlen, F. 1966. “Harbor Resonance,” in Coastline and Estuarine Hydrodynamics, Ippen, A.T., Ed., McGraw-Hill, New York, 281–340. Ramsden, J.D. and Raichlen, F. 1990. “Forces on Vertical Wall Caused by Incident Bores,” J. Waterway Port Costal Ocean Eng., 116 (5), 592–613. Ruscher, C. 1998. “The Sloshing of Trapezoidal Reservoirs,” Ph.D. thesis, University of Southern California, Los Angeles. Satake, K. and Somerville, P. 1992. “Location and Size of the 1927 Lompoc, California Earthquake from Tsunami Data,” Bull. Seismol. Soc. Am., 82, 1710–1725. Shaw, J. and Suppe, J. 1994. “Active Faulting and Growth Folding in the Eastern Santa Barbara Channel, California,” Geol. Soc. Am. Bull., 106, 607–626. Shaw, J. and Suppe, J. 1996. “Earthquake Hazards of Active Blind-Thrust Faults under the Central Los Angeles Basin, California,” J. Geophys. Res., 101 (B4), 8623–8642. Shaw, R.P. 1974. “Long Wave Trapping by Axisymmetric Topographies,” JTRE Internal Report No. 119, Joint Tsunami Research Effort, University of Hawaii, Honolulu. Shuto, N. 1967 “Run-Up of Standing Waves in a Front of a Sloping Dike,” Coastal Eng. Jpn., 10, 23–38. Soloviev, S.L. and Go, Ch.N. 1974. A Catalogue of Tsunamis on the Western Shore of the Pacific Ocean (in Russian), Nauka Publishing, Moscow (English trans. 1984, Canada Institute for Scientific and Technical Information, National Research Council, Ottawa). Soloviev, S.L. and Go, Ch.N. 1975. A Catalogue of Tsunamis on the Eastern Shore of the Pacific Ocean (in Russian), Nauka Publishing, Moscow (English trans. 1984, Canada Institute for Scientific and Technical Information, National Research Council, Ottawa). Stoker, J.J. 1947. “Surface Waves in Water of Variable Depth,” Q. Appl. Math., 5, 1–54. Striem, H.L. and Miloh, T. 1975. “Tsunamis Induced by Submarine Slumpings off the Coast of Israel,” Israel Atomic Energy Commission. Synolakis, C.E. 1986. “The Runup of Long Waves,” Ph.D. thesis, California Institute of Technology, Pasadena. Synolakis, C.E. 1987. “The Runup of Solitary Waves,” J. Fluid Mech., 185, 523–545. © 2003 by CRC Press LLC


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Synolakis, C.E. 1988. “On the Roots of f(z) = J0(z)-iJ1(z),” Q. Appl. Math., 46, 105–107. Synolakis, C.E. 1990. “Generation of Long Waves in the Laboratory,” J. Waterways Port Coastal Ocean Eng., 116, 252–266. Synolakis, C.E. and Skelbreia, J.E. 1993. “Evolution of Maximum Amplitude of Solitary Waves on Plane Beaches,” J. Waterway Port Coastal Eng., 119 (3), 323–342. Synolakis, C.E. and Uslu, B.B. 2003. “Estimates of the Initial Height of Landslide Waves,” Manuscript in preparation. Synolakis, C.E., Imamura, F., Tsuki, Y., Matsutomi, H., Tinti, S., Cook, B., Chandra, Y.P., and Usman, M. 1995. “Damage Conditions of East Java Tsunami 1994 Analyzed,” Eos Trans. Am. Geophys. Union, 76(26), 257, 261–262. Synolakis, C.E., Liu, P., Carrier, G., and Yeh, J. 1997a. “Tsunamigenic Sea-Floor Deformations,” Science, 278 (5338), 598–600. Synolakis, C.E., McCarthy, R., and Bernard, E.N. 1997b. “Evaluating the Tsunami Risk in California,” in Proceedings of the Conference of the American Society of Civil Engineers, California and the World Ocean ’97, San Diego, CA, American Society of Civil Engineers, New York, p. 1225–1236. Synolakis, C.E., Bardet, J.P., Borrero, J.C., Davies, H., Okal, E.A., Silver, E.A., Sweet, S., and Tappin, D.R. 2002a. “Slump Origin of the 1998 Papua New Guinea Tsunami,” Proc. R. Soc. London Ser. A, 458, 763–789. Synolakis, C.E. et al. 2002b. Science Tadepalli, S. and Synolakis, C.E. 1994. “Roots of Jn(z) ± iJn+1(z) and the Evaluation of Integrals with Cylindrical Function Kernels,” Q. Appl. Math., 52, 103–112. Tadepalli, S. and Synolakis, C.E. 1996. “Model for the Leading Waves of Tsunamis,” Phys. Rev. Lett., 77 (10), 2141–2144. Titov, V.V. and Synolakis, C.E. 1993. “A Numerical Study of the Wave Runup of the September 1, 1992, Nicaraguan Tsunami,” in Proc. IUGG International Tsunami Symposium, Wakayama, Japan, pp. 627–634. Titov, V.V. and Synolakis, C.E. 1994. “The Runup of N-Waves on Sloping Beaches,” Proc. R. Soc. London Ser. A, 445, 99–112. Titov, V.V. and Synolakis, C.E. 1995. “Modeling of Breaking and Non-Breaking Long-Wave Evolution and Runup Using VTCS-2,” J. Waterway Port Ocean Coastal Eng., 121 (6), 308–316. Titov, V.V. and Synolakis, C.E. 1997. “Extreme Inundation Flows during the Hokkaido-Nansei-Oki Tsunami,” Geophys. Res. Lett., 24 (11), 1315–1318. Titov, V.V. and Synolakis, C.E. 1998. “Numerical Modeling of Tidal Wave Runup,” J. Waterway Port Ocean Coastal Eng., 124 (4), 157–171. Watts, P. 1997. “Water Waves Generated by Underwater Landslides,” Ph.D. thesis, California Institute of Technology, Pasadena. Watts, P. 1998. “Wavemaker Curves for Tsunamis Generated by Underwater Landslides,” J. Waterway Port Ocean Coastal Eng., 124 (3), 127–137. Watts, P. 2000. “Tsunami Features of Solid Block Underwater Landslides,” J. Waterway Port Ocean Coastal Eng., 126 (3), 144–152. Watts, P. and Borrero, J.C. 2001. “Probability Distributions of Landslide Tsunamis,” in Proc. International Tsunami Symposium, August 7–10, Seattle, WA, pp. 697–710. Wiegel, R.L. 1955. “Laboratory Studies of Gravity Waves Generated by the Movement of a Submerged Body, ”Trans. Am. Geophys. Union, 36(5), 759–774. Wilson, B.W. 1972. “Seiches,” in Advances in Hydroscience, vol. 8, Chow, V.T., Ed., Academic Press, New York, 1–89. Xu, B.Y. and Pachang, V. 1993. “Outgoing Boundary-Conditions for Finite-Difference Elliptic WaterWave Models,” Proc. R. Soc. London Ser. A, 441 (1913), 575–588. Yanenko, N.N. 1971. The Method of Fractional Steps (trans. M. Holt), Springer-Verlag, New York. Yeh, H., Liu, P.F., and Synolakis, C.E. 1992. Long Wave Runup Models, World Scientific, London. Zelt, J.A. 1991. “The Runup of Breaking and Nonbreaking Solitary Waves,” Coastal Eng., 125, 205–246. © 2003 by CRC Press LLC

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10

Soil–Structure Interaction

10.1 Soil–Structure Interaction: Statement of the Problem Elements of SSI Analysis · A Significant SSI Experiment

10.2 Specification of the Free-Field Ground Motion Control Motion and Earthquake Characteristics · Control Point · Spatial Variation of Motion and Kinematic Interaction · Validation of Ground Motion Variation with Depth of Soil · Validation of Kinematic Interaction · Variation of Ground Motion in a Horizontal Plane

10.3 Modeling of the Soil Field Exploration

10.4 Soil–Structure Interaction Analysis SSI Parameters and Analysis · Modeling of the Foundation · Modeling of the Structure

James J. Johnson James J. Johnson and Associates Alamo, CA

10.5 Soil–Structure Interaction Response Defining Terms References

10.1 Soil–Structure Interaction: Statement of the Problem The response of a structure during an earthquake depends on the characteristics of the ground motion, the surrounding soil, and the structure itself. For structures founded on rock or very stiff soils, the foundation motion is essentially that which would exist in the soil at the level of the foundation in the absence of the structure and any excavation; this motion is denoted the free-field ground motion. For soft soils, the foundation motion differs from that in the free field due to the coupling of the soil and structure during the earthquake. This interaction results from the scattering of waves from the foundation and the radiation of energy from the structure due to structural vibrations. Because of these effects, the state of deformation (particle displacements, velocities, and accelerations) in the supporting soil is different from that in the free field. As a result, the dynamic response of a structure supported on soft soil may differ substantially in amplitude and frequency content from the response of an identical structure supported on a very stiff soil or rock. The coupled soil–structure system exhibits a peak structural response at a lower frequency than would an identical rigidly supported structure. Also, the amplitude of structural response is affected by the additional energy dissipation introduced into the system through radiation damping and material damping in the soil.



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Kinematic Interaction Foundation Input motion

Free-field Motion

M F

Soil profile

Foundation Impedance

SSI

Structural Model

FIGURE 10.1 Schematic representation of the elements of soil–structure interaction.

Much of this chapter focuses on structures for which soil–structure interaction (SSI) is an important phenomenon in the design process of the structure and for systems and components housed therein. The type of structure and its foundation determines the importance of SSI. SSI effects can usually be ignored for conventional structures without significant embedment. Even for conventional structures with embedded foundations, ignoring SSI is usually conservative. However, even for conventional structures, it is prudent to consider and evaluate the potential effects of SSI on structure, system, and component design to assure oneself that excessive conservatism is not being introduced. SSI is most important for massive, stiff structures with mat foundations or with foundation systems significantly stiffened by the structure’s load-resisting system. Typical nuclear power plant structures, founded on soil, are particularly affected by SSI. Hence, the references and examples herein are drawn from the nuclear power industry.

10.1.1 Elements of SSI Analysis The analysis of SSI depends on the specification of the free-field ground motion and the idealization of the soil and structure. Modeling the soil involves determining its configuration and material properties. Modeling the structure includes the structure itself and its foundation. The calculated responses must be interpreted in light of differences between the idealized system and the real physical situation, and the uncertainties known to exist in the phenomenon. Figure 10.1 shows the elements of seismic analysis necessary to calculate seismic response, including SSI effects. Table 10.1 lists the various aspects, including interpretation and recognition of uncertainties in the process. The state of knowledge of SSI was well documented in 1980 in a compendium [Johnson, 1981] of contributions from key researchers (Luco, Roesset, Seed, and Lysmer) and drew upon other researchers and practitioners as well (Veletsos, Chopra). This reference provided a framework for SSI over the 1980s and 1990s, which were characterized by the accumulation of substantial data supporting and clarifying the roles of the various elements of the SSI phenomenon. Also, significant progress was made in the development and implementation of SSI analysis techniques. In the international nuclear power industry, © 2003 by CRC Press LLC



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TABLE 10.1 Elements of a Seismic Response Analysis Including Soil–Structure Interaction Specification of the Free Field Ground Motion Control point Control motion (peak ground acceleration and response spectra) Spatial variation of motion (wave propagation mechanism) Magnitude, duration Models of soils and structures Soil Properties Nominal properties (low and high strain) Variability SSI Parameters Kinematic interaction Foundation impedances Structure models Important features (torsion, floor flexibility, frequency reduction with strain, etc.) Variability (frequency and mode shapes, damping) Nonlinear behavior SSI Analysis Interpretation of Responses

the 1980s and 1990s saw a revision of important regulatory practices to conform to the current state of knowledge. Documentation of the state of knowledge of SSI was updated in 1991 and 1993 [Johnson and Chang, 1991; Johnson and Asfura, 1993]. The specific purpose of this update was to identify realistic approaches to the treatment of SSI and its uncertainties. This new understanding of the SSI phenomenon permitted the implementation and use of less conservative, more realistic procedures for the design of structures, systems, and components, and for the evaluation of structures, systems, and components when subjected to beyond-design basis earthquake events. The reader is directed to two other recent references that highlight the current state of the art and practice of SSI analysis. Tseng and Penzien [2000] discuss the SSI problem and its treatment in the context of multi-supported structures, such as bridges. Wolf and Song [2002] summarize numerous elements of the SSI phenomenon and their treatment analytically.

10.1.2 A Significant SSI Experiment Before proceeding further, it is useful to discuss an important SSI experiment. Very few opportunities exist to record free-field motion and structure response for an earthquake. In the mid-1980s, the Electric Power Research Institute (EPRI), in cooperation with Taiwan Power Company (TPC), constructed two scale-model reinforced concrete nuclear reactor containment buildings (one quarter and one twelfth scale). The scale models were located within an array of strong motion instruments (SMART-l, Strong Motion Array Taiwan, Number 1) in Lotung, Taiwan, sponsored by the U.S. National Science Foundation and maintained by the Institute of Earth Sciences of Academia Sciences of Taiwan. The experiment was extensively instrumented in the free field and in the structures. The objectives of the experiment were to measure the responses at instrumented locations due to vibration tests, and due to actual earthquakes, sponsor a numerical experiment designed to validate analysis procedures and to measure free-field and structure response for further validation of the SSI phenomenon and SSI analysis techniques. This Lotung site was chosen based on its known high seismicity. Using this data base, a cooperative program to validate SSI analysis methodologies was sponsored by EPRI, TPC, and the U.S. Nuclear Regulatory Commission (NRC). Numerous publications document the results of the SSI analysis studies. A two-volume EPRI report [EPRI, 1989] contains the proceedings of a workshop held in Palo Alto, California on December 11–13, 1987 to discuss the experiment, data © 2003 by CRC Press LLC


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collected, and analyses performed to investigate SSI analysis methodologies and their application. Johnson et al. [1989] performed one set of analyses from which results are presented here to demonstrate various aspects of the SSI phenomenon. A summary of lessons learned was published [Tseng and Hadjian, 1991]. Finally, a summary of sensitivity studies performed was documented in 1997 as the field experiment was completed. When appropriate throughout this chapter, data from the Lotung experiment are presented and discussed.

10.2 Specification of the Free-Field Ground Motion The term free-field ground motion denotes the motion that would occur in soil or rock in the absence of the structure or any excavation. Describing the free-field ground motion at a site for SSI analysis purposes entails specifying the point at which the motion is applied (the control point), the amplitude and frequency characteristics of the motion (referred to as the control motion and typically defined in terms of ground response spectra, power spectral density functions, and/or time histories), the spatial variation of the motion, and, in some cases, duration, magnitude, and other earthquake characteristics. In terms of SSI, the variation of motion over the depth and width of the foundation is relevant. For surface foundations, the variation of motion on the surface of the soil is important; for embedded foundations, the variation of motion over both the embedment depth and the foundation width should be known.

10.2.1 Control Motion and Earthquake Characteristics The control motion is defined by specifying the amplitude and frequency content of the earthquake to be considered. Two purposes exist for SSI analysis of a structure: design or evaluation of a facility for a specified earthquake level, or the evaluation of a structure for a specific event. In the former case, statistical combinations of recorded or predicted earthquake motions are typically the bases. In the latter case, recorded earthquake acceleration time histories typically comprise the free-field ground motions. The frequency content of the motion is one of the most important aspects of the free-field motion as it affects structure response. For linear structural behavior and equivalent linear SSI, the frequency content of the free-field motion compared to important frequencies of the soil–structure system determines response. For structures expected to behave inelastically during the earthquake (and, in particular, structures for which SSI is not important), structure response is determined by the frequency content of the free-field motion, i.e., in the frequency range from the elastic frequency to a lower frequency corresponding to a certain amount of inelastic deformation. 10.2.1.1 Aggregated Ground Motions A wide variety of ground response spectra has been specified for design of major facilities, such as nuclear power plants, major bridges, critical facilities (e.g., LNG storage and processing plants), and major infrastructure projects. For nuclear power plants, depending on the vintage of the plant and the site soil conditions, the majority of the design ground response spectra has been relatively broad-banded spectra representing a combination of earthquakes of different magnitudes and distances from the site. Construction of such design spectra is usually based on a statistical analysis of recorded motions and frequently targeted to a 50% or 84% nonexceedance probability (NEP). Three points are important relative to these broad-banded spectra. First, earthquakes of different magnitudes and distances control different frequency ranges of the spectra. Small magnitude earthquakes contribute more to the high frequency range than to the low frequency range and so forth. Second, it is highly unlikely that a single earthquake will have frequency content matching the design ground response spectra. Hence, a degree of conservatism is added when broad-banded response spectra define the control motion. Third, a single earthquake can have frequency content that exceeds the design ground response spectra in selected frequency ranges. The likelihood of the exceedance depends on the NEP of the design spectra. Figure 10.2 compares several ground response spectra used in the design or evaluation process. U.S. NRC Regulatory Guide 1.60 [U.S. Atomic Energy Commission, 1973] response spectra defined design criteria © 2003 by CRC Press LLC


10-5


1 Reg Guide 1.60 0.9 84th CR-0098 Soil 0.8

64th CR-0096 Rock

0.7

Acceleration (g)

Median CR-0098 Soil 0.6

Median CR-0098 Rock

0.5 0.4 0.3

5% Spectral Damping Used

0.2 0.1 0 0.1

10

100

Frequency (Hz)

FIGURE 10.2 Examples of aggregated ground motion response spectra.

for U.S. nuclear power plants designed after about 1973. These spectra were targeted to an 84% NEP of the data considered, but exceed this target in selected frequency ranges. Figure 10.2 shows an additional set of broad-banded spectra for rock and alluvial sites and for 50% and 84% NEP. U.S. NRC NUREG0098 is the source. These spectra have been used extensively for defining seismic margin earthquakes, for which beyond design basis assessments have been performed for nuclear power plants in the United States and other countries. This broad-banded spectral shape is also used to define design criteria for new design. In addition to the site-independent ground response spectra discussed above, two additional forms of ground response spectra are being generated and used for site-specific design or evaluations. First, sitespecific spectra are generated by accumulating recorded data that meet the design earthquake characteristics and local site conditions, analyzing the data statistically, calculating ground response spectra of various statistical attributes, and selecting response spectra for design or reevaluation. Figure 10.3 shows an example for a specific site; the 84% NEP was selected. Second, seismic hazard studies are performed to generate families of seismic hazard curves which yield estimates of the probability of exceedance of earthquakes with specified peak ground acceleration (PGA) values or greater. Confidence limits for these seismic hazard estimates are derived from the family of curves. Companion to the seismic hazard curves are uniform hazard spectra (UHS), which are ground response spectra generated for a specified return period or probability of exceedance, with various confidence limits. Figure 10.4 shows example UHS for a specific site, 10–4 probability of occurrence per annum (sometimes termed a “10,000-year return period”), and 15, 50, and 85% confidence limits. Such spectra are generated by the same probabilistic seismic hazard methodology as is used in generating the seismic hazard curves for PGAs. In almost all cases, design ground response spectra are accompanied by ground motion acceleration time histories — artificial acceleration time histories generated with response spectra that match or exceed the design ground response spectra. Artificial acceleration time histories are generated by numerical methods and not recorded motions. Due to the enveloping process, additional conservatism is © 2003 by CRC Press LLC


10-6


0.

1

102

10

101

Max

10

0.

01

0

.0

.84 .50 00 1

100 1.

0.

Pseudo-Velocity 5% (Inches/Second)

0.

0

0.

00

1

Min

0.

01

10−1

10−2

10−1

0.

1

100

101

Period (second)

FIGURE 10.3 Site-specific response spectrum.

introduced. Ground motion time histories are used to generate in-structure response — loads, response spectra, displacements, etc. 10.2.1.2 Individual Recorded Events The previous sections discussed aggregated motions as derived from recorded data or empirical models based on recorded data. These aggregated motions do not represent a single event. They have been developed for various design and evaluation purposes. It is informative to present recorded motions from actual earthquakes and visualize differences between a single event and the aggregated motions. Two earthquakes of note from a SSI standpoint were the May 20, 1986 and November 14, 1986 events which affected the Lotung scale model structures. Figure 10.5 contains response spectra generated from the acceleration time histories recorded on the soil-free surface for the May 20, 1986 event. Each earthquake produced PGAs greater than about 0.2 g in the horizontal direction with principally low frequency motion, i.e., less than about 5 Hz. 10.2.1.3 Magnitude Effects Ground motion frequency content is strongly dependent on specific factors of the earthquake and site. Two particularly important characteristics of the earthquake are its magnitude and epicentral distance from the site. Small magnitude events are characterized by narrow-banded response spectra and high frequency in comparison to moderate magnitude events. Figure 10.6 [Chang et al., 1985] illustrates the effect of magnitude on response spectral shape. In the figure, the response spectral shape obtained from a series of small magnitude (ML < 4) earthquakes is compared with the response spectral shape from a moderate magnitude (ML = 6.5) event. As shown, the small magnitude earthquakes are characterized by a narrow-banded response spectral shape and greater high frequency content than the moderate magnitude event. © 2003 by CRC Press LLC


10-7


10−4 spectra

103

Spectral Velocity (cm/sec)

102

85 101 50

15 100

10−1 10−2

10−1

100

101

Period (sec)

FIGURE 10.4 Uniform hazard spectra.

10.2.1.4 Soil vs. Rock Sites One of the most important parameters governing amplitude and frequency content of free-field ground motions is the local site conditions, i.e., soil vs. rock and shallow, soft soil overlying a stiff soil or rock. Two sets of data dramatically demonstrate the difference in motions recorded on rock vs. soil for the same earthquake and sites in close proximity. The Ashigara Valley in Japan is located about 80 km southwest of Tokyo. A digital strong-motion accelerograph array network [Kudo et al., 1988] was installed in this seismically very active area. The geological profile of the Ashigara Valley is shown in Figure 10.7. The valley is an alluvial basin with rock outcrops at the mountain side and soft sedimentary soil layers at the basin. Accelerometers were installed in the rock outcrop (KR1), at the surface of the soft layers (KS1 and KS2) and inside the soil (KD2). Figure 10.8 shows response spectra of motions recorded at the rock outcrop (KR1) and at the surface of soft layers (K2S) for an earthquake occurring on August 5, 1990. The figure clearly shows differences in motions due to different site conditions. High frequencies of about 10 Hz and greater are dominant at the rock site and frequencies below about 5 Hz are dominant at the soil surface. Figure 10.8 clearly shows the large amplification of the low frequency waves due to the soil response and the deamplification of the high frequency waves due to the filtering effect of the soft soil. The Loma Prieta earthquake, October 17, 1989, with epicenter near San Francisco, provided the opportunity to collect and evaluate recorded motions on rock and soft soil sites, in some cases immediately © 2003 by CRC Press LLC


10-8


x 100 .5

E-W Component

x 100 .5 .4 Acceleration

Acceleration

.4 .3 .2

x 101 .14

100 101 Frequency (Hz)

102

Vertical Component

.2

.0 10−1


102

Notes: All acceleration in g All spectra at 5% damping

.12 Acceleration

.3

.1

.1 .0 10−1

N-S Component

.10 .8 .6 .4 .2 .0 10−1


102

FIGURE 10.5 Response spectra of free-field ground surface motions of the May 20, 1986 earthquake, recorded at Lotung, Taiwan.

adjacent to each other. Figure 10.9 compares response spectra for recorded motions on rock (Yerba Buena Island) and on soil (downtown Oakland). Significant differences in amplification are obvious, with the rock motions being less. Similar observations were made when comparing response spectral amplification factors for soil (Treasure Island) vs. rock (Yerba Buena Island). For horizontal motions, significant amplification of soil over rock is apparent. For vertical motions, the relationship between the rock and soil values was not as clear. As observed in other locations, it is surmised that the presence of a high water table and its effect on vertical ground motion are uncertain. Note that Treasure Island and Yerba Buena Island are the north and south ends of a single land mass (Yerba Buena Island is a natural island with highest elevation several hundred feet above the San Francisco Bay, while the contiguous Treasure Island is of similar areal extent, only a few feet above the bay, and was created by hydraulic land fill in the 1930s). The evidence supporting the differences between rock and soft soil motions continues to mount, emphasizing the effect of local site conditions on the amplitude and frequency content of the motion.

10.2.2 Control Point The term control point designates the location at which the control motion is defined. The control point should always be defined on the free surface of soil or rock at the site of interest. Specifying the control point at locations other than a free surface ignores the physics of the problem and the source of data used in defining the control motion. Past nuclear regulatory practice specified the control point to be at foundation level in the free field, which is technically untenable. It not only ignores the physics of the problem and the source of recorded data, but also results in motions on the free surface whose response spectra display peaks and valleys associated with frequencies of the embedment layer that are unrealistic. The frequencies of these peaks correspond to the frequencies of the soil layer between the foundation and the free surface. These free surface motions are dependent on the foundation depth rather than © 2003 by CRC Press LLC


10-9


Spectral Acceleration Fast Ground Acceleration

7

6

EXPLANATION 1979 Imperial Valley, California Earthquake (ML 6.6) 1975 Oroville, California Earthquake after shocks, and 1980 Mammoth Lakes, California Earthquake (Records from Earthquake with ML 4.0 + 0.2)

5

Damping Rate = 0.02

4

3

2

1

0 0.01

0.03

0.1

0.3 Period, sec

1

3

10

FIGURE 10.6 Illustration of effect of earthquake magnitude on response spectral shape obtained from statistical analysis.

free-field site characteristics. In addition, the peak acceleration of the resulting free surface motion is typically calculated to be significantly greater than the control motion. Hence, by all seismological definitions, a design or evaluation earthquake is increased. A 0.25-g earthquake may become a 0.35-g earthquake, or greater, depending on the embedment depth, soil properties, and control motion characteristics. Finally, specification of the control point at foundation level rather than the soil free surface effectively penalizes partially embedded structures compared to surface-founded structures, which contradicts common sense and observations. Simplistic SSI analyses frequently ignore wave scattering effects (kinematic interaction) for embedded foundations. In so doing, the foundation input motion is assumed to be identical to the control motion. Implicit in this assumption is the definition of the control point as any point on the foundation and no spatial variation of ground motion. This assumption is almost always conservative and frequently extremely conservative. Recognition of this conservatism is important in interpreting the results of the SSI analysis.

10.2.3 Spatial Variation of Motion and Kinematic Interaction Spatial variations of ground motion refer to differences in amplitude and/or phase of ground motions with horizontal distance or depth in the free field. Spatial variations of ground motion are associated with different types of seismic waves and various wave propagation phenomena, including reflection at the free surface, reflection and refraction at interfaces and boundaries between geological strata having © 2003 by CRC Press LLC


10-10

TP(m)


KR1

100

50

KS1 Vs 150m/s Vs 700m/s

0

KS2

Vs 70m/s

Vs 400m/s

−50 Vs 700m/s

SCALE 0

500(m) Vs 800m/s

KD2

−100

FIGURE 10.7 Ashigara Valley, Japan.

different properties, and diffraction and scattering induced by nonuniform subsurface geological strata and topographic effects along the propagation path of the seismic waves. A vertically incident body wave propagating in such a medium will include ground motions having identical amplitudes and phase at different points on a horizontal plane (neglecting source-to-site attenuation effects over short horizontal distances). A plane wave propagating horizontally at some apparent phase velocity will induce ground motion having identical amplitudes but with a shift in phase in the horizontal direction associated with the apparent horizontal propagation velocity of the wave. In either of these ideal cases, the ground motions are considered to be coherent, in that amplitudes (acceleration time histories and their response spectra) do not vary with location in a horizontal plane. Incoherence of ground motion, on the other hand, may result from wave scattering due to inhomogeneities of soil/rock media and topographic effects along the propagation path of the seismic waves. Both of these phenomena are discussed below. In terms of the SSI phenomenon, variations of the ground motion over the depth and width of the foundation (or foundations for multifoundation systems) are the important aspect. For surface foundations, the variation of motion on the surface of the soil is important; for embedded foundations, the variation of motion on both the embedded depth and foundation width is important. Spatial variations of ground motions are discussed in terms of variations with depth and horizontal distances.

10.2.4 Validation of Ground Motion Variation with Depth of Soil 10.2.4.1 Variation of Ground Motion with Depth of Soil For either vertically or nonvertically incident waves, ground motions vary with depth. These variations can generally be expressed in terms of peak amplitudes, frequency content, and phase. Variations of ground motion with depth due to vertically and nonvertically incident body waves and surface waves have been extensively studied analytically by many investigators [Chang et al., 1985]. These studies, based



10-11


.10 KS2S, Comp. 090, Alluvium Site .9

KR1S, Comp. 090, Rock Site 5% Damping

.8 .7

Sa (g)

.6 .5 4 .3 .2 .1 .0 .01 .02

.05

1

(a)

2 5 1 Period (sec)

2

5

10

.10 KS2S, Comp. 000, Alluvium Site KR1S, Comp. 000, Rock Site

.9

5% Damping

.8 .7

Sa (g)

.6 .5 .4 .3 .2 .1 .0 .01

(b)

.02

.05

.1

.2 5 Period (sec)

1

2

FIGURE 10.8 Response spectra at rock and alluvium sites, Ashigara Valley, Japan.


5

10


10-12


.8 Oakland 2_STY BLDG (No.56224). Comp. 200. Soil Site. .7

Yerba Buena Island (No.58163). Comp. 000. Rock Site. 5% Damping

.6

Sa (g)

.5

.4

.3

.2

.1

.0

.01 .02

.05

.1

(a)

.2 .5 Period (sec)

1

2

5

10

.8 Oakland 2_STY BLDG (No.56224). Comp. 290. Soil Site. .7

Yerba Buena Island (No.58163). Comp. 090. Rock Site.

.6

5% Damping

Sa (g)

.5

.4

.3

.2

.1

.0 .01

(b)

.02

.05

.1

.2 .5 Period (sec)

1

2

FIGURE 10.9 Response spectra at rock and soil sites, Loma Prieta earthquake.


5

10


10-13


TABLE 10.2 Free-Field Downhole Arrays Location

Instrument Depth (m)

Natimasu, Tokyo Waseda, Tokyo Menlo Park, CA Richmond Field Station, CA Ukishima Park, Tokyo Futtsu Cape, Chiba Kannonzaki, Yokosuka City Tokyo International Airport Ohgishima Station, Kawasaki City Earthquake Research Institute Miyako, Tokyo Tomakomai, Hokkaido Tateyama, Tokyo Higashi-Matsuyama City, Saitama Shuzenji-cho, Shizuoka Choshi City, Chiba Beatty, Nevada Fukushima Nuclear Power Plant Lotung, Taiwan, ROC

–1, –5, –8, –22, –55 –1, –17, –67, –123 GL, –12, –40, –186 GL, –14.5, –40 GL, –27, –67, –127 GL, –70, –110 GL, –80, –120 GL, –50; GL, –65 GL, –15, –38, –150 GL, –82 –0.5, –18, –26.5 GL, –30, –50 –26; –38, –100 –1, –58, –121 –36, – 100, –49, –74 GL, –18 GL, –41 GL, –50; –0.5, –3, –8.5, –23.5 GL, –6, –11, –17, –47

Turkey Flat, CA Ashigara Valley, Japan Games Valley, CA

GL, –10, –20 GL, –30, –95 GL, –6, – 15, –22, –220

Reference Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Gazetas, G. and Bianchini, G. (1979) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Yanev et al. (1979); Tanaka et al. (1973) Chang et al. (1990); Chang et al. (1991); Hadjian et al. (1991) Cramer (1991); Proceedings (1992) Proceedings (1992); Midorikawa (1992) Seale and Archuleta (1991)

on the physics of plane wave propagation through layered media, all indicate that, due primarily to the free surface effect, ground motions generally decrease with depth. The nature of the variation is a function of frequency content and wave type of the incident waves, soil layering, and dynamic soil properties of each soil layer, including shear and compressional wave velocities, damping ratio, and mass density. 10.2.4.2 Free-Field Motion A review and summary of observational data on the variations of earthquake ground motion with depth was conducted by Seed and Lysmer [Johnson, 1981] and Chang et al. [1985] reflecting the state of knowledge as of 1980 and 1985, respectively. Recordings from two downhole arrays in Japan were analyzed [Chang et al., 1985] and a review of published data from a number of downhole arrays in Japan and the United States was conducted. Based on the review of these data on the variations of ground motion with depth, it was concluded that there is a good body of data to show that, in general, both peak acceleration and response spectra decrease significantly with depth in the range of typical embedment depths of structures, i.e., less than approximately 25 m; and it appears that deconvolution procedures assuming vertically propagating shear waves provide reasonable estimates of the variations of ground motion with depth. Table 10. 2 summarizes the sources of data evaluated by Seed and Lysmer [Johnson, 1981] and Chang et al. [1985]. Since 1985, substantial additional data have been recorded and evaluated. These sources are included in Table 10.2 and one of the most relevant is discussed next. 10.2.4.3 Lotung, Taiwan As part of the Lotung experiment, downhole free-field data were recorded at depths of 6, 11, 17, and 47 m. Figure 10.10 [EPRI, 1989] shows the configuration of the arrays. Equivalent linear deconvolution analyses and nonlinear convolution analyses were performed. Deconvolution analysis has as the starting point the free-field surface motion with the objective being to calculate the motion at various depths in the soil. For the Lotung experiment, the depths at which the earthquake responses were calculated corresponded to the



10-14


FA1-5 DHB

30.48m Arm 1 6.10m

1.5m

5.10m 3.05m

FA1-1 FA2-1

FA3-1 FA3-5

Arm 3

Arm 2

Triaxial accelerometers

Limits of Backfill FA2-5

(a) Surface Instrument Arrays

3.2m 1/4-scale model 4.57m 10.52m

45.7m

DHA 6m

DHB 6m DHB6 DHB11

11m 17m

DHB17

5m 6m

30m

47m

DHB47

(b) Downhole Instrument Arrays

FIGURE 10.10 Location of (a) surface and (b) downhole accelerographs at the Lotung, Taiwan site.

locations of the downhole accelerometers for comparison purposes. Convolution analysis is the inverse process, i.e., starting with the recorded motion at depth in the soil, calculate the earthquake motion at the free surface or at other depths. These extensive studies investigating analytical modeling of the phenomenon clearly support the observed and analytically determined variation of motion with depth in the soil and, in fact, a reduction of motion with depth as expected. In addition, the assumption of vertically propagating shear waves, and an equivalent linear representation of soil material behavior, well models the wave propagation phenomenon, especially at depths in the soil important to SSI [EPRI, 1989]. Figure 10.11 compares recorded and analytically predicted responses for one of the models.



10-15

Spectral Acceleration (g)





E−W

−5

N−S

−4 −3 −2

DHB6

DHB6

DHB11

DHB11

DHB17

DHB17

−1 0 −5 −4 −3 −2 −1 0 −5 −4 −3 −2 −1 0 −5 −4

Recorded (CDS4.7DHB) Computed (S7CDe12080)

−3 −2

DHB47

DHB47

−1 0 −1 −2 −5

1 2 5 10 20 50 100 −1 −2 −5 1 2 5 10 20 50 100 Frequency (Hz) Frequency (Hz)

FIGURE 10.11 Comparison of recorded and computed response spectra (5% damping), deconvolved with iterated strain-compatible properties, Event LSST07.

10.2.5 Validation of Kinematic Interaction 10.2.5.1 Foundation Response The SSI phenomenon can be thought of as two elements: kinematic and inertial interaction. Kinematic interaction is the integrating effect that occurs as portions of the structure and foundation that interface with the soil or rock are subjected to differing free-field ground motion. Variations in translational freefield ground motion result in net translations and accompanying rotations due to this integration or averaging process. Kinematic interaction is typically treated separately from a conceptual standpoint and frequently from a calculational standpoint. The result of accounting for kinematic interaction is to generate an effective input motion, which is denoted foundation input motion. The mathematical transformation from the free-field surface motion to the foundation input motion is through the scattering matrix. Inertial interaction denotes the phenomenon of dynamic behavior of the coupled soil–structure system. The base excitation is defined by the foundation input motion accounting for kinematic interaction. The behavior of the foundation on the soil is modeled by foundation impedances (generalized soil springs) that describe the force-displacement and radiation damping characteristics of the soil. The structure is modeled by lumped mass and distributed stiffness models representing its dynamic response characteristics. These elements are combined to calculate the dynamic response of the structure, including the effects of SSI. © 2003 by CRC Press LLC


10-16


T−5/GL−1m Y

1.5

T−5/GL−1m Y 10.0

Fourier Spectral Ratio

5.0 1.0

Ground 1.0 0.5

Estimated Input Motion Bottom slab

0.5

0.1 0.05

0.0 0.0

2.0

4.0 Frequency (Hz)

6.0

8.0

0.01 0.05 0.1

0.5

1.0

5.0 T (sec)

FIGURE 10.12 Observed transfer function between foundation level motion (–26.2 m) of a large-scale belowground LNG tank and free-field (–l m) horizontal motion. (——), observed average value over 18 earthquakes; (– – – –), theoretical.

Validation of the component pieces of the process proceeds by considering kinematic interaction. A comparison of motions recorded in the free field and on the base of partially embedded structures provides excellent data validating the effects of kinematic interaction and the spatial variation of ground motion. All recorded data on structures include the effects of SSI to some extent. For purposes of validating the spatial variation of motion with depth in the soil, observations of kinematic interaction are sought. The ideal situation is one where free-field surface motions and foundation motions are recorded for a structure whose embedded portion is stiff, approaching rigid behavior, and the dynamic characteristics of the structure are such that inertial interaction is a minimal effect. 10.2.5.2 Free-Field Surface Motions vs. Foundation Response Typically, differences in peak values, time histories, and response spectra were observed and transfer functions relating foundation response to free-field surface motion were generated. These frequencydependent transfer functions are, in essence, one element of the scattering matrix when inertial interaction effects are minimal, i.e., the component relating foundation input motion to horizontal free-field surface motion. In no case was enough information available to generate the rocking component of the scattering matrix from recorded motions. To do so requires recorded rotational acceleration time histories or the ability to generate them from other measurements. 10.2.5.3 LNG Tanks, Japan Eighteen deeply embedded LNG tanks of varying dimensions were instrumented and motions recorded on their foundations and in the free field for a large number of earthquakes. Many of the earthquakes were microtremors, but detailed response for at least one larger event was obtained. Transfer functions between free-field surface motions and foundation response were generated and compared with a calculated scattering element. Results compared well. A significant reduction in foundation response from the free surface values was observed. The mass and stiffness of the tanks were such that kinematic interaction dominated the SSI effects. Figure 10.12 presents the data [Ishii et al., 1984]. 10.2.5.4 Humboldt Bay Nuclear Power Plant The Humboldt Bay Nuclear Power Plant in northern California has experienced numerous earthquakes over the years. Four events of note are the Ferndale earthquake of June 7, 1975 and the Lost Coast earthquake sequence of April 25, 1992. Accelerometers in place in the free field and on the base of a deeply embedded caisson structure (80 ft) recorded acceleration time histories. Figure 10.13 compares



10-17


EXPLANATION

1.2

Free-field finished grade

1.0 0.8

Sa (g’s)

Base of Reactor Caisson (84 ft Embedment Depth)

Transverse Direction Damping Ratio = 0.05

0.6 0.4 0.2

0 0

Medium to stiff clay Medium dense sand Dense sand Very stiff clay

50 75

0.025

CAISSON

Depth - ft

25

1.2

1.0

2.5

1.0

2.5

Longitudinal Direction Damping Ratio = 0.05

1.0

Dense sand

0.1 Period (seconds)

0.8 Sa (g’s)

100 125

0.6 0.4 0.2 0 0.025

0.1 Period (seconds)

FIGURE 10.13 Comparison of response spectra of accelerograms recorded at finished grade in the free field and at the base of the reactor caisson at the Humboldt Bay plant during the June 6, 1975, Femdale, California earthquake.

TABLE 10.3 Peak Accelerations (Surface/Caisson) Earthquake

E-W

N-S

Vertical

6/1/75 4/25/92 (11:06 PDT) 4/26/92 (00:14 PDT) 4/26/92 (04: 18 PDT)

0.35/0.16g 0.22/0.14g 0.25/0.12g 0.13/0.07g

0.26/0.12g 0.22/0.11g 0.23/0.12g 0.098/0.057g

0.06/0.10g 0.05/0.08g 0.05/0.12g 0.031/0.037g

free-field surface response spectra with those recorded on the caisson’s base for the 1975 event. Table 10.3 shows a comparison of peak accelerations. For horizontal motions, significant reductions are apparent, i.e., reductions up to 55%. For vertical motions, peak accelerations remained the same or slightly increased. Additional data for vertical motions will undoubtedly illuminate this phenomenon. The major interest for the design and evaluation of structures is horizontal motions, which clearly exhibit reduction with depth. The dominant SSI phenomenon here, as for the LNG tanks, is likely to be kinematic interaction due to the deep embedment of the caisson. Numerous other data exist and are highlighted in other sources, e.g., Johnson and Asfura [1993]. 10.2.5.5 Buildings With and Without Basements A series of buildings in close proximity to each other, with and without basements, subjected to the San Fernando earthquake of 1971 were investigated. Comparing recorded basement motions for buildings © 2003 by CRC Press LLC


10-18


7,150

11 10

6

2,000

2,390

4,000 0

2,900

5,000

5

4,150

2,000

4

GL

3

6,800

2

3,650

1

6,000

Pickups of seismograph

FIGURE 10.14 Cross section through chemical engineering plant model, Chiba Field Station.

with and without embedment documented the effects of kinematic interaction. The results show a definite reduction in motion of embedded foundations compared to surface foundations or free-field surface values. Numerous comparisons are presented by Chang et al. [1985]. 10.2.5.6 Model Structures Two model structures in Japan and the Lotung scale model structures in Taiwan have been instrumented and have recorded ground motions from a number of earthquakes. One model structure is located at the Fukushima Nuclear Power Plant site in northern Japan. Tanaka et al. [1973] report on data recorded in the free field and structure. A reduction in peak acceleration of about 20% is observed from free-field surface motion to foundation. The second model structure is located at Chiba Field Station, Institute of Industrial Science, University of Tokyo. The purpose of the model was to instrument it for earthquakes, record earthquake motions, and investigate variability in ground motion and response. Figure 10.14 [Shibata, 1978; Shibata, 1991] shows a cross section through the scale model structure including components (piping, hanged tank, and vessel) and instrument locations. As of 1978, Shibata shows graphically that the mean response factor for peak acceleration on the foundation compared to the free field is about 0.68, with a coefficient of variation of 0.125 in the horizontal direction, and 0.83, with a coefficient of variation of 0.136 in the vertical direction. A clear reduction in response of the foundation is observed. The third model structure is the Lotung, Taiwan case. Comparing the May 20, 1986 measured free-field surface response with foundation response demonstrates the reduction in free-field motion with depth.

10.2.6 Variation of Ground Motion in a Horizontal Plane Variations observed in the motions of two points located on a horizontal plane are mainly due to the difference in arrival times of the seismic waves at the two points and to the amplitude and frequency © 2003 by CRC Press LLC



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modification that those seismic waves undergo due to the geotechnical characteristics of the media between the two points. The former is sometimes referred to as a first-order effect and is characterized by an apparent horizontal wave propagation velocity (speed and, in some cases, direction). The latter is often denoted a second-order effect and is characterized by a set of horizontal and vertical ground motion “coherency functions.” Understanding of the variation of ground motion over a horizontal extent was significantly advanced with the installation of several dense accelerograph arrays, e.g., SMART 1 and LSST arrays in Taiwan, El Centro and Parkfield in California, and the Chusal differential array in the former U.S.S.R., and the analysis of the recorded data collected from them. Thus, the spatial variation of ground motions over a horizontal plane is characterized by an apparent horizontal wave propagation velocity, which in the absence of detailed site data is generally assumed to be on the order of 2 to 3 km/ sec. Complex-valued, frequency-dependent coherency functions have been derived from the recorded data of the differential arrays discussed above. These functions strongly depend on the distance between recording or site locations and on the frequency of the seismic waves. This spatial variation of ground motions is a critical element in the seismic analysis of structures on large foundations and in the analysis of long structures on multiple foundations, such as bridges [Tseng and Penzien, 2000]. For long structures on multiple foundations, accounting for both aspects of horizontal spatial variation of ground motion is essential. For these cases, apparent horizontal wave propagation velocities and coherency functions are used directly in the SSI analysis. For structures supported on large, stiff foundations, recorded data support a “base averaging” effect on the free-field ground motions. That is, certain frequency ranges may be filtered out of the foundation input motion due to the base averaging effect. In the absence of performing detailed SSI analyses incorporating the coherency functions, a simpler approach may be taken, i.e., a filtering of motions. For a 50-m plan dimension foundation, reductions in spectral accelerations of 20% in the > 20-Hz frequency range, of 10% to 15% in the 10- to 20-Hz range, and of 5% in the 5- to 10-Hz range are supported by the data.

10.3 Modeling of the Soil For soil sites, describing the soil configuration (layering or stratigraphy) and the dynamic material properties of soil is necessary to perform SSI analysis and predict soil–structure response. Determining soil properties to be used in the SSI analysis is the second most uncertain element of the process — the first being specifying the ground motion. Modeling the soil can be visualized in two stages: determining the low strain in situ soil profile and associated material properties; and defining the dynamic material behavior of the soil as a function of the induced strains from the earthquake and soil–structure response. In general, dynamic stress–strain behavior of soils is nonlinear, anistropic, elastoplastic, and loading path dependent. It is also dependent on previous loading states and the degree of disturbance to be expected during construction. Practically speaking, all of these effects are not quantifiable in the current state of the art and, hence, contribute to uncertainty in describing soil stress–strain behavior. In a majority of cases, soil is modeled as a linear or equivalent linear viscoelastic medium in SSI analyses for earthquake motion. In some instances, in particular where foundations or footings are founded underwater, it is important to characterize nonlinear behavior of the supporting medium, albeit with substantial uncertainty taken into account. In addition, there have been numerous studies where nonlinear behavior of soil has been analyzed for research objectives. The assumption in this chapter is that the majority of SSI analysis cases of interest to the reader are those where the nonlinear behavior of soil may be treated appropriately as equivalent linear viscoelastic material. In other cases, the reader is referred to sources such as Tseng and Penzien [2000]. A linear viscoelastic material model is defined by three parameters — two elastic constants (frequently shear modulus and Poisson’s ratio, although shear modulus and bulk or constrained modulus may be more appropriate) and material damping. The equivalent linear method approximates the nonlinear stress–strain relation with a secant modulus and material damping values selected to be compatible with the average shear strain induced during the motion using an iterative procedure. Requirements for this model are low strain shear modulus and Poisson’s ratio (or bulk or constrained modulus), material © 2003 by CRC Press LLC


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damping values, and their variations with strain. The following discussion assumes an equivalent linear viscoelastic material model for soil. Three aspects of developing soil models are field exploration, laboratory tests, and correlation of laboratory and field data. Much of the discussion refers to Woods [1978], which is the most comprehensive documentation of the state of the art at the time of publication. In the ensuing years, a number of authors have published updates to selected aspects of the subject, in particular, measurement of parameters for nonlinear models of soil material behavior, liquefaction, and lateral spreading. Two such publications are CH2M Hill [1991] and Ishihara [1996].

10.3.1 Field Exploration Field exploration, typically, relies heavily on boring programs, which provide information on the spatial distribution of soil (horizontally and with depth) and produce samples for laboratory analysis. In addition, some dynamic properties are measured in situ, for example, shear wave velocity which leads to a value of shear modulus at low strains. Woods [1978] provides a summary of field exploration, in general, and of boring, sampling, and in-situ testing, in particular. Low strain shear and compressional wave velocities are typically measured in the field. Various field techniques for measuring in situ shear and compressional wave velocities exist, including the seismic refraction survey, seismic cross-hole survey, seismic downhole or uphole survey, and surface wave techniques. The advantages and disadvantages of these techniques are discussed by Woods [1978]. For sites having a relatively uniform soil profile, all of these techniques are appropriate. However, for sites having layers with large velocity contrasts, the most appropriate technique is the cross-hole technique. The cross-hole data are expected to be the most reliable because of better control over and knowledge of the wave path. The downhole technique does not permit as precise resolution because travel times in any layer are averaged over the layer. Most seismic field survey techniques are capable of producing ground motions in the small shearing strain amplitude range (less than 10–3 %). Hence, field exploration methods yield the soil profile and estimates of important low strain material properties (shear modulus, Poisson’s ratio, water table location). 10.3.1.1 Laboratory Tests Laboratory tests are used principally to measure dynamic soil properties and their variation with strain: soil shear modulus and material damping. Currently available laboratory testing techniques have been discussed and summarized by Woods [1978]. These techniques include resonant column tests, cyclic triaxial tests, cyclic simple shear tests, and cyclic torsional shear tests. Each test is applicable to different strain ranges. The resonant and torsional shear column tests are capable of measuring dynamic soil properties over a wide range of shear strain (from 10–4 to 10–2 % or higher). The cyclic triaxial test allows measurement of Young’s modulus and damping at large strain (larger than 10–2 %). Typical variations of shear modulus with shear strain for clays, compiled from laboratory test data, are depicted in Figure 10.15. Generally, the modulus reduction curves for gravelly soils and sands are similar. Figure 10.16 shows material damping as a function of shear strain, also for clays. Shear modulus decreases and material damping increases with increasing shear strain levels. 10.3.1.2 Correlation of Laboratory and Field Data Once shear modulus degradation curves and material damping vs. strain curves have been obtained, it is necessary to correlate laboratory-determined low strain shear modulus values with those in situ. Laboratory-measured values of shear moduli at low levels of strain are typically smaller than those measured in the field. Several factors have been found to contribute to lower moduli measured in the laboratory. These factors include effects of sampling disturbance, stress history, and time (aging or period under sustained load). Thus, when the laboratory data are used to estimate in situ shear moduli in the field, considerations should be given to these effects. When laboratory data do not extrapolate back to the field data at small strains, one of the approaches used in practice is to scale the laboratory data up to the field data at small strains. This can be done by proportionally increasing all values of laboratory moduli to match the field data at low strain values or by other scaling procedures.



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1.0

0.8 Typical Sand Curve

G/Gmax

0.6

0.4

0.2

0.0 10−4

10−3

10−2 10−1 Shear Strain, percent

1

10

FIGURE 10.15 Normalized modulus reduction relationship for clays with plasticity index between 40 and 80.

Damping Ratio, percent

40 Seed and Idris (1970)

30

20

10

0 10−4

10−3

10−2 10−1 Shear Strain, percent

1

10

FIGURE 10.16 Strain-dependent damping ratios for clays.

10.3.1.3 Equipment Linear Soil Properties Given the low-strain soil profile determined from the combination of field and laboratory tests, and the variation of material parameters with strain level, a site response analysis is performed to estimate equivalent linear soil properties for the SSI analysis. The computer program SHAKE [Schnabel et al., 1972] has become an international standard for such analyses. 10.3.1.4 Uncertainty in Modeling Soil/Rock at the Site There is uncertainty in each aspect of defining and modeling the site soil conditions for SSI analysis purposes. The soil configuration (layer or stratigraphy) is established from the boring program. Even after such a program, some uncertainty exists in the definition of the soil profile. Soils are seldom homogeneous, and they seldom lie in clearly defined horizontal layers — the common assumptions in



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SSI analysis. In general, complicated soil systems introduce strong frequency dependence in the site behavior. Modeling the dynamic stress–strain behavior of the soil is uncertain in two respects. First, modeling soil as a viscoelastic material with parameters selected as a function of average strains is an approximation to its complex behavior. Second, there is uncertainty in defining low strain shear moduli and in defining the variations in shear modulus and observed damping with strain levels, Variability can be observed in reporting test values for a given site and for reported generic test results. The range of coefficients of variation on “stress–strain behavior” estimated by the American Society of Civil Engineers (ASCE) Committee on Reliability of Offshore Structures [ASCE, 1979] is 0.5 to 1.0. Similarly, the ASCE Standard, Seismic Analysis of Safety-Related Nuclear Structures and Commentary [1998] recommends implementation of a variation in low-strain shear moduli of 0.5 to 1.0 depending on specific site data acquired and its quality. In the former case, one is dealing with offshore structures with foundations founded underwater, which certainly adds to the uncertainty in the dynamic behavior of soil foundation. In the latter case, variation in shear moduli is intended to account for sources of uncertainty in the SSI analysis process in addition to the uncertainty in soil material behavior. Considering only uncertainty in soil shear modulus itself and the equivalent linear estimates to be used in the SSI analysis, a coefficient of variation of 0.35 to 0.5 on soil shear modulus is estimated. Uncertainty in low strain values is less than uncertainty in values at higher strains. The Lotung SSI experiment provides a unique opportunity to quantify the uncertainty in estimates of equivalent linear soil properties. The bases for determining the equivalent linear soil properties included field and laboratory tests and the results of forced vibration tests on the structure. The latter responses permitted system identification techniques to be employed to refine estimates of the low strain profile. Soil property data were extracted from Chang et al. [1985] and are plotted in Figures 10.17 and 10.18. Ten independent sets of data were available and their variability is apparent from the figures. To quantify this variability, the data were evaluated statistically and a weighted coefficient of variation (COV) calculated for soil shear modulus and damping; the weighting factors were soil thickness to a depth of about 100 ft. The resulting COVs for shear modulus and damping were 0.48 and 0.39, respectively. This emphasizes that uncertainty in soil behavior should be taken into account in any SSI analysis.

10.4 Soil–Structure Interaction Analysis 10.4.1 SSI Parameters and Analysis Several approaches for categorizing SSI analysis methods have been used [Johnson, 1981; Tseng and Penzien, 2000]. Two approaches are direct methods, which analyze the soil–structure system in a single step, and the substructure approach, which treats the problem in a series of steps, e.g., determination of the foundation input motion and the foundation impedances, modeling of the structure, and the analysis of the coupled system. For truly nonlinear analysis, the direct method must be employed, since the equations of motion are solved time step by time step, accounting for geometric and material nonlinearities, as appropriate. In the context of the present discussion, it is informative to continue to view the SSI phenomenon in the steps of the substructure approach. Figure 10.1 shows schematically the substructure approach. The key elements not previously discussed follow below. 10.4.1.1 Foundation Input Motion Section 10.2.3 introduced the concept of foundation input motion which differs from the free-field ground motion in all cases, except for surface foundations subjected to vertically incident waves, provided the spatial variation of the free-field ground motion is taken into account. This is due, first, to the variation of free-field motion with depth in the soil, and second, due to the scattering of waves from the



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LEGEND EIE 0

OHSAKI TAJIMI CRIEPI BASLER HOFFMAN EQE

−50

BECHTEL IMPELL DEPTH (ft)

SARGENT & LUNDY UCSD −100

−150

−200 0

500

1000 1500 2000 SHEAR MODULUS (ksl)

2500

3000

FIGURE 10.17 Variability of equivalent linear shear modulus due to different SSI analyses, earthquake, May 20, 1986, Lotung, Taiwan.

soil-foundation interface, because points on the foundation are constrained to move according to its geometry and stiffness. 10.4.1.2 Foundation Impedances Foundation impedances describe the force-displacement characteristics of the soil. They depend on the soil configuration and material behavior, the frequency of the excitation, and the geometry of the foundation. In general, for a linear elastic or viscoelastic material and a uniform or horizontally layered soil deposit, each element of the impedance matrix is complex-valued and frequency-dependent. For a rigid foundation, the impedance matrix is 6 × 6, which relates a resultant set of forces and moments to the six rigid-body degrees of freedom. 10.4.1.3 SSI Analysis The final step in the substructure approach is the actual analysis. The result of the previous steps — foundation input motion, foundation impedances, and structure models — are combined to solve the equations of motion for the coupled soil–structure system. The entire process is sometimes referred to as a complete interaction analysis, which is separated into two parts: kinematic interaction described by the scattering matrix and inertial interaction comprised of the effects of vibration of the soil and structure. In terms of SSI parameters, the scattering functions model kinematic interaction and the foundation impedances model inertial interaction. It is these two parameters which are highlighted in the ensuing sections.



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0

−50 LEGEND

DEPTH (ft)

EIE OHSAKI −100

CRIEPI BASLER HOFFMAN EQE BECHTEL IMPELL

−150

SARGENT & LUNDY UCSD

−200 0

5

10 DAMPING (percent)

15

20

FIGURE 10.18 Variability of equivalent linear damping due to different SSI analyses, earthquake, May 20, 1986, Lotung, Taiwan.

One other point is that the SSI analysis, typically, calculates overall dynamic response of the soil–structure system. The overall structural response is then applied to a detailed structure model as appropriate load cases for structure element and foundation design. In-structure response spectra are delivered to equipment and commodity designers for their seismic qualification. Hence, the SSI analysis is often an intermediate step, albeit an essential one.

10.4.2 Modeling of the Foundation Three aspects of modeling structure foundations are important: stiffness, embedment, and geometry. 10.4.2.1 Stiffness The stiffness of a structural foundation is of importance because in almost all SSI analyses, by either direct or substructure methods, foundation stiffness is approximated. Most substructure analysis approaches assume the effective foundation stiffness to be rigid. For direct methods, various representations of foundation stiffness have been used depending on the geometry and other aspects of the structure–foundation system. Most foundations of the type common to major building structures cannot be considered rigid by themselves. However, structural load-resisting systems, such as shear wall systems, significantly stiffen their foundations. Hence, in many instances, the effective stiffness of the foundation is very high and it may be assumed rigid. One study which has investigated the effects of foundation flexibility on structure response for a complicated nuclear power plant structure of large plan dimension was performed [Johnson and Asfura, 1993]. In this study, the stiffening effect of the structure on the foundation was treated exactly. Even though the structure had nominal plan dimensions of 350 ft by 450 ft, the effect of foundation flexibility on structure response was minimal. The largest effect was on rotational accelerations of the foundation segment as one would expect. Translational accelerations and response spectra, © 2003 by CRC Press LLC



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quantities of more interest, on the foundation and at points in the structure were minimally affected (5%). This conclusion emphasizes the importance of considering the stiffening effect of walls and floors on the foundation when evaluating its effective stiffness. A counter example is encountered when considering a relatively thin slab supporting massive structurally independent components, such as dry nuclear spent fuel storage casks [Bjorkman et al., 2001]. In the referenced study, sensitivity studies were performed on the dynamic response of dry fuel storage casks and the reinforced concrete pad supporting them. Numerous combinations of number of casks, thickness of pad, and stiffness of soil were considered. In order of significance, the most important parameters affecting cask dynamic response were thickness of the pad, arrangement and number of casks on the pad, and stiffness of the soil. Hence, practically speaking, for design and evaluation of major structures with stiff load-resisting systems, the assumption of rigid foundation behavior is justified. For predicting the response of a structure to a single recorded event, more refined modeling of the foundation may be required. For structure–foundation conditions of differing characteristics, appropriate sensitivity studies need to be performed to justify all assumptions made, including those related to foundation stiffness modeling. 10.4.2.2 Embedment Foundations are typically fully embedded and structures are partially embedded. Foundation embedment has a significant effect on SSI. Both the foundation input motion and the foundation impedances differ for an embedded foundation compared to a surface foundation. Foundation input motion for embedded foundations was discussed extensively in Section 10.2. Foundation impedances comprise a second aspect of foundation modeling. As discussed above, a common and appropriate assumption for many cases is rigid foundation behavior. For a rigid foundation, the impedance matrix describing force-displacement characteristics is, at most, a 6 × 6 complex-valued, frequency-dependent matrix. The literature, as summarized by Johnson [1981], contains numerous exact and approximate analytical representations of foundation impedances. Also, many analytical/experimental correlations exist with relatively good results reported. Figure 10.19 shows one such example. Figure 10.20 demonstrates the effect of embedment on foundation response for embedded and nonembedded configurations of an assumed rigid foundation. Forced vibration tests were performed. The results clearly demonstrate the effect on inertial interaction of embedment. 10.4.2.3 Geometry The geometry of major structure foundations can be extremely complicated. Fortunately, many aspects of modeling the foundation geometry are believed to have second-order effects on structure response, in particular, modeling the precise shape of the foundation in detail. However, other overall aspects, such as nonsymmetry, that lead to coupling of horizontal translation and torsion and vertical translation and rocking, can be very important and need to be considered. Modeling the foundation is important with respect to structure response. This is one area where knowledge and experience of the practitioner are invaluable. Complicated foundations must be modeled properly to calculate best estimates of response, i.e., including the important aspects as necessary. Foundation modeling plays a key role in assessing whether two-dimensional models are adequate or three-dimensional models are required.

10.4.3 Modeling of the Structure 10.4.3.1 Linear Dynamic Behavior Structures for which SSI analysis is to be performed require mathematical models to represent their dynamic characteristics. The required detail of the model is dependent on the complexity of the structure or component being modeled and the end result of the analysis. Structure models are typically of two types: lumped-mass stick models and finite element models. Lumped-mass stick models are characterized by lumped masses defining dynamic degrees of freedom.



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×108t/m Method A C

×1011tm/rad

1.5

B D

Method A C

B D

− K R(REAL)

− K H(REAL)

2.0

0

0 −2.0 0

4

6

0

Hz

×108t/m

2

4

6

Hz

×1011tm/rad

1.5

− K R(IMAG.)

2.0

− K H(IMAG.)

2

0

0 −2.0 0

2 4 (a) swaying spring

6

0

Hz

2 4 (b) rotational spring

6

Hz

FIGURE 10.19 Analytical/experimental foundation impedances.

30

Amplitude (µm/ton)

Non-embedment: 20 Half-embedment: 10 Full-embedment:

0 0

10

20

30 (Hz)

FIGURE 10.20 Comparison of horizontal displacement resonance curves at foundation bottom, forced vibration test.

For buildings, masses are usually lumped at floor slab elevations and simplified assumptions as to diaphragm or floor behavior are made; in particular, floors are frequently assumed to behave rigidly inplane and, often, for out-of-plane behavior, also. Diaphragm flexibility can be modeled when necessary. Connections between lumped masses are usually stiffness elements whose stiffness values represent columns and/or groups of walls running between the floor slabs. In some instances, an offset is modeled between the center of mass and center of rigidity at each floor elevation to account for coupling between horizontal translations and torsion. Also, lumped-mass stick models are frequently used to model other © 2003 by CRC Press LLC



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regular structures, an example being cylindrical structures (tanks, containment shells, caissons, etc.). Finite element models are used to represent complex structures. They permit a more accurate representation of complicated situations without requiring significant simplifying assumptions. Either model type may be adequate depending on the structural configuration, the detail included in the model, and the simplifying assumptions. Lumped-mass stick models are mathematically simpler than finite element models and usually have a smaller number of degrees of freedom. Lumped-mass stick models take advantage of the judgment of the analyst as to the expected behavior of the structure. Modeling methods and techniques will not be discussed in detail here. The ASCE Standard, Seismic Analysis of Safety-Related Nuclear Structures and Commentary [1998] presents many aspects of modeling and a bibliography from which additional information may be obtained. Modal equivalent models can be used for computational efficiency and to maintain equivalency between the dynamic characteristics of a detailed model in the SSI analysis. A modal equivalent model is comprised of a family of single-degree-of-freedom (SDOF) models, each having the dynamic characteristics of an individual mode of the detailed model (finite element or otherwise). Each SDOF has a mass equal to the modal mass of the detailed model mode, the mass is located at the point above the base to produce the equal moment on the base, and the stiffness elements are selected to reproduce the frequency of the detailed model mode. Each of these SDOFs is exactly equivalent to including the detailed model mode. One p oint of note for shear wal l structures is that o ver the last half of the 1980s, testing o f shear walls as indi vidual elements and as a p ortion of a structure asse mblage has b een performed. One result o f these t ests is the ap parent reduction in stiffness fr om the linear ly calculat ed values d ue to small cracks and othe r phenomena. The ASCE D ynamic Analysis Committee’s Working Group o n Stiffness o f Concrete [1992] e valuated the r elevant data and r ecommended approaches to account for increases and d ecreases in st iffness p reviousl y not treated explicitl y. Increases r esult fr om items such as incr ease d concrete strength d ue to ag ing and a chieving minim um specified strengths in a conservative manner. 10.4.3.2 Nonlinear Structure Models The nonlinear behavior of structures is important in two regards: (1) evaluating the capacity of structural members and the structure itself and (2) estimating the environment (in-structure response spectra and structural displacements) to which equipment and commodities are subjected. Nonlinear structural behavior is characterized by a shift in natural frequencies to lower values, increased energy dissipation, and increased relative displacement between points in the structure. Four factors determine the significance of nonlinear structural behavior to dynamic response. 10.4.3.3 Frequency Content of the Control Motion vs. the Frequencies of the Structure Consider a rock-founded structure. Depending on the elastic structure frequencies and characteristics of the control motion, the shift in structure frequency due to nonlinear structural response may result in a relatively large reduction in structure response with a substantial reduction in input to equipment when compared to elastic analysis results. If the structure elastic frequency is located on the peak or close to the peak of the control motion’s response spectra, the frequency shift will result in a decrease in response. If the elastic frequency is higher than the peak of the control motion’s response spectra, the shift in frequency tends to result in increased response. The same type of reduction occurs for structures excited by earthquakes characterized by narrow-band response spectra where the structure elastic frequency tends to coincide closely with the peak of the ground response spectra. 10.4.3.4 Soil–Structure Interaction Effects The effect of nonlinear structure behavior on in-structure response (forces, accelerations, and response spectra) appears to be significantly less when SSI effects are important at the site. This is principally due to the potential dominating effect of SSI on the response of the soil–structure system. The soil can have a controlling effect on the frequencies of the soil–structure system. Also, if SSI is treated properly, the input motion to the system is filtered such that higher frequency motion is removed, i.e., frequency © 2003 by CRC Press LLC


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content which may not be suppressed by nonlinear structural behavior if the structure were founded on rock. SSI can have a significant effect on the energy dissipation characteristics of the system due to radiation damping and material damping in the soil. Accounting for the effect of the inelastic structural behavior on structure response must be done carefully for soil-founded structures to avoid doublecounting of the energy dissipation effects. 10.4.3.5 Degree of Structural Nonlinearity The degree of structural nonlinearity to be expected and permitted determines the adequacy assessment for the structure and can have a significant impact on in-structure responses. Past reviews of testing conducted on shear walls have indicated that element ductilities of up to about four or five can be accommodated before significant strength degradation begins to occur. However, the allowable achieved ductility for many evaluations will be substantially less. The effect of nonlinear structure behavior on instructure response spectra has been considered to only a limited extent. In general, increased levels of nonlinearity lead to increasingly reduced in-structure response spectra for a normalized input motion. However, in some instances, higher frequency, i.e., higher than the fundamental frequency, peaks can be amplified. This is an area in which research is currently being performed, which will provide guidance in the future. 10.4.3.6 Magnitude Effects Earthquake magnitude as it affects the control motion has been discussed earlier. Recall, however, smaller magnitude, close-in earthquakes may be narrow-banded, which are significantly affected by nonlinear behavior as described above.

10.5 Soil–Structure Interaction Response Numerous guidelines exist defining the required steps to perform SSI analysis for design or evaluation purposes. All methods of analysis are treated. Selected guideline documents are: ASCE Standard, Seismic Analysis of Safety-Related Nuclear Structures and Commentary [1998] EPRI Guidelines for Soil–Structure Interaction Analysis [Tseng and Hadjian, 1991] Earthquakes and Associated Topics in Relation to Nuclear Power Plant Siting [IAEA, 1991] Seismic Design and Qualification for Nuclear Power Plants [IAEA, 1992] The validation of SSI analysis through field data has been difficult due to the lack of well-documented and instrumented structures subjected to earthquakes. Very few cases exist where the data necessary to effectively analyze a soil–structure system have been developed or measured. In addition, for those with data, typically, not all aspects of the SSI phenomenon are important. One case in point is the Lotung one quarter scale model. All appropriate data have been developed and measured but the high stiffness of the structure and the very soft soil conditions eliminate structure vibration as a significant phenomenon. Comparisons of measured and calculated response produced an excellent match. Hence, elements of the SSI analysis process were validated. In addition to the Lotung experiment, there is a recognition in the technical community that additional data appropriate for SSI analysis methods benchmarking and development are necessary. One example was an additional experiment, denoted the Hualien large-scale seismic test for SSI research, constructed in Taiwan in the early 1990s. This experiment intended to eliminate some of the deficiencies of the Lotung experiment by siting a model structure on a stiffer site than Lotung, thereby bringing dynamic structure response into importance. Unfortunately, this experiment has not received the funding necessary to progress. Instrumenting large bridge structures in seismically active areas would be an additional source of data to be pursued. Many aspects of SSI are well understood and any valid method of analysis is able to reproduce them. Sections 10.2, 10.3, and 10.4 detailed the various aspects of the problem and the current capability to model them. Clearly, uncertainties exist in the process: randomness associated with the earthquake ground motion itself, and the dynamic behavior induced in soil and structures. Even assuming perfect © 2003 by CRC Press LLC



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modeling, randomness in the response of structures and components is unavoidable. Perhaps the best evidence of such randomness is the Chiba Field Station. Shibata [1991] reports the results of 20 years of recorded motion on the model structure; 271 events when taken in total. Analyzing the measured responses of the hung tank yields a coefficient of variation of response of about 0.45 conditional on the horizontal peak ground accelerations of the earthquake. Of course, arguments can be made that many of the events were low amplitude, that grouping events by epicentral area reduced variability, etc. However, the indisputable fact is that significant variability in response of structures and components due to earthquakes is to be expected. No deterministically exact solution of the SSI problem can be obtained by existing techniques. However, given the free-field ground motion and data concerning the dynamic behavior of soil and structure, reasonable response predictions can be made. These responses can confidently be used in design and evaluation procedures. It is on this premise that analysis guidelines cited above are based. In addition, uncertainties in each of the elements do not necessarily combine in such a fashion as to always increase the uncertainty in the end item of interest (structure response). Finally, when evaluating the SSI model and the resulting analytical results, one should evaluate intermediate and end results including: • Fixed-base vs. soil-structure system frequencies • Amount of soil stiffness softening due to earthquake excitation compared to low strain values • Effect of soil property variations on dynamic model parameters, such as system frequency, important response parameters, and structural damping values used For partially embedded structures, response at grade level floors should, as a general rule, be less than the free-field ground surface motion.

Defining Terms Control motion — Amplitude and frequency characteristics of the input motion. Control point — Point at which input motion is applied, in an SSI analysis. Free field — The ground surface in the absence of any structures. Free-field ground motion — Motion that would essentially exist in the soil at the level of the foundation in the absence of the structure and any excavation.

Uniform hazard spectra (UHS) — Ground response spectra generated so as to have the same probability of exceedance for all structural frequencies of interest.

References ASCE. (1998). “ASCE Standard, Seismic Analysis of Safety-Related Nuclear Structures and Commentary,” ASCE 4–98, American Society of Civil Engineers, Reston, VA. ASCE Committee on Reliability of Offshore Structures, Subcommittee on Foundation Materials. (1979). Probability Theory and Reliability Analysis Applied to Geotechnical Engineering of Offshore Structure Foundations, American Society of Civil Engineers, Reston, VA. ASCE. (1992). Dynamic Analysis Committee Working Group Report on Stiffness of Concrete, American Society of Civil Engineers, Reston, VA. Bjorkman, G.S., Moore, D.P., Nolin, J.J., and Thompson, V.J. (2001). “Influence of ISFSI Design Parameters on the Seismic Response of Dry Storage Casks,” W01/3, Proc. Structural Mechanics in Reactor Technology, August 12–17, Washington, D.C., SMIRT Secretariat, North Carolina State University, Raleigh. CH2M Hill. (1991). Proc. NSF/EPRI Workshop on Dynamic Soil Properties and Site Characterization, EPRI NP-7337, vol. 1, Electric Power Research Institute, Palo Alto, CA.



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Chang, C.-Y., Power, M.S., Idriss, I.M., Somerville, P.G., Silva, W., and Chen, P.C. (1985). “Engineering Characterization of Ground Motion, Task II: Observational Data on Spatial Variations of Earthquake Ground Motion,” NUREG/CR-3805, vol. 3, prepared for the U.S. Nuclear Regulatory Commission, Washington, D.C. Chang, C.-Y. et al. (1990). “Equivalent Linear Versus Nonlinear Ground Response Analyses at Lotung Seismic Experiment Site,” Proc. Fourth U.S. National Conference on Earthquake Engineering, Palm Springs, CA. Chang, C.-Y. et al. (1991). “Development of Shear Modulus Reduction Curves Based on Lotung Downhole Ground Motion Data,” Proc. Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, St. Louis, MO. Cramer, C.H. (1991). “Turkey Flat, USA Site Effects Test Area, Report 6 Weak-Motion Test: Observations and Modeling,” Technical Report No. 91–1, California Department of Conservation, Division of Mines and Geology, Earthquake Shaking Assessment Project, Sacramento, CA. EPRI. (1989). Proc. EPRI/NRC/TPC Workshop on Seismic Soil Structure Interaction Analysis Techniques Using Data from Lotung, Taiwan, EPRI NP-6154, vols. 1 and 2, Electric Power Research Institute, Palo Alto, CA. Gazetas, G. and Bianchini, G. (1979). “Field Evaluation of Body and Surface-Wave Soil-Amplification Theories,” Proc. Second U.S. National Conference on Earthquake Engineering, Electric Power Research Institute, Stanford University, Palo Alto, CA. Hadjian, A.H. et al. (1991). “A Synthesis of Predictions and Correlation Studies of the Lotung Soil Structure Interaction Experiment,” Report No. NP-7307-M, Electric Power Research Institute, Palo Alto, CA. IAEA. (1991). “Earthquakes and Associated Topics in Relation to Nuclear Power Plant Siting: A Safety Guide,” Safety Series No. 50-SG-S1 (Rev. 1), International Atomic Energy Agency, Vienna, Austria. IAEA. (1992). “Seismic Design and Qualification for Nuclear Power Plants: A Safety Guide,” Safety Series No. 50-SG-D15, International Atomic Energy Agency, Vienna, Austria. Ishihara, K. (1996). Soil Behavior in Earthquake Geotechnics, Oxford Engineering Science Series, no. 46, Oxford University Press, London. Ishii, K., Itoh, T., and Suhara, J. (1984). “Kinematic Interaction of Soil-Structure System Based on Observed Data,” Proc. 8th World Conference on Earthquake Engineering, San Francisco, vol. 3, Earthquake Engineering Research Center, Berkeley, CA, pp. 1017–1024. Johnson, J.J. (1981). Soil Structure Interaction: The Status of Current Analysis Methods and Research,” Lawrence Livermore National Laboratory (LLNL), UCRL-53011, NUREGICR-1780, prepared for the U.S. Nuclear Regulatory Commission, Washington, D.C. Johnson, J.J. and Asfura, A.P. (1993). “Soil Structure Interaction (SSI): Observations, Data, and Correlative Analysis,” in Developments in Dynamic Soil-Structure Interaction, P. Gulkan and R.W. Clough, eds., Kluwer Academic Publishers, Dordrecht, pp. 219–258. Johnson, J.J. and Chang, C.-Y. (1991). “State of the Art Review of Seismic Input and Soil-Structure Interaction,” Appendix E in A Methodology for Assessment of Nuclear Power Plant Seismic Margin (Rev. l), EPRI NP-6041-SL, Electric Power Research Institute, Palo Alto, CA. Johnson, J.J., Maslenikov, O.R., Mraz, M.J., and Udaka, T. (1989). “Analysis of Large-Scale Containment Model in Lotung; Taiwan: Forced Vibration and Earthquake Response Analysis and Comparison,” Proc. EPRI/NRC/TPC Workshop on Seismic Soil Structure Interaction Analysis Techniques Using Data From Lotung, Taiwan, EPRI NP-6154, vols. 1 and 2, Electric Power Research Institute, Palo Alto, CA, pp. 13-1–13-44. Kudo, K., Shima, E., and Sakane, M. (1988). “Digital Strong Motion Accelerograph Array in Ashigara Valley — Seismological and Engineering Prospects of Strong Motion Observations,” Proc. 9th World Conference on Earthquake Engineering, vol. 8, Earthquake Engineering Research Center, Berkeley, CA, pp. 119–124.




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Midorikawa, S. (1992). “A Statistical Analysis of Submitted Predictions for the Ashigara Valley Blind Prediction Test” (Subcommittee for the Prediction Criteria of the Ashigara Valley Blind Prediction Test), Proc. International Symposium on the Effects of Surface Geology on Seismic Motion, Odawara, Japan. Newmark, N.M. and Hall, W.J. (1978). Development of Criteria for Seismic Review of Selected Nuclear Power Plants, NUREG/CR-0098, prepared for the U.S. Nuclear Regulatory Commission, Washington, D.C. Proceedings of the International Symposium on the Effects of Surface Geology on Seismic Motions. (1992). Odawara, Japan. Schnabel, P.B., Lysmer, J., and Seed, H.B. (1972). SHAKE: A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites, Report No. EERC 72–12, Earthquake Engineering Research Center, University of California, Berkeley. Seale, S.H. and Archuleta, R.J. (1991). “Analysis of Site Effects at the Games Valley Downhole Array Near the San Jacinto Fault,” Proc. Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, Paper No. 8.13, St. Louis, MO. Seed, H.B. and Idriss, I.M. (1970). Soil Moduli and Damping Factors for Dynamic Response Analysis, Report No. EERC 70–10, Earthquake Engineering Research Center, University of California, Berkeley. Shibata, H. (1978). “On the Reliability Analysis for Structural Design Including Pipings and Equipment,” presented at the Seminar on Probabilistic Seismic Analysis of Nuclear Power Plants, January 16–19, Berlin. Shibata, H. (1991). “Uncertainty in Earthquake Engineering in Relation to Critical Facilities,” Bulletin of Earthquake Resistant Structure Research Center, Institute of Industrial Science, University of Tokyo, No. 24, 93–104. Tanaka, T. et al. (1973). “Observations and Analysis of Underground Earthquake Motions,” Proc. 5th World Conference on Earthquake Engineering, Rome, vol. 1, pp. 658–667. Tseng, W.S. and Hadjian, A.H. (1991). “Guidelines for Soil Structure Interaction Analysis,” EPRI NP7395, Electric Power Research Institute, Palo Alto, CA. Tseng, W.S. and Penzien, J. (2000). “Soil-Foundation-Structure Interaction,” in Bridge Engineering Handbook, W.F. Chen and L. Duan, eds., CRC Press, Boca Raton, FL, pp. 42-1–42-52. U.S. Atomic Energy Commission. (1973). “Regulatory Guide 1.60, Design Response Spectra for Seismic Design of Nuclear Power Plants,” Rev. 1, U.S. Atomic Energy Commission, Washington, D.C. Wolf, J.P. and Song, C. (2002). “Some Cornerstones of Dynamic Soil-Structure Interaction,” Eng. Struct., 24, 13–28. Woods, R.D. (1978). “Measurement of Dynamic Soil Properties,” Proc. ASCE Specialty Conference on Earthquake Engineering and Soil Dynamics, vol. 1, Pasadena, CA, pp. 91–178. Yanev, P.I., Moore, T.A., and Blume, J.A. (1979). “Fukushima Nuclear Power Station, Effect and Implications of the June 12, 1978, Miyagi-ken-Oki, Japan, Earthquake,” prepared by URS/John A. Blume & Associates, Engineers, San Francisco.


0068_Section 03_fm Page 1 Friday, August 16, 2002 3:09 PM

III

Structural Aspects



11

Building Code Provisions for Seismic Resistance 11.1 Introduction 11.2 Historical Development Early Prescriptive Codes · Early Lateral Force Requirements · 1927 Uniform Building Code · Code Development in the 1930s and 1940s · 1958 Uniform Building Code · Code Development 1958 to 1970 · 1971 San Fernando Earthquake · National Seismic Provisions

11.3 2000 NEHRP Recommended Provisions Overview · Performance Intent and Objectives · Seismic Hazard Maps and Ground Motion Parameters · Seismic Design Categories · Permissible Structural Systems · Design Coefficients · Analysis Procedures · Load Combinations and Strength Requirements · Drift Limitations · Structural Detailing

Ronald O. Hamburger Simpson Gumpertz & Heger, Inc. San Francisco, CA

11.4 Performance-Based Design Codes Defining Terms References Further Reading

11.1 Introduction The purpose of building codes is to promote and protect the public welfare. The public welfare may be broadly construed to include considerations of the health and safety of individual citizens, as well as the economic well-being of the community as a whole. Building codes accomplish this purpose by setting minimum standards for the materials of construction that may be used for structures of different types and occupancies, the minimum permissible strength of these structures, and the amount of deformation that may be tolerated under design loading. Governments have the power to enforce these standards through the code adoption process, i.e., converting the code into a legal standard. If building code criteria were not specified in a uniform manner, design and construction practice would vary widely, and many structures would be unable to afford their occupants adequate protection against collapse. Design loading levels are typically set by building codes at levels that have a moderate to low probability of occurrence during the life of the structure. For example, buildings may be designed for earthquake shaking likely to be experienced one time every 500 years, wind loads anticipated, on the average, one time every 100 years, or for snow loads that would be anticipated to occur, on average, one time every



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20 years. The significant difference in recurrence intervals adopted by codes for these various hazards is a function of the hazard itself, and the adequacy of a given return period to capture a maximum, or near maximum, credible event. Building code provisions typically require design for such loading to accomplish two main objectives. The first is to provide a low probability of failure under any likely occurrence of the loading type. This is typically accomplished through prescription of minimum required levels of structural strength. The second is to provide sufficient stiffness such that deflections do not affect the serviceability of the structure, or result in cracking or other damage that would require repair following routine loading. For most structural elements and most loading conditions, these dual design criteria result in structures that are capable of resisting the design loading with either elastic or near-elastic behavior. Consequently, engineered buildings rarely experience structural damage as a result of the effects of dead, live, wind, or snow loads, and rarely completely fail under such loading. Building code provisions for earthquake-resistant design are unique in that, unlike the provisions for other load conditions, they do not intend that structures be capable of resisting design loading within the elastic, or near-elastic range of response — that is, some level of damage is permitted. Building codes intend only that buildings resist large earthquake loading without life-threatening damage and, in particular, without structural collapse or creation of large, heavy falling debris hazards. This unique earthquake design philosophy evolved over time based primarily on two motivating factors. First, even in zones of relatively frequent seismic activity, such as regions around the Pacific Rim, intense earthquakes are rare events, affecting a given region at intervals ranging from a few hundreds to thousands of years. Most buildings will never experience a design earthquake and, therefore, design to resist such events without damage would be economically impractical for most structures. The second reason for this design approach relates to the development history for building code seismic provisions, which is briefly discussed in the next section. Building code provisions governing design for earthquake resistance may be traced back as far as building regulation enacted in Lisbon, Portugal, following the great earthquake of 1755 [Tobriner, 1984]. Early building code provisions for seismic resistance focused on prohibiting certain types of construction observed to behave poorly in past earthquakes, and to require the use of certain construction details and techniques observed to provide better performance. These features remain an important part of modern codes. However, modern codes supplement these prescriptive requirements with specifications of minimum permissible structural strength and stiffness. Although most developed countries develop and enforce their own building codes, the seismic provisions currently used throughout the world generally follow one of four basic models: • NEHRP Recommended Provisions, developed by the Building Seismic Safety Council in the United States [BSSC, 1997] • Building Standards Law of Japan • New Zealand Building Standards Law • Eurocode 8 Although each individual code has many unique requirements and provisions, in general all are based on and incorporate similar concepts. This chapter principally discusses the NEHRP Recommended Provisions which, together with related publications by the Structural Engineers Association of California [SEAOC, 1999], forms the basis for most building codes in use in the Americas today as well as in other parts of the world.

11.2

Historical Development

Building code provisions for earthquake resistance may generally be traced to one of three bases. The first of these, herein termed the experience basis, consists of observation of the behavior of real structures in earthquakes, and the development of prescriptive rules intended to prevent construction of buildings with characteristics that are repeatedly observed to result in undesirable behavior. © 2003 by CRC Press LLC


Building Code Provisions for Seismic Resistance

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The second basis is herein termed the theoretical basis. It consists of the body of analytical and laboratory research that has been developed over the years, largely by the academic community, and which provides an understanding of the way structures of different types respond to earthquakes and why. The final basis is one of designer judgment. The building design community and, in particular, structural engineers — primarily through the SEAOC, the American Society of Civil Engineers (ASCE), the Building Seismic Safety Council (BSSC), and other similar groups — have historically taken a leadership role in the development of these building code provisions. These structural engineers have consistently tempered and moderated the information obtained from the experience and theoretical bases, with their independent design judgment, assuring political acceptability of the building code within the design community, if not completely rational or justifiable provisions.

11.2.1 Early Prescriptive Codes The earliest building code provisions were strictly experience based. It was observed that certain types of construction consistently performed poorly, so rules were developed to regulate the features of these construction types to improve their performance. In the United States this process is thought to have been initiated with the observation of the poor performance of unreinforced brick masonry bearing wall buildings in the San Francisco Bay Area, following the Hayward earthquake of 1868. It was observed in this and other early California earthquakes that brick masonry walls frequently pulled away from the floor and roof systems, then toppled to the ground. It was similarly observed that the brick walls were not strongly bonded together, and that the walls would literally fall apart, into the component brick pieces (Figure 11.1). Based on these observations, some building codes in California began to include prescriptive provisions regulating the construction detailing of unreinforced masonry buildings. To avoid the frequently observed out-of-plane failure of masonry walls, in which they would pull away from the floors and roofs and topple to the ground, codes FIGURE 11.1 Typical failure of masonry walls started to require the provision of out-of-plane anchors in unreinforced masonry bearing wall buildings, between the walls and floor and roof diaphragms. 1989 Loma Prieta earthquake. (Courtesy U.S. Anchors were not designed for specific forces, but rather Geological Survey) were specified to be of a standard size and spacing. The most common such anchors consisted of steel rods that extended to the exterior face of the masonry wall, typically terminating with a round plate washer or rosette for bearing against the masonry, and tying to the floor framing by means of a 90ο bend that “dogged” into the side of the wood members. Evidence of these anchors can be commonly observed on older unreinforced masonry structures in the form of rows of rosette plates along the exterior faces of walls just below the floor and roof levels, typically at 6- to 8-ft spacing. To address the commonly observed in-plane failures of unreinforced masonry walls, some codes in the San Francisco Bay Area required the placement of “bond irons” in the masonry. These bond irons consisted of 1/4-in. thick flat bars, laid horizontally in the mortar courses of masonry walls at approximately 24-in. vertical spacing. Riveted together at lap joints, these bond irons were a primitive form of reinforcing. Neither code-required wall anchors nor bond irons were designed for a specified loading. In fact, engineers of the day had little understanding of the strength of earthquake ground shaking, the © 2003 by CRC Press LLC


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mechanisms by which this shaking induced forces in building components or the magnitude of these forces. They did observe, however, that unreinforced masonry buildings constructed without wall anchors and bond irons tended to collapse when earthquakes occurred and that this resulted in life loss. Thus, the primary goal of these first earthquake provisions in building codes was simply to avoid building collapse and the resulting life endangerment. Over the years, as the building codes evolved, this goal remained as the primary objective of building code earthquake provisions.

11.2.2 Early Lateral Force Requirements In the early 20th century, building codes around the world began to introduce requirements that structures intended to resist earthquakes be provided with sufficient strength to resist a specified lateral force. These requirements, though substantially refined, are retained in most building codes today as a basic design method and are frequently termed the equivalent lateral force (ELF) technique. Perhaps the first of these requirements appeared in the building code published by the City of San Francisco, following the great 1906 earthquake. This code required that all buildings be designed for a lateral pressure of 30 pounds per square foot on the projected area of the building façade, as a protection against both wind and earthquake. Following a devastating magnitude 7.5 earthquake in Messina, Italy, that caused 80,000 casualties in 1908, a special committee of practicing engineers and engineering professors was commissioned to recommend improved construction requirements. The resulting report included a recommendation that the first story of structures be designed for a horizontal force equal to 1.5% of the weight above and the second and third stories be designed for one eighth of the building weight above. This appears to have been the first formal recommendation to provide earthquake resistance by providing lateral strength equal to a fraction of the structure’s supported weight [Housner, 1984]. The ELF concept was introduced in Japan in 1914, but not required. Following the great 1923 Tokyo earthquake, the Japanese Urban Building Law Enforcement Regulations were revised to require lateral design for a strength equal to 10% of the structure’s supported weight.

11.2.3 1927 Uniform Building Code The first modern code containing seismic provisions is generally acknowledged to be the first edition of the Uniform Building Code published by the Pacific Coast Building Officials in 1927 [PCBO, 1927], following the 1925 Santa Barbara earthquake. The Pacific Coast Building Officials later became the International Conference of Building Officials, and continued to publish the Uniform Building Code (UBC) for another 70 years, the last edition being published in 1997 [ICBO, 1997]. The seismic provisions of the UBC were based primarily on the SEAOC recommendations and remained in a leadership role over the full 70 years. The 1927 edition of the UBC incorporated the lessons engineers had learned in observing a series of earthquakes that had affected California during the period 1868 to 1925. These included the 1868 Hayward, 1906 San Francisco, and 1925 Santa Barbara earthquakes, as well as other smaller events. The earthquake requirements of the 1927 code were included in a nonmandatory appendix, where they remained for nearly 30 years. In addition to the vulnerability of unreinforced masonry structures already discussed, the 1927 code built upon engineers’ observations that the primary damaging effect to structures appeared to be a lateral shaking motion and that this lateral shaking tended to be much more severe in areas with deep, soft soil deposits, termed infirm soils. The code required design of such structures for the simultaneous application of a lateral force at each roof and floor level equal to 10% of the structure’s weight tributary to that floor. Structures sited on firm soils were designed for one third of this force, recognizing in an approximate manner, the reduced intensity of ground shaking on sites with firm soil profiles. Since there were no records of actual ground motion available in 1927 (the first accelerometer had yet to be installed), and structural dynamics was a newly developing science, the selection of a 10% design lateral strength level must surely have been judgmental, and may have been influenced in part by the © 2003 by CRC Press LLC



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similar requirement that had been recently adopted in Japan. However, it did set an important precedent. As engineers began to design structures to these new code requirements, they also began to rely on a lateral strength equal to 10% of the supported weight as being adequate to provide earthquake resistance. Even as dramatic improvements in understanding of ground motion and structural response occurred, over the years, engineers tended to apply judgment and scale code provisions so that they produced design forces approximating this same level. With the publication of the 1927 code, the process of observing the behavior of buildings designed to the code began, and of modifying the code to produce better performing structures and incorporate the findings of engineering research. It is important to stress that the observation of earthquake damage to engineered structures has been as significant a factor in this development as analytical and laboratory work performed by the academic community.

11.2.4 Code Development in the 1930s and 1940s In the years between 1927 and 1940 seismic provisions in codes changed relatively little, as relatively few earthquakes occurred, and engineering knowledge was limited. However, following the 1933 Long Beach earthquake, which caused extensive damage to unreinforced masonry buildings, and in particular, several public schools (Figure 11.2), the State of California adopted a number of regulations that would later have significant impact on the UBC. First, California prohibited further construction of unreinforced masonry buildings. The UBC would later pick up this same prohibition in zones of high seismicity. Also, California adopted two acts, the Riley Act and Field Act, which regulated building construction for earthquake resistance. The Riley Act required that all buildings in California be provided with a lateral strength equal to 3% of the weight of the structure, making seismic design mandatory. This provision was also adopted by the UBC and remains in the NEHRP Provisions today, albeit in somewhat modified form. The Field Act established the Office of the State Architect and charged this department with responsibility for the regulation of public school construction. The Office of the State Architect established rigorous standards for structural design, plan review, and inspection of construction that would affect structural engineering practice throughout California and eventually find its way into the building code requirements applicable to all forms of construction.

FIGURE 11.2 Collapse of John Muir School, 1933 Long Beach, CA earthquake. (Courtesy NOAA, www.ngdc.gov, photo: W.L. Huber.)



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In the 1937 edition of the UBC the concept of differentiating seismic risk by means of a zonation map was introduced. This first map divided the continental United States into three seismic zones and the required lateral strength for a structure was regulated based on these seismic zones. In the 1940s, engineers began to understand the science of structural dynamics. Based on rudimentary understanding of this science and on observations that tall structures seemed to perform better in earthquakes than low-rise construction, a base shear equation was introduced into the 1946 edition of the UBC. For structures located in the highest seismic zone, this base shear equation adjusted the design lateral forces for a structure, based on the number of stories present: V=

0.6 W N + 4.5

(11.1)

where N is the number of stories and W is the building weight. Short structures were designed for the most severe lateral forces, equivalent to 10% of the structure’s weight, while the design forces for taller structures could be reduced in proportion to the number of stories, representing in an approximate manner the concept of spectral amplification.

11.2.5 1958 Uniform Building Code At about this same time, Biot, Housner, and other researchers at the California Institute of Technology began to formalize the concepts of dynamic spectral response. In 1952 these researchers, acting under the auspices of the American Society of Civil Engineers, together with practicing structural engineering members of the Structural Engineers Association of California, formed a joint volunteer committee to develop recommendations for incorporation of these concepts into the building codes. The report of this joint committee, known as the Separate 66 Report [Anderson et al., 1952], presented the first formalized recommendations for relating design lateral forces to structural period, based on spectral response concepts. These recommendations were incorporated by SEAOC into the first edition of the Recommended Lateral Force Requirements and Commentary [SEAOC, 1999], commonly known as the Blue Book, and were adopted into the 1958 edition of the UBC. In that building code, the total lateral force, now commonly known as the base shear, was given by the formula: V = ZKCW

(11.2)

In this equation, Z was a zone coefficient that related the design force to regional seismicity, as portrayed in a national seismic zonation map (Figure 11.3). Four seismic zones were presented ranging from 0 to 3. Zone 3 represented the most severe seismic environment and was assigned a zone coefficient Z having a value of 1.0. In zone 0 there was no requirement for seismic design. In zones 1 and 2, the design coefficient Z was assigned fractional values, for example, 1/2 or 1/4, that effectively adjusted the required seismic design forces in lower zones, relative to those required in zone 3. K was a structural system coefficient that adjusted the magnitude of seismic design forces based on the typical performance observed of structures of different construction types in past earthquakes. Four basic classes of structural systems were recognized: • The first of these were buildings of light timber frame construction, such as is commonly used in residential and light commercial construction in the United States. For this class of construction, the K coefficient was assigned a value of 1.0. • The second structural system was the building frame system. In this system, dead and live loads were carried to the foundations by columns while lateral forces were resisted either by diagonal bracing or shear walls that did not participate in the vertical load resisting system. This system was also assigned a K value of 1.0. • The third structural system was known as a “box system.” In this system, bearing walls or diagonal braced frames carried both vertical loads and lateral forces. This category of structures included © 2003 by CRC Press LLC



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Statute Miles 100 50 0

100

200

300

400

Kilometers 10050 0

200

400

600

800

Zone 0 - no damage Zone 1 - minor damage Zone 2 - moderate damage Zone 3 - major damage

FIGURE 11.3

Seismic zonation map, 1958 Uniform Building Code.

a number of building types, such as unreinforced masonry structures, that had repeatedly been observed to perform poorly in earthquakes. Recognizing this poor performance and also the fact that earthquake-induced damage to lateral-force-resisting elements in buildings of this type could also result in loss of vertical load carrying capacity, a K coefficient of 1.33 was assigned to this building type, requiring design forces that were 33% larger than those for either of the other two systems. • The fourth system was moment-resisting frames in which beams and columns were rigidly connected to provide lateral stability. Based on the observation that these structures were often highly redundant, and also that steel frames, the most common form of such structures, had performed well in the 1906 San Francisco earthquake and again in the 1925 Santa Barbara and 1933 Long Beach earthquakes, this system was assigned a preferential K value of 0.67, permitting them to be designed with two thirds of the lateral strength required for light frame and building frame systems. The C coefficient accounted for spectral amplification of ground motion by buildings having certain fundamental response periods. The C coefficient was given by the equation: C=

0.05 T

(11.3)

where T was the fundamental mode natural period of vibration of the structure, calculated using an empirical formula contained in the code, based on strong motion recordings from buildings. Alternatively, more exact techniques for establishing the structural period, such as the Rayleigh method, were also permitted. W was the total dead weight of the structure. Additional provisions of the code limited the value of C such that for structures qualifying for a K value of 1.0, the design base shear force would not have to exceed a value of 0.1, preserving the judgment contained in earlier building codes that most structures could survive a strong earthquake if provided with a lateral strength equal to 10% of their supported weight. In addition, a lower bound value of 0.03 was provided to conform to the Riley Act requirements adopted following the 1933 Long Beach earthquake.



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Once the base shear was determined, using Equation 11.3, lateral forces were distributed to each level of the structure, in proportion to the mass supported at that level, using the so-called uniform distribution method. The lateral forces at each level were distributed to the various vertical elements of the lateral-force-resisting system, considering both the stiffness of the individual vertical elements and the horizontal diaphragms, and the vertical elements were required to be designed, using allowable stress design procedures, for the combined shearing and overturning effects of these forces, taken together with gravity loads. Allowable stresses for load conditions containing earthquake forces were permitted to be increased by one third relative to those specified for gravity load resistance.

11.2.6 Code Development 1958 to 1970 During the 10 years following publication of the 1958 edition of the UBC, the seismic provisions remained quite stable and changes tended to be subtle, though in some cases important. Perhaps the most significant development introduced during this period was philosophical and related to a formalized statement of the intent of the code provisions, as published by SEAOC in its Blue Book. Specifically, the Blue Book recognized during this period that the actual forces imposed on structures by strong earthquakes were significantly larger than those that had historically been used for design purposes. It was postulated that, perhaps, the actual forces would be three to four times those used for design. However, it was rationalized, based largely on the observation of actual structure behavior, that structures designed for a fraction of the real imposed loading could survive earthquake shaking with damage but not collapse, as long as they were provided with continuous and tough lateral-force-resisting systems. Recognizing that actual earthquake forces resulting from design earthquake shaking were potentially significantly larger than the design strength of the structure, SEAOC also recognized that it was inevitable that structures designed in this manner would be damaged. SEAOC proposed that structures designed in accordance with the Blue Book recommendations would provide the following multitiered performance capabilities: • Resist minor earthquake shaking without damage • Resist moderate earthquake shaking without structural damage but possibly with some damage to nonstructural features • Resist major levels of earthquake shaking with both structural and nonstructural damage, but without endangerment of the lives of occupants This final goal came to be known as the life-safety criterion and it became commonly discussed among engineers, if not the public, that the intent of the code was to protect life safety, and not prevent damage or preserve capital investments in real property. Over time, the life-safety criterion was expanded to include the concept that the damaged building would retain adequate stability to avoid collapse while victims were extracted, and later still, that damage to buildings in major levels of shaking would be sufficiently limited, that occupants would be able to exit the buildings unassisted. In addition to the life-safety criterion, commentary in the Blue Book noted that buildings designed in accordance with its provisions should be capable of resisting the most intense levels of ground shaking ever likely to affect the building without collapse. This four-level performance criterion developed by SEAOC in the 1960s remains the intent of building code provisions to this day, though significant refinement and quantification of these performance goals has since occurred. Together with the recognition and admission that buildings were designed to be damaged, came the parallel recognition of the importance of toughness and redundancy to earthquake resistance, so that structures could sustain damage of their structural elements without collapse. These concepts were then used to rationalize and justify the K values that earlier had been assigned to the various structural systems. In particular, the high K value for box systems was justified on the basis of a lack of redundancy, and the fact that earthquake-induced damage of lateral-force-resisting elements could trigger vertical collapse. Similarly, building frame systems and repetitive light frame systems were viewed as highly redundant, justifying their presumed superior performance. Moment-resisting frames, in addition to © 2003 by CRC Press LLC



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having significant redundancy, relating to the large number of beams and columns participating in lateral resistance, were rationalized to have significant toughness, again justifying the reduced design forces for building conforming to that system. In parallel with these philosophical developments, researchers began to investigate the postyield behavior of typical framing elements. With this research, it began to be discovered that the way in which structural elements and their connections are detailed could have substantial impact on the toughness and ductility of the structural system. In particular, it was noted that reinforced concrete frames exhibited brittle behavior unless they are (1) detailed to provide for reversed loading, which favors flexural yielding as opposed to shear nonlinearity, and (2) provided with sufficient transverse reinforcement to provide confinement of the concrete cores of framing elements. The first provisions for ductile detailing of reinforced concrete frames were introduced into the 1967 edition of the UBC. In subsequent years these ductile detailing provisions would be refined and expanded, then developed to cover other structural systems as well, including systems of structural steel, masonry, and timber construction. As the concepts were slowly introduced, engineers began to believe that they had developed a rational and reliable set of building code provisions, able to reliably attain desired earthquake performance.

11.2.7 1971 San Fernando Earthquake The magnitude 6.6 earthquake that occurred February 9, 1971, near Sylmar, California was one of the more significant earthquakes of modern times, with regard to building code development. This large magnitude event, which occurred at the rim of the rapidly developing San Fernando Valley to the north of metropolitan Los Angeles, demonstrated that then-current building code provisions were not capable of meeting the performance goals suggested in SEAOC’s Blue Book. This earthquake caused partial and total collapse of a number of modern, code-conforming buildings, including a number of low-rise industrial and commercial buildings, single-family residences, and a recently completed county healthcare complex (Figure 11.4). It also induced the collapse of a number of older buildings, including several hospitals. It was evident that major revisions to the codes were necessary and that SEAOC could not accomplish this with the voluntary efforts of its members alone. As a result, SEAOC formed the Applied Technology Council (ATC) as a not-for-profit applied research agency, specifically to seek funding to perform the required structural engineering research and advance the practice of structural engineering. In 1978, ATC published its ATC-3.06 (1978) report, a seminal work in the development of seismic provisions. The ATC-3.06 report represented a major milestone in the development of building code provisions and remains as the foundation for current building code seismic provisions in the United States today. Among the milestone improvements introduced in the ATC-3.06 report was the formal introduction of dynamic analysis as the basis for building design for earthquake forces. The report introduced response spectrum analysis methods as the preferred procedure for design and rationalized and reformatted the equivalent lateral force procedure to clarify its use as a simplification of the more exact technique. By doing this, the report was able to directly relate design force levels to anticipated ground shaking accelerations and to the anticipated inelastic response capability of different structural systems. It also introduced the concepts of structural regularity and prohibited the construction of structures with certain types of irregularity. Although the ATC-3.06 report was a landmark in the development of building codes, it was not actually adopted as the basis for building codes until 12 years after its publication, when the seismic provisions of the 1988 UBC were rewritten by SEAOC and reformatted to adopt this approach. In the period of nearly 20 years between the occurrence of the 1971 San Fernando earthquake and the adoption of the 1988 UBC, many important incremental improvements were introduced into the SEAOC provisions that continued to serve as the basis of the UBC until 1988. These improvements were largely the result of observations of damage caused by the 1971 earthquake, but also earthquakes that occurred in Imperial Valley, California in 1979, and Mexico City in 1985. Noteworthy enhancements that occurred during this period included: © 2003 by CRC Press LLC


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FIGURE 11. 4 Partial collapse and extensive damage to the newly completed Olive View Hospital in the 1971 San Fernando earthquake.

• Introduction of a site factor to account for the effect of site soils on the frequency content and amplitude of ground shaking • Introduction of an occupancy importance factor to provide for more conservative design of important facilities • A one third increase in the minimum design force levels for all structures, as a general reaction to the poorer than anticipated performance of buildings • Requirements for positive direct interconnection of building components, particularly heavy wall panels connected to timber diaphragms, and requirements to develop the resulting anchorage forces into the lateral-force-resisting system • Introduction of interstory drift limits • Requirements to design anchorage for nonstructural components and to provide for the effects of interstory drift In addition to these important features introduced into the building code during this period, extensive prescriptive requirements for structural detailing of nearly all structural systems were introduced. These detailing requirements were based in part on observation of earthquake performance of buildings and in part on laboratory research, and are intended to provide for structural elements capable of extensive inelastic response, without degradation or failure.

11.2.8 National Seismic Provisions Although the provisions of the UBC were intended to be nationally applicable, the UBC was commonly adopted only in the western United States. Further, its provisions were dominated by the recommendations of SEAOC and were largely based on western United States and, in particular, California design practice. In the mid-1980s, using funding provided by the Federal Emergency Management Agency © 2003 by CRC Press LLC



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(FEMA), the Building Seismic Safety Council (BSSC) was formed as an independent council under the auspices of the National Institute of Building Sciences. BSSC was charged with converting the ATC-3.06 recommendations into a set of nationally applicable seismic provisions that could be adopted by building codes nationwide. BSSC’s work is performed by a Provisions Update Committee and a series of technical subcommittees. Membership on the committees is voluntary and by appointment. Committee participation is carefully selected to represent the best available knowledge in earthquake and structural engineering, while maintaining a balance in the geographic distribution of committee membership as well as uniform participation by design engineers, engineering researchers, code officials, and construction and materials industry interests. The work of the committees is subject to a national consensus balloting process, which enables rapid acceptance of the resulting provisions by the building regulation, design, and construction communities. The BSSC provisions were first published in 1985 as the NEHRP Recommended Provisions for Seismic Regulation for Buildings (NEHRP Provisions) and have since been updated and published on a 3-year cycle, matching that of the building codes. In 1993, the 1991 edition of the NEHRP Provisions was adopted as the basis of the seismic provisions in ASCE-7 [1991], which was then adopted by reference into two of the three model building codes used in the United States at that time. In 2000, the three model building codes that had served as the basis for building regulation for many years in the United States were replaced by a single code, the International Building Code (IBC) [ICC, 2000], published by a consortium of the organizations that developed the three prior codes. At the same time, the National Fire Protection Association (NFPA) began work on a competing building code, NFPA5000, scheduled to be published in 2002. The seismic design provisions in the IBC are transcribed from the 1997 edition of the NEHRP Provisions with some modification. The NFPA-5000 code will adopt seismic provisions by reference to the nearly identical 2002 edition of ASCE-7, which will be based on the 2000 edition of the NEHRP Provisions. The balance of this chapter focuses on the design requirements contained in the 2000 NEHRP Provisions.

11.3 2000 NEHRP Recommended Provisions 11.3.1 Overview The 2000 NEHRP Recommended Provisions for Seismic Regulation for Buildings and Other Structures (NEHRP Provisions) represents the current state of the art in prescriptive, as opposed to performancebased, provisions for seismic-resistant design. Its provisions form the basis for earthquake design specifications contained in the 2002 edition of ASCE-7, Minimum Design Loads for Buildings and other Structures, either through reference or direct incorporation, the seismic regulations in the 2003 edition of the IBC and also the 2002 edition of the NFPA 5000 Building Code [NFPA, n.d.]. As such, it will form the basis for most earthquake-resistant design in the United States, as well as other nations that base their codes on U.S. practices, throughout much of the first decade of the 21st century. The NEHRP Provisions assume significant amounts of nonlinear behavior will occur under design level events. The extent of nonlinear behavior that may occur is dependent on the structural systems employed in resisting earthquake forces, the configuration of these systems, and the extent to which the structural systems are detailed for ductile behavior under large cyclic inelastic deformation. The NEHRP Provisions may therefore be thought to consist of two component parts: • One part relates to specification of the required design strength and stiffness of the structural system • The second part relates to issues of structural detailing For this second part, the NEHRP Provisions adopt, with modification, design standards and specifications developed by industry groups such as the American Concrete Institute or the American Institute of Steel Construction. This second part of the NEHRP Provisions is not discussed in this chapter, but is covered in detail in each of the following chapters, which treat the individual structural materials. Instead,



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this chapter focuses primarily on the manner in which the NEHRP Provisions regulate the required strength and stiffness of structures.

11.3.2 Performance Intent and Objectives The NEHRP Provisions are intended to provide a tiered series of performance capabilities for structures, depending on their intended occupancy and use. Under the NEHRP Provisions, each structure must be assigned to a seismic use group (SUG). Three SUGs are defined and are labeled I, II, and III: • SUG-I encompasses most ordinary occupancy buildings, including typical commercial, residential, and industrial structures. For these facilities the basic intent of the NEHRP Provisions, just as with earlier codes, is to provide a low probability of earthquake-induced life safety endangerment. • SUG-II includes facilities that house large numbers of persons, persons who are mobility impaired, or large quantities of materials that, if released, could pose substantial hazards to the surrounding community. Examples of such facilities include large assembly facilities, housing several thousand persons, day care centers, and manufacturing facilities containing large quantities of toxic or explosive materials. The performance intent for these facilities is to provide a lower probability of life endangerment, relative to SUG-I structures, and a low probability of damage that would result in release of stored materials. • SUG-III includes those facilities such as hospitals and emergency operations and communications centers deemed essential to disaster response and recovery operations. The basic performance intent of the NEHRP Provisions with regard to these structures is to provide a low probability of earthquake-induced loss of functionality and operability. In reality, the probability of damage resulting in life endangerment, release of hazardous materials, or loss of function should be calculated using structural reliability methods as the total probability of such damage over a period of time [Ravindra, 1994]. Mathematically, this is equal to the integral, over all possible levels of ground motion intensity, of the conditional probability of excessive damage given that a ground motion intensity is experienced and the probability that such ground motion intensity will be experienced in the desired period of time. Although such an approach would be mathematically and conceptually correct, it is currently regarded as too complex for practical application in the design office. Instead, the NEHRP Provisions design for desired limiting levels of nonlinear behavior for a single design earthquake intensity level, termed maximum considered earthquake (MCE) ground shaking. In most regions of the United States, the MCE is defined as that intensity of ground shaking having a 2% probability of exceedance in 50 years. In certain regions, proximate to major active faults, this probabilistic definition of MCE motion is limited by a conservative deterministic estimate of the ground motion intensity anticipated to result from an earthquake of characteristic magnitude on these faults. The MCE is thought to represent the most severe level of shaking ever likely to be experienced by a structure, though it is recognized that there is some limited possibility of more severe motion occurring. Structures categorized as SUG-I are designed with the expectation that MCE shaking would result in severe damage to both structural and nonstructural elements, with damage perhaps being so severe that following the earthquake, the structure would be on the verge of collapse. This damage state has come to be termed collapse prevention, because the structure is thought to be at a state of incipient but not actual collapse. Theoretically, SUG-I structures behaving in this manner would be total or near total financial losses, in the event that MCE shaking was experienced. To the extent that shaking experienced by the structure exceeds the MCE level, the structure could actually experience partial or total collapse. SUG-III structures are designed with the intent that when subjected to MCE shaking they would experience both structural and nonstructural damage; however, the structures would retain significant residual structural resistance or margin against collapse. It is anticipated that when experiencing MCE shaking, such structures may be damaged to an extent that they would no longer be suitable for occupancy, until repair work had been instituted, but that repair would be technically and economically feasible. This superior performance relative to SUG-I structures is accomplished through specification that © 2003 by CRC Press LLC



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SUG-III structures be designed with 50% greater strength and more stiffness than their SUG-I counterparts. SUG-II structures are designed for performance intermediate to that for SUG-I and SUG-III, with strengths and stiffness that are 25% greater than those required for SUG-I structures.

11.3.3 Seismic Hazard Maps and Ground Motion Parameters The NEHRP Provisions incorporate a series of national seismic hazard maps for the United States and territories, developed by the United States Geologic Survey (USGS) specifically for this purpose (available at http://geohazards.cr.usfs.gov/eq/index.html). Two sets of maps are presented. One set presents contours of MCE, 5% damped, elastic spectral response acceleration at a period of 0.2 sec, termed SS. The second set presents contours of MCE, 5% damped, elastic spectral response acceleration at a period of 1.0 sec, termed S1. In both cases, the spectral response acceleration values are representative of sites with subsurface conditions bordering between firm soil or soft rock. Contours are presented in increments of 0.02 g in areas of low seismicity and 0.05 g in areas of high seismicity. By locating a site on the maps, and interpolating between the values presented for contours adjacent to the site, it is possible to rapidly estimate the MCE level shaking parameters for the site, given that it has a soft rock or firm soil profile. Figure 11.5 shows, for a portion of the western United States, contours of the 0.2-sec spectral acceleration with a 90% probability of not being exceeded in 50 years. As indicated in the figure, in zones of high seismicity these contours are quite closely spaced, making use of the maps difficult. Therefore, the USGS has furnished software, available both over the Internet (at the URL indicated above) and on a CD-ROM, that permits determination of the MCE spectral response acceleration parameters based on longitude and latitude. Since many sites are located neither on soft rock nor firm soil sites, it is necessary to correct the mapped values of spectral response acceleration to account for site amplification and deamplification effects. To facilitate this process, a site is categorized into one of six site class groups, labeled A through F. Table 11.1 summarizes the various site class categories. Once a site has been categorized within a site class, a series of coefficients are provided that are used to adjust the mapped values of spectral response acceleration for site response effects. These coefficients were developed based on observed site response characteristics in ground motion recordings from past earthquakes. Two coefficients are provided: • The Fa coefficient is used to account for site response effects on short period ground-shaking intensity • The Fv coefficient is used to account for site response effects of longer period motions Tables 11.2 and 11.3 indicate the values of these coefficients as a function of site class, and mapped MCE ground-shaking acceleration values. Site-adjusted values of the MCE spectral response acceleration parameters at 0.2 and 1 sec, respectively, are found from the following equations:

SMS = FaSS

(11.4)

SM1 = Fv S1

(11.5)

The two site-adjusted spectral response acceleration parameters, SMS and SM1, permit a 5% damped, maximum considered earthquake ground-shaking response spectrum to be constructed for the building site. This spectrum is constructed as indicated in Figure 11.6 and consists of a constant response acceleration range, between periods of T0 and TS, a constant response velocity range for periods in excess of TS and a short period range that ramps between an estimated zero period acceleration given by SMS /2.5 and SMS. Site-specific spectra can also be used. Regardless of whether site-specific spectra or spectra based on mapped values are used, the actual design values are taken as two thirds of the MCE values. The resulting design parameters are labeled, respectively, SDS and SD1 and the design spectrum is identical to the MCE spectrum, except that the ordinates are taken as two thirds of the MCE values. The reason for © 2003 by CRC Press LLC


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0.2 sec Spectral Accel. (%g) with 10% Probability of Exceedance in 50 Years site: NEHRP B-C boundary -124°

-122°

-120°

-118°

-116°

42°

-114°

42°

40°

%g 400 200 160 120 80 60 50 40 30 20 18 16 14 12 10 8 6 4 2 0

40°

38°

38°

36°

36°

34°

34°

32°

32° -124°

-122°

-120°

-118°

-116°

-114°

FIGURE 11.5 MCE seismic hazard map (0.2-sec spectral response acceleration) for the western United States. (Courtesy U.S. Geological Survey) Shown as Color Figure 11.5. TABLE 11.1 Site Categories Site Class A B C D E F

Description Hard rock Rock Very firm soil or soft rock Stiff soil Soil Special soils

Shear Wave Velocity –vs

Penetration – Resistance N

>5,000 ft/sec 2,500 ft/sec < –vs ≤ 5,000 ft/sec 1,200 ft/sec < –vs ≤ 2,500 ft/sec >50 >2,000 psf 600 ft/sec < –vs ≤ 1,200 ft/sec 15 to 50 1,000–2,000 psf v–s < 600 ft/sec 25 ft [8 m] with PI > 75) 4. Very thick soft/medium stiff clays (H > 120 ft [36 m])

– Note: –vs , N, –su represent the average value of the parameter over the top 30 m (100 ft) of soil. © 2003 by CRC Press LLC

Unconfined Shear Strength –su


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TABLE 11.2 Coefficient Fa as a Function of Site Class and Mapped Spectral Response Acceleration Mapped Maximum Considered Earthquake Spectral Response Acceleration at Short Periods Site Class A B C D E F

SS = 0.25

SS = 0.50

SS = 0.75

SS = 1.00

SS > 1.25

0.8 1.0 1.2 1.6 2.5 a

0.8 1.0 1.2 1.4 1.7 a

0.8 1.0 1.1 1.2 1.2 a

0.8 1.0 1.0 1.1 0.9 a

0.8 1.0 1.0 1.0 a a

Note: a — indicates site-specific evaluation required.

TABLE 11.3 Coefficient Fv as a Function of Site Class and Mapped Spectral Response Acceleration Mapped Maximum Considered Earthquake Spectral Response Acceleration at 1-sec Periods Site Class A B C D E F

S1 = 0.1

S1 = 0.2

S1 = 0.3

S1 = 0.4

S1 > 0.5

0.8 1.0 1.7 2.4 3.5 a

0.8 1.0 1.6 2.0 3.2 a

0.8 1.0 1.5 1.8 2.8 a

0.8 1.0 1.4 1.6 2.4 a

0.8 1.0 1.3 1.5 a a

Spectral Response Acceleration, Sa

Note: a — indicates site-specific evaluation required.

S MS Sa = SM 1

S MS

T

2 .5

T0=0.2TS

TS Period, T

FIGURE 11.6

Maximum considered earthquake response spectrum.

using design values that are two thirds of the maximum considered values is that the design procedures, described in later sections, are believed to provide a minimum margin against collapse of 150%. Therefore, if design is conducted for two thirds of the MCE ground shaking, it is anticipated that buildings experiencing MCE ground shaking would be at incipient collapse, the desired performance objective for SUG-I structures.

11.3.4 Seismic Design Categories The seismicity of the United States, and indeed the world, varies widely. It encompasses zones of very high seismicity in which highly destructive levels of ground shaking are anticipated to occur every 50 to © 2003 by CRC Press LLC


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TABLE 11.4 Categorization of Structures into Seismic Design Category, Based on Design Short Period Spectral Response Acceleration, SDS, and Seismic Use Group Seismic Use Group

Value of SDS SDS < 0.167 g 0.167 g ≤ SDS < 0.33 g 0.33 g ≤ SDS < 0.50 g 0.50 g ≤ SDS

I

II

III

A B C Da

A B C Da

A C D Da

a

SUG-I and -II structures located on sites with mapped MCE spectral response acceleration at 1-sec period, S1, equal to or greater than 0.75 g shall be assigned to SDC-E and SUG-III structures located on such sites shall be assigned to SDC-F.

TABLE 11.5 Categorization of Structures into Seismic Design Category, Based on Design 1-sec Period Spectral Response Acceleration, SD1 , and Seismic Use Group Seismic Use Group

Value of SD1 SD1 < 0.067 g 0.067 g ≤ SD1 < 0.133 g 0.133 g ≤ SD1 < 0.20 g 0.20 g ≤ SD1 a

I

II

III

A B C Da

A B C Da

A C D Da

See footnote to Table 11.4.

100 years and zones of much lower seismicity in which only moderate levels of ground shaking are ever anticipated. The NEHRP Provisions recognize that it is neither technically necessary nor economically appropriate to require the same levels of seismic protection for all buildings across these various regions of seismicity. Instead, the NEHRP Provisions assign each structure to a seismic design category (SDC) based on the level of seismicity at the building site, as represented by mapped shaking parameters, and the SUG. Six SDCs, labeled A through F, are defined. SDC A represents the least severe seismic design condition and includes structures of ordinary occupancy located on sites anticipated to experience only very limited levels of ground shaking. SDC F represents the most severe design condition and includes structures assigned to SUG-III and located within a few kilometers of major, active faults, anticipated to produce very intense ground shaking. A designer determines to which SDC a structure should be assigned by reference to a pair of tables, reproduced as Tables 11.4 and 11.5. A structure is assigned to the most severe category indicated by either table. Nearly all aspects of the seismic design process are affected by the SDC to which a structure is assigned. This includes designation of the permissible structural systems, specification of required detailing, limitation on permissible heights and configuration, the types of analyses that may be used to determine the required lateral strength and stiffness, and the requirements for bracing and anchorage of nonstructural components.

11.3.5 Permissible Structural Systems The NEHRP Provisions define more than 70 individual seismic-force-resisting system types. These systems may be broadly categorized into five basic groups that include bearing wall systems, building frame systems, moment-resisting frame systems, dual systems, and special systems:




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• Bearing wall systems include those structures in which the vertical elements of the lateral-forceresisting system comprise either shear walls or braced frames in which the shear-resisting elements (walls or braces) are required to provide support for gravity (dead and live) loads in addition to providing lateral resistance. This is similar to the “box system” contained in earlier codes. • Building frame systems include those structures in which the vertical elements of the lateral-forceresisting system comprise shear walls or braces, but in which the shear-resisting elements are not also required to provide support for gravity loads. • Moment-resisting frame systems are those structures in which the lateral-force resistance is provided by the flexural rigidity and strength of beams and columns, which are interconnected in such a manner that stress is induced in the frame by lateral displacements. • Dual systems rely on a combination of moment-resisting frames and either braced frames or shear walls. In dual systems, the braced frames or shear walls provide the primary lateral resistance and the moment-resisting frame is provided as a back-up or redundant system, to provide supplemental lateral resistance in the event that earthquake response damages the primary lateral-forceresisting elements to an extent that they lose effectiveness. • Special systems include unique structures, such as those that rely on the rigidity of cantilevered columns for their lateral resistance. Within these broad categories, structural systems are further classified in accordance with the quality of detailing provided and the resulting ability of the structure to withstand earthquake-induced inelastic, cyclic demands. Structures that are provided with detailing believed capable of withstanding large cyclic inelastic demands are typically termed “special” systems. Structures that are provided with relatively little detailing, and are therefore incapable of withstanding significant inelastic demands, are termed “ordinary.” Structures with limited levels of detailing and inelastic response capabilities are termed “intermediate.” Thus, within a type of structure, for example moment-resisting steel frames, or reinforced concrete bearing walls, it is possible to have special moment-resisting frames or bearing walls, intermediate moment-resisting frames or shear walls, and ordinary moment-resisting frames or shear walls. The various combinations of such systems and construction materials result in a wide selection of structural systems to choose from. The use of ordinary and intermediate systems, regarded as having limited capacity to withstand cyclic inelastic demands, is generally limited to SDC A, B, and C and to certain low-rise structures in SDC D.

11.3.6 Design Coefficients Under the NEHRP Provisions, required seismic design forces, and therefore required lateral strength, is typically determined by elastic methods of analysis, based on the elastic dynamic response of structures to design ground shaking. However, since most structures are anticipated to exhibit inelastic behavior when responding to the design ground motions, it is recognized that linear response analysis does not provide an accurate portrayal of the actual earthquake demands. Therefore, when linear analysis methods are employed, a series of design coefficients are used to adjust the computed elastic response values to suitable design values that consider probable inelastic response modification. Specifically, these coefficients are the response modification factor, R, the overstrength factor, Ω0, and the deflection amplification coefficient, Cd. Tabulated values of these factors are assigned to a structure, based on the selected structural system, and the level of detailing employed in that structural system. The response modification coefficient, R, is used to reduce the required lateral strength of a structure, from that which would be required to resist the design ground motion in a linear manner, to that required to limit inelastic behavior to acceptable levels, considering the characteristics of the selected structural system. Structural systems deemed capable of withstanding extensive inelastic behavior are assigned relatively high R values, as large as 8, permitting minimum design strengths that are only one eighth of that required for elastic response to the design motion. Systems deemed to be incapable of providing



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reliable inelastic behavior are assigned low R values, approaching unity, requiring sufficient strength to resist design motion in a nearly elastic manner. The deflection amplification coefficient, Cd , is used to estimate the total elastic and inelastic lateral deformation of the structure, when subjected to design earthquake ground motion. Specifically, lateral deflections calculated for elastic response of the structure to the design ground motion, reduced by the response modification coefficient R, are amplified by the factor Cd to obtain this estimate. The Cd coefficient accounts for the effects of viscous and hysteretic damping on structural response, as well as the effects of inelastic period lengthening. Structural systems that are deemed capable of developing significant amounts of viscous and hysteretic damping are assigned Cd values somewhat less than the value of the R coefficient. This results in an estimate of total lateral deformation that is somewhat lower than would be anticipated for pure elastic response. For structural systems with relatively poor capability to develop viscous and/or hysteretic damping, the Cd value may exceed R, resulting in estimates of lateral drift that exceed that calculated for elastic response. The overstrength coefficient, Ω0, is used to provide an estimate of the maximum force likely to be delivered to an element in the structure, considering that due to effects of system and material overstrength, this may be larger than the force calculated by elastic analysis of the structure’s response to design ground motion, reduced by the response modification coefficient R. This overstrength factor is used to compute the strength required to resist behavioral modes that have limited capacity for inelastic response, such as column buckling, or connection failure in braced frames. Figure 11.7 illustrates the basic concepts behind these design coefficients. The figure contains an elastic design response spectrum, an elastic response line, and an inelastic response curve for an arbitrary structure, all plotted in lateral inertial force (base shear) vs. lateral roof displacement coordinates. Response spectra are more familiarly plotted in coordinates of spectral response acceleration (Sa) vs. structural period (T). It is possible to convert a spectrum plotted in that form to the spectrum shown in the figure, through a two-step process. The first step consists of converting the response spectrum for Sa vs. T coordinates to Sa vs. spectral response displacement (Sd) coordinates. This is performed using the following relationship between Sa, Sd, and T: Sd =

T2 S 4π 2 a

(11.6)

Then the response spectrum is converted to the form shown in Figure 11.7 by recognizing that for a structure responding in a given mode of excitation, the base shear is equal to the product of the mass participation factor for that mode, the structure’s mass and the spectral response acceleration, Sa , at that period. Similarly, the lateral roof displacement for a structure responding in that mode is equal to the spectral response displacement times the modal participation factor. For a single degree of freedom structure, the mass participation factor and modal participation factor are both unity, and the lateral base shear, V, is equal to the product of the spectral response acceleration at the mode of response and the mass of the structure, while the lateral roof displacement is equal to the spectral response displacement. The dashed diagonal line in Figure 11.7 represents the elastic response of the arbitrary structure. It is a straight line because a structure responding in an elastic manner will have constant stiffness, and therefore, a constant proportional relationship between the applied lateral force and resulting displacement. The intersection of this diagonal line with the design response spectrum indicates the maximum total lateral base shear, VE , and roof displacement, DE , the structure would develop if it responded to the design ground motion in an elastic manner. The third plot in the figure represents the inelastic response characteristics of this arbitrary structure, sometimes called a pushover curve. The pushover curve has an initial elastic region having the same stiffness as the elastic response line. The point Vy , Dy on the pushover curve represents the end of this region of elastic behavior. Beyond Vy , Dy , the curve is represented by a series of segments, with sequentially reduced stiffness, representing the effects of inelastic softening of the



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Elastic response

R

Design response spectrum

VM

Inelastic response

Ω0

Base Shear V

VE

VY

DY

Cd

DI DE

Lateral Roof Displacement ∆ FIGURE 11.7

Schematic illustration of design coefficients.

structure. The lateral base shear force, VM, at the peak of the pushover curve, represents the maximum lateral force that the structure is capable of developing at full yield. The response modification coefficient, R, is used in the provisions to set the minimum acceptable strength at which the structure will develop its first significant yielding, Vy . This is given by the simple relationship:

VY =

VE R

(11.7)

The coefficient Ω0, is used to approximate the full yield strength of the structure through the relationship:

VM = Ω 0VY

(11.8)

The maximum total drift of the structure, DI, is obtained from the relationship:

DI = Cd DY

(11.9)

11.3.7 Analysis Procedures The NEHRP Provisions permit the use of five different analytical procedures to determine the required lateral strength of a structure and to confirm that the structure has adequate stiffness to control lateral drift. The procedures permitted for a specific structure are dependent on the structure’s SDC and its regularity. 11.3.7.1 Index Force Procedure The index force procedure is permitted only for structures in SDC A. In this procedure, the structure must be designed to have sufficient strength to resist a static lateral force, equal to 1% of the weight of the structure, applied simultaneously to each level. The forces must be applied independently, in two orthogonal directions. Structures in SDC A are not anticipated ever to experience ground shaking of © 2003 by CRC Press LLC


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sufficient intensity to cause structural damage, provided that the structures are adequately tied together and have a complete lateral-force-resisting system. The nominal 1% lateral force function used in this procedure is intended as a means of ensuring that the structure has a complete lateral-force-resisting system, of nominal, though somewhat arbitrary, strength. In addition to providing protection for the low levels of ground motion, anticipated for SDC A structures, this procedure is also considered to be a structural integrity provision, intended to provide nominal resistance against blast and other possible loading events. 11.3.7.2 Equivalent Lateral Force Analysis Equivalent lateral force (ELF) analysis may be used for any structure in SDC B and C, for any structure of light frame construction, and for all regular structures, with a calculated structural period T, not greater than 3.5Ts, where Ts is as previously defined in Figure 11.6. ELF analysis consists of a simple approximation to modal response spectrum analysis. It only considers the first mode of a structure’s lateral response, and presumes that the mode shape for this first mode of response is represented by that of a simple shear beam. For structures having sufficiently low periods of first mode response (T < 3.5Ts) and regular vertical and horizontal distribution of stiffness and mass, this procedure approximates modal response spectrum analysis well. However, for longer period structures, higher mode response becomes significant and neglecting these higher modes results in significant errors in the estimation of structural response. Also, as the distribution of mass and stiffness in a structure becomes irregular, for example, the presence of torsional conditions or soft story conditions, the assumptions inherent in the procedure with regard to mode shape also become quite approximate, leading to errors. In SDCs D, E, and F, this method is permitted only for those structures where these inaccuracies are unlikely to be significant. The procedure is permitted for more general use in other SDCs both because it is felt that the severity of design ground motion is low enough that inaccuracies in analysis of lateral response are unlikely to result in unacceptable structural performance and also because it is felt that designers in these regions of low seismicity may not be able to implement the more sophisticated and accurate methods properly. As with the index force analysis procedure, the ELF consists of the simultaneous application of a series of static lateral forces to each level of the structure, in each of two independent orthogonal directions. In each direction, the total lateral force, known as the base shear, is given by the formula: V=

SDS W RI

(11.10)

This formula gives the maximum lateral inertial force that acts on an elastic, single-degree-of-freedom structure with a period that falls within the constant response acceleration (periods shorter than Ts) portion of the design spectrum, reduced by the term R/I. In this formula, SDS is the design spectral response acceleration at short periods, W is the dead weight of the structure and a portion of the supported live load, R is the response modification coefficient, and I is an occupancy importance factor, assigned based on the structure’s SUG. For SUG-I structures, I is assigned a value of unity. For SUG-II and -III structures, I is assigned values of 1.25 and 1.5, respectively. The effect of I is to reduce the permissible response modification factor, R, for structures in higher SUGs, requiring that the structures have greater strength, thereby limiting the permissible inelasticity and damage in these structures. The base shear force given by Equation 11.10 need never exceed the following: V=

SD1 W ( R I )T

(11.11)

Equation 11.11 represents the maximum lateral inertial force that acts on an elastic, single-degree-offreedom structure with period T that falls within the constant response velocity portion of the design spectrum (periods longer than Ts), reduced by the response modification coefficient, R, and the occupancy © 2003 by CRC Press LLC


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importance factor, I. In this equation, all terms are as previously defined except that SD1 is the design spectral response acceleration at 1 sec. For short period structures, Equation 11.10 will control. For structures with periods in excess of Ts, Equation 11.11 will control. The shape of the design response spectrum shown in Figure 11.6 is not representative of the dynamic characteristics of ground motion found close to the fault rupture zone. Such motions are often dominated by a large velocity pulse and very large spectral displacement demands. Therefore, for structures in SDC E and F, the seismic design categories for structures located close to major active faults, the base shear may not be taken less than the value given by Equation 11.12. Equation 11.12 approximates the effects of the additional long period displacements that have been recorded in some near-field ground motion records: 0.5S1 RI

V=

(11.12)

The total lateral base shear force given by Equations 11.10, 11.11, and 11.12 must be distributed vertically for application to the various mass or diaphragm levels of the structure. For a structure with n levels, the force at diaphragm level x is given by the equation: Fx = C vxV

(11.13)

w x hx

(11.14)

where C vx =

n

∑w h

i i

i =1

and hx and hi, respectively, are the heights of levels x and i above the base of the structure. These formulas are based on the assumption that the structure is responding in its first mode, in pure sinusoidal motion, and that the mode shape is linear. That is, it is assumed that at any instant of time, the displacement at level x of the structure is equal to: δx =

hx δ hn n

(11.15)

where δx and δn are the lateral displacements at level x and the roof of the structure, respectively, and hn is the total height of the structure. For a structure responding in pure sinusoidal motion, the displacement δx, velocity vx, and acceleration ax, of level x at any instant of time t is given by the equations:  2π  δ x = δ x max sin  t  T  v x = δ x max

2π  2π  cos  t  T  T

ax = − δ x max


4 π  2π  sin  t  T  T2

(11.16)

(11.17)

(11.18)


11-22


Since acceleration at level x is directly proportional to the displacement at level x, the acceleration at level x in a structure responding in pure sinusoidal motion is given by the equation: ax =

hn a hx n

(11.19)

where an is the acceleration at the roof level. Since the inertial force at level x is equal to the product of mass at level x and the acceleration at level x, Equation 11.14 can be seen to be an accurate distribution of lateral inertial forces in a structure responding in a linear mode shape. The lateral forces given by Equation 11.13 are applied to a structural model of the building and the resulting member forces and building interstory drifts are determined. The analysis must consider the relative rigidity of both the horizontal and vertical elements of the lateral-force-resisting system, and when torsional effects are significant, must consider three-dimensional distributions of stiffness, centers of mass and rigidity. The structure must then satisfy two basic criteria. First, the elements of the lateralforce-resisting system must have sufficient strength to resist the calculated member forces, in combination with other loads, and second, the structure must have sufficient strength to maintain computed interstory drifts within acceptable levels. The specific load combinations that must be used to evaluate member strength and the permissible interstory drifts are described in succeeding sections. In recognition of the fact that higher mode participation can result in significantly larger forces at individual diaphragm levels than is predicted by Equation 11.14, forces on diaphragms are computed using an alternative equation, as follows:

∑ = ∑

n

Fpx

i=x n i=x

Fi

w px

(11.20)

wi

where Fpx is the design force applied to diaphragm level x, Fi is the force computed from Equation 11.14 at level i, wpx is the effective seismic weight at level x, and wi is the effective weight at level i. 11.3.7.3 Response Spectrum Analysis Response spectrum analysis is permitted for the design of any structure. The procedure contained in the NEHRP Provisions uses standard methods of elastic modal dynamic analysis, which are not described here, but are well documented in the literature [e.g., Chopra, 1981]. The analysis must include sufficient modes of vibration to capture participation of at least 90% of the structure’s mass in each of two orthogonal directions. The response spectrum used to characterize the loading on the structure may be either the generalized design spectrum for the site, shown in Figure 11.6, or a site-specific spectrum developed considering the regional seismic sources and site characteristics. Regardless of the spectrum used, the ground motion is scaled by the factor (I/R), just as in the equivalent lateral force technique. The NEHRP Provisions require that the member forces determined by response spectrum analysis be scaled so that the total applied lateral force in any direction not be less than 80% of the base shear calculated using the ELF method for regular structures nor 100% for irregular structures. This scaling requirement was introduced to ensure that assumptions used in building the analytical model not result in excessively flexible representation of the structure, and consequently, an underestimate of the required strength. 11.3.7.4 Response History Analysis Response history analysis is also permitted to be used for the design of any structure but, due to the added complexity, is seldom employed in practice except for special structures incorporating special base isolation or energy dissipation technologies. Either linear or nonlinear response history analysis is permitted to be used. When response history analysis is performed, input ground motion must consist of a suite of at least three pairs of orthogonal horizontal ground motion components, obtained from records




11-23

of similar magnitude, source, distance, and site characteristics as the event controlling the hazard for the building’s site. Each pair of orthogonal records must be scaled such that with a period range approximating the fundamental period of response of the structure, the square root of the sum of the squares of the orthogonal component ordinates envelopes 140% of the design response spectrum. Simple amplitude, rather than frequency domain scaling, is recommended. Actual records are preferred, though simulations may be used if a sufficient number of actual records representative of the design earthquake motion is not available. If a suite of less than seven records is used as input ground motion, the maximum of the response parameters (element forces and deformations) obtained from any of the records is used for design. If seven or more records are used, the mean values of the response parameters obtained from the suite of records may be used as design values. This requirement was introduced with the understanding that the individual characteristics of a ground motion record can produce significantly different results for some response quantities. It was hoped that this provision would encourage engineers to use larger suites of records, and obtain an understanding of the variability associated with possible structural response. When linear response history analyses are performed, the ground motion records, scaled as previously described, are further scaled by the quantity (I/R). The resulting member forces are combined with other loads, just as they would be if the ELF or response spectrum methods of analysis were performed. When nonlinear response history analyses are performed, they must be used without further scaling. Rather than evaluating the strength of members using the standard load combinations considered with other analysis techniques, the engineer is required to demonstrate acceptable performance capability of the structure, given the predicted strength and deformation demands. The intention is that laboratory and other relevant data be used to demonstrate adequate behavior. This is a rudimentary introduction of performance-based design concepts, which will likely have significantly greater influence in future building codes.

11.3.8 Load Combinations and Strength Requirements Structures must be proportioned with adequate strength to resist the forces predicted by the lateral seismic analysis, together with forces produced by response to vertical components of ground shaking as well as dead and live loads. Unless nonlinear response history analysis is performed using ground motion records that include a vertical component of motion, the effects of vertical earthquake shaking are accounted for by the equation: E = QE ± 0.2SDS D

(11.21)

where QE are the element forces predicted by the lateral seismic analysis, SDS is the design spectral response acceleration at a 0.2-sec response period, and D are the forces produced in the element by the structure’s dead weight. The term 0.2SDSD represents the effect of vertical ground shaking response. For structures in zones of high seismicity, the term SDS has a value approximating 1.0 g and therefore, the vertical earthquake effects are taken as approximately a 20% increase or decrease in the dead load stress demands on each element. In fact, there are very few cases on record where structural collapse has been ascribed to the vertical response of a structure. This is probably because design criteria for vertical load resistance incorporate substantial factors of safety and also because most structures carry only a small fraction of their rated design live loads when they are subjected to earthquake effects. Therefore, most structures inherently have substantial reserve capacity to resist additional loading induced by vertical ground motion components. In recognition of this, most earlier codes neglected vertical earthquake effects. However, during the formulation of ATC-3.06, it was felt to be important to acknowledge that ground shaking includes three orthogonal components. The resulting expression, which was somewhat arbitrary, ties vertical seismic forces to the short period design spectral response acceleration, as most structures are stiff vertically and have very short periods of structural response for vertical modes. © 2003 by CRC Press LLC


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The earthquake forces on structural elements derived from Equation 11.21 are combined with dead and live loads in accordance with the standard strength level load combinations of ASCE-7. The pertinent load combinations are: Q = 1.4 D ± E

(11.22)

Q = 1.4 D + 0.75 ( L + E )

(11.23)

where D, L, and E are, respectively, the dead, live, and earthquake forces. Elements must then be designed to have adequate strength to resist these combined forces. The reduction factor of 0.75 on the combination of earthquake and live loads accounts for the low likelihood that a structure will be supporting full live load at the same time that it experiences full design earthquake shaking. An alternative set of load combinations is also available for use with design specifications that utilize allowable stress design formulations. These are essentially the same as Equations 11.22 and 11.23 except that the earthquake loads are further reduced by a factor of 1.4. The NEHRP Provisions recognize that it is undesirable to allow some elements to experience inelastic behavior as they may be subject to brittle failure and in doing so, compromise the ability of the structure to develop its intended inelastic response. The connections of braces to braced frames are an example of such elements. The provisions also recognize that inelastic behavior in some elements, such as columns supporting discontinuous shear walls, could trigger progressive collapse of the structure. For these elements, the earthquake force E that must be used in the load combination Equations 11.22 and 11.23 is given by the formula: E = Ω0QE ± 0.2SDS D

(11.24)

where the term 0.2SDSD continues to represent the effects of vertical ground shaking response and the term Ω0QE represents an estimate of the maximum force likely to be developed in the element as a result of lateral earthquake response, considering the inelastic response characteristics of the entire structural system. In Equation 11.24, the term Ω0QE need never be taken larger than the predicted force on the element derived from a nonlinear analysis or plastic mechanism analysis.

11.3.9 Drift Limitations It is important to control lateral drift in structures because excessive drift can result in extensive damage to cladding and other nonstructural building components. In addition, excessive lateral drift can result in the development of P-∆ instability and collapse. Lateral drift is evaluated on a story by story basis. Story drift, δ, is computed as the difference in lateral deflection at the top of a story and that at the bottom of the story, as predicted by the lateral analysis. If the lateral analysis was other than a nonlinear response history analysis, design story drift, ∆, is obtained from the computed story drift, δ, by the equation: ∆ = Cd δ

(11.25)

where Cd is the design coefficient previously discussed. The design interstory drift computed from Equation 11.25 must be less than a permissible amount, dependent on the SUG and structural system as shown in Table 11.6. The provisions require evaluation of potential P-∆ instability through consideration of the quantity θ given by the equation: θ=


Px ∆ Vx hxCd

(11.26)


11-25


TABLE 11.6 Permissible Drift Limits Seismic Use Group

Structure Structures, other than masonry shear wall or masonry wall frame structures, four stories or less in height with interior walls, partitions, ceilings, and exterior wall systems that have been designed to accommodate the story drifts Masonry cantilever shear wall structures Other masonry shear wall structures Masonry wall frame structures All other structures

I

II

III

0.025 hsx

0.020 hsx

0.015 hsx

0.010 hsx 0.007 hsx 0.013 hsx 0.020 hsx

0.010 hsx 0.007 hsx 0.013 hsx 0.015 hsx

0.010 hsx 0.007 hsx 0.010 hsx 0.010 hsx

In this equation, Px is the dead weight of the structure above story x, ∆ is the design story drift, computed from Equation 11.25, Vx is the design story shear obtained from the lateral force analysis, hx is the story height, and Cd is the coefficient previously discussed. If the quantity θ computed by this equation is found to be less than 0.1, P-∆ effects may be neglected. If the quantity θ is greater than 0.1, P-∆ effects must be directly considered in performing the lateral force analysis. If the quantity θ exceeds 0.3, the structure should be considered potentially unstable, and must be redesigned. This approach to P-∆ evaluation has remained essentially unchanged since its initial introduction in ATC-3.06. It was introduced in that document as a placeholder, pending the development of a more accurate method for evaluating drift-induced instability. Obvious deficiencies in this current approach include the fact that it evaluates drift effects at the somewhat artificial design-base shear levels. A more realistic evaluation would consider the actual expected lateral deformations of the structure, as well as the yield level shear capacity of the structure at each story. As contained in the current provisions, evaluation of P-∆ effects seldom controls a structure’s design.

11.3.10 Structural Detailing Structural detailing is a critical feature of seismic-resistant design but is not generally specified by the NEHRP Provisions. Rather, the provisions adopt detailing requirements contained in standard design specifications developed by the various materials industry associations, including the American Institute of Steel Construction, the American Concrete Institute, the American Forest Products Association, and the Masonry Society. Other chapters in this handbook present the requirements of these various design standards.

11.4 Performance-Based Design Codes Starting about 1990, the international design community began to be interested in the development of performance-based design concepts. Whereas current building code provisions are prescriptive in nature and require that buildings be designed with minimum specified strength and stiffness, performancebased procedures permit the designer to directly demonstrate that a design is capable of meeting certain standard performance objectives, independent of meeting prescriptive strength and stiffness criteria. Acceptable performance may be demonstrated through a variety of means, including prototype testing or analytical simulation. For many years, building codes have permitted such performance-based designs through language that allowed the application of alternative procedures, justified by rational engineering analysis to be capable of providing equivalent performance. However, these earlier codes provided little quantification of the performance objectives to be attained, making application of alternative approaches largely impractical.



11-26


In the early 1990s, a series of performance-based design procedures intended for application to seismic rehabilitation of structures were published under efforts sponsored by FEMA [BSSC, 1997a] and the California Seismic Safety Commission [1996]. These documents began the process of formalizing the concept of performance objectives, as quantifiable levels of damage, for specified levels of hazard. These concepts were adopted and extended by SEAOC, in a preliminary manner, for application to the design of new construction [SEAOC, 1996]. Also, in a project supported by FEMA [SAC, 2000] to address unanticipated damage experienced by steel moment frame structures in the 1994 Northridge and 1995 Kobe earthquakes, a formal structural reliability basis was applied to these concepts. The International Code Council has published a performance-based code [ICC, 2001] that permits the application of performance-based concepts for design for a variety of structural, fire, and health hazards. The new NFPA-5000 code also includes specific provisions intended to permit performancebased design approaches. While these new codes do a better job of quantifying the performance objectives with which a design must comply, they do little to regulate how such compliance is demonstrated. Therefore, application of these concepts is likely to be limited. It is anticipated, however, that substantial development of performance-based design approaches will continue to occur and that future codes will include more guidance on their application.

Defining Terms Base shear — The total lateral force for which a structure is designed using equivalent lateral force techniques.

Damping — Energy dissipation that occurs in a dynamically deforming structure, either as a result of frictional forces, viscous behavior, or structural yielding. Increased damping tends to reduce the amount that a structure responds to ground shaking. Damage — Permanent cracking, yielding, or buckling of a structural element or structural assemblage. Degradation — A behavioral mode in which structural stiffness or strength is reduced as a result of inelastic behavior. Elastic — A mode of structural behavior in which a structure displaced by a force will return to its original state upon release of the force. Ground shaking — A random, rapid cyclic motion of the ground produced by an earthquake. Hysteresis — A form of energy dissipation that is related to inelastic deformation of a structure. Inelastic — A mode of structural behavior in which a structure, displaced by a force, exhibits permanent unrecoverable deformation. Mass participation — That portion of total mass of a multidegree of freedom structure that is effective in a given mode of response. Maximum considered earthquake (MCE) — The earthquake intensity forming the basis for design, in the NEHRP Provisions. Mode shape — A deformed shape, in which a structure can oscillate freely, when displaced. Natural mode — A characteristic dynamic property of a structure, in which it will oscillate freely. Participation factor — A mathematical relationship between the maximum displacement of a multidegree of freedom structure and a single degree of freedom structure. Period — The amount of time it takes a structure that has been displaced in a particular natural mode and then released to undergo one complete cycle of motion. Response spectrum — A graphical representation, usually as a function of period, of the maximum acceleration, displacement or velocity response of a structure, subjected to a given level of ground shaking excitation. Spectral acceleration — The maximum response acceleration that a structure of given period will experience when subjected to a specific ground motion. Spectral displacement — The maximum response displacement that a structure of given period will experience when subjected to a specific ground motion.




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Spectral velocity — The maximum response velocity that a structure of given period will experience when subjected to a specific ground motion.

Viscous — A form of energy dissipation that is proportional to velocity. Yielding — A behavioral mode in which a structural displacement increases under application of constant load.

References American Society of Civil Engineers. 1991. Minimum Design Loads for Buildings and Other Structures, Standard No. ASCE-7, American Society of Civil Engineers, Reston, VA. Anderson, J., Blume, J.A., Degenkolb, H.K. et al. 1952. “Lateral Forces of Earthquake and Wind,” Trans. Am. Soc. Civ. Eng., 117. Applied Technology Council. 1978. Tentative Recommended Provisions for Seismic Regulation of Buildings, Report no. ATC-3.06, Applied Technology Council, Redwood City, CA. Applied Technology Council. 1996. Evaluation and Upgrade of Reinforced Concrete Buildings, Report no. ATC-40, California Seismic Safety Commission, Sacramento, CA. BSSC. 1997a. NEHRP Guidelines for Seismic Rehabilitation of Buildings, Building Seismic Safety Council Report no. FEMA 273, Federal Emergency Management Agency, Washington, D.C. BSSC. 1997b. NEHRP Recommended Provisions for Seismic Regulations for Buildings and Other Structures, Building Seismic Safety Council Report no. FEMA 302/303, Federal Emergency Management Agency, Washington, D.C. Chopra, A.K. 1981. Dynamics of Structures, A Primer, Earthquake Engineering Research Institute, Oakland, CA. Housner, G. 1984. “Historical View of Earthquake Engineering,” in Proc. Post-Conf. Volume, Eighth, World Conf. on Earthquake Engineering, Earthquake Engineering Research Institute, Oakland, CA. ICBO. 1997. Uniform Building Code, Volume 2: Structural Engineering Provisions, 1997 ed., International Conference of Building Officials, Whittier, CA. ICC. 2000. International Building Code 2000, International Code Council, published by International Conference of Building Officials, Whittier, CA, and others. ICC. 2001. International Performance Code 2001, International Code Council, published by International Conference of Building Officials, Whittier, CA, and others. NFPA. n.d. NFPA 5000 Building Code, National Fire Protection Association, Cambridge, MA (publication pending). Otani, S. 1995. “A Brief History of Japanese Seismic Design Requirements,” Concrete Int., 17(12), 46–53. PCBO. 1927. Uniform Building Code. Pacific Coast Building Officials. Ravindra, M.K. 1994. “Seismic Risk Assessment,” in Probabilistic Structural Mechanics Handbook: Theory and Applications, Sundararajan, C., Ed., Chapman & Hall, New York. SAC Joint Venture. 2000. Recommended Seismic Design Criteria for Steel Moment-Frame Structures, Report no. FEMA-350, Federal Emergency Management Agency, Washington, D.C. SEAOC. 1996. Vision 2000, A Framework for Performance-based Seismic Design, Structural Engineers Association of California, Sacramento, CA. SEAOC, Seismology Committee. 1999. Recommended Lateral Force Requirements and Commentary, Structural Engineers Association of California, Sacramento, CA. Tobriner, S. 1984. “The History of Building Codes to the 1920s,” Proc. SEAOC, Sacramento, CA.

Further Reading There is an extensive body of literature on building codes, although it is surprisingly deficient in the history of the development of the seismic aspects. Neglecting the historic development, the following three references will give the reader an excellent overview of the current state of seismic design requirements:



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Structural Engineers Association of California, Seismology Committee. 1999. Recommended Lateral Force Requirements and Commentary. Structural Engineers Association of California, Sacramento, CA. Building Seismic Safety Council. 1997. NEHRP Recommended Provisions for Seismic Regulations for Buildings and Other Structures, Report no. FEMA 302/303. Federal Emergency Management Agency, Washington, DC. Structural Engineers Association of California. 1996. Vision 2000, A Framework for Performance-based Seismic Design, Structural Engineers Association of California, Sacramento, CA. This chapter has focused on U.S. practice and codes. Some useful sources re seismic code provisions in other countries include: Earthquake Resistant Design Codes in Japan, January, 2000, Japan Society of Civil Engineers, Tokyo, 2000. International Handbook of Earthquake Engineering: Codes, Programs, and Examples (IHEE), edited by Mario Paz, Kluwer Academic Publishers, Dordrecht, 1995. Regulations for Seismic Design: A World List, 1996 (RSD). Rev. ed. (update of Earthquake Resistant Regulations: A World List, 1992). Prepared by the International Association for Earthquake Engineering (IAEE), Tokyo, 1996; and its Supplement 2000: Additions to Regulations for Seismic Design: A World List, 1996. Available from Gakujutsu Bunken Fukyu-Kai (Association for Science Documents Information) c/o Tokyo Institute of Technology, 2-12-1 Oh-Okayama, Meguro-Ku, Tokyo, Japan 152-8550 (telephone: +81-3-3726-3117; fax:+81–3-3726-3118; e-mail: [email protected]). The last is a comprehensive compendium of seismic regulations for more than 40 countries, which includes Eurocode 8 (the European Union’s seismic provisions).



12

Seismic Design of Steel Structures 12.1 Introduction 12.2 Historic Development and Performance of Steel Structures 12.3 Steel Making and Steel Material Physical Properties of Structural Steel · Mechanical Properties of Structural Steel

12.4 Structural Systems Braced Frames · Design Approach

12.5 Unbraced Frames

Ronald O. Hamburger Simpson Gumpertz & Heger, Inc. San Francisco, CA

Niaz A. Nazir DeSimone Consulting Engineers San Francisco, CA

Special Moment-Resisting Frames · Intermediate MomentResisting Frames · Ordinary Moment Frames · Special Truss Moment-Resisting Frames

Defining Terms References Further Reading Appendix A

12.1 Introduction In many ways structural steel is an ideal material for the design of earthquake-resistant structures. It is strong, light weight, ductile, and tough, capable of dissipating extensive energy through yielding when stressed into the inelastic range. Given the seismic design philosophy of present building codes, which is to rely on the inherent ability of structures to undergo inelastic deformation without failure, these are exactly the properties desired for seismic resistance. In fact, other construction materials rely on these basic properties of steel to assist them in attaining adequate seismic resistance. Modern concrete and masonry structures, for example, attain their ability to behave in a ductile manner through the presence and behavior of steel reinforcing. Timber structures derive their ability to withstand strong ground motion through the ductile behavior of steel connection hardware, including bolts, nails, and various steel straps and assemblies used to interconnect wood framing. Steel is a mixture of iron and carbon, with trace amounts of other elements, including principally manganese, phosphorus, sulfur, and silicon. Steel is differentiated from the earlier cast and wrought irons by the reduced amounts of carbon relative to these other alloys and the reduced amounts of other trace elements. These differences make steel both stronger and more ductile than cast and wrought irons, both of which tend to be quite brittle. Although iron alloys have been in use for centuries, steel is a relatively modern material. For practical purposes the advent of steel as a construction material can be traced to



12-2


the mid-19th century, when Sir Henry Bessemer developed the iron-to-steel conversion process that allowed production of steel in large quantities. Initial uses of steel were in the railroad industry, where it was used extensively to produce rails, and for armaments, including rifle and gun barrels. Andrew Carnegie imported the Bessemer process to the United States and constructed his first steel mill in 1870, initially for rail and machinery production. By the 1890s, however, steel was being applied to building construction and, with the advent of the elevator and high-rise construction, rapidly became the building material of choice for the new generation of tall buildings. The same properties that make it a desirable material for high-rise construction (light weight, strength, ease of fabrication and erection) also make it a popular construction material for structures involving long, clear spans. Today it is used in a variety of construction applications ranging from bridges to industrial plants to buildings. Throughout the relatively brief history of their use, structural steel buildings have been among the best performing structural systems and, prior to January 1994, when previously unanticipated connection failures were discovered in some buildings following the Northridge earthquake (M 6.7), many engineers mistakenly regarded such structures as nearly earthquake-proof. A year later, the Kobe earthquake (M 6.9) caused collapse of 50 steel buildings, confirming the potential vulnerability of these structures. This experience notwithstanding, structural steel buildings, if properly designed, can provide outstanding earthquake performance. To assure good behavior of steel structures, it is necessary to: • Configure the structural steel system so that inelastic behavior is well distributed throughout the structure, rather than concentrated in a few stories or elements • Provide columns with sufficient strength to resist earthquake-induced overturning loads without buckling • Provide adequate lateral bracing for flexural members to prevent lateral-torsional buckling • Proportion connections with sufficient strength that inelastic behavior occurs in the members themselves • Select compact sections for those members intended to experience inelastic behavior, to avoid local buckling and the rapid loss of strength that accompanies such behavior In addition, as with all structural materials, it is very important to assure that the structures are actually constructed as designed, that quality is maintained in fabrication and field welding operations, and that the structure is maintained over its life. This chapter discusses the historic performance of steel structures in earthquakes, the basic manufacturing processes and properties of structural steel, the basic structural systems used in steel structure design, and the current code requirements for the design of steel structures.

12.2 Historic Development and Performance of Steel Structures Prior to the late 1800s, the most common building materials were either timber or masonry. Timber structures were limited in height by the strength of the material and seldom exceeded three or four stories. Masonry buildings could be constructed taller than this; however, it was necessary to make the loadbearing walls quite thick, 30 in. or more, in buildings of six stories or taller. Until the advent of the elevator, these were not limiting factors on construction, as it was impractical to inhabit structures taller than four or five stories. With the elevator, however, it became practical to construct buildings that were ten or more stories in height. The elevator, together with structural steel being on the order of ten times stronger than masonry, enabled such construction to occur. The Home Insurance building, a 9-story structure erected in Chicago in 1885 and later expanded to 11 stories in 1891, is generally credited with being the first skyscraper [Chicago Public Library, 1997]. Throughout the 1890s and early 1900s, major cities in industrialized nations around the world began to build tall steel structures. The use of structural steel as a building construction material also found rapid application in long-span industrial structures, where the high strength and light weight of the material found practical application in the construction




FIGURE 12.1

Large steel spans (left) detail St. Pancras Station, London; (right) Hamburg Hauptbahnof.

FIGURE 12.2

Typical built-up member in early steel construction.

12-3

of trusses to span over large manufacturing operations. Throughout the early 20th century, these two applications, high-rise and industrial construction, were the primary applications of steel construction in the building industry. Later in the 20th century, as labor became more expensive in industrialized countries, steel began to find application in low- and mid-rise construction as well, replacing the more labor-intensive concrete and masonry construction practices. As compared with other construction materials, steel construction requires a significant industrial infrastructure and a skilled labor force. Therefore, even today, it is commonly used as a building material only in industrialized nations (Figure 12.1). Steel building construction is typically of two basic types: braced frames or unbraced frames (also commonly called moment-resisting frames), or a combination of these types. Prior to the 1920s, members of steel frames commonly were constructed as complex built-up members with gusset plates and built-up connections, as illustrated in Figure 12.2. The members and connections were riveted, and the entire steel frame was normally encased in masonry or concrete for fire protection, and also to provide walls and partitions for the structure. Few, if any, of these steel structures were designed for seismic loading, since only wind load was considered prior to about 1930 (see Chapter 11). These buildings invariably included many stiff and strong unreinforced masonry walls and partitions. Structural engineers relied upon these walls and partitions to help resist lateral loads, but they performed no calculations of the stiffness and resistance provided by these walls [Roeder, 2000]. © 2003 by CRC Press LLC


12-4

FIGURE 12.3


Typical semirigid beam column connections with rolled structural shape.

Changes in steel frame construction began to evolve around 1920. Labor costs for the built-up elements were increasing at this time, and standard hot rolled shapes for beams and columns became the normal practice. The AISC Specification and Manual [AISC, 1928] was first developed in this period. These rolled shapes commonly were connected with riveted angles and T-sections as illustrated in Figure 12.3, and members and the connections were still encased in concrete for fire protection. These framing practices became standard and were designed with relatively simple calculations for the next 20 to 30 years. Unreinforced masonry curtain walls and partitions were still used, and the combined effect of the added strength and stiffness provided by these walls and the composite action due to the encasement supplied a major portion of the structural stiffness and resistance to lateral loads. These early structures tended to be highly redundant in that every beam–column connection was a semirigid moment-resistant connection, with a large but uncalculated stiffness, and significant uncalculated resistance was also provided by nonstructural elements such as architectural masonry walls and the concrete encasement for fire protection. This construction was commonly used until the mid-1950s or early 1960s. After about 1960, high strength bolts began to replace the rivets in the T-stub and double-flange-angle connection, but the connection details and geometry remained essentially the same as those used for riveted construction. Concrete encasement was also discontinued in favor of lighter fire protection materials. However, buildings of the 1950s and 1960s still had a substantial uncalculated strength and stiffness due to cladding and partitions, and they were very redundant, since the moment-resisting connections were used at every beam-to-column joint. This construction continued into the early 1970s, at which time field welding began to replace field bolting, particularly for application to moment-resisting connections and, at about the same point in time, single plate shear connections began to replace double angles and tees for non-moment-resisting connections. The period 1970 to 1994 is characterized by a gradual trend of building frames with reduced redundancy, in which fewer but larger framing elements were used to provide lateral resistance for structures. Moment-resisting connections were typically fabricated using a standard welded flange, bolted web connection (Figure 12.4). Failure of a number of these connections in the 1994 Northridge earthquake resulted in revised practice, discussed in later sections. Given the relatively short history of steel building construction and the fact that this construction material was widely used only in industrialized nations, the earthquake performance history for steel structures is rather limited. It begins with the 1906 San Francisco earthquake (M 7.9) and fire. At the time of the FIGURE 12.4 Typical welded flange, bolted web moment-resisting connecSan Francisco earthquake, construction in the city predomition commonly in use 1970 to 1994. nantly consisted of low-rise timber frame and masonry bearing © 2003 by CRC Press LLC



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FIGURE 12.5 View of downtown San Francisco following the 1906 earthquake and fire, and showing the survival of a number of taller steel frame buildings.

FIGURE 12.6 Tall building (left) on fire, 1906 earthquake; (right) in 1999, with newer cladding. (Photos: (left) anonymous; (right) C. Scawthorn)

wall buildings and taller steel frame buildings with unreinforced masonry infill walls. Engineers surveying the damage following the earthquake and fire remarked that damage to the taller steel frame buildings was much lighter than for other structures [USGS, 1907] (Figure 12.5), and, in fact, a number of these buildings are still in service today (Figures 12.6 and 12.7). The superior performance of steel buildings observed in this earthquake initiated the perception, commonly held by some engineers until the mid-1990s, that steel frame buildings were practically invulnerable to earthquake-induced structural damage. Reis and Bonowitz [2000] postulate that this perception was more a result of a lack of exposure of steel frame buildings to strong motion, rather than a significant body of data of good performance. However, it is probable that this perception evolved, at least in part, from the fact that the early steel frame structures, with extensive infill masonry, did perform remarkably better than contemporary structures of pure masonry or reinforced concrete construction. Hadley (n.d.), for example, reports that at the time of the great Kanto, Japan earthquake of 1923, steel © 2003 by CRC Press LLC


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FIGURE 12.7 Market Street at Third Street in San Francisco, April 1906. The tall steel frame building to the right is still in service today. (Source: anonymous)

building construction had been in use only for about 5 years in Japan. Four large steel buildings had been completed and two were almost complete. These buildings, with extensive masonry infill walls and partitions, suffered little to no damage of the frames, though extensive damage to the masonry infill is reported. Hundreds of collapses of masonry structures were reported. Similarly, reports of the 1925 Santa Barbara earthquake [CISC, n.d.] indicate that although 17 concrete and masonry buildings were destroyed or eventually demolished, 2 steel frame buildings with masonry infill, located closer to the epicenter, were barely damaged. The first earthquake to affect a large number of modern steel buildings was probably the 1971 San Fernando (M 6.6), California earthquake. Steinbrugge et al. [1971] reported on a study of 30 completed steel buildings in the greater Los Angeles area, noting some damage to stairs, concrete walls, and nonstructural elements, but no structural damage to the completed steel frames. However, two noteworthy steel buildings, the two 52-story ARCO Towers then under construction in downtown Los Angeles, did experience damage to their structural frames. These buildings probably saw ground motion with a peak horizontal acceleration on the order of 0.15 g. Damage consisted of cracking of welded beam to column connections and of welded connections in transfer trusses. These cracks were ascribed to poor weld quality, and as the buildings were then under construction, were repaired as part of the ongoing construction work. Osteraas and Krawinkler [1989] note that the 1985 Mexico City earthquake (M 8.1) was probably the first event in which a significant number of steel buildings, including modern ones, were subjected to a severe test. They report data on 79 steel structures, including 41 moment-resisting frames, 17 braced frame structures and 21 structures with concrete shear walls. Of these, 12 buildings were reported as having moderate to severe damage, including 2 buildings in the Piño Suarez complex that were total collapses (Figure 12.8). Piño Suarez was a five-building complex constructed over a subway station. A 21-story, braced frame structure collapsed onto an adjacent 14-story structure, also causing its collapse. Osteraas and Krawinkler ascribe this collapse to overstrength in the steel braces of the structure, which delivered greater overturning forces to the building’s built-up columns then they could withstand, inducing local, and then complete, buckling failure of the columns and building collapse. Study of this failure led to introduction of requirements in the building codes that columns in steel structures be designed considering the potential overstrength of the supported structure. © 2003 by CRC Press LLC



12-7

FIGURE 12.8 Pino Suarez collapse, 1985 Mexico City earthquake. (Courtesy National Oceanographic and Atmospheric Agency) Shown as Color Figure 12.8.

Numerous other reports of damage to braced frame structures in various earthquakes may be found in the literature. Typical damage includes buckling of compression braces, fracture of braces at weak net sections and in the vicinity of local buckling of thin-walled brace sections, and failure of bolted end connections of braces. Figure 12.9, for example, shows a buckled brace in the three-story California Federal Savings Bank data center in Rosemead, California following the 1987 Whittier Narrows (M 5.9) earthquake. Such damage has typically been readily repairable. Extensive damage to welded moment-resisting connections was reported in buildings following the 1994 Northridge California (M 6.7) earthquake [Youssef et al., 1995]. The damage typically consisted of fractures, initiating at the root of complete penetration welded joints between beam bottom flanges and columns. Once initiated, these fractures would extend in a variety of paths and, in some cases, extended nearly completely across columns (Figure 12.10). Although only one structure, a two-story building owned by the California State Automobile Association, was damaged so severely that it was deemed irreparable, the widespread occurrence of this unanticipated damage caused great concern in the design community. Responding to this concern, the Federal Emergency Management Agency (FEMA) sponsored a 6year, $12 million research program known as the SAC Steel Program, to determine the cause of the damage and recommend design and construction procedures to mitigate the problems identified. The FEMA/SAC program concluded that the damage was a result of large stress and strain concentrations induced by the typical connection configuration, the frequent presence of large defects and flaws in the welded joints, and the common use of low toughness weld metals. An extensive series of design [SAC, 2000a], construction, and quality assurance [SAC, 2000b] recommendations were published by the FEMA/SAC project and are slowly being incorporated into standard design specifications. The project also developed procedures for seismic performance evaluation of steel structures [SAC, 2000c], postearthquake damage assessment criteria [SAC, 2000d], and an extensive collection of background technical report documents. On January 17, 1995, exactly 1 year after the Northridge earthquake, the Hyogo Ken Nambu earthquake (M 6.9) struck the city of Kobe, Japan and surrounding areas. This earthquake also caused extensive brittle fracture damage to steel structures. Nakashima [2000] reports 988 damaged steel buildings, including 432 moment-resisting frames, 168 buildings with braced frames, and 388 with unidentified framing systems. Figure 12.12 presents a breakdown of the severity of damage, by building height. More than 50 © 2003 by CRC Press LLC


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FIGURE 12.9

FIGURE 12.10


Buckled brace in California Federal Savings building, Rosemead, California.

Fracture through a column flange and web at a moment-resisting connection.

steel buildings collapsed in the Kobe earthquake, but none in excess of seven stories in height. Most of the collapsed buildings were older structures, employing tubular steel columns. Many of these buildings were very slender and experienced brittle fractures at column splices, resulting in overturning failures. As a result of the number of collapsed and severely damaged buildings, a study similar to that conducted in the United States following the Northridge earthquake was conducted by Japanese investigators. This study concluded that the failures were largely due to older construction practices and did not result in recommendations for major changes to design or construction practice.

12.3 Steel Making and Steel Material The behavior of steel structures in earthquakes is dependent on key mechanical properties of the steel material, including its strength, ductility, and toughness. These properties, in turn, are dependent on © 2003 by CRC Press LLC



12-9

FIGURE 12.11 Brittle fractures in massive braced frames of Ashiyahama Complex. (Photo: C. Scawthorn)

FIGURE 12.12 Distribution of steel building damage in the Kobe earthquake by severity and building height. (From Nakashima, M., 2000. Appendix C, State of the Art Report on Past Performance of Steel Buildings in Earthquakes, FEMA-355E, Federal Emergency Management Agency, Washington, D.C.)

the processes used to produce the material. Structural steel is a mixture of iron and carbon with varying amounts of other elements — primarily manganese, phosphorus, sulfur, and silicon. These and other elements are either unavoidably present or intentionally added in various combinations to achieve specific characteristics and properties of the finished steel product. Table 12.1, excerpted from Frank et al. [2000], lists the primary elements found in structural steel and their effects on steel properties. Various steel-making furnaces have been developed over the years. The modern age of bulk production of steel was initiated with the Bessemer Converter. This was later replaced by the open hearth furnace and, more recently, the basic oxygen and electric arc furnaces. Steel making begins with a source of raw iron, either in the form of iron ore, reduced in a blast furnace, or scrap metal. The blast furnace reduces iron ore and other iron-bearing materials, coke, and limestone into pig iron. Coke is a carbon-rich material obtained by baking coal in an oxygen-free environment. The limestone acts as a cleaning agent by reacting with impurities in the ore. The iron ore and other iron-bearing materials, coke, and limestone proceed slowly down through the body of the furnace as they are exposed to a blast of hot air that burns the coke, releasing heat and gas, and reduces the iron ore to metallic iron. This metallic iron contains several chemical elements, including carbon, manganese, sulfur, phosphorus, and silicon in amounts higher than permitted for steel. Thus, it is drawn off periodically, to be refined further in a steel-making furnace. © 2003 by CRC Press LLC


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TABLE 12.1 Principle Elemental Components of Structural Steel Carbon

Manganese Phosphorus

Sulfur

Silicon Aluminum Vanadium and Columbium Titanium Nickel Chromium Copper Nitrogen Boron

Principal hardening element in steel, increases strength and hardness, decreases ductility, toughness, and weldability Moderate tendency to segregate Increases strength and toughness Controls negative effects of sulfur Increases strength and hardness, decreases ductility and toughness Considered as an impurity, but sometimes added for atmospheric corrosion resistance Strong tendency to segregate Considered undesirable except for machineability. Decreases ductility, toughness, and weldability Adversely affects surface quality Strong tendency to segregate Used to deoxidize or “kill” molten steel Increases strength Used to deoxidize or “kill” molten steel Refines grain size, thus increasing strength and toughness Small additions increase strength Refines grain size, thus increasing strength and toughness Small amounts refine the grain size, thus increasing toughness Increases strength and toughness Increases strength Increases atmospheric corrosion resistance Primary contributor to atmospheric corrosion resistance Increases strength Increases strength and hardness May decrease ductility and toughness Small amounts increase hardenability, used only in aluminum-killed steels Most cost effective at low carbon levels

The most common steel-making furnaces today are the basic oxygen furnace and electric arc furnace (EAF). In either furnace, the metallic iron from a blast furnace or scrap iron is charged into the furnace together with limestone and melted by gas jets, electric arcs, and oxygen lances. Fluxes are added to reduce sulfur and phosphorus contents to desired levels. As the melt progresses and a liquid pool can be contacted, the lanced oxygen “burns” dissolved oxidizable elements, such as carbon, manganese, silicon, and aluminum contained in the liquid; the energy from this reaction elevates the temperature of the liquid metal pool. In the final stages of melting, the oxygen is used to decarburize the melt. Sacrificial carbon is also commonly blown into the covering slag layer to react with excess oxygen. This reaction liberates additional energy. Working of the steel continues until the desired tap temperature and carbon level have been obtained. When this has occurred, the heat will be tapped into a refractory-lined ladle. Typical EAF heats range from 80 to 360 tons. Once the liquid steel has been processed to achieve the desired chemistry and temperature, it must be put into a solid form suitable for use by the rolling mill. The process of producing this solid product is known as casting. In traditional (historic) steel making, the liquid steel was poured from the ladle into a series of cast iron molds, cooled, and solidified into an ingot. Most modern steel production uses the continuous casting method. All structural shapes of domestic origin and the majority of foreign-produced shapes are continuously cast. In this process molten steel is continuously poured into a mold. The molds are made of copper, formed in the cross-sectional shape and size of the desired casting, and water-cooled. During steady-state casting, the steel streams into the open top of the mold and fills the mold cross section. Liquid steel that comes in direct contact with the water-cooled mold surface quenches to form a solid shell and joins to the existing shell already formed along the perimeter of the mold. As the shell forms, it is continually withdrawn from the bottom of the mold. During the short residence time within the mold, the thermal transfer is sufficient such that the shell grows to a thickness that is capable of maintaining its cross-sectional shape while containing a core of liquid steel. Outside of the mold, water and/or air sprays are employed to continue shell thickening. Mechanical restraint may also be used to help maintain the cast shape. Continuously cast shapes include billets, blooms, slabs, beam blanks, and near net shapes. © 2003 by CRC Press LLC


12-11


Lamellar fracture

Plate subjected to thru-thickness tension strain

Welded joint

FIGURE 12.13 Schematic of lamellar tear-type fracture in heavy weldment.

Most structural shape and plate is produced from castings by the hot rolling process. The process consists of passing the hot cast material between a set of rolls revolving in opposite directions, and spaced such that the distance between the rolls is less than the thickness of the material entering the rolls. The rolls grip the piece, reducing its cross-sectional area and increasing its length. This process forms the steel into the desired cross-sectional shape, while improving the mechanical properties by modifying the original cast structure. Hot rolling causes grain refinement and elongation of those grains, deformable inclusions, and inhomogeneities in the rolling direction. The preferential alignment of structure along the rolling direction results in a shape with anisotropic properties. This is particularly true for ductility and fracture toughness. Hot rolling also tends to elongate segregated elements, such as sulfur, into flat discontinuities. When rolled steel is subjected to through-thickness tensile stresses, these discontinuities can produce planes of weakness that can later result in a form of failure known as lamellar tearing. Lamellar tearing is characterized by a step-like fracture surface, generally running parallel to the rolling direction (Figure 12.13). Lamellar tearing has occasionally occurred in thick materials under highly constrained conditions, such as in certain welded joint details. The tearing usually occurs during fabrication as a result of thru-thickness shrinkage strains and tensile stresses that occur as welded joints cool. Nondestructive testing procedures, including ultrasonic testing (UT) and radiographic testing (RT), can be used to detect zones of lamellar tearing. Modern steel produced by the EAF and continuous casting processes has reduced levels of sulfur relative to historic steels, and such steel is thought to be less susceptible to lamellar tearing.

12.3.1 Physical Properties of Structural Steel On the microstructural level, all metals are composed of grains. Grains are a three-dimensional matrix of atoms arranged in a regular and repeating crystal structure. The characteristics and properties of steels are a function of the microstructure and grain distribution. Microstructure, in turn, is determined by the chemistry, deformation, and thermal history of the steel. The microstructure of most common structural steels consists of a primary matrix of ferrite grains with a small dispersion of pearlite. The characteristics of the ferritic grain structure of steel dictate the properties and behavior at normal service temperatures. A fine grain size promotes increased strength, toughness, and weldability. The past thermal history of steel has significant influence upon properties of steel products. The principal thermal history effects are due to phase transformations and grain growth events. Steel is an unusual material in that, as its temperature decreases from the liquid state to ambient, it not only



12-12


undergoes a liquid to solid-state change (freezing), but also two separate and distinct solid-state phase transformations. Very simplistically, solid steel grains are composed of a three-dimensional crystal matrix of regularly arranged iron atoms. The atomic diameter of carbon is roughly half the size of iron. Thus, carbon atoms easily fit into the interstices (spaces) between the iron atoms. The packing arrangement, and hence the interstitial hole size and distribution, is different in the different solid-state phases. Structural steel grades, upon solidification, form a solid phase known as delta-iron (δ-iron). This phase exists only at highly elevated temperatures. Upon further cooling, the atomic arrangement of iron atoms in δ-iron transforms to a different packing configuration known as austenite or gamma-iron (γ-iron). Atomic packing density of iron in the austenitic state is such that up to 2% of carbon can be dissolved into the iron matrix. Further cooling of austenite will induce the iron matrix to transform to a higher packing density known as ferrite or alpha-iron (α-iron). The volume of interstices in the new matrix is reduced, resulting in a maximum carbon solubility of 0.02%. The transformation from austenite to ferrite occurs over a temperature range that is dependent on chemical composition. Under equilibrium conditions, as the temperature is decreased through the transformation range, the excess carbon that is rejected by the formation of ferrite diffuses through the solid steel, concentrates, and forms iron carbide. Iron carbide forms in islands of alternating ferrite and iron carbide, known as pearlite. The total percentage of pearlite developed within steel depends on the carbon content. The pearlite lath spacing is a function of temperature and time of formation. The size of the pearlite islands and the spacing between laths strongly influence the hardness, ductility, and strength of the steel. Examples of structural steels having ferrite-pearlite microstructure are ASTM A36, A572, and A992, all of which are deemed to have suitable toughness, ductility, and weldability for use in seismic force-resisting systems. The solid-state diffusion (transport) of carbon atoms through the solid steel matrix is dependent on both time and temperature. If the temperature of the steel is lowered rapidly (quenched) through the transformation range such that sufficient time for carbon diffusion is not provided, metastable lowtemperature transformation products bainite or martensite will form. These phases are characterized as being harder, stronger, and less ductile than ferrite pearlite steels and not desirable components of seismic force-resisting systems. Martensite and bainite can form in structural steels if rapidly heated by welding, flame or arc cutting unless proper preheating is performed to control the cooling rate and avoid quenching. If after quenching, the temperature of the steel is again raised, sufficient thermal energy will be restored to the system for solid-state carbon diffusion to reinitiate. Ductility and toughness of the steel will be improved, but at the expense of the strength and hardness that bainite and martensite offer. By carefully controlling the temperature and time of reheating, the amount of decomposition can be controlled and thus a balance between increased strength and hardness can be obtained, with acceptable toughness and ductility. This process is known as tempering. ASTM A913 is an example of a structural steel material that is processed through a quenching and tempering process and has excellent properties of toughness and ductility. It is also suitable for use in seismic force-resisting systems.

12.3.2 Mechanical Properties of Structural Steel The primary properties of structural steel that are important to seismic performance are • • • •

Yield strength Tensile strength Ductility Fracture toughness

Each of these depends on the metallurgy and thermomechanical processing history, as discussed in previous sections, as well as the load application rate, temperature, and conditions of restraint at the time of load application.



12-13


YIELD POINT

TENSILE STRENGTH

Fy STRESS f (Ksi)

ε = 0.005

εy 0

0.004

0.008

εsτ 0.012

0.016

0.020

0.024

STRAIN ε (in./in.)

FIGURE 12.14

Typical stress-strain curve for structural steel.

12.3.2.1 Tensile Properties Most mechanical properties important for design are determined from a standard tension test. In this test, a machined specimen, with standard cross section, is loaded in a universal testing machine while loadelongation data are recorded. These data are reduced into the form of a stress-strain curve (Figure 12.14). The initial straight line segment of the stress-strain curve represents the specimen’s elastic behavior where stress is proportional to strain and related by the Young’s Modulus, which has a value of 29,000 ksi for steel. As strain increases, stress and strain become nonlinear and the specimen experiences permanent plastic deformation. Many mild carbon steels exhibit a peak stress immediately after the stress-strain curve deviates from linearity, known as the yield point. Immediately after achieving the yield point, the stress dips with increasing strain, then remains at a constant value, known as the yield strength, for considerable amounts of additional strain. Thereafter, the steel strain hardens with increasing stress, until a peak, or ultimate, tensile strength is reached. With increasing strain beyond the tensile strength, the material exhibits necking and, ultimately, fracture. Standard ASTM material specifications include controls on the yield strength or yield point of the material as well as the tensile strength and elongation of the material at fracture. Although yield point is of no engineering significance, ASTM specifications permit mills to report either yield point or yield strength. Therefore, it is possible that some material conforming to the ASTM material specifications will have slightly lower yield stress than the nominal value contained in the specification. More typically, due to variations in the production process, yield and tensile properties will substantially exceed the minimum specified values, sometimes by as much as 40% or more. In general, tensile properties of steel vary with temperature. Tensile data for various steels show that their yield strength and ultimate strength increase by approximately 60 ksi when the temperature decreases from 70° to –320°F [Barsom, 1991]. Similarly, when steel is elevated to about 900°F it loses about half of its room temperature strength and modulus of elasticity. However, for the range of temperatures of interest for most structures (–60°F < T < 120°F), stress-strain properties of steel may be considered to be essentially constant. Tensile properties also vary with rate of loading. Tensile data for various steels subjected to monotonic dynamic loading show that the yield strength increases by about 4 to 5 ksi for each order of magnitude increase in rate of loading. The difference in yield strength under static loading as opposed to full impact loading (time to fracture 1  

0.9 1 + 600 ε r

(13.23a)

(13.23b)

Tensile stress-strain relationship of concrete: From the tests of panels subjected to shear, it was clear that the tensile stress of concrete, σr , is not zero as assumed in the simple truss model. Based on the tests of 35 full-size panels [Hsu, 1993], a set of formulas was recommended as follows:


If ε r ≤ ε cr ,

σr = Ε c ⋅ ε y

If ε r > ε cr ,

ε  σ r = fcr ⋅  cr   εr 

(13.24) 0.4

(13.25)


13-23


where Ε c = 47, 000 fc' , and both fc' and

fc' are in pounds per square inch

ε cr = strain at cracking of concrete = 0.00008 fcr = 3.75 fc' Stress-strain relationship of steel: The stress-strain curve of a steel bar in concrete relates the average stress to the average strain of a large length of bar crossing several cracks, whereas the stress-strain curve of a bare bar relates the stress to the strain at a local point [Okamura and Maekawa, 1991]. In other words, a steel bar in concrete is stiffened by tensile stress of concrete. If the tensile strength of concrete is neglected, as assumed in most truss models, the following equations are used:

If εt ≤ εty ,

fl = Ε s ε l

(13.26)

If ε l > ε ly ,

fl = fly

(13.27)

where Es = modulus of elasticity of steel bars fly = yield stress of longitudinal steel bars εly = yield strain of longitudinal steel bars It was recommended by Belarbi and Hsu [1995] that both the tensile strength of concrete, presented in the previous section, and the average stress-strain curve of steel stiffened by concrete be taken into account. In this model, the following equations are used for describing the stress-strain relationship of steel:

If ε l Ε s ≤ fly' ,

fl = Ε s ⋅ ε l

If ε l Ε s ≤ fly' ,

 2 − α 45o  fl = 1 −  (0.91 − 2B) fly + (0.02 + 0.25B)Ε s ε l 1000 ⋅ ρl  

(13.28)

[

]

(13.29)

where

(

[ (

B = (1 ρl ) fcr fly

)

(13.30)

)

]

(13.31)

1.5

fly' = 1 − 2 − α 45o 1000ρl (0.93 − 2B) fly 13.4.2.5 Solution Procedures

Figure 13.22 shows a framed shear wall. This kind of shear wall will be analyzed in this section. As discussed by Hsu and Mo [1985], in the design of low-rise structural walls the boundary elements are reinforced to resist the applied bending moment, while the webs are designed to resist the applied shear force. The size and shape of the boundary elements do not have a significant influence on the shear behavior, as long as they are sufficient to carry the required bending moment. The effect of the boundary elements on structural walls has been studied by Mo and Kuo [1998]. Due to the restriction of the boundary elements, the strain of transverse steel in low-rise framed shear walls can be neglected, as verified by the PCA tests, i.e., εt = 0. Therefore, adding Equations 13.20 and 13.21 gives: εr = εl − εd


(13.32)


13-24

VER.DIR.


HOR.DIR.

σdb cos α

τb cot α τb

V

A

I

A

cot α

hw

I

α τ(I)

sα

co

I (b) WALL ELEMENT

(a) GENERAL VIEW

tf b A

C

B

D

d (c) SECTION I-I

FIGURE 13.22 A framed shear wall.

Inserting εt sin2 α = εr – εr cos2 α into Equation 13.20 gives: cos 2 α =

εr − εl εr − εd

(13.33)

Substituting Equations 13.32 and 13.33 into Equation 13.17 results in:

fl =

1 ρl

 (−εd ) − σ (εl − εd )  σ l − σ d ⋅ (εl − 2εd ) r (εl − 2εd )  

(13.34)

Neglecting the tensile strength of concrete, i.e., σr = 0, gives: fl =

1 ρl

 (−εd )  σ l − σ d ⋅ (εl − 2εd )  

(13.35)

For low-rise framed shear walls, the average shear stress τ on the horizontal cross section is defined as: τ=


V bd

(13.36)


13-25


where d is the effective depth, which is defined as the distance between the centroids of the longitudinal bars in the two flanges, b is the width of the web, and V is the horizontal shear force. The deflection at the top of the shear wall, δ, is determined by: δ = γh

(13.37)

where h is the height of the shear wall. Based on the softened truss model theory presented above, the algorithm is shown in Figure 13.23 [Mo and Jost, 1993; Mo and Shiau 1993] and is explained below. Select a given εd . Assume a value of εl . Calculate εr from Equation 13.32. Calculate ζ using Equation 13.23b. Calculate σd from Equation 13.23a. Calculate σr from Equation 13.24 or 13.25. Calculate fl from Equation 13.34 or 13.35. Check fl using Equations 13.26 to 13.27 or Equations 13.28 to 13.31. If the calculated value for fl determined in step 8 is not sufficiently close to the value shown in step 7, repeat steps 2 through 7. 9b. If the calculated value for fl determined in step 8 is sufficiently close to the value shown in step 7, proceed to calculate τ (or V) and γ (or δ) from Equation 13.19 or 13.36 and Equation 13.21 or Equation 13.37, respectively. This will provide one set of solutions. 1. 2. 3. 4. 5. 6. 7. 8. 9a.

Select other values of εd and repeat steps 1 through 9 for each εd . This will provide a number of sets of quantities. From these sets of quantities the shear stress vs. distortion curve (or shear force vs. deflection curve), the longitudinal steel strain vs. deflection curve, and the longitudinal steel strain vs. concrete strain curve can be plotted. In general the maximum εd value can be chosen as 0.003 with an increment of 0.00005.

13.5 Seismic Design 13.5.1 Columns 13.5.1.1 Flexural Plastic Hinge Mechanism To confine a flexural plastic hinge region in a circular column for standard design ductilities, a volumetric reinforcement ratio of:

ρs =

ks fc' f yh

 P  0.5 + 1.25 '  + 0.13 (ρl − 0.01) fc Ag  

(13.38)

is required, based on Priestley et al. [1996], in the plastic hinge zone. Equation 13.38 depends on the longitudinal column reinforcement ratio As/Ag and on a factor ks which is calibrated with experimental results based on an energy balance approach, which compares the vertical strain energy stored in the confined concrete at crushing with the strain energy provided by the horizontal hoop reinforcement up to bar rupture. For mild steel reinforcement hoops ks = 0.16 is applied [Priestley et al., 1996]. Note that P is the axial force and fyh is the yield strength of the horizontal reinforcement. 13.5.1.2 Shear Mechanism Many different models exist to describe the complex transfer of so-called shear forces in a reinforced concrete member. A simple model that seems to fit the experimental data best was put forward by Priestley © 2003 by CRC Press LLC


13-26


Select

εd

Estimate

ε

Calculate

εr

Calculate

ζ

Calculate

σd

Calculate

σr

Calculate

fl

l

NO

Check if the error for

fl

is

acceptable YES Calculate τ , γ , v, δ

NO

Check if

εd > 0.003 YES END

FIGURE 13.23 Algorithm for framed shear wall analysis.

et al. [1993a, 1993b] and assumes a combination of three different mechanisms to contribute to the nominal shear capacity Vn in the form: Vn = Vc + Vs + Vp


(13.39)

0068_C13_fm Page 27 Thursday, August 15, 2002 8:02 AM

13-27


where Vc is the concrete contribution provided primarily in the form of aggregate interlock, which decreases with increasing crack width and flexural ductility, Vs is the horizontal reinforcing steel contribution as part of an assumed truss mechanism, and Vp is the horizontal component from the applied axial load compression strut between the column ends. Due to the aggregate interlock degradation with increasing crack width or flexural ductility, the Vc component needs to be tied to the column displacement ductility level µ∆ in regions where inelastic flexural plastic hinging occurs. Thus, the concrete contribution to the shear resistance needs to be assessed both inside the plastic hinge region Lc as Vci and outside the plastic hinge region over Lv as Vco. Thus, Vci = k fc' Ae   Vco = 3 fc' Ae 

(13.40)

where the effective concrete shear area Ae = 0.8Ag or 80% of the gross column area, and k represents a strength reduction factor based on the column displacement ductility µ∆ in the form of: k=3 k = 5 − µ∆ k = 1.5 − µ ∆ 8 k = 0.5

for for for for

µ∆ < 2   2 ≤ µ ∆ < 4  4 ≤ µ ∆ < 8 µ ∆ ≥ 8 

(13.41)

Note that Equation 13.41 is for shear design and is thus slightly more conservative than concrete shear reductions proposed for assessment of expected capacities in existing columns. The horizontal reinforcing steel contribution Vs can be determined as: Vs = Vs =

π Ah fhy D' cot θ (circular) 2 s nAh fhy D' s

cot θ (rectangular)

(13.42a)

(13.42b)

where Ah n fhy s θ

= = = = =

the area of one leg of the horizontal reinforcement the number of legs of horizontal column ties in the loading direction the yield strength of the horizontal reinforcement the spacing of the horizontal reinforcement or the spiral pitch the angle of the principal compression strut to the column axis or the shear crack inclination D' = the core column dimension in the loading direction from center to center of the peripheral horizontal reinforcement

Conservatively, θ = 45° or cot θ = 1 can be assumed for design or, more accurately for assessment, principal compression strut inclinations of 30° can be assumed for bridge columns and 45° for pier walls. The axial load shear contribution is simply defined as the horizontal component of the inclined compression strut as: Vp = P tanα


(13.43)


13-28


Mass F (t) (a) Low-rise shear wall with a mass at the top

y SPRING

(b) Model for a nonlinear single-degree-of-freedom system

DAMPER

ki ∆ yi

F (t)

Mass

mi ∆ ÿi

∆I

ci ∆ ÿi

(c) Free body diagram showing the incremental inertial force and the incremental external force

FIGURE 13.24 A model for dynamic analysis.

where P represents the axial load at the column top and α the compression strut inclination or angle with the vertical column axis. Thus, tan α can be defined as:

D−c for single bending 2L D−c for double bending L where c represents the distance between the neutral axis and the extreme compression fiber, D the column dimension in the loading direction, and L the clear column height.

13.5.2 Structural Walls 13.5.2.1 Dynamic Analysis In dynamic analysis, a low-rise structural wall can be modeled as a nonlinear single degree of freedom system (Figure 13.24) [Mo, 1988]. The dynamic incremental equilibrium is shown in Figure 13.24c. The equation of the equilibrium is:

m∆˙˙y i + c i ∆y˙ i + ki ∆y i = ∆Fi


(13.44)


13-29


FIGURE 13.25 Linear variation of acceleration during time interval ∆t.

where m is the total mass at roof level plus one third the mass of the wall. The coefficients ci and ki are calculated for values of velocity and displacement corresponding to time t and assumed to remain constant during the increment of time ∆t. ∆ÿi , ∆ y˙ i, and ∆yi are the incremental acceleration, incremental velocity, and incremental displacement, respectively. To perform the step-by-step integration of Equation 13.44, the linear acceleration method is employed. In this method, it is assumed that the acceleration may be expressed by a linear function of time during the time interval ∆t. Let ti and ti +1 = ti + ∆t be, respectively, the designation for the time at the beginning and at the end of the time interval ∆t. When the acceleration is assumed to be a linear function of time for the interval of time ti to ti +1 = ti + ∆t as shown in Figure 13.25, the acceleration may be expressed as: ˙˙y (t ) = ˙˙y i +

∆˙˙y i (t − t i ) ∆t

(13.45)

Integrating Equation 13.45 twice with respect to time between the limits ti and t = ti + ∆t and using the incremental displacement ∆y as the basic variable gives: ∆˙˙y i =

6 6 ∆y − y − 3 ˙˙y i ∆t 2 i ∆t i

(13.46)

∆y˙ i =

3 ∆t ˙˙y ∆y i − 3 y˙ i − ∆t 2 i

(13.47)

and

The substitution of Equations 13.46 and 13.47 into Equation 13.44 leads to the following form of the equation of motion: 6 ∆t   6   3 ˙˙y  + k ∆y = ∆Fi m  2 ∆y i − y˙ − 3 ˙˙y i  + c i  ∆y i − 3 y˙ i −  ∆t   ∆t 2 i i i ∆t i

(13.48)

Transferring in Equation 13.48 all the terms containing the unknown incremental displacement ∆yi to the left-hand side gives: ki ∆y i = ∆Fi


(13.49)


13-30


where ki = ki +

6m 3c i + ∆t 2 ∆t

(13.50)

and ∆t   6   ˙˙y  ∆Fi = ∆Fi + m  y˙ i + 3 ˙˙y i  + c i  3 y˙ i +  ∆t   2 i

(13.51)

It should be noted that Equation 13.49 is equivalent to the static incremental-equilibrium equation and may be solved from the incremental displacement by simply dividing the equivalent incremental load ∆Fi by the equivalent spring constant ki. The displacement yi+1 and the velocity y˙ i+1 at time ti+1 = ti + ∆t are: y i +1 = y i + ∆y i

(13.52)

y˙ i +1 = y˙ i + ∆y˙ i

(13.53)

and

The acceleration ˙˙y i+1 at the end of the time step is obtained directly from the differential equation of motion to avoid the errors that generally might tend to accumulate from step to step. It follows that: ˙˙y i +1 =

[

1 F (t i +1 ) − c i +1 y˙ i +1 − ki +1 y i +1 m

]

(13.54)

where the coefficients ci+1 and ki+1 are now evaluated at time ti+1. It should be noted that according to a Nuclear Regulatory Commission regulatory guide, the damping coefficient ci+1 is 7 and 4% of critical damping ccr for reinforced concrete structures subjected to safe shutdown earthquake (or blast loading) and operating-basis earthquake, respectively: c i +1 = ξ(c cr )i +1 = 2ξ(ki +1m)

1/ 2

(13.55)

After the displacement, velocity, and acceleration have been determined at time ti+1 = ti + ∆t, the procedure just outlined is repeated to calculate these quantities at the following time step ti +2 = ti+1 + ∆t. In general, sufficiently accurate results can be obtained if the time interval is taken to be no longer than one tenth of the natural period of the structure. The natural period T can be expressed as: T = 2π

m k

(13.56)

13.5.3 Design Approach 13.5.3.1 Design Considerations To ensure ductile failure, the two design limitations for over-reinforcement and minimum reinforcement can be derived in terms of the inclination angle α of the diagonal concrete struts. Over-reinforcement: Mo [1987] shows the inclination angle of the diagonal compression struts in the “lower balanced reinforcement,” αlb , to be:


0068_C13_fm Page 31 Thursday, August 15, 2002 12:15 PM

13-31


  ε      8ε 2 1 α lb = cos−1   ly   1 + 20 − 1    ε ly     2  2ε o  

(13.57)

αlb is a function of only one variable, the yield strain of longitudinal steel εly . In under-reinforced design, the angle α should be chosen greater than αlb. Minimum reinforcement: Mo [1987] also shows the inclination angle for minimum reinforcement αm to be: 1/3  f   α m = cos−1  0.0025 ly'   fc     

(13.58)

αm is a function of two variables, the yield strain in longitudinal steel εly and the concrete strength fc' . Equations 13.57 and 13.58 give the lower and upper limits, respectively, for the range of α, which ensures ductile failure. After the range of the inclination angle α is found, a preliminary angle α can be selected within this range. The wall size bd can then be determined by substituting τ = V/bd and σ d = fc' cos α into τ = σ d sin α cos α [Hsu and Mo, 1985; Mo, 1988]: bd =

V fc' sin α cos 2 α

(13.59)

The effective length d in Equation 13.59 is usually given in design, and the web width b needs to be chosen by the designer. After the wall size bd is determined, the actual inclination angle α can be refined by solving α in Equation 13.59. The longitudinal steel can be determined from Al fl = τbd cot α [Hsu and Mo, 1985; Mo, 1988], noting that τbd becomes Vn at maximum shear: Al fly = Vn cot α

(13.60)

The transverse (horizontal) steel can be determined by the specified minimum value [Hsu, 1993]: ρt = 0.0045

(13.61)

13.5.3.2 Design Procedures For a given dynamic loading history (or seismogram) and given material properties ( f c' , f ly , ξ) , the procedures to design the size of the wall, the vertical steel, and the horizontal steel are as follows: 1. Assume a shear force (Vn). 2. Determine the range of αs by Equations 13.57 and 13.58. 3. Select an α value and b find and d from Equation 13.59. After b and d are selected, the actual angle of inclination can be refined. 4. Determine the longitudinal steel by Equation 13.60 and the horizontal steel by Equation 13.61. 5. Determine the load-deflection relationship using the algorithm mentioned in Figure 13.22. 6. Calculate the stiffness at the ultimate state. 7. Determine the natural period at the ultimate state by Equation 13.56. 8. Select the time interval ∆t ≤ 0.1 times the natural period at the ultimate state. 9. Calculate the initial stiffness using the load-deflection relationship. 10. Calculate the damping coefficient by Equation 13.55. 11. Calculate the effective stiffness by Equation 13.50.



13-32


12. 13. 14. 15. 16. 17. 18. 19. 20.

Calculate the incremental effective force by Equation 13.51. Solve for the incremental displacement by Equation 13.49. Calculate the incremental velocity by Equation 13.47. Calculate displacement and velocity at the end of the time interval by Equations 13.52 and 13.53. Calculate shear force using the load-deflection relationship. Calculate acceleration at the end of the time interval by Equation 13.54. Steps 9 through 17 will provide one set of solutions. Repeat steps 9 through 17 for each time interval. This will provide a number of sets of solutions. Determine the calculated maximum shear force in the entire loading history. a. If the value of the calculated maximum shear force is not greater than the shear force assumed, the design is finished. b. If the value of the calculated maximum shear force is greater than the shear force assumed, reassume a new value for shear force Vn and repeat steps 2 through 19 until step 19a is satisfied.

The algorithm presented in this section has been extended to box tubes subjected to dynamic shear and torsion [Mo and Yang, 1996] and to hybrid reinforced concrete frame–steel wall systems [Mo and Perng, 2000, in press]. 13.5.3.3 Design Example A shear wall 10 ft (3.05 m) high by 15 ft (4.57 m) wide (Figure 13.26a) is designed to withstand the missile impact having the force-time relationship shown in Figure 13.26b and acting at the top of the wall. For simplicity, the force-time relationship of the missile impact is used instead of the earthquake seismogram. It is assumed that the mass at the top of the wall and one third the mass of the wall m are 0.5 k⋅sec2/in. (0.088 kN⋅sec2/mm). The material properties are given as follows: fly = 60 ksi (414 MPa), fc' = 4000 psi (27.6 MPa), Es = 29 × 106 psi (2.0 × 105 MPa), εo = 0.002, and ξ = 0.07. The wall thickness b and the reinforcement in the wall ρl and ρt are to be determined. Design of the boundary columns, which should be designed to resist the bending moment, will not be described. Solution: 1. Assume Vn = 1600 kips (7117 kN). 2. Determine the range of α:    1  0.00207  α > cos−1      2  2(0.002)   

2    8(0.002)   1+   1 − 2    0 00207 . ( )    

(13.57)

α = 60.4° 1   0.0025)(60, 000)  3  (  α ≤ cos     4000    −1

α = 70.4°

(13.58)

∴ 60.4° < α ≤ 70.4° 3. Select α = 60.4° and d = 180 in. (4572 mm): b≥

1, 600, 000

(180)(4000) sin 60.4 cos2 60.4

b ≥ 10.48 in. (266 mm)


(13.59)


13-33


y

k · sec2/in.

m = 0.5

1.2 x 103K

F(t) F (t) 10′

ξ = 0.07 t (sec) 0.02

15′

0.1

(b) LOADING

(a) SHEAR WALL 1 k.sec/in. = 0.175 kN· sec/mm 1 ft = 0.3048 m SHEAR FORCE v (kips)

1 k = 4.448 kN 1 in. = 25.4 mm

1500

1000

500

0.1

0.2 0.3 DISPLACEMENT y (in.)

0.4

(c) SHEAR FORCE − DISPLACEMENT RELATIONSHIP

FIGURE 13.26 Shear wall subjected to missile impact.

Let us select b = 12 in. (305 mm). Calculate α = 62.9° from Equation 13.59: α = 62.9° < 70.4° OK 4. Determine ρl and ρt: ρl =

1, 600, 000 cot 62.9 = 0.0063 (12)(180)(60, 000) ρt = 0.0045

(13.60)

(13.61)

5. Determine the load-deflection relationship. Using the algorithm mentioned in Figure 13.22 the load-deflection relationship is determined as shown in Figure 13.26c. 6. Calculate the stiffness at the ultimate state: ku =

1609.9 = 3879.3 k / in. (679 kN / mm 0.415

7. Determine the natural period at the ultimate state: Τu = 2π


0.5 = 0.071 sec 3879.3

(13.56)


13-34


8. Select ∆t : ∆t = (0.1)(0.071) = 0.0071 sec Let us select ∆t = 0.005 sec ∆t = 0.005 sec < 0.0071 sec

OK

9. Calculate the initial stiffness k: k=

572.2 = 7354.8 k / in. (1288 kN / mm) 0.0778

10. Calculate the damping coefficient C:

[

]

C = (0.07)(2) (0.5)(7354.8)

1

2

= 8.49 k ⋅ sec/ in. (1.49 kN ⋅ sec/ mm )

(13.55)

11. Calculate the effective stiffness k : k = 7354.8 +

6 (0.5)

(0.005)

2

+

3 (8.49) = 132, 448.8 k / in. (23194 kN / mm ) 0.005

12. Calculate the incremental effective force: ∆F = 300 kips (1334 kN)   6(0)  0.005 (0)  ∆F = 300 + (0.5)  + 3 (0) + (8.49) 3 (0) +  = 300 kips (1334 kN) 2    0.005  13. Determine the incremental displacement ∆y: ∆y =

300 = 0.002265 in.(0.058 mm) 132, 448.8

(13.49)

14. Determine the incremental velocity ∆y˙ : ∆y˙ =

3 (0.002265) − 3 (0) − 0.005 (0) = 1.359 in. / sec(34.52 mm / sec) 0.005 2

(13.47)

15. Calculate displacement and velocity at the end of the time interval: y i+1 = 0 + 0.002265 = 0.002265 in. (0.058 mm)

(13.52)

y˙ i+1 = 0 + 1.359 = 1.359 in./sec (34.52 mm/sec)

(13.53)

16. Determine shear force V. From Figure 13.26c, V = 16.7 kips (74.3 kN) when y = 0.002265 in. (0.058 mm).



13-35


TABLE 13.1 Nonlinear Response: Linear Acceleration Step-by-Step Method for Design Example sec

kip

in.

in./sec

kip

in./sec

k/in.

k/in.

kip

kip

in.

in./sec

0 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120 0.125 0.130

0 300 600 900 1200 1125 1050 975 900 825 750 675 600 525 450 375 300 225 150 75 0 0 0 0 0 0 0

0 0.0023 0.0172 0.0524 0.1091 0.1807 0.2509 0.3045 0.3311 0.3255 0.2997 0.2698 0.2391 0.2108 0.1874 0.1701 0.1588 0.1519 0.1472 0.1421 0.1342 0.1225 0.1091 0.0963 0.839 0.0715 0.0591

0 1.36 4.86 9.23 13.19 13.64 12.83 8.17 2.28 –4.55 –5.68 –6.17 –6.00 –5.22 –4.10 –2.82 –1.77 –1.07 –0.90 –1.24 –1.97 –2.62 –2.64 –2.49 –2.49 –2.49 –2.49

0 17 126 385 700 1015 1300 1455 1530 989 870 732 590 459 351 271 219 187 165 142 105 51 0 0 0 0 0

0 544 865 947 776 4 –669 –1063 –1347 –280 –164 –31 101 202 253 246 186 90 –19 –116 –183 –67 36 0 0 0 0

7355 7355 7355 7355 5549 4399 4060 2892 2820 4621 4621 4621 4621 4621 4621 4621 4621 4621 4621 4621 4621 4621 4621 0 0 0 0

132,449 132,449 132,449 132,449 129,971 128,341 127,846 126,084 125,976 128,659 128,659 128,659 128,659 128,659 128,659 128,659 128,659 128,659 128,659 128,659 128,659 128,659 120,000 120,000 120,000 120,000 120,000

300 300 300 300 –75 –75 –75 –75 –75 –75 –75 –75 –75 –75 –75 –75 –75 –75 –75 –75 0 0 0 0 0 0 0

300 1977 4658 7514 9309 9004 6852 3349 –709 –3322 –3846 –3948 –3645 –3009 –2232 –1449 –888 –603 –661 –1019 –1502 –1723 –1532 –1491 –1491 –1491 –1491

0.0023 0.0149 0.0352 0.0567 0.0716 0.0702 0.0536 0.0266 –0.0056 –0.0258 –0.0299 –0.0307 –0.0283 –0.0234 –0.0173 –0.0113 –0.0069 –0.0047 –0.0051 –0.0079 –0.0117 –0.0134 –0.0128 –0.0124 –0.0124 –0.0124 –0.0124

1.36 3.50 4.37 3.96 1.45 –1.81 –4.66 –5.89 –6.83 –1.13 –0.49 0.17 0.78 1.13 1.28 1.05 0.69 0.17 –0.34 –0.74 –0.64 –0.03 0.16 0 0 0 0

Note: kN/mm. 1kip = 4.448 kN; 1 in. = 25.4 mm; 1 in./sec= 25.4 mm/sec; 1 in./sec2 = 25.4 mm/sec;2 1 kip/in. = 0.175

17. Calculate acceleration at the end of the time interval: ˙˙y i+1 =

[

]

1 300 − (8.49)(1.359) − 16.7 = 543.5 in./sec2 (13,805 mm/sec2) 0.5

Steps 9 through 17 provide one set of solutions. 18. Repeating steps 9 through 17 for each time interval gives a number of sets of solutions, as illustrated in Table 13.1. 19. Determine the calculated maximum shear force. From Table 13.1, Vmax = 1530 kips (6805 kN) < assumed Vn = 1600 kips (7117 kN). OK The dynamic inelastic response calculated in Table 13.1 is plotted in Figure 13.27. Also plotted for comparison is the linear elastic response obtained by a similar step-by-step analysis. The effect of the inelastic response on the displacement shows up clearly in this comparison.

13.5.4 Detailing Requirements According to the detailing requirements of the ACI code [1995], a brief description is introduced by Nawy [1996], as summarized below.



13-36


36 32

1 in. = 25.4 mm

28 DISPLACEMENT y (10−2 in)

INELASTIC RESPONSE 24 20 ELASTIC RESPONSE

16 12 8 4 0

10

20

30

40

50

-4

60 70 80 90 TIME t (10−3 sec)

100 110 120 130

-8

FIGURE 13.27 Comparison of inelastic with elastic response.

13.5.4.1 Longitudinal Reinforcement 1. In seismic design, when the factored axial load Pu is negligible or significantly less than Ag fc' 10 , the member is considered a flexural member (beam). If Pu > Ag fc' 10 , the member is considered a beam-column, because it is subjected to both axial and flexural loads, as columns are. 2. The shortest cross-sectional dimension ≥ 12 in. (300 mm). 3. The limitation on the longitudinal reinforcement ratio in the beam-column element is: 0.01 ≤ ρ g =

As ≤ 0.06 . Ag

For practical considerations, an upper limitation of 6% is too excessive, because it results in impractical congestion of longitudinal reinforcement. A practical maximum total percentage ρg of 3.5 to 4.0% should be a reasonable limit. 4. A minimum percentage of longitudinal reinforcement in flexural members (beams) is: a. For positive reinforcement,

ρ≥

3 fc' fy

≥

200 fy

(13.62)

≥

200 fy

(13.63)

b. For negative reinforcement,

ρ≥


6 fc' fy


13-37


But under no condition should ρ exceed 0.025. The stresses fc' and fy in these expressions are in psi units. All reinforcement has to be continued through the joint. 5. In building design, main reinforcement should be chosen on the basis of the strong column–weak beam concept of the ACI code:

∑M

col

≥

6 5

∑M

bm

(13.64)

13.5.4.2 Transverse Confining Reinforcement Transverse reinforcement in the form of closely spaced hoops (ties) or spirals has to be adequately provided. The aim is to produce adequate rotational capacity within the plastic hinges that may develop as a result of the seismic forces. 1. For column spirals, the minimum volumetric ratio of the spiral hoops needed for the concrete core confinement is: ρs ≥

0.12 fc' f yh

(13.65)

or A  f' ρs ≥ 0.45  g − 1 c  Ach  f yh

(13.66)

whichever is greater, where ρs = ratio of volume of spiral reinforcement to the core volume measured out to out Ag = gross area of the column section Ach = core area of section measured to the outside of the transverse reinforcement fyh = specified yield strength of transverse reinforcement, psi 2. For column rectangular hoops, the total cross-sectional area within spacing s is: Ash ≥ 0.09shc

fc' f yh

(13.67)

or A  f' Ash ≥ 0.3shc  g − 1 c  Ach  f yh

(13.68)

whichever is greater, where Ash = total cross-sectional area of transverse reinforcement (including cross ties) within spacing s and perpendicular to dimension hc hc = cross-sectional dimension of column core measured c-c of confining reinforcement (in.) Ach = cross-sectional area of structural member, measured out to out of transverse reinforcement s = spacing of transverse reinforcement measured along the longitudinal axis of the member (in.) The maximum allowable spacing is one quarter of the smallest cross-sectional dimension of the member or 4 in., whichever is smaller (UBC code [1997] requires 4 in.).



13-38


3. The confining transverse reinforcement in columns should be placed on both sides of a potential hinge over a distance o . The largest of the following three conditions governs: a. Depth of member at joint face b. One sixth of the clear span c. 18 in. 4. For beam confinement, the confining transverse reinforcement at beam ends should be placed over a length equal to twice the member depth h from the face of the joint on either side or of any other location where plastic hinges can develop. The maximum hoop spacing should be the smallest of the following four conditions: a. One fourth effective depth d b. 8 × diameter of longitudinal bars c. 24 × diameter of the hoop d. 12 in. (300 mm) 13.5.4.3 Beam–Column Connections Test of joints and deep beams have shown that shear strength is not as sensitive to joint (shear) reinforcement as for that along the span. On this basis, the ACI code [1995] has assumed the joint strength as a function of only the compressive strength of the concrete and requires a minimum amount of transverse reinforcement in the joint. The minimal shear strength of the joint should not be taken greater than the forces Vn specified below for normal-weight concrete. 1. Confined on all faces by beams framing into the joint: Vn ≤ 20 fc' A j

(13.69)

2. Confined on three faces or on two opposite faces: Vn ≤ 15 fc' A j

(13.70)

Vn ≤ 12 fc' A j

(13.71)

3. All other cases:

A framing beam is considered to provide confinement to the joint only if at least three quarters of the joint is covered by the beam. The value of allowable Vn should be reduced by 25% if lightweight concrete is used. Also, test data indicate that the value in Equation 13.71 is unconservative when applied to corner joints. Aj = effective cross-sectional area within a joint, in a plane parallel to the plane of reinforcement generating shear at the joint. 13.5.4.4 Development of Reinforcement at the Joint For bars of sizes numbers 3 through 11 terminating at an exterior joint with standard 90° hooks in normal concrete, the development length ldh beyond the column face should not be less than the following:


ldh ≥ f y db 65 fc'

(13.72)

ldh ≥ 8 db

(13.73)


13-39


ldh ≥ 6 in.

(13.74)

where db is the bar diameter. The development length provided beyond the column face must be no less than ld = 2.5ldh when the depth of concrete cast in one lift beneath the bar ≤ 12 in. or ld = 3.5 × ldh when the depth of concrete cast in one lift beneath the bar exceeds 12 in. All straight bars terminated at a joint are required to pass through the confined core of the column boundary member. Any portion of the straight embedment length not within the confined core should be increased by a factor of 1.6. 13.5.3.2 Shear Walls Forces and reinforcement in shear walls and diaphragms: High-rise shear walls with height-to-depth ratio in excess of 2.0 essentially act as vertical cantilever beams. As a result, their strength is determined by flexure rather than shear. If they are subjected to factored in-plane seismic shear forces Vuh > Acv fc' , they have to be reinforced with a minimum percentage ρv ≥ 0.0045. At least two curtains of reinforcement are needed in the wall if the in-plane factored shear forces exceed a value of Vuh > Acv fc' : ρv = Asv Acv

(13.75)

Acv = net area of concrete cross section = thickness × length of section in direction of shear considered Asv = projection on Acv of area of distributed shear reinforcement crossing the plane of Acv If the extreme fiber compressive stresses exceed 0.2 fc', the shear walls have to be provided with boundary elements along their vertical boundaries and around the edges of openings. The nominal shear strength Vn of structural walls and diaphragms of high-rise buildings with aspect ratio greater than 2 should not exceed the shear force calculated from:

(

Vn = Acv 2 fc' + ρn f y

)

(13.76)

where ρn is the ratio of distributed shear reinforcement on a plane perpendicular to the plane of Acv . For low-rise walls with aspect ratio hw l w less than 2, the ACI code [1995] requires that the coefficient 2 in Equation 13.76 be increased linearly up to a value of 3 when the hw l w ratio reaches 1.5 in order to account for the higher shear capacity of low-rise walls. In other words:

(

VN = Acv α c fc' + ρn f y

)

(13.77)

where αc = 2 when hw l w ≥ 2 and α c = 3 when hw l w = 1.5; Vu = φVn φ = 0.6 for designing the joint, if nominal shear is less than the shear corresponding to the development of the nominal flexural strength of the member The nominal flexural strength is determined considering the most critical factored axial loads including earthquake effects. The maximum allowable nominal unit shear strength in structural walls is 8Acv fc' where Acv is the total cross-sectional area (in.2) previously defined and fc' is in psi. However, the nominal shear strength of any one of the individual wall piers can be permitted to have a maximum value of 10Acp fc' , where Acp is the cross-sectional area of the individual pier.



13-40


13.6 Seismic Retrofit 13.6.1 Columns Steel jackets [Aboutaha et al., 1999] and fiber-reinforced plastic composites [Gergely et al., 1998; Saadatmanesh et al., 1996] have been used successfully for the retrofit of bridge columns. At the University of California at San Diego (UCSD), a series of systematic tests [Seible, 1994a, 1994b, 1995a, 1995b, 1995c, 1995d] have been performed on seismic retrofit of columns. A brief summary is introduced by Seible et al. [1997], as shown below. 13.6.1.1 Flexural Plastic Hinge Retrofit For carbon fiber jackets Equation 13.38 can be interpreted as: ρj =

4t j D

=

k j fc'  P  0.5 + 1.25 '  + 0.13 (ρl − 0.01) f ju  fc Ag 

(13.78)

Based on the energy balance considerations [Seible, 1997], the characteristic hoop reinforcement strain energy for elastoplastic stress-strain characteristics of mild steel in the form of [ fhy εhu] can be expressed for carbon jackets with essentially linear elastic stress-strain characteristic in the form of [ 12 fju εju], which for typical mild steel ( fy = 66 ksi, εsu = 15%) and unidirectional carbon tows ( fju = 200 ksi, εju = 1%) would result in an efficiency reduction to approximately 10% for the carbon jacket due to the low strain limits. However, tests on carbon fiber jacketed columns at UCSD [Seible et al., 1994a, 1994b, 1995a, 1995b, 1995c, 1995d] have shown that significantly higher compression strains (by a factor of three to four) can be achieved in the confined concrete than predicted by the energy balance approach, which can be attributed to the reduced concrete dilation due to the lower ultimate strain limits in the carbon jacket. Thus, for carbon jacket retrofit designs the confinement efficiency can conservatively be increased by at least a factor of two, resulting in an equivalent confinement factor of: ks = 5ks = 0.8 2 × 0.1

(13.79)

D fc'  P  0.5 + 1.25 '  + 0.13 (ρl − 0.01) 5 f ju  fc Ag 

(13.80)

kj = or a carbon jacket thickness: tj =

The ultimate compression strain in the confined concrete can be expressed based on Mander et al. [1988b] as: ε cu = 0.004 +

2 × 1.4 ρ j f ju ε ju fcc'

(13.81)

where fcc' = the compression strength of the confined concrete conservatively taken as 1.5 fc' and the factor 2 again represents the conservative estimate of increased compression strains based on the observed experimental data from carbon fiber jacket confined plastic hinges. With this ultimate concrete strain and a depth cu for the flexural compression zone calculated as part of normal flexural strength calculations or from a moment curvature analysis, the resulting ultimate curvature: φu =


ε cu cu

(13.82)


13-41


can be determined. Together with the φy from an equivalent bilinear moment curvature approximation (obtained from the moment curvature section analysis) the curvature ductility: µφ =

φu φy

(13.83)

can be determined, which in turn can be expressed in the form of a member ductility factor:

) L 1 − 0.5 L 

(

µ∆ = 1 + 3 µφ − 1

Lp

Lp

(13.84)

where Lp is the equivalent plastic hinge length defined as: L p = 0.08 L + 0.022 fsydb

(13.85)

where fsy is the yield strength [ksi] and db is the bar diameter of the longitudinal column reinforcement. Note Equation 13.85 is the same as the one used to assess unretrofitted columns since 90° carbon fiber wraps do not contribute to longitudinal column capacities or provide restrictions to the plastic hinge development. Alternatively, for a given εcu , which can directly be derived based on design ductility requirements from back calculation of Equations 13.84 to 13.81, the required jacket thickness can be expressed as: tj =

ρjD 4

= 0.09

D (ε cu − 0.004) fcc' f ju ε ju

(13.86)

which generally results in a more economical jacket thickness than required by the standard confinement Equations 13.38 and 13.80. To prevent column bar buckling in the plastic hinge region [Priestley et al., 1996], a volumetric transverse reinforcement ratio of: ρs =

0.45 ⋅ n ⋅ fs2 E ds Et

(13.87)

is required, where E ds =

(

4E s E i Es + Ei

)

2

(13.88)

and Et = the modulus of elasticity of the transverse reinforcement n = the number of longitudinal reinforcing bars fs = steel stress at a strain of 4% in the longitudinal reinforcement or 74 ksi (510 MPa) for grade 60 steel Es = the secant modulus from fs to fu Ei = the initial elastic modulus of the longitudinal reinforcement



13-42


For longitudinal grade 60 steel Eds can thus be determined as 657 ksi (4530 MPa), resulting in: ρs = 3.75

n Et

(13.89)

with Et in [ksi] units. For a carbon fiber jacket Equation 13.89 can be expressed as: ρs =

4t j D

= 3.75

n E j [ksi]

(13.90)

The antibuckling requirement of Equation 13.90 only needs to be checked for slender columns where Li, the distance between maximum moment location and point of inflection, is greater than 4D, i.e., M/(VD) > 4. Note that all of the above considerations apply to circular columns. 13.6.1.2 Design of Flexural Confinement Retrofits For confinement of flexural plastic hinge regions where the ultimate jacket stress controls the design, a long-term durability strength reduction factor of 0.9 should be employed for the carbon jacket design. For other composite materials appropriate strength reduction factors based on their expected durability characteristics should be assigned. Circular columns: For circular columns with column diameter D, longitudinal reinforcement ratio ρ, expected concrete strength fc' , axial load P, gross section area Ag, and ultimate jacket modulus fju, the carbon jacket thickness t can be determined as:

tj =

Dfc' 4.5 f ju

 P  0.5 + 1.25 '  + 0.13 (ρl − 0.01) fc Ag  

(13.91)

The resulting member ductility should be checked based on Equations 13.81 to 13.84. Alternatively, for a given member ductility µ∆ and required ultimate concrete strain εcu : t j = 0.09

D (ε cu − 0.004) fcc' 0.9 f ju ε ju

= 0.1

D (ε cu − 0.004) fcc' f ju ε ju

(13.92)

can be provided. To prevent column bar buckling for columns with shear span L D = M (V ⋅ D) > 4 a minimum jacket thickness of: tj =

nD [in. ] E j [ ksi ]

(13.93)

should be provided. Rectangular columns: For side aspect ratios ≤ 1.5, rectangular columns can be retrofitted for flexural confinement with rectangular jackets under the following design considerations: 1. The corners need to be rounded to a radius of ≥ 2 in. (1 in. was used in the laboratory tests) 2. The jacket thickness t should be twice that determined from a column with equivalent circular jacket diameter De



13-43


In all other cases where the side aspect ratio > 1.5, oval or circular carbon jackets should be designed by adding oval or circular concrete segments to the bridge column sides prior to wrapping and curing. Extent of flexural hinge confinement retrofit: The jacket thickness tj must be extended beyond the expected plastic hinge region. For bridge columns with typical axial load ratios P / ( fc' Ag ) ≤ 0.3, the confinement length Lc1 should be greater than L/8 and greater than 0.5D, measured from the location of maximum moment. In addition, a reduced jacket thickness of 0.5tj should be extended for a distance Lc2 defined by the same criteria as Lc1 but starting at Lc1. Furthermore, where jackets and/or concrete bolsters add significantly to the column dimension in the loading direction, a gap g between the retrofit measure and the adjacent bridge bent member (cap or footing) needs to be provided to avoid any strength and stiffness increase from the retrofit. For most bridge columns and retrofits a gap of 2 in. (51 mm) is sufficient to meet this objective. Other gap widths can be explicitly calculated based on the maximum expected hinge rotation and column bar buckling considerations. Shear retrofit: Carbon jackets of thickness tj contribute an additional or fourth term to the shear resistance mechanism outlined in Equation 13.39 in the form: π f t D cot θ (circular) 2 jd j V j = 2 f jd t j D cot θ (rectangular) Vj =

(13.94)

where tj is the carbon jacket thickness, fjd the design stress level in the jacket, and D the column dimension in the loading direction. Again, conservatively, a 45° force transfer mechanism, or cot θ = 1 can be assumed for the jacket design. While Equation 13.94 clearly indicates that the jacket contribution depends on the jacket stress, a stress level less than the ultimate capacity fju is assumed to limit the horizontal column dilation. Tests at UCSD [Priestley et al., 1993a, 1993b; Priestley and Seible, 1991] have shown that, when the column dilation exceeds 0.4 to 0.6% in the loading direction, the concrete contribution to the shear capacity degrades rapidly, thus a strain limit rather than a strength limit needs to be employed for the jacket design. A strain limit of εjd = 0.4% is a conservative design value, which is well below the ultimate strain limit of −1% for carbon jacket but higher than the yield strain of the horizontal column reinforcement, which will ensure that the column reinforcement shear contribution in Equation 13.42 will be fully activated. Thus, in Equation 13.94: f jd = 0.004 E j

(13.95)

should be used for the composite jacket shear design. The carbon jacket shear retrofit design can be summarized as follows. The shear design demand originates, based on the capacity design principles, from the plastic column shear or the shear at full over strength Vo . With a shear strength reduction factor φ = 0.85, the column shear design requires that: Vn = Vc + Vs + Vp + V j ≥

Vo φ

(13.96)

Unless more reliable actual plastic shear information is available Vo can be conservatively estimated as 1.5 times Vyi or 1.5 times the ideal shear capacity of the column at ductility µ∆ = 1, or: Vj ≥


(

Vo − Vc + Vs + Vp φ

)

(13.97)


13-44


For circular columns the jacket thickness tj can be determined as:

(

)

(

)

Vo − Vc + Vs + Vp  159  Vo φ = − Vc + Vs + Vp  tj =  π E jD  φ  ⋅ 0.004E j ⋅ D 2

(

)

(13.98)

and for rectangular columns: Vo − Vc + Vs + Vp  125  Vo φ = − Vc + Vs + Vp  tj =  2 × 0.004 E j ⋅ D E jD  φ 

(

)

(13.99)

Since the concrete shear contribution Vc is different inside the plastic hinge confinement region (Lc) and outside (Lv), two jacket thicknesses for shear have to be derived and provided over the regions Liv and Lov , respectively. To avoid shear problems within and in direct proximity to the flexural plastic hinge, the shear retrofit length Liv should be extended to Liv = 1.5D or one and a half times the column dimension in the loading direction measured from the point of maximum moment.

13.6.2 Buildings 13.6.2.1 Problem Statement The soft first story concept [Fintel and Khan, 1969] is an attempt to reduce accelerations in a building by allowing the first-story columns to yield during an earthquake and produce energy-dissipation action. However, excessive drifts in the first story coupled with P-∆ effects on the yielded columns make buildings collapse [Fintel, 1991]. Hence, seismic retrofit of these kinds of buildings is needed. The problem can be corrected by either introducing additional energy dissipation capacity in order to reduce first-story energy or by providing a mechanism to reduce P-∆ effects or both. Such modifications of the soft first story concept are now a reality [Boardman et al., 1983]. More recently, nonductile columns fitted with Teflon sliders were suggested to reduce P-∆ effects on building design [Chen and Constantinou, 1990]. However, it is not practical because nonductile columns to resist strong earthquake forces and remain elastic are not economical. In general, it is accepted that inelastic behavior and thus damage to the building will occur. Inelastic action has the effect of lengthening the fundamental period of the building and of generating damping or energy-absorbing action and in this way reducing the accelerations at the upper levels of the building. The goal should be to reduce the accelerations in buildings to be less than the ground accelerations, and to do this the building must be flexible. Flexibility in a structural frame will cause problems in the fabric of the building. Windows may fall out in the wind; partition walls will crack; floors will vibrate under foot. In a low- or medium-rise building the necessary flexibility can only be achieved at the foundation level by the use of base isolation [Kelly, 1986]. A new approach was proposed by Mo and Cheng [1993]. In this system, Teflon sliders are placed on the top of the first story reinforced concrete framed shear walls. These shear walls are framed by columns and beams, and are designed to carry a portion of the weight of the superstructure and the lateral load determined by the frictional characteristics of the Teflon sliders. The remaining first-story columns are designed for ductile behavior in order to accommodate large drifts. According to this proposed system, an analytical model is described. To determine the effects of variables on the dynamic response of the proposed system, parametric studies are performed, and the results are discussed in detail. 13.6.2.2 Proposed System In the proposed system a major part of the weight of the building is carried by the Teflon sliders placed on top of the most heavily loaded shear wall of the first story. The least loaded columns on the first floor © 2003 by CRC Press LLC


13-45


(a)

(b) m7

m7

K7

4.8 m K7 4.2 m 3.75 m 3.75 m 3.75 m 3.75 m

m1

m1 A

4.2 m

K1 6.2 m

2.7 m 3.9 m

mS kS

K1DC

Shear wall Teflon Slider

(c)

(d) A

m7 K7

I st floor Teflon sheet Stainless steel plate

Shear wall m1

mS Pf(t)

K1DC

kS

FIGURE 13.28 (a) Reinforced concrete seven-story frame; (b) model of the proposed system; (c) detail of the firststory shear wall with Teflon sliders on top; (d) dynamic model of the proposed system.

(termed ductile columns) are designed to accommodate large drifts. Figure 13.28a shows a reinforced concrete seven-story frame. This structure is a hospital located in Tianjing City, China. When the proposed system is applied to this structure, it becomes the form shown in Figure 13.28b. A portion of the weight of the structure is carried by the first-story shear wall, which is fitted with Teflon sliders on top. The first-story shear wall is designed for a lateral load determined by the frictional characteristics of the Teflon sliders [Constantinou et al., 1990]. The proposed system is also able to reduce P-∆ effects, when a framed shear wall is used. The lateral force is shared by the ductile columns and the framed shear wall, which behave in distinctly different ways. Drift in the framed shear wall is very small and P-∆ effects are, therefore, insignificant. 13.6.2.3 Computer Model To illustrate the analytical model of the proposed system, the hospital mentioned previously is employed again. It should be noted that Figure 13.28a is a conventional frame structure; Figure 13.28b is a proposed system; Figure 13.28c is a detailing for the first-story shear wall with Teflon sliders on top; Figure 13.28d © 2003 by CRC Press LLC


13-46


is the dynamic model for the proposed system. In Figure 13.28c, uplift control is not considered because for reinforced concrete construction of up to seven stories, uplift on the bearing will not occur and will be unimportant [Kelly, 1986]. The stiffness of the shear wall, ks, varies depending on stress level. The first-story ductile columns have total initial stiffness K1DC and yield displacement Y1DC given by: K1DC = K1 (1 − n)

(13.100)

Y1DC = Y1R

(13.101)

in which n is the portion of weight carried by the sliders normalized by the total weight, K1 and Y1 are the initial stiffness and yield displacement, respectively, of the first story of the conventionally designed structure, and R is a reduction factor applied to the yield displacement of the first-story columns of the conventional design. The shear wall together with its beam is treated as an inelastic single degree of freedom system with mass, ms: 1 ms = nm1 3

(13.102)

where m1 is the mass at the first floor. The factor 1/3 in Equation 13.102 reflects the fact that the mass of the beam at the top of the shear wall is less than that of the first floor [Chen and Constantinou, 1990]. When R = 1.0 and n = 0.0, we have the conventional design. For n = 0.0, and R less than unity we have a conventional soft first story [Chopra et al., 1973]. Other combinations of n and R result in systems with the characteristics of the proposed system. The equations of motion of the system are: MX˙˙ + CX˙ + KX + Pf = − MX˙˙ g

(13.103)

ms x˙˙s + c s x˙ s + ks x s − p f = −ms X˙˙ g

(13.104)

in which M, C, and K are the mass, damping, and stiffness matrices, respectively. X˙˙ g is the ground acceleration and X is the floor displacement vector with respect to the ground. KX represents the vector of the restoring forces, which are described by Takeda’s degrading stiffness model [Takeda et al., 1970]. ms, cs, and ks are mass, damping, and stiffness, respectively, for the shear wall. xs represents the displacement of the top of the shear wall with respect to ground. ksxs is the restoring force in the shear wall, which is described by Mo’s model [Mo, 1988; Jost and Mo, 1991]. Pf is the vector of frictional force which has one non-zero entry at the first-floor level equal to pf . pf is the frictional force mobilized at the sliding interfaces, and is described by the following equation [Constantinou et al., 1990; Mokha et al., 1990]: p f = µ( x˙ r ) nWZ

(13.105)

in which nW is the portion of the weight carried by the sliding bearings. Z is a parameter taking values in the range (−1, 1) and µ is the coefficient of sliding friction, which is a function of the relative velocity between the first floor and the top of the shear wall, x˙ r = x˙ 1 − x˙ s . For Teflon sliding against polished stainless steel of mirror finish the sliding coefficient of friction is given by:

(

µ = f max − Df × exp − a x˙ r

)

(13.106)

Experimentally determined parameters fmax, Df, and a are friction parameters and are given elsewhere [Mokha et al., 1990]. It should be noted that these parameters depend on the condition of interface and © 2003 by CRC Press LLC


13-47


TABLE 13.2 Parameters in Model of Friction of Teflon Bearings Bearing Pressure (MPa) 6.9 13.8 6.9

Type of Teflon

fmax

Df

a (s/m)

Unfilled Unfilled Glass filled at 15%

0.1193 0.0870 0.1461

0.0927 0.0695 0.1060

23.62 23.62 23.62

Source: Mokha, A. et al., 1990, J. Struct. Eng., 116(2), 438–454.

bearing pressure. fmax is the maximum value of the friction coefficient which is mobilized at large velocities. (fmax − Df) represents the value of the coefficient of friction at essentially zero velocity of sliding. For the cases studied, bearing pressure is 6.9 MPa for which fmax = 0.1193, Df = 0.0927, and a = 23.62 s/m (see Table 13.2). 13.6.2.4 Discussion The structural system described relies on the frictional properties of sliding bearings on top of the shear wall and on the energy absorption capability of a number of accurately designed ductile columns to protect the structure from large lateral forces. In this system the sliding bearings play an important role and, consequently, factors affecting their frictional properties are of paramount importance. The frictional properties of Teflon sliding bearings are influenced by a number of parameters. One of the most influential parameters is the velocity of sliding. This effect has been properly accounted for. However, the value of friction used has been based on experiments that were conducted on fresh and clean specimens with the load sustained for a short interval of time. The effects of surface contamination and dwell of load on the frictional properties are important considerations in design. Surface contamination is known to cause substantial increase in the coefficient of friction. Bearings in service should be provided with skirts or bellows to prevent airborne contamination. The effect of dwell of load is an important consideration in the system described because, unlike bridge applications, the bearings may sustain load for a number of years before any sliding movement occurs. This effect has been studied. A specimen had been under load for almost 2 years before testing. The effect of the 2-year dwell of load on the recorded frictional properties was found to be insignificant. Interestingly in these tests, the polished stainless steel plate in the testing arrangement, which had been stored in a highly humid environment, showed no deterioration and in particular no change in the degree of surface roughness. 13.6.2.5 Algorithm The procedures for the system being described are explained as follows (Figure 13.29). Right after initialization is performed, sliding friction force needs to be determined. As a result, the SDOF shear wall and the MDOF frame can be analyzed for seismic response. The remaining procedures are similar to those for pure frame systems. When the responses are found at the time ti+1, the same procedures as mentioned above are repeated for time until the end of the time history. The algorithm is demonstrated in Figure 13.29. 13.6.2.6 Parametric Studies 13.6.2.6.1 Shear Building Modeling The primary concern of these studies is whether the ductility demand and damage in the upper stories of a building with the proposed system are significantly reduced in comparison with the ductility demand and damage in the conventional design. For this purpose the 1940 El Centro motion, scaled to 0.4 g, is used. The structure analyzed is as shown in Figure 13.28. This structure is a reinforced concrete sevenstory hospital building, located in Tianjing City, China, and was designed according to the Chinese seismic design code for a 0.2 g peak ground acceleration. Following the 1976 Tangshan earthquake, in which the structure suffered a moderate degree of damage, a comprehensive study of it was performed. The actual mass, stiffness, and strength distribution of the structure were determined in the study. Table 13.3 presents the story initial stiffness, yield strength and displacement, and the floor weight in a © 2003 by CRC Press LLC


13-48


Initialize values Find sliding friction force Perform response analysis for SDOF shearwall Perform response analysis for MDOF frame Calculate incremental load

Calculate effective incremental load

Find incremental displacement for extended time interval

Calculate incremental acceleration for extended time interval

Calculate incremental acceleration for normal time interval

Calculate incremental velocity and displacement for normal time interval Calculate displacement and velocity at time ti+1 Calculate acceleration at time ti+1 Output displacement and force, etc.

FIGURE 13.29 Algorithm for dynamic analysis of the proposed system.

TABLE 13.3 Properties of Seven-Story Structure Story

Initial Stiffness Ki (kN/mm)

Yield Strength Yi (mm)

Yield Strength Fyi (kN)

Weight (kN)

1 2 3 4 5 6 7

64.5 63.4 72.2 72.1 68.7 52.3 16.8

17.70 17.28 13.09 10.01 8.56 8.21 15.93

1141 1095 951 722 588 430 268

1011 953 953 934 982 1059 751



13-49


(b) 7

7

6

6

5

5 n = 0.0 R = 1.0 R = 0.5 R = 0.3 R = 0.1

4 3 2 R

1.0

0.5

0.3

Story

Story

(a)

3 2

0.1

R

1

1.0

0.5

0.3

0.1

1 Drift 0.0119 0.0214 0.0281 0.0238

Drift 0.0042 0.0127 0.0186 0.0269 0

0 0.0

1.0

2.0 3.0 4.0 Ductility Demand

0.0

5.0

(c)

1.0


5.0

(d) 7

7

6

6

5

5 n = 0.5 R = 1.0 R = 0.5 R = 0.3 R = 0.1

4 3 2 R

1.0

0.5

0.3

Story

Story

n = 0.3 R = 1.0 R = 0.5 R = 0.3 R = 0.1

4

n = 0.8 R = 1.0 R = 0.5 R = 0.3 R = 0.1

4 3 2

0.1

R

1

1.0

0.5

0.3

0.1

1 Drift 0.0371 0.0340 0.0380 0.0414

Drift 0.0202 0.0300 0.0243 0.0295 0

0 0.0

1.0


5.0

0.0

1.0


5.0

FIGURE 13.30 Displacement response of seven-story structure for scaled El Centro motion.

shear-type representation of the structure. The total weight of the frame is 6643 kN and the fundamental period is 1.15 s. The shear wall used in these studies have the following properties: concrete compressive strength, fc' = 28 Mpa; longitudinal steel yield strength, fly = 420 Mpa; longitudinal steel ratio = 0.0025. The height, width, and thickness are 3.05 m, 4.41 m, and 12.7 cm, respectively, and the bearing pressure of Teflon sliders with unfilled sheet type remains 6.9 MPa for all the cases. Specific values considered are R = 1.0, 0.5, 0.3, and 0.1 and n = 0.0, 0.3, 0.5, and 0.8. For example, the case n = 0.5, R = 0.5 corresponds to a design in which 50% of the superstructure’s weight is carried by sliders and the yield displacement of the first-story ductile columns is half the yield displacement of the original conventional design. The results for ductility demand, damage assessment, fundamental mode shape, restoring forcedisplacement loops, and displacement-time history are discussed below. Figures 13.30 and 13.31 present the displacement ductility demands of the described seven-story building when subjected to the scaled El Centro motion and when the yield strength of the first story is reduced by factor R ( = 1.0, 0.5, 0.3, 0.1) and parameter n takes values of 0.0, 0.3, 0.5, and 0.8, respectively. The case n = 0.0 corresponds to the conventional soft first story. The drifts in the first stories are normalized by story height. Clearly, the ductility demand in the superstructure reduces with increasing values of n and decreasing values of R. Figure 13.32 shows the damage assessment of the described seven-story building when the double index criteria are used. The damage criterion proposed by Chen and Gong [1986], also plotted in Figure 13.32, distinguishes minor, moderate, and severe damage. Minor damage is defined with the occurrence of minor cracks with partial crashing of concrete in columns. Moderate damage corresponds to the occurrence of extensive large cracks, whereas severe damage corresponds to extensive crushing of concrete or collapse. Minor and moderate damage are considered repairable. It can be seen that the damage indices reduce quite a lot when R = 1.0 and n = 0.0 are changed to R = 1.0 and n = 0.5, and the © 2003 by CRC Press LLC


13-50


(b) 7

7

6

6

5

5 R = 1.0 n = 0.0 n = 0.3 n = 0.5 n = 0.8

4 3 2 n

0.0

0.3

0.5

Story

Story

(a)

R = 0.5 n = 0.0 n = 0.3 n = 0.5 n = 0.8

4 3 2

0.8

n

1

0.3

0.5

0.8

Drift 0.0127 0.0214 0.0300 0.0340

0

0 0.0

1.0


5.0

(c)

0.0

1.0


5.0

(d) 7

7

6

6

5

5 R = 0.3 n = 0.0 n = 0.3 n = 0.5 n = 0.8

4 3 2 n

0.0

0.3

0.5

Story

Story

0.0

1 Drift 0.0042 0.0119 0.0202 0.0371

R = 0.1 n = 0.0 n = 0.3 n = 0.5 n = 0.8

4 3 2

0.8

n

1

0.0

0.3

0.5

0.8

1 Drift 0.0186 0.0281 0.0243 0.0380

Drift 0.0269 0.0238 0.0295 0.0414

0

0 0.0

1.0


5.0

0.0

1.0


5.0

FIGURE 13.31 Displacement ductility response of seven-story structure for scaled (0.4 g) 1040 El Centro motion. Drift is normalized by story height (n varies).

7.0 6.0 5.0 Energy Index

Severe damage 4.0 R = 1.0 ; n = 0.0 R = 1.0 ; n = 0.5 R = 0.5 ; n = 0.5

3.0

2.0

Moderate Minor

1.0

No damage 0.0 0.0

1.0

2.0

3.0 4.0 5.0 Ductility Index

FIGURE 13.32 Damage assessment of the seven-story structure.


6.0

7.0


13-51


TABLE 13.4 Natural Period of First Four Modes of Each Case (in sec) Case

Mode 1

Mode 2

Mode 3

Mode 4

C n n n

1.147 1.209 1.310 1.679

0.452 0.466 0.480 0.524

0.302 0.312 0.321 0.338

0.213 0.220 0.225 0.233

3.0

R = 1.0 ; n = 0.0 R = 1.0 ; n = 0.8

Displacement (cm)

2.0 1.0 0.0 −1.0 −2.0 −3.0 0.0

2.0

4.0 6.0 Time (sec.)

8.0

10.0

FIGURE 13.33 Displacement-time history for the top story.

damage indices further reduce significantly when both R and n are changed to 0.5 (i.e., severe damage becomes no damage). The effect of parameter n on the natural period of the seven-story building is also studied. Table 13.4 gives the results for the first four modes. It can be seen from Table 13.4 that the natural period is increased with increasing values of n. Finally, Figure 13.33 gives the deflection-time history for the top story with R = 1.0 and n = 0.0 or 0.8. Clearly, the deflection reduces significantly when parameter n is changed from 0.0 to 0.8. 13.6.2.6.2 Two-Dimensional Modeling The primary concern of these studies is whether the energy dissipation and story drift in the upper stories of a building with the proposed system are significantly reduced in comparison with those in the conventional design. For this purpose the 1940 El Centro motion, scaled to 0.4 g, is used. The structure analyzed is shown in Figure 13.34. The properties of this structure are also shown in this figure. The shear wall used in these studies has the following properties: concrete compressive strength, fc' = 31.1 MPa; longitudinal steel yield strength, fly = 350 MPa; longitudinal steel ratio = 0.0025. The height, width, and thickness are 27.9 cm, 30.5 cm, and 5.0 cm, respectively, and the bearing pressure of Teflon sliders with unfilled sheet type keeps 6.9 MPa [Chen and Constantinou, 1990] for all the cases. Specific values considered are R = 1.0, 0.5, 0.3, and 0.1 and n = 0.0, 0.3, 0.5, and 0.8. For example, the case n = 0.5, R = 0.5 corresponds to a design in which 50% of the superstructure’s weight is carried by sliders and the yield displacement of the first-story ductile columns is half of the yield displacement of the original conventional design. The results for moment-curvature hysteretic loops, steel yield locations, normalized drifts, and displacement history are discussed. Figures 13.35 and 13.36 show the moment-curvature hysteretic loops of the exterior column in the first story. Figure 13.35 indicates the results for the cases when R = 0.5 and n varies, while Figure 13.36 shows those for n = 0.5 and R varies. It can be seen from Figure 13.35 that the energy dissipated by the moment-curvature hysteretic loops increases with increasing value of n. It can also be seen from Figure 13.36 that for the case when R = 1.0 and n = 0.5, the moment-curvature relationship is linear © 2003 by CRC Press LLC


13-52


3 @ 305 mm

1

1

2

2

279 mm

2

2

2

2

3

4

4

3

= 0.227 N-sec2 / mm

2

2

2

mass per floor

3

3

3

3

As2 = 12.75 mm2

2

2

2

As1 = 8.5 mm2

3

3

3

3

fcy = 31.1 MPa

2

2

2

fsy = 350 MPa

3

3

3

3

ρc = 0.268

2

2

2

ρs = 0.0039

3

3

3

3

Ec = 20,733 MPa

2

2

2

Es = 200,000 MPa

3

3

3

3

3

3

3

3

3

3

3 1

8 @ 229 mm

1

1

1

3

3

3

3

3

39 mm

39 mm 6.36

39 mm

As1

As2 6.36

6.36

As2 6.36

As1

section 1

4

4

4

4

50.9 mm

279 mm

cross-section type

39 mm 38.1 mm

1

1

1

section 2 section 3

section 4

FIGURE 13.34 A ten-story frame.

(i.e., no energy dissipated), and the case with R = 0.5 and n = 0.5 has greater energy dissipations than the remaining cases. Figures 13.37 and 13.38 show the steel yield locations in the frame. Figure 13.37 indicates the results for the cases when n = 0.5 and R varies, while Figure 13.38 shows those for R = 0.3 and n varies. It can be seen from Figure 13.37 that the number of steel yield locations decreases with decreasing the value of R. It can also be seen from Figure 13.38 that the number of steel yielding locations decreases with increasing the value of n. In conclusion, a new system for the seismic retrofitted reinforced concrete buildings has been presented, in which first-story shear walls are fitted with Teflon sliders while the remaining first-story columns are designed with reduced yield strength. With this system energy dissipation is increased and the number of steel yield locations, normalized story drifts, and displacements in the superstructure are significantly reduced. © 2003 by CRC Press LLC


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21000

21000

case ; R = 0.5 ; n = 0.0

7000 0 −7000 −14000

7000 0 −7000 −14000

−21000 −0.05

18000

−0.02 0.00 0.02 Curvature (1/cm)

−21000 −0.05

0.05

15000

case ; R = 0.5 ; n = 0.5

−0.03 0.00 0.03 Curvature (1/cm)

0.06

case ; R = 0.6 ; n = 0.6

10000 Moment (N-cm)

12000 Moment (N-cm)

case ; R = 0.5 ; n = 0.3

14000 Moment (N-cm)

Moment (N-cm)

14000

6000 0 −6000 −12000

5000 0 −5000 −10000

−18000 −0.07

−0.03 0.00 0.03 Curvature (1/cm)

−15000 −0.12

0.07

−0.06 0.00 0.06 Curvature (1/cm)

0.12

FIGURE 13.35 Restoring moment curvature loops of the first story.

18000

18000

case ; R = 1.0 ; n = 0.5

6000 0 −6000

6000 0 −6000

−12000

−12000

−18000 −0.0012 −0.0006 −0.0000 0.0006 0.0012 Curvature (1/cm)

−18000 −0.07

15000

10600

case ; R = 0.5 ; n = 0.5

5000 0 −5000 −10000 −15000 −0.10

−0.00 0.03 Curvature (1/cm)

0.07

case ; R = 0.1 ; n = 0.5

3600 0 −3600 −7000

−0.06


0.10

−10600 −0.07

FIGURE 13.36 Restoring moment curvature loops of the first story.


−0.03

7000 Moment (N-cm)

10000 Moment (N-cm)

case ; R = 0.5 ; n = 0.5

12000 Moment (N-cm)

Moment (N-cm)

12000

−0.03


0.07


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R = 1.0 ; n = 0.5

R = 0.5 ; n = 0.5

R = 0.3 ; n = 0.5

R = 0.1 ; n = 0.5

indicates “already yielded” FIGURE 13.37 Yielded locations in the plane frame with n = 0.5.

R = 0.3; n = 0.0

R = 0.3; n = 0.3

R = 0.3; n = 0.5

R = 0.3; n = 0.8

indicates “already yielded” FIGURE 13.38 Yielded locations in the plane frame with R = 0.3.

Defining Terms Bauschinger effect — In the reversed loading of steel, after loading past the yield point in one direction, the yield stress in the opposite direction is reduced. Column — A vertical member of approximately equal dimensions in both horizontal planes, and carrying vertical load. Columns may or may not be part of the lateral-force-resisting system. Confined concrete — Concrete is confined by transverse reinforcement, commonly in the form of closely spaced steel spirals or hoops to increase the ductility of concrete. Damage assessment — An assessment to evaluate the damage of a structure due to large loads. Damping coefficient — The ratio of the viscous damping to the critical damping.




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Ductility — The ratio between the maximum displacement for elastoplastic behavior and the displacement corresponding to yield point.

Energy dissipation — The area bounded by the hysteretic loops of the load-displacement relationships of a structure. Inelastic response — A structure is subjected to a large excitation, resulting in yielding of longitudinal rebars. Load-displacement relationship — The relationship between the load on a structure and the correspond displacement. Low-cycle fatigue — When a rebar is subjected to cyclic loading, the maximum strength is less than the maximum strength of monotonic tensile tests. Natural period — The time interval for a vibration system in free vibration to do one oscillation. P − ∆ effect — The secondary effect on shears, axial forces, and moments of frame members induced by the vertical loads on the laterally displaced building frame. Performance-based design — The integrated effort of design, construction, and maintenance needed to produce engineered facilities of predictable performance for multiple performance objectives. Pinching effect — When a structure is subjected to reversed cyclic loading, the deformation with a small load becomes very large at the beginning of the reloading state. Plastic hinge length — A region in which longitudinal rebars in a member yield. Residual deformation — The remaining deformation after unloading of a structure. Seismic retrofit — A retrofit may be completed if the results of the detailed seismic assessment indicate the seismic demand is greater than the capacity. Shear capacity — The capacity of a member to resist shear force. It is reduced with increasing ductility. Shear retrofit — If the shear demand is greater than the shear capacity, a shear retrofit is needed. Soft first story — An attempt to reduce accelerations in a building by allowing the first-story columns to yield during an earthquake and produce energy dissipation action. Softened branch relation — When a rebar is subjected to cyclic loading, the reversal branch of the stress-strain relationship in each hysteretic loop is a parabolic curve. Softened compression stress-strain relationship of concrete — Viewing the shear action on a membrane element as a two-dimensional problem, the compressive strength of concrete in one direction is reduced by cracking due to tension in the perpendicular direction. Softening parameter — When a membrane element is subjected to shear, the compressive strength of concrete is reduced to approximately 40% to 60%. Stress strain-strain curve of a steel bar in concrete — A steel bar in concrete is stiffened by tensile stress of concrete. It relates the average stress to the average strain of a large length of bar crossing several cracks. Structural wall — An in-plane wall to reduce the relative interstory distortions of a building caused by seismic-induced motions.

References Aboutaha, R.S., Engelhardt, M.D., Jirsa, J.O., and Kreger, M.E. (1999). “Rehabilitation of Shear Critical Concrete Columns by Use of Rectangular Steel Jackets,” ACI Struct. J., 96, 68–78. ACI Committee 318 (1995). Building Code Requirements for Reinforced Concrete (ACI 318–95), American Concrete Institute, Detroit, MI, p. 369. Aschhiem, M., Moehle, J.P., and Werner, S.D. (1992). Deformability of Concrete Columns, Project report under Contract No. 59Q122, California Department of Transportation, Division of Structure, Sacramento, CA, June. Balan, T., Filippou, F., and Popov, E. (1998). “Hysteretic Model of Ordinary and High-Strength Reinforcing Steel,” J. Struct. Eng. (ASCE), 124, 288–297. Belarbi, A. and Hsu, T.T.C. (1994). “Constitutive Laws of Concrete in Tension and Reinforcing Bars Stiffened by Concrete,” Struct. J. Am. Concrete Inst., 91, 465–474. © 2003 by CRC Press LLC


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Belarbi, A. and Hsu, T.T.C. (1995). “Constitutive Laws of Softened Concrete in Biaxial Tension-Compression,” Struct. J. Am. Concrete Inst, 92, 562–573. Blume, J.A. (1970). “Design of Earthquake-Resistant Poured-in-Place Concrete Structures,” in Earthquake Engineering, R.L. Wiegel, Ed., Prentice-Hall, Englewood Cliffs, NJ, chap. 18. Boardman, P.R., Wood, B.J., and Carr, A.J. (1983). “Union House: A Cross Braced Structure with Energy Dissipators,” Bull. NZ Nat. Soc. Earthquake Eng., 16, 83–97. Caltrans. (1995). Memo to Designers Change Letter 02, California Department of Transportation, Sacramento, CA, March. Chen, Y.Q. and Constantinou, M.C. (1990). “Use of Teflon Sliders in a Modification of the Concept of Soft First Story,” Eng. Struct., 12, 243–253. Chen, Y.Q. and Gong, S. (1986). “Double Control Damage Index of Structural Ductility and Dissipated Energy during Earthquakes,” Chinese J. Building Struct., 7, 35–48 (in Chinese). Chopra, A.K., Clough, D.P., and Clough, R.W. (1973). “Earthquake Resistance of Buildings with a Soft First Story,” Earthquake Eng. Struct. Dyn., 1, 347–355. Constantinou, M.C., Mokha, A., and Reinhorn, A.M. (1990). “Teflon Bearings in Base Isolation. II. Modeling,” J. Struct. Eng. ASCE, 116, 455–475. Cusson, D. and Paultre, P. (1995). “Stress-Strain Model for Confined High-Strength Concrete,” J. Struct. Eng. ASCE, 121, 468–478. Diniz, M.C. and Frangopol, M. (1997). “Strength and Ductility Simulation of High-Strength Concrete Columns,” J. Struct. Eng. ASCE, 123, 1365–1373. Eibl, J. and Neuroth, U. (1988). Untersuchungen zur Druckfestigkeit von bewehrtem Beton bei gleichzeitig wirkendem Querzug, Institut für Massivbau and Baustofftechnologie, Universität Karlsruhe, Germany. Fajfar, P. and Krawinkler, H. (1998). “Seismic Design Methodologies for the Next Generation of Codes,” Proc. Sixth SECED Conference on Seismic Design Practice into the Next Century, Oxford, U.K., March 26–27, pp. 459–466. FEMA (Federal Emergency Management Agency) (2000a). “Prestandard and Commentary for the Seismic Rehabilitation of Buildings,” FEMA 356, Federal Emergency Management Agency, Washington, D.C., November. FEMA (Federal Emergency Management Agency) (2000b). “Global Topics Report on the Prestandard and Commentary for the Seismic Rehabilitation of Buildings,” FEMA 357, Federal Emergency Management Agency, Washington, D.C., November. Fintel, M. (1991). “Shearwalls: An Answer for Seismic Resistance?” Concrete International, July, 48–53. Fintel, M. and Khan, F.R. (1969). “Shock-Absorbing Soft Story Concept for Multistory Earthquake Structures,” ACIJ, 66, 381–390. Fujii, M., Kobayashi, K., Miyagawa,T., Inoue, S., and Matsumoto, T. (1988). “A Study on the Application of a Stress-Strain Relation of Confined Concrete,” Proc. JCA Cement Concrete, Japan Cement Assn., Tokyo, Japan, vol. 42, 311–313. Gergely, I., Pantelides, C.P., Nuismer, R.J., and Reaveley, L.D. (1998). “Bridge Pier Retrofit Using FiberReinforced Plastic Composites,” J. Composites Construct., 2, 165–174. Hoshikuma, J., Kawashima, K., Nagaya, K., and Taylor, A.W. (1997). “Stress-Strain for Reinforced Concrete in Bridge Piers,” J. Struct. Eng. ASCE, 123, 624–633. Hsu, T.T.C. (1993). Unified Theory of Reinforced Concrete, CRC Press, Boca Raton, FL. Hsu, T.T.C. and Mo, Y.L. (1985). “Softening of Concrete in Low-Rise Shear Walls,” J. Am. Concrete Inst., 82, 883–889. Hsu, T.T.C. and Zhang, L.X. (1997). “Nonlinear Analysis of Membrane Elements by Fixed-Angle SoftenedTruss Model,” J. Am. Concrete Inst., 94, 483–492. Hsu, T.T.C. and Zhu, R.H. (1999). “Post-Yield Behavior of Reinforced Concrete Membrane Elements: The Hsu/Zhu Ratios,” Proceedings Volume, U.S.–Japan Joint Seminar on Post-Peak Behavior of Reinforced Concrete Structures Subjected to Seismic Loads, Recent Advances and Challenges on Analysis and Design, Tokyo/Lake Yamanaka, Japan, Oct. 25–29, 1999, vol. 1, pp. 43–60. © 2003 by CRC Press LLC



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IBC (2000). International Building Code, International Code Council, Inc., International Conference of Building Officials, Whittier, CA. Iemura, H. and Takahashi, Y. (2001). “Development of High Seismic Performance RC Piers with Unbonded Bars,” Workshop on High Performance Materials in Bridges and Buildings, Hona, HI, July 29–August 3. Jost, S.D. and Mo, Y.L. (1991). “An Algorithm for Seismic Analysis of Low-Rise Structural Walls,” Nuclear Eng. Des., 131, 263–270. Karsan, I.D. and Jirsa, J.O. (1969). “Behavior of Concrete under Compressive Loadings,” J. Struct. Eng. ASCE, 95, 2543–2563. Kelly, J.M. (1986). “Aseismic Base Isolation: Review and Bibliography,” Soil Dyn. Earthquake Eng., 5, 202–216. Kent, D.C. and Park, R. (1971). “Flexural Members with Confined Concrete,” J. Struct. Div. ASCE, 97, 1969–1990. Kollegger, J. and Mehlhorn, G. (1990). “Experimentell Untersuchungen zur Bestimmung der Druckfestigkeit des gerissenen Stahlbetons bei einer Querzugbean-spruchung,” Report 413, Deutscher Ausschuβ für Stahlbetons, Berlin, Germany. Krawinkler, H. (1998). “Issues and Challenges in Performance Based Seismic Design,” Structural Engineers World Congress, San Francisco, CA, July 19–23. Mander, J.B. (1983). “Seismic Design of Bridge Piers,” Ph.D. thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, chap. 8. Mander, J.B., Priestley, M.J.N., and Park, R. (1988a). “Theoretical Stress-Strain Model for Confined Concrete,” J. Struct. Div. ASCE, 114, 1804–1826. Mander, J.B., Priestley, M.J.N., and Park, R. (1988b). “Observed Stress-Strain Behavior of Confined Concrete,” J. Struct. Div. ASCE, 97, 1969–1990. Mander, J.B., Panthaki, F.D., and Kasalanati, A. (1994). “Low-Cycle Fatigue Behavior of Reinforcing Steel,” C J. Mat. Civ. Eng. ASCE, 6, 453–468. Mansour, M.Y. (2001). “Behavior of Reinforced Concrete Membrane Elements under Cyclic Shear: Experiments to Theory,” Ph.D. thesis, Department of Civil and Environmental Engineering, University of Houston, Houston, TX. Mansour, M.Y., Hsu, T.T.C., and Lee, J.Y. (2001a). “Cyclic Stress-Strain Curve of Concrete and Steel Bars in Membrane Elements,” J. Struct. Eng. ASCE, 127, 1402–1411. Mansour, M.Y., Hsu, T.T.C., and Lee, J.Y. (2001b). “Pinching Effect in Hysteretic Loops of R/C Shear Elements,” ACI Special Publication, American Concrete Institute, Toronto, Canada. MCEER (Multidisciplinary Center for Earthquake Engineering Research) (2000). “The Chi-Chi, Taiwan Earthquake of September 21, 1999: Reconnaissance Report,” Technical Report MCEER-00–0003, State University of New York at Buffalo. Mikame, A., Uchida, K., and Noguchi, H. (1991). “A Study of Compressive Deterioration of Cracked Concrete,” Proc. Int. Workshop on Finite Element Analysis of Reinforced Concrete, Columbia University, New York. Miyahara, T., Kawakami, T., and Maekawa, K. (1988). “Nonlinear Behavior of Cracked Reinforced Concrete Plate Element under Uniaxial Compression,” Concrete Library International, Japan Soc. Civ. Eng., 11, 131–144. Mo, Y.L. (1987). “Discussion of ‘Shear Design and Analysis of Low-Rise Structural Walls,’ by S.T. Mau and T.T.C. Hsu,” ACI Struct. J., 84, 91–92. Mo, Y.L. (1988). “Analysis and Design of Low-Rise Structural Walls under Dynamically Applied Shear Forces,” ACI Struct. J., 85, 180–189. Mo, Y.L. (1994). Dynamic Behavior of Concrete Structures, Elsevier, Amsterdam, 37–38. Mo, Y.L. and Chang, Y.F. (1993). “Effect of First Story Shearwalls with Teflon Sliders on EarthquakeResistant Buildings,” Mag. Concrete Res., 45, 293–299. Mo, Y.L. and Jost, S.D. (1993). “Tool for Dynamic Analysis of Reinforced Concrete Framed Shearwalls,” Comp. Struct., 46, 659–667. © 2003 by CRC Press LLC


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Mo, Y.L. and Kuo, J.Y. (1998). “Experimental Studies on Low-Rise Structural Walls,” Mat. Struct., RILEM, 31, 465–472. Mo, Y.L. and Perng, S.F. (2000). “Hybrid RC Frame-Steel Wall Systems,” SP-196, ACI Special Publication on Composite and Hybrid Systems, American Concrete Institute, Detroit, MI, pp. 189–213. Mo, Y.L. and Perng, S.F. (in press). “Analytical Model for Hybrid RC Frame-Steel Wall Systems,” ACI Fall Convention, Dallas, TX, American Concrete Institute. Mo, Y.L. and Rothert, H. (1997). “Effect of Softening Models on Behavior of Reinforced Concrete Framed Shearwalls,” ACI Struct. J., 94, 730–744. Mo, Y.L. and Shiau, W.C. (1993). “Ductility of Low-Rise Structural Walls,” Mag. Concrete Res., 45, 131–138. Mo, Y.L. and Yang, R.Y. (1996). “Dynamic Response of Box Tubes to Combined Shear and Torsion,” J. Struct. Eng. ASCE, 122, 47–54. Mokha, A., Constantinou, M.C., and Reinhorn, A.M. (1990). “Teflon Bearing in Base Isolation. I. Testing,” J. Struct. Eng. ASCE, 116, 438–454. Monti, G. and Nuti, C. (1992). “Nonlinear Cyclic Behavior of Reinforcing Bars Including Buckling,” J. Struct. Eng. ASCE, 118, 3268–3284. Muguruma, H., Watanabe, S., Tanaka, S., Sakurai, K., and Nakaruma, E. (1978a). “A Study on the Improvement of Bending Ultimate Strain of Concrete,” Proc. J. Struct. Eng., 24, 109–116. Muguruma, H., Watanabe, S., and Tanaka, S. (1978b). “A Stress-Strain Model of Confined Concrete,” Proc. JCA Cement and Concrete, Japan Cement Assn., Tokyo, Japan, vol. 34, pp. 429–432. Nawy, E.G. (1996). Reinforced Concrete — A Fundamental Approach, 3rd ed., Prentice-Hall, Upper Saddle River, NJ. Pang, X.B. and Hsu, T.T.C. (1995). “Behavior of Reinforced Concrete Membrane Elements in Shear,” Struct. J. Am. Concrete Inst., 92, 665–679. Pang, X.B. and Hsu, T.T.C. (1996). “Fixed-Angle Softened-Truss Model for Reinforced Concrete,” Struct. J. Am. Concrete Inst., 93, 197–207. Park, R. and Paulay, T. (1975). Reinforced Concrete Structures, John Wiley & Sons, New York. Park, R., Priestley, M.J.N., and Gill, W.D. (1982). “Ductility of Square-Confined Concrete Columns,” J. Struct. Div. ASCE, 108, 929–950. Peter, J. (1964). “Zur Bewehrung von Scheiben and Schalen für Hauptspannungen schiefwinklig zur Bewehrungsrichtung,” Dissertation, Lehrstuhl für Massivbau, Technische Hochschule Stuttgart, Germany. Priestley, M.J.N. and Seible, F., Eds. (1991). “Seismic Assessment and Retrofit of Bridges,” Structural Systems Research Project, Report No. SSRP-93/06, University of California, San Diego, CA, July, p. 426. Priestley, M.J.N., Seible, F., Verma, R., and Xiao, Y. (1993a). “Seismic Shear Strength of Reinforced Concrete Columns,” Structural Systems Research Project, Report No. SSRP-93/06, University of California, San Diego, CA, July, p. 120. Priestley, M.J.N., Verma, R., and Xiao, Y. (1993b). “Shear Strength of Reinforcement Concrete Bridge Columns,” Second Annual Seismic Research Workshop, Caltrans, Division of Structures, March 16–18. Priestley, M.J.N., Verma, R., and Xiao Y. (1994). “Seismic Shear Strength of Reinforcement Concrete Columns,” J. Struct. Eng. ASCE, 120, 2310–2329. Priestley, M.J.N., Seible, F., and Calvi, G.M. (1996). Seismic Design and Retrofit of Bridges, John Wiley & Sons, New York, pp. 147, 686. Razvi, S.R. and Saatcioglu, M. (1999). “Confinement Model for High-Strength Concrete,” J. Struct. Eng. ASCE, 125, 281–289. Robinson, J.R. and Demorieux, J.M. (1968). “Essais de Traction-Compression sur Modeles d’Âme de Poutre en Beton Arme,” Institute de Recherches Appliquées du Beton Arme (IRABA). Part I, June. Robinson, J.R. and Demorieux, J.M. (1972). “Essais de Traction-Compression sur Modeles d’Âme de Poutre en Beton Arme,” Institut de Recherches Appliquées du Beton Arme (IRABA). Part II, May. Rodriguez, M.E., Botero, J.C., and Villa, J. (1999). “Cyclic Stress-Strain Behavior of Reinforcing Steel Including Effect of Buckling,” J. Struct. Eng. ASCE, 125, 605–612. © 2003 by CRC Press LLC



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Saadatmanesh, H., Ehsani, M.R., and Jin, L. (1996). “Seismic Strengthening of Circular Bridge Pier Models with Fiber Composites,” ACI Struct. J., 93, 639–647. Saatcioglu, M. and Razvi, S.R. (1992). “Strength and Ductility of Confined Concrete,” J. Struct. Div. ASCE, 118, 1590–1607. Schlaich, J. and Schafer, K. (1983). “Zur Druck-Querzug-Festigkeit des Stahlbetons,” Beton-and Stahlbetonbau, March, pp. 73–78. Schlaich, J., Schafer, K., and Schelling, G. (1982). Druck und Querzug in bewehrten Betonelementen. Bericht, Institut für Massivbau, Universität Stuttgart, Germany, November. Seible, F. (1997). “Seismic Bridge Damage and Advanced Composite Retrofit of Bridge Columns,” Technical Seminar on Advanced Technologies for Bridge Infrastructure Renewal, National Taiwan University, Taipei, Taiwan, May 21–23. Seible, F., Hegemier, G.A., Priestley, M.J.N., Innamorato, D., Weeks, J., and Policelli, F. (1994a). “Carbon Fiber Jacket Retrofit Test of Circular Shear Bridge Column, CRC-2,” Advanced Composite Technology Transfer Consortium, Report No. ACTT-94/02, University of California, San Diego, September, p. 49. Seible, F., Hegemier, G.A., Priestley, M.J.N., and Innamorato, D. (1994b). “Seismic Retrofitting of Squat Circular Bridge Piers with Carbon Fiber Jackets,” Advanced Composites Technology Transfer Consortium, Report No. ACTT-94/04, University of California, San Diego, November, p. 55. Seible, F., Hegemier, G.A., Priestley, M.J.N., Innamorato, D., and Ho, F. (1995a). “Carbon Fiber Jacket Retrofit Test of Rectangular Flexural Column with Lap Spliced Reinforcement,” Advanced Composites Technology Transfer Consortium, Report No. ACTT-95/02, University of California, San Diego, June, p. 78. Seible, F., Hegemier, G.A., Priestley, M.J.N., Innamorato, D., and Ho, F. (1995b). “Rectangular Carbon Jacket Retrofit of Flexural Column with 5% Continuous Reinforcement,” Advanced Composites Technology Transfer Consortium, Report No. ACTT-95/03, University of California, San Diego, April, p. 52. Seible, F., Hegemier, G.A., Priestley, M.J.N., Innamorato, D., and Ho, F. (1995c). “Carbon Fiber Jacket Retrofit Test of Circular Flexural Columns with Lap Spliced Reinforcement,” Advanced Composites Technology Transfer Consortium, Report No. ACTT-95/04, University of California, San Diego, June, p. 78. Seible, F., Hegemier, G.A., Priestley, M.J.N., Innamorato, D., and Ho, F. (1995d). “Rectangular Carbon Jacket Retrofit Test of a Shear Column with 2.5% Reinforcement,” Advanced Composites Technology Transfer Consortium, Report No. ACTT-95/05, University of California, San Diego, July, p. 50. Seible, F., Priestley, M.J.N., Hegemier, G.A., and Innamorato, D. (1997). “Seismic Retrofit of RC Columns with Continuous Carbon Fiber Jackets,” J. Composites Construct. ASCE, 1, 52–62. Sheikh, S.A. and Uzumeri, S.M. (1980). “Strength and Ductility of Tied Concrete Columns,” J. Struct. Div. ASCE, 106, 1079–1102. Sheikh, S.A. and Uzumeri, S.M. (1982). “Analytical Model for Concrete Confinement in Tied Columns,” J. Struct. Div. ASCE, 108, 2703–2722. Sheikh, S.A., Shah, D.V., and Khoury S.S. (1994). “Confinement of High-Strength Concrete Columns,” ACI Struct. J., 123, 100–111. Sinha, B.P., Gerstle, K.H., and Tulin, L.G. (1964). “Stress-Strain Relation for Concrete under Cyclic Loading,” Am. Concrete Inst. J., 61, 195–211. Takeda, T., Sozen, M.A., and Nielsen, N.N. (1970). “Reinforced Concrete Response to Simulated Earthquakes,” Proc. ASCE, 96, 2557–2573. Takiguchi, K. et al. (1976). “Analysis of Reinforced Concrete Sections Subjected to Biaxial Bending Moments,” Trans. AIJ, 250, 1–8. UBC (1997). 1997 Uniform Building Code, International Conference of Building Officials, Whittier, CA. Ueda, M., Noguchi, H., Shirai, N., and Morita, S. (1991). “Introduction to Activity of New RC,” Proc. Int. Workshop on Finite Element Analysis of Reinforced Concrete, Columbia University, New York.



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Vecchio, F.J. and Collins, M.P. (1981). “Stress-Strain Characteristic of Reinforced Concrete in Pure Shear,” IABSE Colloquium, Advanced Mechanics of Reinforced Concrete, Delft, Final Report, International Association of Bridge and Structural Engineering, Zurich, Switzerland, pp. 221–225. Vecchio, F.J. and Collins, M.P. (1986). “The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear,” ACI Journal, 83, 219–231. Vecchio, F. and Collins, M.P. (1993). “Compression Response of Cracked Reinforced Concrete,” J. Struct. Eng. ASCE, 119, 3590–3610. Vecchio, F.J., Collins, M.P., and Aspiotis, J. (1994). “High-Strength Concrete Elements Subjected to Shear,” ACI Struct. J., 91, 423–433. Watanabe, F. and Nishiyana, M. (2001). “Controlled Yield Sequence of Reinforced in Concrete Memebers,” Workshop on High Performance Materials in Bridges and Buildings, Kona, HI, July 29–Aug.3. Watanabe, F., Lee, J.Y., and Nishiyama, M. (1995). “Structural Performance of Reinforced Concrete Columns with Different Grade Longitudinal Bars,” ACI Struct. J., 92, 412–418. Xiao, Y. and Martirossyan, A. (1998). “Seismic Performance of High-Strength Concrete Columns,” J. Struct. Eng. ASCE, 124, 241–251. Yeh, Y.K., Mo, Y.L., and Yang, C.Y. (2001). “Seismic Performance of Hollow Circular Bridge Piers,” ACI Struct. J., 98, 862–871. Yeh, Y.K., Mo, Y.L., and Yang, C.Y. (2002). “Seismic Performance of Rectangular Hollow Bridge Columns,” J. Struct. Eng. ASCE, 128, 60–68. Zhang, L.X. and Hsu, T.T.C. (1998). “Behavior and Analysis of 100 MPa Concrete Membrane Elements,” J. Struct. Eng. ASCE, 124, 24–34. Zhu, R.H. (2000). “Softened Membrane Model for Reinforced Concrete Elements Considering Poisson Effect.” Ph.D. thesis, Department of Civil and Environmental Engineering, University of Houston, Houston, TX. Zhu, R.H., Hsu, T.T.C., and Lee, J.Y. (2001). “A Rational Shear Modulus for Smeared Crack Analysis of Reinforced Concrete,” Struct. J. Am. Conc. Inst., 98, 343–350.

Further Reading Specific topics related to reinforced concrete structures subjected to earthquake loads can be found in the following references. Dowrick, D.J. (1987). Earthquake Resistant Design, 2nd edition, John Wiley & Sons, New York. FEMA (Federal Emergency Management Agency) (2000a). “Prestandard and Commentary for the Seismic Rehabilitation of Buildings,” FEMA 356, Federal Emergency Management Agency, Washington, D.C., November. FEMA (Federal Emergency Management Agency) (2000b). “Global Topics Report on the Prestandard and Commentary for the Seismic Rehabilitation of Buildings,” FEMA 357, Federal Emergency Management Agency, Washington, D.C., November. Hsu, T.T.C. (1993). Unified Theory of Reinforced Concrete, CRC Press, Boca Raton, FL. JSCE (Japan Society of Civil Engineers). (2000). Earthquake Resistant Design Codes in Japan, Earthquake Engineering Committee, Japan Society of Civil Engineers, Tokyo, Japan. Mo, Y.L. (1994). Dynamic Behavior of Concrete Structures, Elsevier, Amsterdam. Okamura, H. and Maekawa, K. (1991). Nonlinear Analysis and Constitutive Models of Reinforced Concrete, University of Tokyo, Tokyo, Japan. Naeim, F. and Kelly, J. M. (1999). Design of Seismic Isolated Structures, John Wiley & Sons, New York. Paulay, T. and Priestley, M.J.N. (1992). Seismic Design of Reinforced Concrete and Masonry Buildings, John Wiley & Sons, New York. Priestley, M.J.N., Seible, F., and Calvi, G.M. (1996). Seismic Design and Retrofit of Bridges, John Wiley & Sons, New York. Wakabayashi, M. (1986). Design of Earthquake-Resistant Buildings, McGraw-Hill, New York. Williams, A. (1998). Seismic Design of Buildings and Bridges, 2nd edition, Engineering Press, Austin, TX. © 2003 by CRC Press LLC


14

Precast and Tilt-Up Buildings 14.1 Introduction 14.2 Precast and Tilt-Up Buildings Precast Buildings · Tilt-Up Buildings

14.3 Performance of Precast and Tilt-Up Buildings in Earthquakes Precast Buildings · Tilt-Up Buildings

14.4 Code Provisions for Precast and Tilt-Up Buildings Precast Buildings · Tilt-Up Buildings

14.5 Seismic Evaluation and Rehabilitation of Tilt-Up Buildings

Charles Scawthorn Consulting Engineer Berkeley, CA

David L. McCormick ABS Consulting San Francisco, CA

Out-of-Plane Wall Anchors · Girder Anchorage Failures at Pilasters · Retrofit Details and Recommendations · Development of Wall Anchor Loads into Diaphragms · Retrofit Details and Recommendations · Collectors · Retrofit Details and Recommendations

Defining Terms References Further Reading

14.1 Introduction This chapter discusses seismic aspects of precast concrete and tilt-up buildings. Precast concrete refers to concrete components not cast in place but rather, cast off site (usually at precast yards) or in a location different from their final location. Precasting offers economies based on speed of construction and the use of the components as architectural elements. Precast1 components are typically beam, column, floor, roof, or wall units. This chapter addresses buildings assembled in part or entirely of such units, where the units perform a structural function.2 Precast components are typically used where a large number of identical units are required. Due to this mass production in a controlled environment, precast components usually have lower unit cost and more uniform and higher quality, more like a manufactured unit (which they are), than a field-fabricated reinforced concrete beam, for example. The size of precast building components is usually limited only by transport limits — that is, typically, by the largest components that can be transported by truck, or by crane or space limitations. Precast components often utilize prestressing, which is a structural concrete technique involving stresses introduced into the structural member prior to its service, typically similar in magnitude but opposite in

1

Precast is synonymous with precast concrete. Precast concrete components can also perform a nonstructural function, such as exterior building cladding, or precast concrete floor planks — however, this aspect is not addressed in this chapter. 2



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pattern to the stresses expected during the member’s service. Prestressing is usually achieved via highly tensioning steel cables or bars within the member, in such a manner that the tension forces in the steel cable or bar are transferred as compressive forces to the concrete member. Prestressed members can be either pretensioned in the casting yard (cables are pretensioned prior to casting concrete), or post-tensioned at the site, prior to the introduction of loads. Cables may be bonded or unbonded to the concrete. Precast concrete construction was first developed in the 1930s, but was not widely used until the 1960s. It is widely used in certain types of buildings in the United States, such as parking garages and low-rise commercial buildings, and is even more widely employed in certain other countries. In the western United States its use until recently has been limited primarily to gravity framing in parking structures, tilt-up buildings, and architectural cladding. Until recently, precast concrete frames have not been widely used to resist lateral loads in high seismic zones. Several efforts have been made over the last decade to change this situation. For example, the National Science Foundation (NSF), the Precast Concrete Institute (PCI), and the Prestressed/Precast Concrete Manufacturers Association (PCMAC) sponsored the PRESSS (Precast Structural Seismic Systems) program to develop innovative precast framing systems suitable for use in all seismic regions, and to produce comprehensive design guidelines. Recently in phase III of the PRESSS program a complete building was constructed and tested in the laboratory. The structure included precast components connected by unbonded prestressing. Although such structures have relatively little damping, they can undergo large deformations without yielding because the changes in strain are small. Consequently, such a structure will recenter itself after the ground motion stops [Stanton and Nakaki, 2001]. The reader is referred to papers generated as part of the PRESSS project for further information. The National Institute of Standards and Technology (NIST) has also sponsored related research. Several projects have been completed using the results of these studies, including a 39-story building in San Francisco. One of the most common types of precast buildings in the western United States are tilt-up buildings, in which large concrete panels are often cast on the ground at the job site, and then tilted up, to form the building’s walls (tilt-up construction is discussed further below). The next section describes what differentiates precast and tilt-up buildings from other building types. This is followed by a review of the performance of these types of buildings in recent earthquakes in the United States and elsewhere, a brief review of code provisions for precast and tilt-up building design, and then a somewhat lengthier discussion of major seismic deficiencies in existing tilt-up buildings, and their remediation. The chapter concludes with listings of Defining Terms, References, and Further Reading.

14.2

Precast and Tilt-Up Buildings

14.2.1 Precast Buildings A building with various precast elements is shown in Figure 14.1, and is essentially a post-and-beam system in concrete, where columns, beams, or slabs are prefabricated and assembled on site. Various types of members are used: • Vertical load-carrying elements may be typical column shapes, Ts, cross shapes, or arches and are often more than one story in height. Note that columns are often formed with corbels (i.e., beam seats). • Beams are often Ts, double Ts, or rectangular sections. • Wall panels may be several stories in height, and may be load bearing, or nonload bearing (i.e., curtain walls). Precast frames are divided into two broad categories: 1. Emulated moment frames of precast concrete are “those precast beam–column systems that are interconnected using reinforcing and wet concrete in such a way as to create a system that will act to resist lateral loads in a manner similar to cast-in-place concrete systems” [FEMA 274, 1997]. © 2003 by CRC Press LLC



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FIGURE 14.1 Precast concrete building — typical details. (From FEMA 154, 1988, Rapid Visual Screening of Buildings for Potential Seismic Hazards: A Handbook, Earthquake Hazards Reduction Series 41, Federal Emergency Management Agency, Washington, D.C.)

2. Other than emulated cast-in-place moment frames: Frames of this classification “are assembled using dry joints; that is, connections are made by bolting, welding, post-tensioning, or other similar means. Frames of this nature may act alone to resist lateral loads, or they may act in conjunction with shear walls, braced frames, or other elements to form a dual system” [FEMA 274, 1997]. The appendix to Chapter 9 of the 1997 NEHRP Recommended Provisions [FEMA 302, 1998] contains a trial version of code provisions for new construction of this nature, but it was felt to be premature in 1997 to base actual provisions on the material in the appendix. The concern with these types of structures is that because the members are stiffer than the connections, the majority of the deformations must be absorbed in deformation of the connections. The lateral-force-resisting system for a precast building can be a box or shear wall system (where walls act as shear panels to transmit lateral forces between stories), or a moment frame. Figure 14.2 shows, for example, a building under construction, where the shear wall and columns are cast in place, © 2003 by CRC Press LLC


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(A)

(B) FIGURE 14.2 (A) Precast concrete building under construction — note large shear wall. (B) Note precast beam supported by corbel on column. (Photos: C. Scawthorn)

and the beams and floor planks are precast. This sometimes leads to splitting of responsibility between two engineers, one for the precast framing, and one for the lateral-load system.

14.2.2 Tilt-Up Buildings One of the most common low-rise commercial building types in the western United States is the tilt-up building, which utilizes precast wall elements in a box-type lateral-force-resisting system (Figure 14.3). In traditional tilt-up buildings, concrete wall panels are cast on the ground then tilted upward onto their final positions (Figure 14.4). Tilt-up buildings are an inexpensive form of light industrial and commercial construction. Walls are concrete panels, and the roof is typically plywood or oriented strand board (OSB) diaphragms supported by wood purlins and glue-laminated (glulam) wood beams or a light steel deck and truss joist system, supported in the interior on steel pipe columns. Discussions in this chapter will be limited primarily to tilt-ups with wood diaphragms, as they are more common in higher seismic zones. © 2003 by CRC Press LLC


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4 2 3 1

7

5 6

Details: 5. anchor bolted wooden ledger for roof/floor support

Wall systems: 6. cast-in-place columns– square, "T" shape, and "H" shape 7. welded steel plate type panel connection

FIGURE 14.3 Tilt-up building — typical details. (From FEMA 154, 1988, Rapid Visual Screening of Buildings for Potential Seismic Hazards: A Handbook, Earthquake Hazards Reduction Series 41, Federal Emergency Management Agency, Washington, D.C.)

In many cases, panelized roof systems are used to minimize the cost of constructing a wood diaphragm. The primary components of existing buildings typically include 5 1/8 - or 6 3/4 -in. wide glulam beams (usually spaced on 20- to 24-ft modules), 4× sawn lumber purlins (framing to the glulam beams on an 8-ft module), 2 × 4 or 2 × 6 subpurlins (framing to the purlins on a 2-ft module), and plywood sheathing. The 8-ft by 4-ft plywood panels are framed with a subpurlin along each of the long sides and a third subpurlin along the centerline, to span between purlins. Panel sections are fabricated on the ground with purlins and subpurlins overlain with sheets of plywood. The grids are then lifted into position and connected to glulam beams and purlins already in place. Recent code requirements have resulted in 3× subpurlins being used as struts for attachment of wall anchors. In most tilt-up buildings, a ledger member attached to the walls with embedded anchors (Figure 14.5) supports the perimeter of the roof. Diaphragm shear transfers through the nails into the ledgers, and then through the ledger bolts into the wall panels. Ledgers on most modern and nearly all older buildings are solid 3× or 4× sawn lumber members. Some newer buildings have steel ledger angle (L) or channel (C) sections with or without a wood nailer attached at the top. Glulam beams are typically directly supported by the walls or pilasters at the building perimeter and by interior steel columns. (Occasionally steel columns adjacent to the walls support the beams.) Wall supports for glulam beams may either consist of bearing seats on top of pilasters or fabricated steel “bucket” hardware anchored to the walls with reinforcing steel or stud anchors. Glulam beams are usually designed to cantilever over the interior supports to provide economy in member selection. Suspended spans of glulam beams are supported from hinge-type connection hardware by the cantilevered beams (Figure 14.6). Purlins and subpurlins are normally supported at their ends by metal hangers. The metal deck roofs of tilt-up structures are commonly composed of fluted sheets with gage thickness between 22 and 14. Flute depths vary from 1 1/2 to 3 in. in most cases. Decking units are attached to © 2003 by CRC Press LLC


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(A)

(B) FIGURE 14.4 Details of two-story tilt-up building under construction, showing wall panels propped up. (Photos: C. Scawthorn)



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Plywood

Purlin or subpurlin Hanger Ledger Wall panel

FIGURE 14.5 Typical tilt-up wood ledger detail. (From Structural Engineers Association of Northern California, 2001, Guidelines for Seismic Evaluation and Rehabilitation of Tilt-Up Buildings and Other Rigid Wall/Flexible Diaphragm Structures, D. McCormick, Ed., International Conference of Building Officials, Whittier, CA. With permission.)

(N) Side Strap (Both Sides)

Hinge Connector

Plywood

Suspended GLB Cantilevered GLB

Use (N) Steel Shim Plate Each Side of Beam to Clear Hinge Connector

FIGURE 14.6 Typical tilt-up hinge connector detail for cantilevered glulam beam. (From Structural Engineers Association of Northern California, 2001, Guidelines for Seismic Evaluation and Rehabilitation of Tilt-Up Buildings and Other Rigid Wall/Flexible Diaphragm Structures, D. McCormick, Ed., International Conference of Building Officials, Whittier, CA. With permission.)

adjacent units and to structural steel supports by welds (typically puddle welds) or mechanical fasteners. Metal decks with nonstructural concrete fill (e.g., vermiculite) are sometimes used on the roof. Metal decks with structural concrete topping are commonly used on floors for two-story tilt-ups. Reinforcing for the concrete ranges from light wire mesh to a grid of reinforcing bars. Concrete has structural properties that significantly add to diaphragm stiffness and strength. Thus, two-story tiltups often have flexible roof diaphragms and rigid floor diaphragms.

14.3 Performance of Precast and Tilt-Up Buildings in Earthquakes 14.3.1 Precast Buildings The earthquake performance of precast buildings varies greatly and is sometimes poor. This type of building performs well if a lateral-force-resisting system is present, and the details used to connect the structural elements have sufficient strength and ductility (toughness). As noted in FEMA 274 [1997]: © 2003 by CRC Press LLC


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FIGURE 14.7 Collapse of precast concrete building, Leninakan (1988 Armenia earthquake). (Photo: EQE International)

FIGURE 14.8 Collapse of precast concrete building, 1999 Marmara (Turkey) earthquake. (Photo: C. Scawthorn)

Many types of precast concrete frames have been constructed since their inception in the 1950s. Some have inherent limited lateral-load-resisting capacity because of the nature of their construction details and because they were consciously designed for wind or earthquake loads. Except for emulated systems and braced systems…these frames have capacities to resist lateral loads that are limited by elastic level deformations. In many double tee and single tee systems, as well as others, there is a lack of a complete load path. Brittle welded connections are very common. Many columns and beams lack sufficient confinement steel to provide ductility, and some column systems have inadequate shear capacity as well as base anchorage. Other columns have moment capacity at the base plate that is far beyond their ability to accept the deformations imposed by the global system. Each system may contain details or configuration characteristics that make it unique. In older precast buildings, and in certain foreign countries, lateral-force-resisting systems may not be present or adequate, resulting in collapse (Figures 14.7 and 14.8). Because structures of this type often employ cast-in-place concrete or reinforced masonry (brick or block) shear walls for lateral load © 2003 by CRC Press LLC


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(A)

(B) FIGURE 14.9 Collapsed precast parking garage, 1994 Northridge earthquake, illustrating lack of member connectivity/diaphragm adequacy. (Photos: EQE International) Shown as Color Figure 14.9.

resistance, they experience the same types of damage as other shear wall building types. Some of the problems specific to precast buildings include: • • • •

Improper design, or no real lateral-force-resisting system Inadequate diaphragms Poorly designed connections between prefabricated elements Loss of vertical support, which can occur due to inadequate bearing area and/or insufficient connection between floor elements and columns • Preexisting damage due to restraint of drying or thermal shrinkage • Corrosion of metal connectors between prefabricated elements An example of a building with inadequate diaphragm/connections is illustrated in Figure 14.9, which shows a collapsed new, large, three-story, precast, prestressed concrete garage at the Northridge Fashion Center, following the 1994 Northridge earthquake. Figure 14.10 shows a modern, four-level, precast © 2003 by CRC Press LLC


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concrete garage at California State University, Northridge, partially collapsed in the 1994 Northridge earthquake. The structure was only 18 months old and presumably was in nominal conformance with the building code requirements. The design included a perimeter “ductile” concrete frame, with the exterior columns designed to carry all earthquake loads and the interior columns designed to carry only vertical (nonearthquake) loads.

14.3.2 Tilt-Up Buildings Although numerous tilt-up buildings were constructed in the western United States following World War II, these buildings were not subjected to a significant earthquake until the 1964 Alaska earthquake, in which the first known collapse of a tilt-up warehouse occurred (at Elmendorf Air Force Base). The cause of the failure was reported to be pull out of pilaster anchor bolts [SEAONC, 2001]. However, it was not until the 1971 San Fernando (California) earthquake, in which many tilt-ups in the epicentral region performed very poorly, that severe deficiencies in this type of construction were recognized. Typical failures included separation between tilt-up panels and roofs, with and without collapse, roof diaphragm damage, and other damage caused by various connection failures — particularly the connections between the heavy tilt-up panels and the light, timber-frame and plywood-sheathed roofs (Figure 14.11). A fundamental flaw in the typical wall-diaphragm connection was observed (Figure 14.12) involving the wood ledger being placed in cross-grain bending, due to the out-of-plane forces on the wall resulting from the seismic acceleration of the wall’s mass. Wood is especially weak in cross-grain bending, and codes of that era and design practice did not consider this aspect of the lateral force path. In reaction to the numerous failures observed in the 1971 San Fernando earthquake, relevant seismic requirements of the Uniform Building Code (UBC) were extensively modified in 1973 (direct wall anchor connections, pilaster ties, continuous ties), 1976 (subdiaphragms), and again in 1979 (wall anchor forces). It was expected that tilt-up buildings conforming to these more stringent requirements would generally perform better than would older, unstrengthened structures. The detail shown in Figure 14.12 was modified to have a positive connection between the beam, purlin or subpurlin, and the wall (Figure 14.13). Additional modifications to the code were made in 1991 (introduction of amplified forces in the middle of the diaphragm), based on research from the 1984 Morgan Hill, the 1987 Whittier-Narrows, and the 1989 Loma Prieta events. In the 1994 Northridge earthquake, however, a large proportion of concrete tiltup buildings located in the region of strong shaking had serious structural damage, including partial collapses. The City of Los Angeles estimated that more than 400 of the 1200 tilt-up buildings in the San Fernando Valley had significant structural damage, including partial roof collapse and collapse of exterior walls [Brooks, 1994]. It was estimated that about 40% of the pre-1973/1976 and 25% of the post-1973/ 1976 tilt-up and reinforced masonry buildings had roof connection failures. Figure 14.14, for example, is an aerial view of an industrial park taken shortly after the Northridge earthquake, in which several buildings can be seen to be missing wall panels or roof bays. Another example of tilt-up damage is Figure 14.15, which shows a large commercial building that lost its rear tilt-up wall when the wall-to-roof connections failed. These connections appeared to conform to typical code standards dating from 1973 to 1990. The particular detail involved steel brackets anchored into the wall and bolted through the wood roof beams. The collapse was caused by the bolts pulling through the ends of the wood beams. This particular structure, however, may have undergone particularly strong ground motions because it was located on soft alluvium, next to a river channel.

14.4 Code Provisions for Precast and Tilt-Up Buildings 14.4.1 Precast Buildings Section 1921.2.1.6 of the 1997 UBC requires that precast lateral-force-resisting systems shall either be designed to “emulate the behavior of monolithic reinforced concrete construction…or…rely on the unique properties of a structural system composed of interconnected precast elements.” That is, unless © 2003 by CRC Press LLC



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(A)

(B)

(C) FIGURE 14.10 International)

Collapsed precast Cal State Northridge parking garage, 1994 Northridge earthquake. (Photo: EQE



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FIGURE 14.11 Collapse of tilt-up building, 1971 San Fernando earthquake. (Photo: EQE International)

FIGURE 14.12 Ledger detail showing cross-grain bending, typical of pre-1971 tilt-up buildings.

it can be shown otherwise (i.e., via testing and analysis), the lateral-force-resisting system of precast frame buildings must emulate the behavior of reinforced concrete construction. However, precast buildings can be constructed where the gravity load-carrying system is of precast construction, and the lateral-forceresisting system is, for example, a monolithic reinforced concrete shear wall, etc. (see Figure 14.2).

14.4.2 Tilt-Up Buildings Design of tilt-up buildings is governed by the applicable building code. The discussion herein is in the context of the 1997 UBC, which embodied a major change from previous codes, involving a move from service level to strength level design (see SEAONC, 2001 for a discussion of previous codes governing design of tilt-ups in the western United States), as well as modifications based on lessons learned in the 1994 Northridge earthquake. The 2000 International Building Code (IBC) has similar design provisions [International Code Council, 2000]. Other relevant documents include the 1997 Uniform Code for Building Conservation (UCBC), Appendix Chapter 5, and its successor, Chapter 2 of the Guidelines for Seismic Retrofit of Existing Buildings (GSREB) [ICBO, 2001]. The base shear equation and other equations used to determine design forces in the 1997 UBC are: V = Cv IW/RT © 2003 by CRC Press LLC

(14.1a)


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"Hold-Down" Type Connector Plywood Sheathing

Ledger Embedded Anchor

Glulam Beam

Wall Panel

FIGURE 14.13 Revised detail for wall-diaphragm connection. (Photo: EQE International)

FIGURE 14.14 Aerial view showing damaged tilt-ups, 1994 Northridge earthquake. (Photo: EQE International)

but need not exceed: V = 2.5CaIW/R

(14.1b)

where W is the building weight, I is the importance factor (normally 1.0), and the other factors are discussed below. Equation 14.1b serves as an upper cap for the value of the base shear in Equation 14.1a, and corresponds to the plateau on the design spectrum for short period structures. Tilt-up buildings typically are designed for the capped value as they are considered stiff structures. The values for Ca and Cv are determined from Tables 16-Q and 16-R of the 1997 UBC, respectively, and are functions of both the soil type and seismic zone. In seismic zone 4, Ca and Cv are also dependent on the near-source factors Na and Nv , respectively. The near-source factors are related to both proximity to a major fault and maximum capable magnitudes and slip rates of the faults, as set forth in Tables 16-S, © 2003 by CRC Press LLC


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16-T, and 16-U. For major faults (moment magnitude greater than 7 and slip rate of 5 mm/year or more) Na varies from 1.5 (located less than 2 km to the fault) to 1.0 (greater than 10 km). The value of Na used to determine Ca need not exceed 1.1 for regular, redundant (see below) structures located at a site with a soil profile of SA through SD . Simple tilt-up buildings can qualify for this exemption. The soil classifications have been expanded from a four-tier (S1 through S4) to a six-tier (SA through SF) scheme (Section 1636 of the 1997 UBC). If the soil properties are not known in sufficient detail to determine the soil profile type, type SD shall be used (Section 1629.3). For zone 4, Ca varies from 0.32Na (for SA) to 0.44Na (for SD), and Cv varies from 0.32Nv to 0.96Nv . R in Equation 14.1 is a numerical coefficient representative of the inherent overstrength and global ductility capacity of lateral-force-resisting systems. For shear wall systems that are also bearing walls R has a value of 4.5. Thus, for a typical tilt-up building of standard importance in seismic zone 4 (more than 10 km from a major fault) for which no soil information is known, the base shear equation yields V = 2.5CaIW/R = (2.5)(0.44)(1)W/4.5 = 0.24W. Consideration of vertical earthquake loads does not have a significant effect on the design of tilt-up buildings and will not be considered here. A redundancy/reliability factor ρ is incorporated into design load combinations, which is intended to increase the design forces for less redundant structures. The redundancy/reliability factor ρ is defined by:

[

ρ = 2 − 20 rmax AB

]

(14.2)

where rmax is the maximum element-story shear ratio and AB is the ground floor area of the structure in square feet. ρ shall not be taken less than 1.0 (highly redundant) and need not be greater than 1.5. Thus, the effect ranges from either leaving the base shear from Equation 14.1 unchanged to increasing it by up to 50%. This increase in load applies only to the vertical resisting elements and foundations, and typically not to collectors, the diaphragm, and other components (including the design of wall anchors). For a given direction of loading, the general definition of ri is the ratio of the design story shear in the most heavily loaded single element divided by the total design story shear for level i. (rmax is the highest value for ri in the bottom two thirds of the structure.) However, for buildings with shear walls a more specific definition is provided. For tilt-up buildings, ri shall be taken as the maximum value of the product of the wall shear and 10/lw (lw is the length of solid wall in feet) divided by the total story shear. This in effect penalizes buildings with shorter length walls, thereby increasing base shear for buildings that depart significantly from the original box-system concept. It may also penalize buildings with reentrant corners or interior walls regardless of the total length of wall available. This is because the short wall at the reentrant corner may resist up to 50% of the base shear based on tributary area. The redundancy/reliability factor has been widely debated since its introduction, and numerous modifications have been proposed. The overstrength factor Ωo is incorporated into special design load combinations (e.g., to axial forces in columns supporting discontinuous walls, and for collectors and collector connections.) It is intended to account for structural overstrength and has a value of 2.8 for shear wall systems. It is analogous with the use of 3Rw/8 in previous editions of the UBC. The application of this amplification to collectors and collector connections (Section 1633.2.6) is a new provision in the 1997 UBC. The value of the wall anchor force can be determined by the lesser of Equations 32–1 and 32–2 of the 1997 UBC:

Fp = 4.0 Ca I pWp ,  h  a pCa 1 + 3 x  hr   F p= Wp Rp


(14.3a)

(14.3b)



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where ap Ca Ip Wp hx

is the in-structure component amplification factor. is the seismic coefficient, as set forth in Table 16-Q of the UBC. is the importance factor specified in Table 16-K of the UBC. is the weight of an element or component. is the element or component attachment elevation with respect to grade. hx shall not be taken less than 0.0. hr is the structure roof elevation with respect to grade. Rp is the component modification factor that shall be taken from Table 16-O. Note that the equation for determining wall anchor forces in the 2000 IBC is not dependent on diaphragm height with respect to roof diaphragm height. Equation 14.3b can be simplified for wall anchorage for the roof by setting hx = hr (element or component attachment level equals the height of the roof). The value of hx should not mistakenly be taken as the center of gravity of the walls. Then Equation 14.3b becomes Fp = 4apCa IpWp /Rp . ap is the instructure component amplification factor that varies from 1.0 to 2.5. Section 1632.2 states that the component response modification factor Rp shall be reduced to 1.5 if shallow anchors (embedment length to diameter less than 8) are used, and 1.0 if nonductile materials are used. However, Section 1623.2.8.1 states that Rp = 3 shall be used for wall anchorage, regardless of anchor type. Using the ap and Rp values provided for bearing walls and flexible diaphragms in Section 1633.2.8.1 (1.5 and 3, respectively), Equation 14.3b becomes 4CaIpW/3, which obviously is less than in Equation 14.3a. For a typical structure of standard importance in seismic zone 4 with Ca = 0.44 (soil type SD and distant from a major fault), Equation 14.3b yields an anchor force of 0.88W. This force must be multiplied by 0.85, 1.0, and 1.4 for the design of wood elements, concrete embedments, and steel elements in the wall anchorage system, respectively. These factors were introduced in an attempt to provide similar factors of safety for all materials. (The 1.4 factor is used for all materials in the 2000 IBC.) Multiplying by these factors results in strength design anchor forces of 0.75W, 0.88W, and 1.23W for wood, concrete, and steel, respectively. Unlike earlier codes (1991 and 1994 UBC), the design wall anchorage force is not amplified only in the center of the diaphragm. A constant amplified value was assigned over the full length of the diaphragm because a flexible diaphragm is a shear yielding beam, not a flexural beam. Finally, a change in the 1997 UBC is the restriction that subdiaphragm length-to-depth ratios should be limited to 2.5:1 instead of 4:1 as permitted in previous codes. This effectively limits subdiaphragm shear stresses. Appendix Chapter 5 of the 1997 UCBC and Chapter 2 of the 2001 GSREB include design forces that are reduced with respect to the UBC. In the case of the GSREB, the loads are 75% of those in the 1997 UBC, and the primary focus is on the wall anchorage system. It is not required that diaphragms or wall stresses be evaluated. It appears that both the 2001 GSREB and FEMA 356 will be incorporated or referenced in the 2003 International Existing Building Code (IEBC).

14.5 Seismic Evaluation and Rehabilitation of Tilt-Up Buildings The evaluation and rehabilitation of tilt-up buildings consist of identifying and remediating deficiencies in the lateral-force-resisting system. The following discussion on evaluation and rehabilitation of deficiencies is based on a recent Structural Engineers Association of Northern California (SEAONC) publication [SEAONC, 2001], to which the reader is referred for additional detail as well as a methodology for prioritization of identified deficiencies. The guidelines identify eight features or components of tilt-up structures that can be evaluated for deficiencies. Although it is not possible to state absolute priorities for all buildings, the component priorities are generally judged to be:



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• High: wall anchors, continuity ties and subdiaphragms, and collectors • Moderate: diaphragms and shear walls loaded in plane • Low: chords, ledgers, and out-of-plane loading on walls These priorities are based on knowledge of performance in past earthquakes. Only issues associated with the High category of deficiencies will be discussed herein, and the reader is referred to the SEAONC guidelines for more detail, as well as discussion of the Moderate and Low categories of priorities. Although relative priorities remain basically the same regardless of the expected severity of ground shaking, the priorities are basically applicable to seismic zone 4 of the UBC. When trying to compare the significance of deficiencies in different seismic regions, judgment should be used to increase these priorities for structures located near major active faults, and decrease the priorities for structures in lower seismic zones.

14.5.1 Out-of-Plane Wall Anchors The absence of wall anchors (or a wall anchorage system) is the most critical deficiency that a tiltup structure can possess. As first dramatically illustrated in the San Fernando earthquake, inadequate anchorage can lead to a sudden roof and wall collapse once the walls and roof framing separate (Figure 14.11). During the 1994 Northridge earthquake even structures designed and built to the requirements of the latest building codes experienced serious damage, including partial collapses (Figure 14.15) in areas of strong ground shaking. Although there is some speculation regarding the relative roles of inadequate design provisions, quality of construction, and designer errors, improvements in the as-built capacity of wall anchorage systems are clearly necessary. Analysis of the damage observed after the Northridge earthquake suggested that: 1. Peak ground accelerations (PGAs) are amplified by flexible diaphragms in accordance with the amplified portion of response spectrum. 2. The effects of relative stiffness and eccentric loads (especially on subpurlins) must be considered. 3. The implicit code philosophy of assuming ductility in wall anchors that are inherently brittle is inappropriate. 4. The effects of overstrength of the diaphragm are not considered in design. The typical wall anchor detail for buildings constructed prior to the 1971 San Fernando earthquake consisted of the plywood diaphragm nailed to the wood ledger that is in turn bolted to the wall (Figure 14.5). Manufactured metal hangers for purlins and subpurlins provide bearing support but no direct tension connection to the walls. As clearly demonstrated in the San Fernando earthquake, this detail is extremely weak and subject to failure at even moderate levels of shaking (e.g., PGAs of approximately 0.20 g). Glulam beams and girders were typically supported on pilasters and anchored to the top of the pilasters with anchor bolts and beam seat hardware. Thus, in the direction parallel to the glulam beams, some wall anchorage capacity was provided locally, but cross-grain bending in the ledgers also occurred near the midspan of the panels. Ledgers failed and pilaster–glulam connections were too weak and failed. Parallel to purlins where no wall anchorage was provided, the wall anchor capacity for unretrofitted pre-1971 buildings relies totally on the combination of cross-grain bending of the ledgers, transfer of shear through the nails, and tension in the plywood (Figure 14.12). Typical wall anchorage detailing utilized by designers following adoption of the 1973 UBC is depicted in Figure 14.16. All of the details provide an alternative load path to the one described above (i.e., crossgrain bending); however, anchor flexibility, installation problems, and eccentric loads caused these details to remain prone to damage. During the Northridge earthquake, failures of all types of anchors of all ages were observed [Hamburger et al., 1995]. A study of 88 buildings [SEAOSC, 1994] in the epicentral area revealed virtually no difference in performance of buildings of different ages constructed after 1971. However, buildings that had been retrofitted did perform better than buildings that had not been retrofitted. This suggests that the types of anchors used in retrofit (i.e., stiffer anchors such as © 2003 by CRC Press LLC


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(A)

(B) FIGURE 14.15 Aerial view (A) and close-up (B) showing failed wall in tilt-up building, 1994 Northridge earthquake. (Photos: EQE International) Part (B) shown as Color Figure 14.15.

hold-downs) have a larger overstrength than the steel strap-type anchors (tension ties) that are cast in walls and bent over to attach to framing. The Northridge earthquake demonstrated that, due to lack of appreciation of the different factors of safety for the wood, reinforced concrete, and steel components of the wall anchorage system, the performance of the system once the seismic loads exceeded those associated with working stresses was not adequately predicted. Manufactured steel hardware had safety factors (defined as the ratio of allowable load, including 1.33 factor, to ultimate strength) ranging from 1.8 for steel straps to 2.5 or more for holddown devices. Not surprisingly, tension ties were observed to fail more frequently than hold-down devices. Consequently, new material load factors (intended to provide consistent overstrengths in the 3+ range) were introduced into the 1996 UBC and UCBC Supplements. Wall anchorage systems designed using post-Northridge design provisions are expected to be capable of resisting loads associated with diaphragm accelerations of over 1.2 g if detailed properly. © 2003 by CRC Press LLC


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A. Hold-Down Type Anchor

D. Twisted Strap Anchor With Metal Ledger

B. Twisted Strap Anchor

E. V- Strap

C. Top Strap Anchor

F. Splayed-Strap Anchor

FIGURE 14.16 Examples of wall anchorage details. (Photo: EQE International)

Failures associated with tension ties observed during the Northridge earthquake include: • • • • •

Brittle fracture at the first bolt or rivet hole Nail pull-out Buckling Brittle failure where the strap is bent over ledger (at face of wall) Embedment pull-out

Failures of the steel portions of manufactured metal strap anchors (as opposed to the fasteners) are more likely for the longer straps because many manufacturers use straps with a single cross-sectional area for tension ties of different capacity and length. Thus, a shorter strap will be governed by the nail capacity, while a longer strap with more fasteners is governed by the capacity of the steel strap. Nail failure has been observed to be significantly more ductile and desirable than failure of the straps. Consequently shorter straps used at more locations (due to the lower capacities) are preferred in design and retrofit. Net-section failures at connector holes were noted for twisted straps and tension ties with rivets. Presumably, these failures occurred because the ultimate capacity at the net section was less than the © 2003 by CRC Press LLC



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yield capacity at the gross section. Some of the manufactured hardware is made with ASTM A446 (grade A) steel with an ultimate tensile stress of 45 ksi and a yield stress of 33 ksi. The ratio of the ultimate stress to yield stress is only 1.4, significantly less than the 1.6 for A36 steel determined by using Fu = 58 ksi and Fy = 36 ksi. However, recent tests for A36 steel indicated Fu/Fy values can be much lower because no attempt was made to control the ratio. It is recommended that hardware with bolt holes be conservatively sized or, alternatively, hardware with nail holes only (minimal reduction in gross section) be used instead. The capacity of twisted straps installed at significant angles from the horizontal is limited in three ways: 1. The horizontal component of the force in the inclined portion of a strap must match the horizontal wall anchorage load. Thus, the design load for the strap increases with installation angle. Although some manufacturers currently specify maximum installation angles, no limit was specified in older catalogs. Inclinations of 45° or more have been observed in the field. 2. The fasteners must develop perpendicular-to-the-grain stresses to resist the vertical component of the load. The perpendicular-to-the-grain capacity of the strut is lower than the parallel-to-grain capacity, which is the basis of the capacity included in the catalog. For installations with large angles with respect to the horizontal, the strength of the bolted connection should be calculated using Hankinson’s formula for the angle of load to grain. Calculations should include reductions due to inadequate edge distance for perpendicular-to-the-grain-loading. 3. The vertical component is limited by the dead load on the member plus the uplift capacity of the joist hanger (which is typically low). For a typical purlin, dead load reactions can range from 800 to 1,600 lb. For subpurlins, they are significantly less. If the vertical component of the anchor force exceeds the dead load, flexural stresses are developed in the strap at the first bolt hole. The combined axial tension and flexure act on the net section of the strap. Thus, twisted straps with high loads can fail for members with light gravity loads (i.e., subpurlins). Failure modes for tension ties applied over the top of roofing framing members included: • • • •

Tension failures at the net section Pull-out due to improper anchor embedment Fastener failure Buckling at the wall interface

The buckling of the tension ties can probably be attributed to the flexibility in the wall anchorage system in combination with the presence of a gap between the anchored framing member and the ledger. Poor alignment of tension ties can result in the installation of fewer nails than required by the manufacturer, as well as large installation angles, and subsequently less capacity. It is believed that installation procedures involving bending straps upwards during construction to allow for panel erection and framing installation, and then bending them back down after the roof framing was installed, contributed to tension tie failure. Although manufacturers indicate that they believe bending the straps back into place once is acceptable, the extra number of bends that some straps encounter during the construction process weakens the ties. During the Northridge earthquake failures of subpurlins (typically 2 in. wide by 4 or 6 in. deep) with single-sided (anchors located on only one vertical face of the framing member) hold-down devices were noted. Splitting is the typical ultimate failure mode in bolted connections, but many failures seemed to have been caused prematurely by eccentric loading. The eccentric loading induces bending about the minor axis of the framing member, which combines with the axial loads due to seismic, and the bending stresses due to gravity loads in the framing members. Until very recently, such stresses were not considered in any hardw