Learning from failure: long-term behaviour of heavy masonry structures

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Learning from Failure Long-term Behaviour of Heavy Masonry Structures

WITPRESS WIT Press publishes leading books in Science and Technology. Visit our website for the current list of titles. www.witpress.com

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Managing Editor F. Escrig Escuela de Arquitectura Universidad de Sevilla Spain

Honorary Editors C. A. Brebbia Wessex Institute of Technology UK

P. R. Vazquez Estudio de Arquitectura Mexico

Associate Editors C. Alessandri University of Ferrara Italy

K. Ishii Yokohama National University Japan

F. Butera Politecnico di Milano Italy

W. Jäger Technical University of Dresden Germany

J. Chilton University of Lincoln UK

M. Majowiecki University of Bologna Italy

G. Croci University of Rome, La Sapienza Italy

S. Sánchez-Beitia University of the Basque Country Spain

A. de Naeyer University of Ghent Belgium

J. J. Sendra Universidad de Sevilla Spain

W. P. De Wilde Free University of Brussel Belgium

M. Zador Technical University of Budapest Hungary

C. Gantes National Technical University of Athens Greece

R. Zarnic University of Ljubljana Slovenia

K. Ghavami Pontificia Univ. Catolica, Rio de Janeiro Brazil

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Learning from Failure Long-term Behaviour of Heavy Masonry Structures Editor: L. Binda Politecnico di Milano, Italy

Editor: L. Binda Politecnico di Milano, Italy

Published by WIT Press Ashurst Lodge, Ashurst, Southampton, SO40 7AA, UK Tel: 44 (0) 238 029 3223; Fax: 44 (0) 238 029 2853 E-Mail: [email protected] http://www.witpress.com For USA, Canada and Mexico WIT Press 25 Bridge Street, Billerica, MA 01821, USA Tel: 978 667 5841; Fax: 978 667 7582 E-Mail: [email protected] http://www.witpress.com British Library Cataloguing-in-Publication Data A Catalogue record for this book is available from the British Library ISBN: 978-1-84564-057-6 ISSN: 1368-1435 Library of Congress Catalog Card Number: 2007922340 The texts of the papers in this volume were set individually by the authors or under their supervision. No responsibility is assumed by the Publisher, the Editors and Authors for any injury and/ or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. The Publisher does not necessarily endorse the ideas held, or views expressed by the Editors or Authors of the material contained in its publications. © WIT Press 2008 Printed in Great Britain by Athenaeum Press Ltd. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the Publisher.

Contents

Preface ............................................................................................................ xiii Chapter 1 Failures due to long-term behaviour of heavy structures........................... L. Binda, A. Anzani & A. Saisi 1.1 1.2

1.3

1.4

1.5

Introduction ............................................................................................. The collapse of the Civic Tower of Pavia: search for the cause .................................................................................................. 1.2.1 Description and historic evolution of the tower ......................... 1.2.2 First experimental results and interpretation of the failure causes .................................................................... 1.2.2.1 Structure and morphology of the walls....................... 1.2.2.2 Geotechnical investigation.......................................... 1.2.2.3 Physical, chemical and mechanical tests on the components ...................................................... 1.2.2.4 Compression tests on masonry prisms........................ 1.2.3 Long-term tests ........................................................................... 1.2.3.1 Fatigue tests ................................................................ 1.2.3.2 Constant load tests ...................................................... Long-term behaviour of masonry structures ........................................... 1.3.1 Deformation during mortar hardening........................................ 1.3.2 First, secondary and tertiary creep in rock and hardened masonry....................................................................... Collapse and damage of towers due to long-term heavy loads............... 1.4.1 St. Marco bell-tower and St. Maria Magdalena tower in Goch ....................................................................................... 1.4.2 The bell-tower of Monza Cathedral and the Torrazzo of Cremona ................................................................................. The role of investigation on the interpretation of the damage causes ......................................................................................... 1.5.1 The bell-tower of the Cathedral of Monza ................................. 1.5.2 The ‘Torrazzo’ of Cremona........................................................

1 1 2 3 4 4 6 7 8 9 9 11 12 12 15 16 16 16 17 18 21

1.6 1.7

Comparison between the two towers ...................................................... 25 Conclusions ............................................................................................. 26

Chapter 2 Experimental researches into long-term behaviour of historical masonry........................................................................................... 29 A. Anzani, L. Binda & G. Mirabella Roberti 2.1 2.2

2.3

2.4

Introduction ............................................................................................. Tests on the masonry of the Civic Tower of Pavia ................................. 2.2.1 Characterization by sonic tests ................................................... 2.2.2 Monotonic tests on prisms of different dimensions ................... 2.2.3 Fatigue tests ................................................................................ 2.2.4 Creep tests on prisms of 300 × 300 × 510 mm........................... 2.2.5 Pseudo-creep tests on prisms of 100 × 100 × 180 mm............... 2.2.6 Pseudo-creep tests on prisms of 200 × 200 × 350 mm............... Tests on the masonry of the crypt of the Cathedral of Monza ................ 2.3.1 Preparation of prisms of 200 × 200 × 350 mm........................... 2.3.2 Characterization by sonic tests ................................................... 2.3.3 Monotonic tests........................................................................... 2.3.4 Fatigue tests ................................................................................ 2.3.5 Creep test on one prism of 300 × 300 × 510 mm ....................... 2.3.6 Pseudo-creep tests, first series .................................................... 2.3.7 Pseudo-creep tests, second series ............................................... Comments................................................................................................

29 31 33 33 35 36 39 39 42 42 44 45 45 48 48 50 52

Chapter 3 Collapse prediction and creep effects............................................................ 57 P.B. Lourenço & J. Pina-Henriques 3.1 3.2

3.3

3.4

Introduction ............................................................................................. Short-term compression: failure analysis and collapse prediction using numerical simulations .................................................. 3.2.1 Experimental results ................................................................... 3.2.2 Continuum model ....................................................................... 3.2.3 Particle model ............................................................................. 3.2.4 Discussion of the results ............................................................. Long-term compression: experimental assessment................................. 3.3.1 Tested specimens........................................................................ 3.3.2 Standard compression tests......................................................... 3.3.3 Short-term creep tests ................................................................. 3.3.4 Long-term creep tests ................................................................. 3.3.5 Discussion of the results ............................................................. Conclusions and future work ..................................................................

57 58 58 59 62 63 66 66 68 69 71 74 78

Chapter 4 Effects of creep on new masonry structures................................................. 83 N.G. Shrive & M.M. Reda Taha 4.1 4.2 4.3

4.4

4.5 4.6 4.7

Introduction ............................................................................................. The step-by-step in time approach to modeling time-dependent effects ............................................................................ Case 1: An axially loaded column .......................................................... 4.3.1 Creep model................................................................................ 4.3.2 Effect of coupling creep and damage in concentrically loaded columns........................................................................... 4.3.3 Examining the effect of rehabilitation ........................................ Case 2: Composite structural element subject to bending ...................... 4.4.1 Development of model ............................................................... 4.4.2 Application to a beam................................................................. 4.4.3 Masonry walls subject to axial load and bending....................... New mathematical approaches to modeling creep.................................. Discussion ............................................................................................... Conclusions .............................................................................................

83 84 85 85 89 91 92 92 97 103 103 104 105

Chapter 5 Experimental study on the damaged pillars of the Noto Cathedral ..................................................................................... 109 A. Saisi, L. Binda, L. Cantini & C. Tedeschi 5.1 5.2 5.3

Introduction ............................................................................................. The collapse and the decision for reconstruction.................................... On-site investigation on the remaining parts of the collapsed pillars....................................................................................................... 5.3.1 Layout of the section and of the masonry morphology.............. 5.3.2 General characterisation of the materials ................................... 5.3.3 Damage description .................................................................... 5.3.4 Laboratory testing....................................................................... 5.3.4.1 Mortars........................................................................ 5.3.4.2 Stones.......................................................................... 5.3.4.3 Injectability tests ......................................................... 5.3.5 On-site tests ................................................................................ 5.3.5.1 Flat-Jack tests.............................................................. 5.3.5.2 Application of sonic pulse velocity test to pillars........................................................................... 5.3.6 Design decisions ......................................................................... 5.3.7 The dismantling of the remaining pillars....................................

109 109 110 111 111 114 114 115 115 117 117 117 118 119 120

Chapter 6 Monitoring of long-term damage in long-span masonry constructions.................................................................................... 125 P. Roca, G. Martínez, F. Casarin, C. Modena, P.P. Rossi, I. Rodríguez & A. Garay 6.1 6.2 6.3 6.4

6.5

6.6 6.7

6.8

Introduction ............................................................................................. Monitoring and long-term damage.......................................................... Role of monitoring in the study of ancient constructions ....................... Monitoring: methodology and requirements........................................... 6.4.1 Technology ................................................................................. 6.4.2 Distinction between dynamic and static monitoring .................. 6.4.3 Requirements .............................................................................. Measuring damage and deformation related to historical or long-term processes ............................................................................ 6.5.1 Monitoring and long-term damage ............................................. 6.5.2 Structural deformation................................................................ 6.5.3 Tensile damage in arches and vaults .......................................... 6.5.4 Damage of compressed members ............................................... 6.5.5 Fragmentation............................................................................. Structural modelling and monitoring ...................................................... Case studies ............................................................................................. 6.7.1 Dynamic monitoring of Mallorca Cathedral .............................. 6.7.2 S. Maria Assunta Cathedral, Reggio Emilia, Italy ..................... 6.7.3 Vitoria Cathedral ........................................................................ Conclusions .............................................................................................

125 125 127 128 128 129 131 133 133 133 135 135 139 140 141 141 145 148 151

Chapter 7 Modelling of the long-term behaviour of historical masonry towers ............................................................................................... 153 A. Taliercio & E. Papa 7.1 7.2

7.3

7.4

Introduction ............................................................................................. A continuum damage model for masonry creep ..................................... 7.2.1 Unidimensional viscoelastic model with damage ...................... 7.2.2 Three-dimensional viscoelastic model with damage.................. 7.2.3 Identification of the model parameters and comparisons with experimental results............................................................ Structural analyses of two masonry towers............................................. 7.3.1 The Civic Tower of Pavia........................................................... 7.3.2 The bell-tower of Monza Cathedral............................................ Remarks and future perspectives ............................................................

153 154 154 157 160 166 166 167 171

Chapter 8 Repair techniques and long-term damage of massive structures ......................................................................................................... 175 C. Modena & M.R. Valluzzi 8.1 8.2 8.3

8.4

8.5

Introduction ............................................................................................. The bed reinforcement technique............................................................ The experimental campaigns................................................................... 8.3.1 Laboratory tests on the use of stainless steel bars ...................... 8.3.2 Laboratory tests on the use of CFRP bars and thin strips........... Case studies ............................................................................................. 8.4.1 The bell-tower of the Basilica of S. Giustina in Padua .............. 8.4.2 The pillars of S. Sofia church in Padua ...................................... 8.4.3 The bell-tower of S. Giovanni Battista Cathedral in Monza (Milan)........................................................................ Final remarks...........................................................................................

175 176 178 179 183 197 197 199 199 201

Chapter 9 Simple checks to prevent the collapse of heavy historical structures and residual life prevision through a probabilistic model .......................... 205 L. Binda, A. Anzani & E. Garavaglia 9.1 9.2

9.3 9.4

9.5 9.6

Introduction ............................................................................................. The safety of ancient towers ................................................................... 9.2.1 A survey on Italian cases ............................................................ 9.2.2 Comments on the observed crack patterns ................................. 9.2.3 Elaboration of the collected data ................................................ A probabilistic model for the assessment of historic buildings .............. Fragility curves from the experimental data ........................................... 9.4.1 Fragility curve F versus σ applied to creep tests ...................... 9.4.2 Comparison between vertical and horizontal strain-rate ............ 9.4.3 Fragility curve F versus σ applied to pseudo-creep tests ......... 9.4.4 Comparison between vertical and horizontal strain-rate ............ Application to the bell-tower of Monza .................................................. Conclusions .............................................................................................

205 205 206 206 209 210 215 215 215 216 218 219 221

Conclusions...................................................................................................... 225


Preface On March 17 1989, the Civic Tower of Pavia collapsed without any apparent warning signs – killing four people. Subsequently, L. Binda, together with four colleagues from DIS, Politecnico of Milan, was nominated a member of a Committee that had the aim of helping the Prosecutor of the Procura della Repubblica in Milan find the causes of the collapse. After an experimental and analytical investigation lasting nine months, the collapse cause was found. Progressive damage dating back many years, due mainly to the heavy dead load put on top of the existing medieval tower with the addition of a massive bell-tower in granite, was to blame. This type of long-term behaviour of masonry structures was not as well researched as it was for concrete and steel structures and for rocks. Experimental research aimed at showing the reliability of this interpretation was carried out, and is still continuing, that is more than sixteen years of research since 1989. After careful interpretation of the experimental results, also based on experiences from rock mechanics and concrete, the modelling of the phenomenon for massive structures, such as creep behaviour of masonry, was implemented by collaboration with E. Papa and A. Taliercio from the same department. Other case histories were collected such as the collapse of the Sancta Maria Magdalena bell-tower in 1992 in Dusseldorf, the damage to the bell-tower of the Monza Cathedral, Italy, and to the Torrazzo in Cremona, Italy. Later on, in 1996 the collapse of the Noto Cathedral, Italy, showed that similar progressive damage can take place in pillars of churches and cathedrals. Collaborations on the topic first started with the University of Padua (C. Modena) and later on with the University of Minho, Portugal (P. Lourenco). Then the University of Calgary, Canada (N. Shrive) and the University of Barcelona (P. Roca) were involved. The editor would like to thank the technicians Mr Antico, Mr Cucchi and Mr Iscandri for their collaboration in the experimental research and Mrs C. Arcadi for her help in the editing of the chapters. The Editor 2007


CHAPTER 1 Failures due to long-term behaviour of heavy structures L. Binda, A. Anzani & A. Saisi Department of Structural Engineering, Politecnico di Milano, Milan, Italy.

1.1 Introduction The authors’ interest towards the long-term behaviour of heavy masonry structures started after the collapse of the Civic Tower of Pavia in 1989, when L. Binda was involved in the Committee of experts supporting the Prosecutor in the trial, which involved the Municipality and the Cultural Heritage Superintendent after four people died under the debris of the tower. The response required by the Committee concerned the cause of the failure; therefore an extensive experimental investigation on site, in the laboratory and in the archives was carried out and the answer was given within the time of nine months. Several hypotheses were formulated and studied before finalizing the most probable one, from the effect of a bomb to the settlement of the soil caused by a sudden rise of the water-table, to the effect of air pollution, to the traffic vibration and so on. Several documents were collected concerning the sudden collapse of other towers even before the San Marco tower failure and the results of the investigation were interesting. In fact, the failure of some towers apparently happened a few years after a relatively low intensity shock took place. In other cases, the collapse took place after the development of signs of damage, such as some crack patterns, for a long time. This suggests that some phenomena developing over time had probably to be involved in the causes of the failure, combined in a complex synergetic way with other factors. As for the experimental investigation carried out on some prisms cut out from the large blocks of the collapsed walls of the Pavia tower found on the site, the

2

Learning from Failure

attention was more and more concentrated on the dilatancy of the masonry under compressive monotonic and creep tests and on the fatigue behaviour of masonry under cycling loads. This chapter discusses the investigation carried out on the materials of the Civic Tower of Pavia and the conclusion reached by the previously mentioned Committee. Furthermore, the phenomena of early and retarded deformations of historic masonry structures will be described together with the results of an investigation carried out on other damaged structures. Finally the research campaign carried out on site and in laboratory on the belltower of the Cathedral of Monza and the bell-tower of the Cathedral of Cremona. The investigation shows that the damaged state of the structures or of structural elements can be precociously detected by the recognition of the typical crack patterns, based on simple visual investigation. Collapses may be prevented by detecting the symptoms of structural decay, particularly the crack patterns, through on-site survey, monitoring the structure movements for long enough periods of time, choosing appropriate analytical models and appropriate techniques for repair and strengthening the structures at recognized risk of failure.

1.2 The collapse of the Civic Tower of Pavia: search for the cause The Civic Tower of Pavia, an eleventh-century tower apparently made of brickwork masonry, suddenly collapsed on 17 March 1989 (Fig. 1.1). Several hypotheses were

Figure 1.1: The ruins after the collapse, seen from the arcade opposite to the Cathedral.

Failures due to Long-Term Behaviour of Heavy Structures

3

made about the causes of that sudden failure, from soil settlements to the presence of a bomb, from vibrations caused by traffic to the passage of super sonic jets. For a thorough understanding of the real causes of the collapse, an experimental investigation was carried out on site and in the laboratory, on the large amount of material coming from the remains of the tower. 1.2.1 Description and historic evolution of the tower The tower, about 60 m high with a square base measuring 12.3 × 12.3 m was located close to the north-west corner of the Cathedral. Each of the four facades was divided horizontally into six orders (Fig. 1.2a and b). The first four from the bottom were divided into five parts by four pilaster strips topped by two small arches. The third and fourth orders had no pilaster strips, but were topped by similar hanging arches. The fifth order terminated in a cornice. A large mullioned window with two apertures opened out on each side of the sixteenth-century belfry. Inside the tower two timber floors were situated at a height of approximately 11 and 23 m.

(a)

(b)

Figure 1.2: (a) The Civic Tower and Cathedral of Pavia, Italy. (b) Geometry of the Civic Tower and Cathedral of Pavia, Italy.

4


According to the few historical documents found, the first order and half of the second order can be dated between 1060 and 1100 AD [1, 2], the part from the middle of the second order and the fifth perhaps were built between the twelfth and thirteenth centuries; the tower was surmounted by a brick belfry and a timber roof. Between 1583 and 1598 the granite belfry weighing 3,000 tons, designed by the famous architect Pellegrino Tibaldi was set on top of the tower. A staircase built into the wall ran along all four walls from the south-west corner up to the belfry. The staircase was covered by a small barrel vault apparently made of conglomerate. 1.2.2 First experimental results and interpretation of the failure causes The few documents available at the time of the collapse [3] were insufficient to give an accurate geometric configuration of the tower. Consequently, in order to draw prospects and sections of the tower the following operations, described in detail in [4, 5], were carried out: • topographic survey of the remains of the tower (Fig. 1.3), and partial rectification of existing photographs to define the precise plan and the thickness and morphological features of the cross-section of the masonry; • reconstruction of the geometry of the belfry from a survey of the granite parts, practically all recovered from the internal portion of the remaining part of the tower; • assessment of the overall height of the tower from an existing aerial photogrammetric survey; • perspective plotting from existing photographs to reconstruct the geometry of the staircase and the arrangement of the architectural elements. 1.2.2.1 Structure and morphology of the walls The medieval walls, built according to the techniques normal at that time for towers, were characterized by two external brick cladding ranging from 120 to 400 mm

Figure 1.3: Photogrammetric survey of the remains of the tower.


5

with an average of 150 mm, with the intermediate portion of the walls consisting of irregular courses of large pebbles of brick and stones alternated with mortar, constituting a sort of conglomerate (Fig. 1.4). The walls of the second building phase were characterized by a much more irregular filling and by thinner external facings. Figure 1.5 shows one of the large blocks among the remains revealing part of the section of the wall with the external cladding. Figure 1.6 shows a complete cross-section of the wall of the present remains of the tower (south side), the ratio between the thickness of the external leaf of the wall and the internal one was approximately 1:16. The section of the wall near the staircase was composed by an external wall similar to the one described above, but 1400 mm thick, a stairwell 800 mm wide, and an internal wall 600 mm thick. The latter wall was of the rubble type and was particularly heterogeneous.

Figure 1.4: Cross-section of the wall of the Civic Tower of Pavia.

Figure 1.5: Part of the section of the bearing wall (2.8 m thick), showing the external brick cladding.

Figure 1.6: View of the complete section of the bearing wall. Note how thin the external facing is in comparison with the total thickness of the wall.

6


1.2.2.2 Geotechnical investigation The remains of the lower part of the tower left standing reached a height from 0.1 to 5 m still visible at the moment, since it was decided to leave the remains as they were without reconstructing the tower. The outside main wall is continuous and does not show any appreciable signs of dislocation or displacement from its original position. This, as well as the behaviour of the tower over time (there is no evidence of any specific surveys, but no appreciable settlement appears ever to have been reported), suggests that the collapse cannot be attributed to failure of the foundation soil. At most, possible differential settlements, caused by abnormal variations in the groundwater level in the previous years, could have worsened the stress–strain distribution within the structure, leading to the collapse. The settlements were, however, very limited and their effect is considered to be negligible. These qualitative considerations have been confirmed by calculation [5]. The soil consists mainly of sandy deposits, sometimes silty or with lithoid elements, intercalated with highly impermeable strata of clayey, sandy silt. The most important clayey, silty strata are found between 7.5 and 10 m, 13.5 and 15 m and between 29.5 and 32 m below ground level. These are over consolidated materials with a medium to low degree of plasticity. On-site and laboratory geotechnical surveys were carried out to obtain the mechanical parameters of the soil [5]. The on-site survey consisted of two geognostic drillings in which undisturbed samples were taken and measurements made with a standard penetrometer (SPT); two seismic cone penetration tests (SCPT) and four cone penetration tests (CPT) were also carried out. The samples taken during the drillings were subjected to identification, three-axial and oedometric compressibility tests. The penetrometric resistances give a similar picture of the pattern of the resistance of the soil. The values measured are as follows: from the base of the tower to a depth of approximately 14 m Nspt ranging from 8 to 30 blows/foot, Nscpt ranging from 5 to 23 blows/foot, Qc ranging from 4.0 to 9.0 N/mm2; from 14 m down to the maximum depth reached, Nspt ranging from 34 to 65; Nscpt ranging from 26 to 56; Qc ranging from 14.5 to 28.0 N/mm2. The shearing strengths were determined: (i) for sandy soils on the basis of the correlations presented in the literature between Nspt or Qc, effective vertical pressure sv and friction angle j (ϕ was subsequently suitably reduced to take into account the presence of silt); (ii) for silty soils by means of laboratory tests (threeaxial tests and direct shear tests). To calculate the bearing capacity, for safety’s sake, the soil from a depth of 4 to 14 m was considered. This depth range showed mean j values of 34° and 33°, respectively, depending upon the correlations adopted. To get at least an indicative value of the ultimate capacity, the foundation was initially considered in the two extreme situations of a continuous beam with width equal to 2.8 m (thickness of the foundation walls) and of a square foundation with a side equal to 12.3 m (base of the tower). By adopting the smallest shear resistance angle j = 33°, and prudently assuming the groundwater to be at the foundation level, an ultimate capacity of 2788 kN/m2


7

and the second case 4583 kN/m2 was calculated. The unit load on the soil was 1161 kN/m2 and the safety factor was therefore 2.4 and 3.95, respectively. The effective safety factor will lie between these and even the lower value can be considered sufficient to guarantee the stability of the foundation. In the period from January 1987 to February 1989, the maximum measured variation in level was 400 mm. Even though there are no reasons to believe that the variations around the tower were greater, the effect of an abnormal drop in level of 3 m was examined. The soil was considered deformable down to the depth at which Δsv the variation in pore pressure stale is about 0.2 of the s¢v geostatic pressure. The average settlement calculated was 8 mm. Since the ground around the tower is relatively uniform, it must be assumed that the differential settlements are negligible. In order to evaluate the maximum theoretical distortion possible, penetrometric profiles were calculated at opposite sides using all the minimum and maximum values recorded during the various tests at various depths. Maximum settlements of 11 mm and a minimum of 6 mm were obtained. The ultimate differential settlement would, therefore, be 5 mm and consequently of negligible effect on the stress–strain condition within the structure.

1.2.2.3 Physical, chemical and mechanical tests on the components To determine the effect of any possible chemical or physical degradation of the masonry, numerous samples of mortar were taken from the large blocks of masonry. The bricks and stones showed no signs of degradation except in the outermost area; in fact, even in the most deteriorated areas of the examined blocks, the degradation did not penetrate any deeper than 80–100 mm. Chemical and mineralogical/petrographic analyses were performed on 22 samples of mortars. The chemical analyses revealed that the binder used for the mortars during the first building phase consisted chiefly of lime putty (soluble silica 0.28–0.40%) and that the aggregate was mainly siliceous (unsoluble residue between 69.94 and 82.04%). The binder/aggregate ratio varied from 1:3 to 1:5. Similar values were obtained for the mortars of the second and third building phases. The porosity was around 12–13% and the bulk density about 18.5 kN/m3. In most cases, the sulphur trioxide content was negligible (around 0.06). Optical inspection of thin sections of the mortar revealed numerous porous areas which were sometimes covered by a layer of carbonates of relatively recent formation, thus making the surface of the mortar far more resistant. This could be the result of calcareous matter being deposited by flows of water. Similar deposits have been found in different areas of the masonry [6] and in each case the covering layer strengthened the surface of the mortar. Thin section mineralogical/petrographic analysis also confirmed the total carbonation of the mortars and the siliceous nature of the aggregate and revealed corrosion along the surface of contact between certain aggregates (pebbles of stained quartz and flintstone, etc.) and the binder. As it is quite common [7], however, the reaction products cause no fissures inside the mortars. The adhesion

8


between mortar, bricks and stone was also fairly good (except in cases where the building techniques had left large voids). The mortars were consistent, as the mechanical tests confirmed, had a low content of sulphates and did not show heavy deterioration except for the outermost ones. The possibility of any significant reduction in structural strength of the masonry due to the chemical or physical degradation of the mortars or other materials was, therefore, excluded. Since the collapse was not caused by the degradation of the building materials or sudden or differential settlement, attention was turned to how dead and live loads might have affected the mechanical behaviour of the materials over time. Compression tests were performed on small cubes of mortar [5] (with sides ranging from 2.7 to 3.5 mm) taken from the mortar joints of the inner conglomerate. The strength was 2.92–13.37 N/mm2, with a mean value of 6.45 N/mm2 and SD 49% (n = 11). Since the specimens are very small these results are merely indicative. Nevertheless it can be said that the results confirm the chemical and physical analyses; in general, the mortar was consistent despite its heterogeneity and very hard and strong when sampled. The compressive strength of the bricks, on the other hand, as tested on cubes with sides of 40–50 mm was rather low: the mean value was 13.37 N/mm2, with SD 26% (over 50 specimens). The elastic modulus between 20 and 60% of the peak stress was 1973 N/mm2 for the bricks and 905 N/mm2 for the mortars [5]. Tests reported later show that the strength of the masonry was less than that of the mortar, suggesting that the low carrying capacity of the masonry was mainly due to the construction technique.

1.2.2.4 Compression tests on masonry prisms Compression tests were performed on prisms of masonry, cut from large blocks that had remained intact, in order to obtain the stress–strain curve up to and beyond failure [5]. Fatigue tests were then performed using a load value reproducing the stress induced by the dead load and applying a cyclic load, the amplitude of which reproduced the stress variations due to the effects of the wind. Lastly, a survey of the effects of the dead load of the tower on the behaviour of the materials over time was carried out by means of constant load tests. Prisms measuring 4000 × 600 × 700 mm approximately were obtained from the recovered blocks. These dimensions were chosen so as to simulate the behaviour of the masonry, which was very thick (2.8 m) compared to height (60 m) and plan form (12.3 × 12.3 m) of the tower. The load-control or displacement-control compression tests were carried out with a 2250 kN, servo-controlled MTS hydraulic press, with programmed cycles. Monotonic compression tests to failure were conducted on seven masonry prisms from the first two building phases. The tests were carried out under displacement-control, at rates of 3.85 × 10–3 mm/s and 9.62 × 10–4 mm/s.


Figure 1.7: s–e curves of prisms subjected to monotonic compression tests.

9

Figure 1.8: s–e curve obtained for a cyclic compression test.

Figure 1.7 shows the curves obtained for the seven prisms, two of which (102A and 102B) were tested by applying the load in the direction of the horizontal joints. The peak strengths and ultimate strain values vary quite considerably: low ultimate strains appear to correspond to higher strengths. Strength varies from 2.0 to 4.1 N/mm2, ultimate strains from 3.0 to 5.5 × 10–3 and the modulus of elasticity, defined between 20 and 40% of the peak stress, varies from 719 to 1802 N/mm2. Five prisms were tested to failure by means of loading and unloading cycles applied every 0.5 N/mm2 under displacement-control conditions up to and beyond the peak stress. Strength varied from 1.8 to 3.3 N/mm2, the elastic modulus from 544 to 1455 N/mm2 and the ultimate strains from 3.6 to 8.5 × 10–3. A typical curve is shown in Fig. 1.8. Although on average the strength is lower than that of the seven prisms subjected to the monotonic tests, the cycles appear not to have any great influence on the s–e curve, the peaks of which at each loading approximate well to points of the monotonic curve. 1.2.3 Long-term tests The behaviour detected from cycling tests and particularly the evident increase in deformation while the stress was kept constant (Fig. 1.8) led to a study of the effects of fatigue and long-term tests at constant load. The experimental research is described in the following sections. 1.2.3.1 Fatigue tests It is well known that repeated load cycles cause damage to the material. The damage originates from imperfections in the material itself, such as small cracks which

10


get larger as the cycling load is applied. Generally, failure occurs at peak load value lower than that measured when the load is statically applied. In the case of a masonry structure, fatigue may be caused by the repeated action of horizontal loads such as wind or seismic loads. In the particular case of the tower, no appreciable seismic effects have been recorded, whereas the effects of the wind must certainly have been felt over the centuries, causing significant variations in the stress due to the static load of the tower. As mentioned above, the damage caused by repeated cycles of loading and unloading is not very high when the average load applied is low and cycles are not frequent. However, significant damage may be caused if the cycles are repeated at an average stress close to the ultimate capacity [8]. Three prisms were subjected to cyclic loads corresponding to calculated stress variations of 0.2 N/mm2 starting from very high compression values similar to those produced by the dead load as calculated at the most loaded points of the structure. Cyclic loads corresponding to repeated wind effects, simulated according to the Italian Code, produced no appreciable damage except for higher strains (Fig. 1.9), when the loads starting from stress values very close to failure were applied. The fact that the load history included one or more cycling phases did not reduce the failure values (which remained 1.7, 2.7 and 4.4 N/mm2) obtained during the monotonic tests.

Figure 1.9: s–e curve obtained during the fatigue test performed to simulate wind effects.

Figure 1.10: s–e and e–t curves obtained during a step-by-step constant load test.


11

1.2.3.2 Constant load tests Displacements measured on the prisms during loading showed a tendency to increase at constant load suggesting that the behaviour of the material could be time-dependent. During the constant load tests, almost all the prisms were tested under load control up to 1.0–1.5 N/mm2. The stress was then increased in steps of 0.14 N/mm2, at intervals of at least 15 min. The increase in the effects of strain was on average 1.6 × 10–3 for each 15-min interval at constant load. At higher stresses close to the ultimate strength of the material, the time-dependent effects of the constant load evolved more rapidly. No further load increases were made until the increase in strain stopped. At the last step the strain rate continued to increase rapidly until failure occurred suddenly after a period of time varying between 10 min and 2 or 3 h. It seems reasonable to assume that the time needed to reach collapse is a function of the ratio between the load applied and the maximum load the specimen is able to withstand. The curves of strain as a function of time, (Fig. 1.10) clearly show the type of behaviour described earlier. At loads over approximately 70% of the ultimate compression strength, a small number of cracks appeared on one of the sides of the tested specimens. The cracks were found chiefly on the bricks and at the surfaces of contact between the mortar and the stone or bricks of the inner face of the wall. The cracks, which were always vertical, were hardly visible right up to the moment of collapse (see Fig. 1.11a and b). Although the tests were carried out under load control, it was almost always possible to keep the collapse under check and thus prevent the sudden spalling, which often characterizes the failure of prisms of solid bricks arranged in regular courses, and/which is often an indication of a brittle failure of the bricks. Structural analysis carried out by a FE (finite element) elastic model [5] revealed that some parts of the tower were subjected to severe stress, very often close to the failure limits found experimentally. This probably led to the gradual evolution of micro-fissures which, over the centuries, may have contributed to the sudden collapse of the material for no apparent immediate cause and without the appearance (a)

(b)

Figure 1.11: Width of cracks after (a) 22 min and (b) 60 min under a constant stress of 2.0 N/mm2 (peak stress).

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Figure 1.12: Vertical cracks on the external wall of the tower (1968). of warning signs, such as large cracks or spalling, even during the days immediately preceding the collapse. A careful examination of the photographs taken by archaeologists for the Civic Museums in 1968 reveals that even at this time there were thin vertical cracks largely diffused on the outer face of the wall. These cracks were extremely difficult to see from the Piazza and were similar to those that appeared on the specimens during the tests (see Fig. 1.12).

1.3 Long-term behaviour of masonry structures Masonry is a composite material and its mechanical and physical behaviour strongly depends on that of its components (mortar and brick/stone). Mortar influences mainly the deformability and bricks or stones influence mainly the strength. Historic buildings are very often characterized by high values of deformations, which may have taken place in the past or may still be in progress and may lead the building even to unexpected failure. Early deformation due to delayed hardening of hydrated mortars based on carbonation is typical of ancient buildings presenting thick mortar joints; multiple leaf masonry is usually characterized by differential creep displacements induced by the different deformability of the leaves; persistent and cyclic loads can give rise to a creep–fatigue interaction and to greatly retarded strain. 1.3.1 Deformation during mortar hardening It has been shown that early creep behaviour, due to the carbonation process of fresh mortar, can last for a long time particularly when mortar was made with


13

hydrated lime [9]. This can be the case, for instance, of very thick ancient walls or of masonry characterized by very thick mortar joints like those of St. Vitale in Ravenna shown in Fig. 1.13 [10]. Increasing deformation due to heavy dead or cyclic loads can vary the geometry of masonry walls in a visible way already during the construction. These modifications can occur locally, or involve a whole structural element. Large displacements and deformations frequently involve piers and columns like those of gothic cathedrals (Fig. 1.14) [11] due to the horizontal thrust exerted by vaults and arches or due to soil and structure settlements. Generally speaking, old or ancient structures are continuously subjected to modifications concerning their geometry and their state of stress and strain. J.L. Taupin [12] says that ‘time moulds the structure of towers, cathedrals, bridges etc. which we would like to consider immutable.’ Time plays a role both in the short and in the long run dispersing and returning energy in three ways: through deformations and settlements, through vibration, and through material modification or deterioration. Figure 1.15 shows a detail of the well-known Hagia Sophia at Istanbul, where the rotation of a column and the deformation of an arch in the north gallery can be clearly observed [13]. Figure 1.16 shows a much less famous small Romanesque church, St. Maria la Rossa in Milan, dating from the tenth to thirteenth century. This single aisled brickwork masonry building is covered by a timber gable roof, with a chancel comprised by two small chapels besides the choir, terminating with a semicircular apse. The church was subjected to different transformations during centuries, and its present aspect is due to the restoration works done in the 1960s. In the picture the tilt of the lateral walls and the deformation of the central arch can be seen [14].

Figure 1.13: View of the Basilica of San Vitale in Ravenna (Sixth century AD).

14


Figure 1.14: Pillar of the Cathedral of Salisbury [11].

Figure 1.15: Hagia Sophia, north gallery looking west.

Figure 1.16: Church of St. Maria la Rossa, view of the central nave looking east.


15

1.3.2 First, secondary and tertiary creep in rock and hardened masonry The influence of time on the mechanical behaviour of stiff clays, soft rocks, fresh cement mortar, concrete and hardened concrete becomes evident when both uniaxial–triaxial compressive test at different rate of loading and compressive test at vertical constant load are carried out. On the one side, when testing compression of soft porous materials a decrease of the rate of loading produces a decrease of the vertical peak stress and of the stiffness of the material (Fig. 1.17 v. Cook). On the other side, if a constant load is applied an increase of deformation develops which is commonly subdivided into three phases: the so-called primary, secondary and tertiary creep (Fig. 1.18 v. Cook) [15]. The appearance of one or more of these phases and the strain rate of the secondary creep phase depend on the stress level. Very poor research was done before the collapse of the Civic Tower in Pavia, on the creep behaviour of masonry structures, apart from the papers published by Lenczner [16].

Figure 1.17: Dependency of strain on the loading rate.

Figure 1.18: First, secondary and tertiary creep.

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The influence of time on the mechanical behaviour of masonry structures under high states of stress became evident after the collapse of the Tower of Pavia, when the identification of a time-dependent behaviour, probably coupled in a synergetic way to cyclic loads [17], was identified as a possible explanation of the sudden collapse.

1.4 Collapse and damage of towers due to long-term heavy loads The failure of monumental buildings is fortunately an exceptional event; nevertheless, when their safety assessment is required, any risk factor that may affect the integrity of the buildings has to be taken into account. Ancient buildings often show diffused crack patterns, which may be due to different causes in relation to their original function, to their construction technique and to their load history. In many cases it is simply the dead load, usually very high in massive monumental buildings, which plays a major role into the formation and propagation of the crack pattern. The only way to prevent the occurrence of these failures is continuous observation and maintenance of these structures. 1.4.1 St. Marco bell-tower and St. Maria Magdalena tower in Goch The first well-studied example of the collapse of a tower in Italy was certainly the one of the bell-tower of St. Marco in Venice in 1902 (Fig. 1.19) [18]. The tower collapsed suddenly with no previous evident signs of heavy damage. In the long debate following the tower collapse and in the long report made by Luca Beltrami in [18], the settlement of foundation was excluded from the causes and it was clearly described that the damage was interesting considering the structure and the repairs made 45 years earlier by confining the bearing corners of the tower with steel reinforcements (Fig. 1.20). A similar situation occurred in June 1902 with the collapse of a bell-tower in Corbetta, near Milan, in the same year. The tower was under modification, being elevated from the original 24 m to 41 m in 1860 and by adding a spire in 1900. In 1993, the bell-tower of Sancta Magdalena church in Goch collapsed suddenly during the night (Fig. 1.21); it had already been decided a few years earlier to start a repair intervention due to the extent of the damage detected. Probably the waiting time was too long, taking into account that the tower was badly cracked for a long time and also damaged during the last world war. 1.4.2 The bell-tower of Monza Cathedral and the Torrazzo of Cremona The bell-tower of the Cathedral of Monza is a sixteenth-century building made of solid brick masonry, at present subjected to a repair intervention. Its walls were showing large vertical cracks crossing the whole transversal section of the walls on the west and east (Fig. 1.22a and b), which were continuously widening at a constant rate [19, 20]. These cracks were certainly present before 1927, when they were roughly monitored. Wide cracks were also present in the corners of the tower


Figure 1.19: The bell-tower of the St. Marco Basilica in Venice.

17

Figure 1.20: Detail of the collapse with the reinforced pillar [18].

at a height of 30 m, together with a damaged zone at a height of 11–25 m with a multitude of very thin and diffused vertical cracks. A similar crack pattern is visible on the Torrazzo, a medieval brickwork tower adjacent to the Cathedral of Cremona (Fig. 1.23a and b) [21]. The precise date of construction is not known but is assumed to be around the thirteenth century. It belongs to a group of monuments, including the Cathedral, the Baptistery, the Town Hall Palace, the Militia Loggia, which forms one of the most beautiful Italian squares. The external load-bearing walls of the tower, which is about 112 m tall, have been showing several cracks for many years [21]; since the crack pattern has experienced an evolution, a time-dependent behaviour of the material may possibly be assumed to cause the phenomenon.

1.5 The role of investigation on the interpretation of the damage causes On the basis of the previous experience the authors have developed investigation procedures for the safety of these structures; the idea came first when studying the collapse of the Civic Tower in Pavia.

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Figure 1.21: The church of St. Magdalena in Goch (Germany) after the collapse of the bell-tower, 1993. The procedure is based on the following steps: (i) historic research to know the evolution of the structure over time, (ii) geometrical and crack pattern surveys, which allow one to understand the evolution of the structure, to calculate weights and give a first interpretation of the crack pattern, (iii) geognostic investigation and monitoring, to understand the soil–structure interaction, (iv) on-site mechanical and non-destructive testing (radar, sonic, etc.) to define local states of stress and stress– strain behaviour of the material, (v) chemical, physical and mechanical tests on mortars, brick and stones to find their composition and their characteristics, (vi) if necessary, passive and active dynamic tests on site to survey the overall structural behaviour and (vii) monitoring system applied to the structure when necessary. 1.5.1 The bell-tower of the Cathedral of Monza The bell-tower of the Cathedral of Monza, is a masonry structure 70 m high, with a square plan (a side is 9.7 m long) with solid brick walls 140 cm thick. The tower construction started in 1592, probably following the design of Pellegrino Tibaldi, the architect of the Pavia tower belfry, and ended in 1605 [19, 22]. The only damage to the tower reported by the documents occurred in 1740 and was due to a fire which started in the bell-tower and caused the collapse of the belfry dome and roof and the fall of the bells with their supporting frame down to the vault of the


Figure 1.22: Survey of the crack pattern for the bell tower of the Cathedral of Monza: (a) west and (b) east sides.

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Figure 1.23: Survey of the crack pattern for the Torrazzo tower: (a) west and (b) east sides.

first floor at 11 m. No damages were reported in other known calamities, such as lightning or thunderstorms through the centuries. Nevertheless cracks are present since 1927 or even before, as mentioned above. From 1978 the cracks have been surveyed with removable extensometers: they show a slow increase of their opening through time. From 1988 the rate of opening seems to be increasing faster. The trend of widening of the three main cracks was calculated as 30.6, 31.3 and 39.7 μm/year from 1978 to 1995. Actually if this trend is considered from 1988 to 1997 the values change, respectively, into 41.2, 35.2 and 56.2.

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The first step of the investigation procedure [19] was the geometrical survey [20]. A geodetic network set up in the square of the Cathedral in 1993, was used as support. No relevant leaning was measured due to the small subsidence which is taking place in the square. Two distinct products were obtained: (i) a detailed three-dimensional model from which the external and internal prospects and the vertical sections were obtained and (ii) a simplified model for which only the essential aspects of the geometry were preserved for the structural analysis. The survey of the crack pattern showed that the tower walls have a dangerous distribution of passing-through cracks on the western and eastern load-bearing walls for more than 50 years, and of a net of thin vertical cracks from a level of 11 m up to 30 m (Fig. 1.22). Other cracks can be seen on the internal walls of the tower; they are very thin, vertical and diffused along the four sides of the tower and deeper at the sides of the entrance where the stresses are more concentrated. The thin diffused cracks run 450 mm deep inside the section, reducing its total working thickness from 1400 mm to no more than 900 mm. From laboratory tests it was found that the mortar is very weak and made with putty lime and siliceous aggregates; also the bricks were of poor strength (between 4 and 12 N/mm2 measured on 40 mm-side cubes). On-site single flat-jack tests were carried out at different heights of the tower (5.4, 5.6, 13.0, 14.0, 31.5 and 38.0 m) and the stress values against the height are plotted in Fig. 1.24. The maximum compressive stress acting in the tower, measured on site by the flat-jack test, is about 2.2 N/mm2. The most interesting information came from the double flat-jack test results, where it was possible to see the real risky situation if compared with the local state of stress measured by the single flat-jack (Fig. 1.25). Passive dynamic tests using the bell ringing were also carried out monitoring the dynamic excitation of the extensometers applied across the

Figure 1.24: Single flat-jack tests of Monza.

21

Failures due to Long-Term Behaviour of Heavy Structures (b)

3.00

2.50

Local state of stress

2.00 1.50 1.00

Stress [N/mm2]

2.50

Stress [N/mm2]

3.00

2.00


(a)

1.50 1.00 0.50

0.50

εh

εv

0.00

0.00

εh

εv

-2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00

-2.00 -1.00 0.00

1.00

2.00

3.00

4.00

5.00

Strain [μm/mm]

Strain [μm/mm]

Figure 1.25: Monza tower stress–strain plot at (a) 5 m and (b) 13 m height.

main cracks, giving under these cycling stresses a maximum peak to peak (opening to closing) of 28 μm that has to be compared with a daily variation of 100 μm due to the temperature effects. The diagnosis based on the experimental survey and on the FE modelling lead to the conclusion that the bell-tower was a high risk building and needed a quick intervention. In Chapter 8 the preservation and repair intervention which is still being carried out is illustrated. 1.5.2 The ‘Torrazzo’ of Cremona The bell-tower of the Cathedral of Cremona, an interesting historic town not far from Milan (Italy), is known by the nickname ‘il Torrazzo’ from long time ago. The tower is situated at the northern side of the Cathedral and it is connected to it by a Loggia called ‘Bertazzola’. The geometry of the tower is rather complex, being composed of a lower part (Romanesque tower) with a square plan of 13 m side and 70 m high, an upper part, the Ghirlandina, with an octagonal plan (2.5 m side), more than 40 m high. The Torrazzo is known as the tallest medieval belltower in Europe being 112 m high [23]. The lower part of the tower, with a square plan, is a massive construction with few openings localized on the western and eastern sides. The upper Ghirlandina appears as a light structure with arches and large openings on all the four sides. The staircase from the lowest level up to the Ghirlandina level was built within the thickness of the walls (approximately 3.3 m thick). Along the staircase, covered with a barrel vault, the thickness of the external wall is approximately 1 m, while the thickness of the internal wall is 0.7–1 m with the span of the staircase measuring 1.3–1.6 m. The staircase allows one to reach some internal vaulted rooms.

22


Archive research did not clarify the date of construction; nevertheless the highest number of reference data collected locates the date of construction between the eighth and the thirteenth centuries. In 1491, the porch of the Bertazzola was added connecting the Torrazzo with the Cathedral and in 1519 the Loggia was built resting on the arches of the porch. Maintenance works were carried out starting from the fifteenth century. These works mainly concerned the highest part of the tower damaged by storms and lightening, especially the stone and brick columns which were sometimes substituted. The last intervention at the Ghirlandina was carried out in 1977. The works performed were the following: connection of structural and decorative elements, construction of a concrete frame sustaining the twin columns of the ‘Stanza delle Ore’ (at 85 m height) and surface treatments of stone and brick elements with an epoxy resin. The first step of the investigation carried out in 1998 was the geometrical survey. A principal network defining fixed points in the horizontal and vertical plan was set up having 21 nodes inside and around the tower made with fixed nails. The co-ordinates of the nodes were determined with a T2000 WILD equipment. The vertical and horizontal profiles were determined by rays starting from the network nodes, using a TC1600 DIOR system and an auto scanning Laser System MDL. A photogrammetric survey of the external prospects was also carried out using TC1600-DIOR and T460* DISTO equipment. The prospects were obtained by a Rollei special software, MSR. The survey enabled the finding of some irregularities of the structure: (i) a 21 cm horizontal displacement of the centre of the tower in direction north-east, calculated from the ground level to the top at 112 m, (ii) a non-symmetrical reduction of the plan dimensions from the ground level to the top at 31 cm for the north-east corner and 66 cm for the south-west corner, (iii) the Ghirlandina not being perfectly centred on the square part of the tower, but with a slight counter-clockwise rotation toward west. The presence of a diffused crack pattern particularly on the western and the eastern sides of the tower and on the Ghirlandina can indicate high states of stress due to the dead loads, the temperature variations and/or to a slight leaning. The survey was carried out on the outer surfaces by reaching the height of 60 m thanks to a special crane. The crack pattern is certainly also influenced by differential movements due to temperature variation between one side and the other of the tower. The highest variations certainly occur between the north and the south side. The west side has a diffused fissuration with passing-through cracks; the cracks are mostly vertical and start from approximately 20 m. Important cracks appear also between 48 and 60 m from the ground level (Fig. 1.23a). The north side is cracked in the centre between 27 and 40 m and at the north-east corner. The east side is cracked between 6 m and 20 m from the ground level and between 35 and 60 m (Fig. 1.23b). The south side has few cracks located between 14 m and 27 m. The Ghirlandina shows the most important cracks, on the buttress and on the brick columns particularly on the south-west corner. Also the internal part of the tower, along the staircase and inside the rooms shows a diffused crack pattern with some passing-through cracks. Three thresholds were established concerning the measure of the opening of the cracks: 10 mm. The crack


23

pattern survey helped one to understand and interpret roughly the mechanical damage and to locate the position for the monitoring system. The inspection of the masonry surface and the inside of the walls leads to the following description: (i) the walls are made with solid bricks and no rubble was used for the inner part of the section; (ii) the bricks are regular with varying dimensions: 240–280 × 100–1200 × 55–70 mm; (iii) the external walls of the Ghirlandina are irregularly scaled and tooled; (iv) the colour of the bricks is variable red, dark red, yellow, orange etc.; (iv) the mortar joints are regular with thickness variable from 10 to 30 mm; (v) different techniques of jointing and pointing can be found and often the vertical joints seem to be void or recessed; (vi) the masonry texture is also regular with header and stretcher alternatively positioned; (vii) an external leaf one brick thick with a weak collar joint is certainly present along the staircases, in the internal rooms and at the level of the Bertazzola and more research is needed to test the real extension of this leaf along the tower; (viii) in the staircase walls a row composed of 4–22 headers is repeated at rather regular intervals as if it should represent a connection of the external leaf to the internal one; (ix) several scaffolding holes externally closed can be seen along the masonry walls; and (x) numerous restorations by brick substitution can also be seen externally and internally. Together with the geometric survey an accurate survey of the material decay was carried out. Concerning the reinforced concrete frame (85 m level) the columns between the north and north-east and the east and south-east side show washout of the binder, formation of carbonates near the stirrups with partial detachment of the reinforcement cover (no more than 1 cm thick) and reinforcement corrosion. Sixteen samples of bricks and mortars were collected from the masonry: five from the facades, four inside from the walls of the internal rooms, four along the staircase and three from the external and internal walls of the Ghirlandina. The maximum depth of sampling was 300 mm. All sampling operations were documented graphically or photographically. Laboratory tests were carried out on mortar and bricks. Chemical analyses showed that the mortar binder was hydrated lime (probably lime putty) and the aggregates were mainly siliceous. Two types of bricks were used, which differ in colour (red and brown) and also in properties. The red bricks have high absorption (21–28.8%), low strength 8–12.4 N/mm2 in compression and in tension (0.1–1.6 N/mm2) and low modulus of elasticity (1000–2175 N/mm2); the brown bricks have lower absorption (18.5–21.7%), higher compressive strength (9.4–25.43 N/ mm2) and tensile strength (2.2–2.6 N/mm2) and modulus of elasticity (1725–4417 N/mm2). The two types of bricks are present everywhere in the tower, so an average between the two bricks can be considered as reference. In order to detect the suspected existence of an external cladding in use during the Middle Age as a false curtain to hide the roughness of the real wall, bricks were sampled from the external wall of the Bertazzola at 6 m level and from the walls of the ‘Stanza dei Contrappesi’ at 13.6 m level. This external leaf was confirmed and its thickness is around 12 cm. The sampling allowed one to find large areas

24


where the leaf seems to be detached from the rest of the wall; following these results the application of NDT technique was required in order to map the detached areas which represent structurally a reduction of the wall section to be taken into account when modelling. All the areas from where samples were taken were then repaired with similar bricks and mortars. Flat-jack tests: Single and double flat-jack tests were carried out on the Torrazzo. The single flat-jack test was also used to study the behaviour of the external leaf of the wall. Different types and dimensions of flat-jacks were used: (i) 240 mm × 12 mm rectangular jacks where the detachment of the external leaf was suspected, (ii) 400 mm × 200 mm rectangular jacks and (iii) 350 mm × 240 mm semicircular jack where no detachment was suspected and for the double jack-test. Twenty-one tests were carried out, of which 19 were with single flat-jack and 2 with double flat-jack: 3 single flat-jack tests at between 1 and 5 m from the ground, 7 single flat-jack tests at 7 m, 10 single flat-jack between 15 and 18 m and 1 single flat-jack at 22 m. The double flat-jack tests were carried out at 7.2 and 19 m from the ground. The results of the single jack tests are reported in Fig. 1.26 and show clearly two situations: a state of stress varying between 0.4 and 0.9 N/mm2 where the test found a detached leaf and a state of stress varying from 1.01 and 1.81 N/mm2 where no detachment was found. Also double flat-jack tests were performed and Fig. 1.27 shows the stress–strain plots. It was impossible to carry out tests at higher levels due to the lack of scaffolding and of appropriate means for carrying the jack equipment. In future other tests will be carried out.

3.50 masonry section 3.3 m

3.00

masonry section 1 m

15.2-16.5 m

presence of veneer inner walls (rooms)

Stress [N/mm2]

2.50

16-17.8 m 16.6-17.8 m

2.00

7.2-7.7 m

7.2-7.4 m 15.4-19.1 m 7-7.7 m

1.50 1.7 m

5m

1.00 0.50 0.00

Figure 1.26: Single flat-jack tests of Cremona.


3.50

3.50

3.00

3.00


2.00 1.50 1.00

2.00 1.50 1.00

0.50 0.00

2.50 Local state of stress

2.50

Stress [N/mm2]

(b) 4.00

Stress [N/mm2]

(a) 4.00

25

0.50

εh

εv

-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00

0.00

εh

εv

-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00

Strain [μm/mm]

Strain [μm/mm]

Figure 1.27: Stress–strain plot at (a) 7.2 m and (b) 19 m height.

1.6 Comparison between the two towers Since the bell-tower of Monza is considered a building with high risks of collapse, a comparison between the data collected on both towers seems to be useful to understand better the real situation of the Torrazzo. As mentioned above, the mortar composition of the two bell-towers does not differ much from one another, though the Torrazzo mortar seems to be more consistent. The bricks of the Monza tower are generally weaker than those of the Torrazzo (Fig. 1.28a and b) except for the brown type, which is mainly used on the outside surface of the bearing walls and very seldom used in the interior. On the contrary the brown and the red bricks are evenly distributed in the Torrazzo walls. It is also interesting to compare the results of single and double flat-jack tests carried out on the two towers. The results of four tests, two for each tower are discussed. In Fig. 1.27a and b maximum stress reached with the double flat-jack test on the Torrazzo together with the values obtained with the single one, respectively, at 7 and 19 m height are considered, showing an elastic linear behaviour up to, respectively, 2.45 and 2.7 N/ mm2. The maximum stress level when cracks clearly appear is, respectively, 3.77 and 3.77 N/mm2 and the state of stress measured is 1.5 and 1.5 N/mm2. So in these two cases the safety coefficient at collapse is certainly more than 3. In Fig. 1.25a and b the results of two tests at the height of 5 and 13 m, out of the four carried out on the walls of the Monza tower, are considered. Here the linear elastic behaviour stops at, respectively, 1.65 and 1.1 N/mm2 and the maximum stress reached before cracks propagated was 2.62 and 1.87 N/mm2. The measured local state of stress was, respectively, 1.67 and 0.98 N/mm2. In these two cases the safety

26


32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0

(b) 26

σ

Stress [N/mm2]

Stress [N/mm2]

(a) 34

red brick brown brick

εh -20 -16 -12 -8 -4 0 4 8 Strain [μm/mm]

εv

24 22 20 18 16 14 12 10 8 6 4 2 0

σ

red brick brown brick

εh -20 -16 -12 -8 -4 0 4 8 Strain [μm/mm]

εv 12

16 20

12 16 20

Figure 1.28: Stress–strain plot for (a) Monza tower bricks and (b) Torrazzo bricks.

coefficient at failure is much lower than in the first one and certainly less than 2. Furthermore in the case of the Torrazzo the modulus of elasticity is much higher and the Poisson ratio much lower than in the case of the Monza tower.

1.7 Conclusions The investigation carried out on the specimens cut from the walls of the Pavia tower after its collapse allowed formulating for the first time on an ancient masonry the hypothesis of a collapse due to the long-term behaviour of the material. Probably since the construction of the bell-tower in the sixteenth century the structure was under a high state of stress and the damage very slowly but continuously increasing until the collapse. The creep behaviour of the material was shown clearly during the experimental research which started in 1989 and is still developing, as will be shown in Chapter 2. Examples of other similar situations were found in the history of collapses of towers and damages or collapses of churches (Noto cathedral). The two experiences of investigation on tall towers allow some concluding remarks: • the on-site and laboratory tests carried out following the methodology described in the first section allowed one to detect situations of danger and to characterize the materials and calculate input parameters for the structural analysis; • the laboratory tests were able to show the difference of properties of the masonry in the two buildings and that where the materials used are weaker, the damage is more;


27

• the flat-jack test is a powerful tool to calculate the actual state of stress in compression and to detect the mechanical behaviour of the masonry, so that two different situations (Torrazzo and Monza towers) can be compared; • the investigation allowed the authors to state that the situation of the Monza tower is very difficult and that a quick intervention has to be started; • for the Torrazzo, even if the state of damage is not considered dangerous, a monitoring system has been set up, and the tower will be under control for 4–5 years at least in order to study its further evolution; in the meantime some repairs are being done for the external surfaces. FE numerical models were used for the static and dynamic analysis of the two towers [19, 23]. The results of the experimental research were used to calibrate the FE models.

References [1] [2] [3] [4]

[5]

[6] [7] [8]

[9]

[10]

[11]

Panazza, G., Campanili Romanici a Pavia, Arte Lombardia, pp. 18–27, 1956. Ward-Perkins, B., Scavi nella Torre Civica di Pavia, Sibrium, 12, pp. 177– 185, 1973–75. Milano, F. & Toscani, X., Il fond di documenti relativi alla Torre Civica esistence nell’Archivio Comunale di Pavia, Sibrium, 12, pp. 467–493, 1973–75. Anti, L. & Valsasnini, L., Indagini preliminari all’analisi strutturale ed alle prove sui materiali della Torre Civica di Pavia, TEMA J., L’Arsenale, Venezia, 1991. Binda, L., Gatti, G., Mangano, G., Poggi, C. & Sacchi Landriani, G., The collapse of the Civic Tower of Pavia: a survey of the materials and structure. Masonry International, 6(1), pp. 11–20, 1992. Knoffel, D.F.E. & Wisser, S.G., Microscopic investigation of some historic mortars, Proc. 10th Int. Conf. Cement Microscopic, S. Antonio, Texas, 1988. Baronio, G. & Binda, L., Reazioni di aggregati in intonaci antichi, Conv. Intonaco: Storia, Cultura e Tecnologia, Bressanone, pp. 269–276, 1985. Binda, L., Anzani, A. & Mirabella Roberti, G., The failure of ancient towers: problems for their safety assessment, Int. Conf. on Composite Construction - Conventional and Innovative, IABSE, Insbruck, pp. 699– 704, 1997. Ferretti, D. & Bazant, Z.P., Stability of ancient masonry towers: moisture diffusion, carbonation and size effect, Cement and Concrete Research, 36, pp. 1379–1388, 2006. Binda, L., Lombardini, N. & Guzzetti, F., St. Vitale in Ravenna: a survey on materials and structures, Int. Conf. Historical Buildings and Ensembles, invited lecture, Karlsruhe, pp. 113–124, 1996. Gordon, J.E., Strutture, ovvero Perche’ le cose stanno in piedi, Edizioni Scientifiche e Tecniche, Mondadori, 1979.

28 [12] [13] [14]

[15] [16]

[17]

[18] [19]

[20]

[21]

[22] [23]


Taupin, J.L., Réflexions sur la cathedrale Saint-Pierre de Beauvais. ANAGKH, 12, pp. 86–100, 1995. Mainstone, R.J. Haghia Sophia: Architecture, Structure and Liturgy of the Justinian’s Great Church, Thames and Hudson, 1985. Binda, L., Mirabella Roberti, G. & Guzzetti, F., St. Vitale in Ravenna: a Survey on materials and structures, International Symp. on Bridging Large Spans (BLS) from Antiquity to the Present, Istanbul, Turkey, pp. 89–99, 2000, ISBN 975-93903-02. Jaeger, J.C. & Cook N.G., Fundamentals of Rock Mechanics, 2nd edn, Chapman & Hall: London, 1976. Lenczner, D. & Warren, D.J.N., In situ measurement of long-term movements in a brick masonry tower block. Proceedings of the 6th IBMaC, Rome, pp. 1467–1477, 1982. Anzani, A., Binda, L. & Mirabella Roberti, G., The behaviour of ancient masonry towers under long-term and cyclic actions, in Proc. Computer Methods in Structural Masonry – 4, Computer & Geotechnics: Swansea, pp. 236–243, 1998. Fradeletto, A., et al., Il campanile di S. Marco riedificato. Studi, ricerche, relazioni, ed. Comune di Venezia, Carlo Ferrari: Venezia, 1912. Binda, L., Tiraboschi, C. & Tongini Folli, R., On site and laboratory investigation on materials and structure of a bell-tower in Monza. Int. Zeitschrift für Bauinstandsetzen und baudenkmalpflege, 6, Jahrgang, Aedification Publishers, Heft 1, pp. 41–62, 2000. Binda, L., Tongini Folli, R. & Mirabella Roberti, G., Survey and investigation for the diagnosis of damaged masonry structures: the ‘Torrazzo of Cremona’. 12th Int. Brick/Block Masonry Conf., Madrid, Spain, pp. 237–257, 2000. Binda, L. & Poggi, C., Ricerca volta a stabilire le condizioni statiche ed il comportamento meccanico della muratura del campanile del Duomo di Cremona. Relazione Finale, Contratto Consiglio della Chiesa Cattedrale di Cremona, 1999. Scotti, A., L’età dei Borromei in Monza. Il Duomo nella storia e nell’arte, Electa: Milano, 1989. Binda, L., Falco, M., Poggi, C., Zasso, A., Mirabella Roberti, G., Corradi, R. & Tongini Folli, R., Static and dynamic studies on the Torrazzo in Cremona (Italy): the highest masonry bell tower in Europe. Int. Symp. on Bridging Large Spans from Antiquity to the Present, Istanbul, Turkey, pp. 100–110, 2000.

CHAPTER 2 Experimental researches into long-term behaviour of historical masonry A. Anzani1, L. Binda1 & G. Mirabella Roberti2 1Department

of Structural Engineering, Politecnico di Milano, Milan, Italy. 2Department of History of Architecture, University Iuav of Venice, Venice, Italy.

2.1 Introduction The time-dependent behaviour of ancient masonry structures, often characterized by non-homogeneous load-bearing sections, is considered among the factors affecting the structural safety of monumental buildings. Together with other synergetic aspects, this has proved to be involved in collapses, which occurred during the last thirty years. Exploiting the ancient (from the Middle Ages to the sixteenth century) masonry coming from the ruins of the collapsed tower of Pavia, several experimental procedures have been adopted to understand the phenomenon, from creep to pseudo-creep tests at different time intervals, and various rheological models have been applied to describe the creep evolution and creep-induced damage, as explained later in this book in Chapter 7. Purpose of the testing activity has been initially the identification of the creep behaviour as a possible cause of the collapse of buildings, then the study of factors affecting creep (rate of loading, stress level, etc.) and the set-up of the most suitable testing procedures to understand the phenomenon, and finally the individuation of significant parameters (e.g. strain rate of secondary creep phase) that may be referred to as risk indicators in real structures. After the first tests carried out on prisms of dimension 400 × 600 × 700 mm described in Chapter 1, long-term tests on six prisms coming from the ruins of the tower of Pavia and one from the crypt of Monza were performed, some of which lasted 1000 days. Considering that long-term tests require constant

30


thermo-hygrometric conditions and especially designed testing apparatus, a more rapid and therefore more convenient testing procedure was subsequently preferred. The so-called pseudo-creep tests were carried out applying the load by subsequent steps corresponding to a constant value (generally 0.25 or 0.3 MPa) kept constant for a specific time interval. Different durations of the time interval have been experimented (from 300 to about 30,000 seconds) that allowed one to indirectly observe the influence of the rate of loading. In fact, these tests characterized by a regular load history tend to simulate, by discrete load steps, monotonic tests where the load increases continuously at an equivalent rate that can be calculated. They give the opportunity to satisfactorily catch the limit between primary and secondary creep phase. Considering tertiary creep, pseudo-creep tests imply a disadvantage. In fact, the load value that in a monotonic test at the equivalent rate of loading would cause failure may not correspond exactly to one of the applied load steps, but to an intermediate value (Fig. 2.1). Therefore, if the applied load is higher than that which would have caused tertiary creep and failure, the specimen collapses instantaneously, without showing the tertiary creep phase. The latter is not particularly important in itself; what is interesting is the secondary creep strain rate just before failure. The problem could be solved by simply prolonging the time interval of the last load step so as to reach the failure limit curve (see Fig. 2.1) in constant load conditions instead of at increasing load. Actually, before reaching it, the stress at failure is not known; however, the failure conditions may be roughly previewed by estimating the ultimate stress through sonic tests and by controlling accurately the strain rate in real time during the pseudo-creep test. In some of the cases described below tertiary creep was therefore recorded.

σv

failure limit curve

viscosity limit curve εv

Figure 2.1: Pseudo-creep testing: simulation of monotonic test at an equivalent rate of loading.

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY 31 In the case of the masonry from the Pavia tower, different prism dimensions were adopted in order to use as much as possible the material coming from the irregular blocks taken from the ruins, compatibly with the capacity of the testing machine. On the contrary, from the crypt of Monza two big blocks were purposely extracted from which prisms of the same dimensions were obtained. When relevant, comments on the influence of the specimen dimensions on the test results will be given. The mechanical test series were carried out on the prisms previously capped with 1:3 cement mortar; PTFE sheets were interposed between the sample bases and the machine platens (Fig. 2.2a); a hydraulic compressive machine MTS (2500 KN) was used, connected with a control unit for data-acquisition, a plotter producing load-displacements diagrams, a PC for storing data. If not differently specified, vertical and horizontal displacements were measured directly on the prisms using four LVDT with a base of 150 mm and four LVDT with a base of 180 mm, respectively; two overall vertical readings were also taken from plate to plate of the machine in case the other LVDTs had fallen during the tests (Fig. 2.2b and c).

2.2 Tests on the masonry of the Civic Tower of Pavia After the sudden collapse of the Civic Tower of Pavia (built from eleventh to sixteenth century), during the investigation into the causes, many prisms of different dimensions were obtained out of the large blocks coming from the ruins of the tower and constituting the medieval trunk of the structure (Fig. 2.3). The prisms, subjected to mechanical tests, had mainly been obtained from the conglomerate forming the very thick inner core of the 2800 mm three-leaf walls (Fig. 2.4); a few of them were coming from the fairly regular external layers made of roman brick masonry of thickness varying between 150 and 490 mm; no specimens were initially sampled from the plain masonry belonging to the sixteenth-century belfry, as it was not involved in the initiation of the collapse [1] although this addition may be suspected as a remote trigger responsible for the collapse [2].

(a)

(b)

(c)

Figure 2.2: Preparation and instrumentation of the prisms for mechanical testing.

32


Sixteenth century

Eleventh– twelfth centuries

Figure 2.3: Civic Tower of Pavia before failure.

Inner leaf

Outer leaf

Figure 2.4: Detail of the cross-section of the 2800 mm thick medieval masonry.

Figure 2.5: Cutting the sixteenthcentury plain masonry.

Only recently, it was decided to study also the sixteenth-century plain masonry belonging to the upper part (Figs 2.5, 2.6). In fact, its behaviour may provide a useful comparison for other structures of the same age and constructive technique, being a historical masonry not usually available for mechanical testing. Prisms of larger dimensions were cut first and progressively smaller specimens were also obtained subsequently in order to exploit the historical material as much as possible. The 400 × 600 × 700 mm masonry prisms were identified by a number

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY 33

(a)

(b)

(c)

Figure 2.6: Civic tower of Pavia: (a) medieval outer leaf, (b) medieval inner leaf, (c) sixteenth-century plain masonry. (indicating the block which they came from) and a letter, (since more than one specimen had been cut from the same block). Smaller specimens were named in a similar way, including a second number after the first figure, which indicates the dimension of the base of the prism [3]. 2.2.1 Characterization by sonic tests Before designing the load history to which the prisms were to be submitted, sonic tests were carried out for non-destructive strength estimation. In the case of prisms of 400 × 600 × 700 mm and in the case of prisms of 300 × 300 × 510 mm, eight trajectories in each of the two horizontal directions were adopted to test the prisms by transparency; in the case of prisms of 200 × 200 × 350 mm four trajectories in each of the two horizontal directions were adopted (Fig. 2.7). Figure 2.8 shows a direct relationship between the mean sonic velocity and the compressive strength of the medieval inner leaf, tested monotonically as described below. 2.2.2 Monotonic tests on prisms of different dimensions Monotonic uniaxial compression tests on the masonry of the inner leaf have been carried out, respectively, on seven prisms of dimensions 400 × 600 × 700 mm [1], on one prism of dimensions 200 × 200 × 350 mm and on five prisms of dimensions 100 × 100 × 180 mm [4]. The test results are summarized in Table 2.1. As expected, the smaller prisms exhibited higher values of the peak vertical stress and lower values of the ultimate deformation.

34

Learning from Failure 4.0

σm [N/mm2]

3.5 3.0 2.5 2.0 1.5 1.0 1000

Figure 2.7: Apparatus for sonic tests.

1200

1400 1600 sonic velocity [m/s]

1800

2000

Figure 2.8: Compressive strength vs. sonic velocity: tests on 400 × 600 × 700 mm masonry prisms.

Table 2.1: Results of monotonic tests on the masonry of the inner leaf. Sample 67C 94B 94D 100C 100D 102A 102B Y 18-10M 19-10A 19-10H 102-10B 102-10A

Dimensions (mm) 400 × 600 × 700

200 × 200 × 350 100 × 100 × 180

s fv (MPa)

e fv (×103)

2.0 3.1 2.5 3.0 2.5 2.4 4.1 2.26 3.86 3.60 3.00 3.90 4.80

4.0 3.0 3.0 3.9 5.5 5.2 4.4 2.5 2.20 3.90 2.90 2.14 2.04

s fv, ave (MPa)

e fv, ave (×103)

2.8

4.14

– 3.83

– 2.63

Two prisms of the sixteenth-century plain masonry of dimension 200 × 200 × 350 mm were tested, the results of which are reported in Table 2.2. A higher peak stress and a lower value of maximum vertical strain than in the case of the inner leaf have been registered, indicating an important influence of the construction technique on the masonry mechanical behaviour. The stress–strain diagrams of the larger size prisms are shown in Figs 2.9 and 2.10. Considering the vertical strains, the marked initial ‘locking’ branch appearing in Fig. 2.9 is due to the fact that, in this case, the plotted strain has not been read directly on the specimens, but calculated from the displacement between the machine platens. In all cases, a linear part can be seen during which no visible

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY 35 Table 2.2: Results of monotonic tests on the sixteenth-century plain masonry. Dimensions (mm)

s fv (MPa)

e fv (×103)

s fv, ave (MPa)

e fv, ave (×103)

200 × 200 × 350

5.80 6.00

1.79 2.1

5.9

1.945

Sample

7

7

6

6

5

5

X

σv [N/mm2]

σf [N/mm2]

R X

4 3

100C

2

X

4

R

R

3 2

Y

Y

67C

1

1

0 0

2

4 6 εv [μm/mm]

8

Figure 2.9: Monotonic tests on prisms of 400 × 600 × 700 mm from the inner leaf.

10

0 -20

εv

εh -15

-10

-5 0 ε [μm/mm]

5

10

Figure 2.10: Monotonic tests on prisms of 200 × 200 × 350 mm: (---) inner leaf, (—) plain masonry.

cracks appear, but probably steady diffusion of micro-cracks takes place; in the case of specimens R and X belonging to the plain masonry, this basically continues up to the peak stress, showing a brittle behaviour. Vice-versa, in the case of the masonry of the inner leaf a non-linear part up to the peak stress value shows, corresponding to first visible crack appearance. Finally a ‘softening’ branch, characterized by a decrease of the vertical stress with increasing strain, can be observed in all cases. 2.2.3 Fatigue tests Following the monotonic tests, cyclic tests were performed. Two cycles of loadingunloading were applied every 0.5 MPa under displacement control and diagrams similar to those presented in Fig. 2.11 were obtained. A behaviour similar to that shown by the prisms tested monotonically can be observed. An interesting tendency of the samples to deform under constant load can also be seen. This is indicated by an almost horizontal line in the stress–strain diagram just before the unloading phase initiates, corresponding to the time elapsed while measuring the horizontal displacements [5]. Values of secant modulus have been calculated on the linear part of the unloading diagrams: this is particularly interesting because it describes the elastic stiffness referred to recoverable strain only, whereas the secant modulus based on the loading branch of the diagram is influenced by elastic and permanent strain. The obtained

Learning from Failure 5

5

4

4 σv [N/mm2]

σv [N/mm2]

36

3 2

3 2 1

1 0 0

2

4 6 εv (×103)

8

Figure 2.11: Results of a cyclic test on a 400 × 600 × 700 mm masonry prism.

10

0 0.0

1.0

2.0

3.0

εv (×103)

Figure 2.12: Results of a cyclic test on a 200 × 200 × 400 mm masonry prism.

values followed an increasing trend up to the peak stress, and in general were higher than the values of the tangent modulus calculated for monotonic tests [6]. More specific tests were then carried out on 100 × 100 × 200 mm prisms to understand the effect of cyclic actions, e.g. that of wind or that of thermal cycles. Figure 2.12 shows the results obtained on a sample which was loaded monotonically and submitted to cycles of 0.5 Hz frequency and ± 0.05 N/mm2 amplitude, at different stress levels. Cycles acting within a relatively small load range proved capable of provoking noticeable material strain. When applied at a high stress level, relative to the material strength, load cycles appeared particularly effective, having induced failure at a lower stress level than the estimated peak stress [3]. 2.2.4 Creep tests on prisms of 300 ¥ 300 ¥ 510 mm Six prisms of dimensions 300 × 300 × 510 mm were tested in compression in controlled conditions of 20°C and 50% RH at ENEL-CRIS Laboratory (Milan), using hydraulic machines capable of keeping constant a maximum load of 1000 KN. The dimensions adopted for the prisms were the maximum compatible with the testing machine. The load was applied in subsequent steps, kept constant until either the creep strain reached a constant value or a steady state was attained. The first stress level was chosen between 40 and 50% of the static peak stress of the prisms, estimated by sonic tests. The test results are reported in Table 2.3 and in Fig. 2.13a and b. From the experimental data, the development of all the creep phases was evident, with secondary creep showing even at 41% of the estimated material peak stress and tertiary creep showing at about 70%; material dilation took place under severe compressive stress corresponding to high values of the horizontal strain due to slow crack propagation until failure [3].

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY 37 Table 2.3: Results of long-term tests on inner leaf prisms of 300 × 300 × 510 mm. Sample

Test duration (days)

s fv (MPa)

e fv (×103)

19-30A 19-30B 67-30B* 47-30A 41-30B 102-30A Average

1170 1082 163* 524 894 894 –

2.0 2.0 1.3* 2.0 2.3 2.9 2.24

4.75 2.92 0.70* 3.50 2.70 2.90 3.35

*Collapsed by premature failure; not included in average calculation.

(a) 4

Secondary creep Tertiary creep

εv (×103)

3 Primary creep

2 1 0 -1

-3

(b) 3.0 dilation

2.5

-4

σv [N/mm2]

εh (×103)

-2

-5 -6 -7

2.0 1.5 1.0 0.5

-8

0.0 0

200

400

600 800 time [days]

1000

1200

0

200

400

600 800 time [days]

1000 1200

Figure 2.13: Results of creep tests on prisms of 300 × 300 × 510 mm from the inner leaf. The strain vs. time values of one of the prisms tested are reported in Fig. 2.14a and b. Due to technical problems, after 630 days from the beginning of the test the load was unintentionally lowered to zero for 90 days. Undesired unloading caused only partial strain recovery without affecting very much the test results. Despite the apparent scatter due to the sensitivity of the calculated value to random reading errors, the volumetric strain seems nearly constant during the first load steps of the test. Subsequently it starts to decrease markedly: the slope of the plot

38

Learning from Failure (b)

4

4

2

2

0

ε'v evol

0

ε 'h

-2

-2

-4

-8

0

-8

100 200 300 400 500 600 700 800 900 1000

0

2.8 MPa

2.6 MPa

0 MPa

2.4 MPa

2.4 MPa

2 MPa

2.8 MPa

2.6 MPa

0 MaP

2.4 MPa

-6 2.4 MPa

2 MPa

-6

2.2 MPa

-4

2.2 MPa

εh (×103)

6

ε (×103)

εv (×103)

(a) 6

100 200 300 400 500 600 700 800 900 1000

time [days]

time [days]

Figure 2.14: (a) Vertical and horizontal strain vs. time on prism 102-30A. (b) Deviatoric and volumetric strain vs. time on prism 102-30A.

(a)

(b)

Figure 2.15: Prism of the inner leaf: (a) face A at the beginning of the test; (b) crack pattern of face B at the end of the test.

(i.e. the strain rate) increases and the curve becomes negative until collapse is reached; negative deformation corresponds to dilation due to fracturing and cracks opening. The creep behaviour is evident since the beginning from the deviatoric strain plots [7]. Two faces of the prism at the beginning and at the end of the test are shown in Fig. 2.15a and b. The highly irregular texture of the wall is evident, with a great part of the masonry being occupied by mortar. The crack pattern is characterized by the presence of vertical and sub-vertical cracks.

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY 39 2.2.5 Pseudo-creep tests on prisms of 100 ¥ 100 ¥ 180 mm Twelve prisms of dimensions 100 × 100 × 180 mm were tested in compression by subsequent load steps corresponding to 0.3 MPa kept constant for different time intervals, respectively, of 300, 900, 3600 and 10800 s, as indicated in Table 2.4. An initial step of 0.6 MPa was first applied. Before the application of any new load step, the sample was completely unloaded so the unloading Young modulus could be evaluated [4]. Looking at Table 2.4, it is interesting to notice that the average peak stress tends to decrease and the corresponding strain tends to increase at extending the time interval, indicating that the stress–strain behaviour is strongly time-dependent. The results of a test carried out at 10800 s are reported, as an example, in Fig. 2.16: at each load step primary creep occurred and, during the last load step, secondary and tertiary creep. 2.2.6 Pseudo-creep tests on prisms of 200 ¥ 200 ¥ 350 mm A first series of four prisms, three coming from the external layers of the masonry and one coming from the inner part constituting the trunk of the tower of Pavia, was tested applying constant load steps of 0.25 MPa and keeping them constant for 10800 s. The test results are reported in Table 2.5 and in Fig. 2.17. Strictly speaking, a direct comparison between these results and those previously presented could not be done, due to various factors: different testing procedures, different dimensions of the specimens, non-homogeneity of the material, different texture of these prisms with respect to the previous ones. Anyway, this last aspect seems to have played a major role, since higher values of peak stress and lower values of the corresponding strain have on average been obtained in this case. Table 2.4: Results of pseudo-creep tests on inner leaf prisms of 100 × 100 × 180 mm at different time intervals. Sample 18-10A 18-10B 18-10C 18-10D 18-10E 18-10F 18-10G 18-10H 18-10I 18-10J 18-10K 18-10L

Time interval (s)

s fv (MPa)

300

3.24 4.18 3.63 2.69 2.99 2.52 2.89 2.39 2.15 2.59 2.88 2.58

900

3600

10800

e fv (×103) 3.19 3.60 2.73 4.71 4.15 3.75 5.48 3.94 2.96 5.78 10.21 1.65

s fv, ave (MPa)

e fv, ave (×103)

3.68

3.17

2.73

4.20

2.47

4.12

2.68

5.87

40


σv [N/mm2]

2.5 2.0 1.5 1.0

t [min]

0.5 0 0.0

3

6

εv (×103) 9

12

60 120 180

Figure 2.16: Pseudo-creep tests on a 100 × 100 × 180 mm prism of the inner leaf.

Table 2.5: Results of compression tests on medieval outer leaf prisms of 200 × 200 × 350 mm, at constant load step. Sample 40-20B 40-20C 57-20A Average 102-20A*

Test interval (s)

s fv (MPa)

e fv (×103)

10800

5.25 7.00 4.50 5.583 3.50

1.17 1.27 1.80 1.413 0.90

*Inner leaf, not considered for average calculation.

The horizontal strain takes higher absolute values than the vertical strain, indicating that at failure dilation takes place. The results of a test on a single specimen of the first series are shown in Fig. 2.18a and b. Considering the trend of the stress– strain plot (Fig. 2.18a), a linearly elastic behaviour can be observed below a stress value of 3.25 MPa. Correspondingly, the strain–time plot shows that within this interval only primary creep develops. After that level, the stress–strain diagram indicates non-linear behaviour; and the strain–time plots exhibit the steady-state (or secondary creep) and, eventually, the tertiary creep phases. The volumetric strain (Fig. 2.18b) keeps almost naught values approximately during the first twelve load steps and subsequently gets decreasing negative values until collapse. As appears also from the data previously presented, decreasing volumetric strain can be certainly interpreted as a sign of increasing material damage.


εv (×103)

8 4

102-20a

57-20a

40-20c

0 -4

εvol (×103)

40-20b

57-20a

-8 -12

40-20c

102-20a -16 40-20b

-20 0

100000

200000

300000

400000

time [sec]

Figure 2.17: Pseudo-creep tests of the first series.

(b) 20

4 2 0

time [sec] 12000 8000 4000

ε'v

10

1

2

3

4

5

6

εv (×103) 7 8

ε (×103)

σv (Mpa)

(a) 6

0 ε'h

-10 -20

evol

-30 0

40000

80000 120000 160000 200000 240000

time[sec]

Figure 2.18: (a) Vertical stress vs. vertical strain and vertical strain vs. time on prism 40-20B. (b) Deviatoric and volumetric strains vs. time on prism 40-20B. Figure 2.19 shows the crack pattern of a prism after the test. A more regular texture than that appearing in Fig. 2.15 characterizes this sample, with the presence of whole bricks lying horizontally; nevertheless a great difference between the four faces of the same prism has to be pointed out. The vertical cracks tend to follow the directions corresponding to the interfaces between mortar and bricks and split the prism faces from bottom to top. A second series of pseudo-creep test was then carried out on additional prisms recently obtained from the ruins of the tower. A total of four prisms coming from the inner medieval masonry (labelled Q, B, M and S) and four coming from the sixteenth-century solid masonry (labelled Ec, W, K and In) were tested applying subsequent load steps of 0.3 MPa kept constant for intervals of 28800 s (Table 2.6). On the average, higher peak stresses (sf) and lower strains at failure (evmax, ehmax) were registered on the plain masonry.

42


Face A

Face B

Face C

Face D

Figure 2.19: Prism of the outer leaf: crack pattern at the end of the test. Table 2.6: Results of pseudo-creep tests of the second series. Specimen

Masonry

sf (MPa)

evmax (μm/mm)

ehmax (μm/mm)

Prism Q Prism B Prism M Prism S Average

Sixteenth-century solid masonry

6.07 4.36 5.27 4.13 4.96

9.52 5.98 4.67 7.19 6.84

–20.39 –26.46 –15.56 –17.23 –19.91

Prism Ec Prism W Prism K Prism In Average

Medieval inner leaf

3.59 2.75 1.56 2.47 2.59

8.43 4.00 3.99 4.78 5.30

–11.84 –7.89 – 45.35 –18.30 –20.85

In Fig. 2.20 the results of the pseudo-creep tests of the second series on the inner leaf and on the plain masonry are compared. As expected, the prisms of the inner leaf reached failure well before the prisms of the plain masonry. In Figs 2.21 and 2.22 the results of a test carried out on the masonry of the inner leaf and those of a test carried out on the plain masonry are, respectively, shown. In both cases, all the creep phases are visible.

2.3 Tests on the masonry of the crypt of the Cathedral of Monza 2.3.1 Preparation of prisms of 200 ¥ 200 ¥ 350 mm After the plane rearrangement of the Museum of the Cathedral of Monza in 1994, the removed material, resulting from a door opening on the northern wall of the

εv (×103)

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY 43 10

Ec S B K In W

5

M

Q

0 -5 W

-10

Ec

-15 -20

M

S

In

Q

εh (×103)

-25 B

-30 -35 K

-40 0

200000

400000 time [sec]

600000

800000

σv [N/mm2]

5 4 3 2 1 0

5 4 3 2 1 0

10000

10000

20000

20000

30000

εh 40000 -45 -40 -35 -30 -25 -20 -15 -10 -5 [μm/mm]

εv 0

5

10

Figure 2.21: Results obtained on prism K of the inner leaf.

t [sec]

t [sec]

σv [N/mm2]

Figure 2.20: Pseudo-creep curves: (---) inner leaf, (—) solid masonry.

30000

εh 40000 -45 -40 -35 -30 -25 -20 -15 -10 -5 [μm/mm]

εv 0

5

10

Figure 2.22: Results obtained on prism B of the solid masonry.

crypt, was collected for experimental testing. According to historical information, the construction of the crypt (concluded in 1577) is nearly contemporary to the construction of the bell tower (1592–1605), a building made of solid brick masonry that was badly damaged by compression and is now undergoing a repair intervention [8]. As it has become clear after the collapses of the last fifteen years, towers as well as pillars of the cathedrals turn out to be particularly vulnerable to the effects of persistent loading; therefore, achieving a better experimental knowledge on their creep behaviour became crucial. Since considerable amounts of historical masonry are not normally available, it was a good opportunity of gaining original sixteenth-century masonry (Fig. 2.23). Two large blocks were extracted by coring their perimeter in order to obtain as much as possible undisturbed material. Subsequently, they were cut by a diamond

44


Figure 2.23: Sampling of the masonry from the crypt of the Cathedral of Monza.

(a)

(b)

(c)

Figure 2.24: Cutting scheme of the masonry sampled from the crypt of the Cathedral of Monza. saw into prisms of dimensions 200 × 200 × 350 mm to be subjected to different mechanical testing (Fig. 2.24). As shown in Fig. 2.24c, the crypt is mainly made of solid brick masonry apparently regularly laid which nevertheless includes stones, voids and cracks, and has therefore to be considered as a non-homogeneous material. In fact, the different prisms appeared damaged to rather different extents, those subjected to monotonic tests showing the most evident signs of damage. 2.3.2 Characterization by sonic tests Before mechanical tests, the prisms were characterized by sonic tests as described in Section 2.2.1. The results are reported in Fig. 2.25.

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY 45 m/s 2500 2000 1500 1000 500 0 I5

II 8

II 2

I8

II 5 II 16

II 4 II 12

I4

II11

Figure 2.25: Results of sonic tests.

Table 2.7: Results of monotonic tests. Sample

sm (MPa)

ev at sm

Ei (MPa)

3.70 3.75 3.50

4.41 5.21 5.38

2810 2110 1775

IIp6 IIp9 IIp13

2.3.3 Monotonic tests Monotonic tests on three prisms were carried out initially, to have a first indication on the static compressive strength of the masonry; the tests were performed in displacement control with a velocity of 1 μm/sec and data acquisition every 10–20 sec. The results obtained are reported in Table 2.7, where the peak stress (sm), the vertical strain at peak stress, the initial elastic modulus and the test duration to reach sm are indicated. In Fig. 2.26 stress vs. vertical and volumetric strain diagrams are plotted for all the tested samples. 2.3.4 Fatigue tests Three fatigue tests were carried out in load control. The samples were loaded monotonically up to a stress value of 2.25 MPa, equal to 65% of the average static compressive strength previously obtained with monotonic tests; cyclic actions of ± 0.15 MPa at 1 Hz were then applied for a period of 5400 s. After this, the vertical stress was increased of 0.25 MPa, a new cyclic phase was applied and the sequence repeated until failure. When a single test lasted more than one day, the sample was unloaded at night for safety reasons and reloaded the day after. The results obtained are reported in Table 2.8 where the maximum vertical stress, the vertical strain at failure, the initial elastic modulus calculated during the monotonic phase and the test duration are shown. The ratio between the vertical stress at

46


IIp9 IIp6

IIp9

IIp6

σv [MPa]

3

IIp13

IIp13

2

1

0 -15

-10

-5 εvol

0

5 εv

(×103)

10

15

(×103)

Figure 2.26: Monotonic tests.

Table 2.8: Results of fatigue tests. Sample Ip1 Ip6 Ip7

sm (MPa)

ev (×103) at failure

Ei (MPa)

sm/sm*

Test duration (no. of cycles)

5.00 5.00 4.25

9.21 6.13 4.14

3118 3774 2805

0.97 0.81 0.92

110286 51507 24243

failure and the estimated static maximum stress (sm*) is also indicated the latter having been calculated on the basis of the initial elastic modulus. In fact, the average ratio between the initial elastic modulus and the maximum vertical stress obtained with monotonic tests on samples IIp6 and IIp9 was used for the calculation; the results obtained on prism IIp13 were not included in calculating the average, as the stress–volumetric strain diagram of this sample showed a very dilatant behaviour, probably due to some local effects of the material. Of course, the estimated values of sm* cannot be considered statistically relevant, but still they can give an indication on the severity of the testing procedure with respect to the strength of the material [9]. In Fig. 2.27 vertical stress vs. vertical and volumetric strain diagrams obtained on prism Ip1 are shown as an example. It can be observed that during the application of the cyclic load a deformation takes place. Moreover, considering the volumetric strain, it appears that dilation occurs to the material after very low stress values are reached. The strain rate per cycle was calculated for the prisms tested cyclically, as presented by Taliercio and Gobbi [10] relatively to cyclic tests on concrete specimens.

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY 47 6

σv [MPa]

5 4 3 2 1 0 -24

-20

-16

-12 -8 -4 εvol (×103)

0

4

8 12 εv (×103)

16

Figure 2.27: Results of a fatigue test carried out on prism Ip1. 2.5

Ip1

2.0

Δεv/ Δn (×106)

Ip6 Ip7

1.5

1.0

0.5

0.0 0

2000

4000 6000 cycles

8000

10000

Figure 2.28: Strain rate vs. number of cycles in the last series of cycles. It was interesting to notice that plotting the strain rate vs. the number of cycles allows the primary, secondary and tertiary creep phases to be distinguished quite clearly. Figure 2.28 shows the results relative to the last series of cycles obtained on each prism: though the number of test results is not particularly significant, a relationship between the strain rate of the secondary creep phase, corresponding to the portion of the diagram with horizontal tangent, and the fatigue life of the material, corresponding to the total number of cycles at failure, can be found. In particular, the higher the strain rate of the secondary creep phase, the shorter the fatigue life.

48


2.3.5 Creep test on one prism of 300 ¥ 300 ¥ 510 mm The creep test was carried out at the ENEL-CRIS laboratory (Milan) in an especially designed apparatus, in controlled conditions of 20°C temperature and 50% RH. During the 630-day test, three load increments of 1.4, 2 and 2.25 MPa and an unloading phase were applied. In Fig. 2.29 the vertical and volumetric strain are plotted vs. time. It appears that after load removal, it took more than 100 days for the material to completely recover the accumulated creep strain. 2.3.6 Pseudo-creep tests, first series Compression tests in displacement control were carried out loading the prisms monotonically until a stress value of 2.25 MPa equal to 65% of the average short term strength obtained by monotonic tests and then applying the load in subsequent steps kept constant for periods of about 5400 s, during which creep strain took place. In this case also unloading reloading cycles had been necessary overnight. Table 2.9 shows the results obtained with this test series: the maximum vertical stress, the vertical strain at failure, the initial elastic modulus calculated during the monotonic phase, the test duration and the ratio between the maximum vertical stress and the static maximum stress are reported. Figure 2.30 shows the diagrams obtained from all the tested prisms and Fig. 2.31 shows the results obtained on a single prism. Results similar to those obtained by the pseudo-creep tests previously presented can be seen. A clear dilatancy phenomenon is evident, with considerable volumetric strain developing when approaching failure, as a typical feature of brittle materials.

εv (×103)

4 3 2 1

-1

0

90

180

2.25 MPa

0 MPa

-3 -4

2 MPa

-2 1.4 MPa

εvol (×103)

0

270 360 time[days]

450

Figure 2.29: Creep test.

540

630

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY 49 Table 2.9: Results of pseudo-creep tests, first series. Sample

sm (MPa)

ev (×103) at failure

eh (×103) at failure

Ei (MPa)

sm/sm*

2.75 2.80 4.25 5.30

7.57 5.07 8.87 3.98

7.57 5.07 8.87 3.98

2122 2159 3024 4298

0.79 0.79 0.85 0.75

IIp4 Ip5 Ip4 IIp11

10 II 4p

I 4p

εv (×103)

I 5p 5

II 11p

0

εvol (×103)

-5

-10

-15 I 5p II 4p

I 4p II 11p

-20 0

20000 40000 60000 80000 100000 120000 140000 160000 180000 200000

tempo [sec]

Figure 2.30: Pseudo-creep tests: first series.

Comparing the strength values obtained on the masonry of Monza with the different test series, it appears unexpectedly that the prisms tested monotonically showed the lowest strength values, which apparently is not coherent with viscous behaviour. Actually, some aspects which may have influenced the results have to be considered: first of all, masonry does not fulfil the conditions of continuity, homogeneity and isotropy which have normally to be assumed in continuous mechanics. In addition, the masonry studied here is an ancient one; at present it is damaged. Moreover, the amount of cracks already present before testing was not the same for all the samples, those tested monotonically showing more signs of damage. However, if the ratio between the actual maximum vertical stress and the static strength (sm/sm*) is evaluated through the initial elastic modulus as shown

50


σv [MPa]

6

4

2 1

2

3

4

5

6

7

εv(×103) 8 9

0

time [sec]

2000 4000 6000 8000

Figure 2.31: Results of a compression test with constant load steps on prism Ip4.

Table 2.10: Results of pseudo-creep tests, second series. Sample

sm (MPa)

II8pN II2pN I8pN II16pS II12pS II5pS

2.00 3.25 4.00 4.00 4.25 4.75

ev (×103) at failure 13 4 6 4 8 6

eh (×103) at failure 16 9 9 12 9 9

in Tables 2.8 and 2.9, it appears that cyclic and constant load step tests damaged the material lowering its strength on average by 85%. 2.3.7 Pseudo-creep tests, second series The second series followed a more regular procedure: no monotonic phase was carried out; the load steps were applied since the start of the test and kept constant for a time interval of 10800 s (Table 2.10). As shown in Figs 2.32 and 2.33 more regular data were obtained. Considering the trend of the stress–strain plot, it can be noted that in this case also the behaviour can be considered linearly elastic below a stress value of 2.5 MPa. Correspondingly, the strain–time plot shows that within this interval only primary creep develops. After that level, the stress–strain diagram indicates

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY 51 10 εv (×103)

II 12 5

II 8

II 16 I 8 II 5

II 2

0

-5

εvol (×103)

II 16 -10

II12 II 5

I8

II 2 -15 II 8

-20 0

40000

80000 120000 Time [sec]

160000

200000

Figure 2.32: Pseudo-creep tests: second series. 5

σv[MPa]

4 3 2 1 0 3600 Time [sec]

7200 10800 14400 18000 21600 -10

-8

-6

-4

εvol (×103)

-2

0

2

4

6

8

10

εv(×103)

Figure 2.33: Results obtained on prism II 12. non-linear behaviour, and correspondingly the strain–time plots exhibit the steadystate (or secondary) and, eventually, the tertiary creep phases. In Fig. 2.34 the crack pattern across the specimen at the end of the test is represented. It is apparent from the drawings that the prism was characterized by the presence of a large portion of stone, occupying most of face D and large parts of faces A and C. The crack pattern has basically developed in sub-vertical direction, with

52


II 8

II 2 II 16 I 8

II 8

II2

I8

II8

II 8

II2

II 16 I

II 16 II 2

II16 I 8

II 2

II 8

II 16 I8

II 16

I8

II 2

II 8

II 8

II 2 II 16 I 8

II

II 16

I8

II 2

I8

II8

Figure 2.34: Crack pattern of prism II 12 at the and of the test, faces A, B, C and D.

fissures opening preferably along discontinuities already present at start of the test, whereas bricks were not cracked.

2.4 Comments The effect of persistent loads on the damage of ancient masonry has been experimentally studied and their effects on the mechanical properties of the material have been shown. Constant load step tests turned out to be a suitable procedure for analysing creep behaviour, having the advantage of being carried out more easily than long-term tests. Primary, secondary and tertiary creep phases have been clearly observed, together with their relationship with the stress level, a damage development being associated to an increase of the stress level. The action of cyclic and persistent loads has proved to cause a severe damage on the mechanical properties of ancient masonry. The fatigue life of masonry under uniaxial cyclic compression is related to the secondary creep strain rate, which is the strain rate during the phase of stable cyclic damage growth. Having tested the masonry coming from two historical buildings and built by different constructive techniques, a comparison can be made by using different mechanical parameters. In Fig. 2.35 the compressive peak stress obtained through pseudo-creep tests have been plotted vs. the sonic velocity. A strong linear correlation can be clearly observed; the prisms obtained from the outer leaf of the medieval part of the tower of Pavia achieved the highest strength values, whereas those from the inner leaf present the lowest ones, being the sixteenth-century plain masonry in between. In fact, this is coherent with the texture characteristics of the three materials (Figs 2.19 and 2.24). The outer leaf is the highest quality one, built to be the visible part of the structure; the inner leaf is constituted by rubble masonry. The values of the crypt of Monza, the texture of which shows an intermediate pattern between the previous two, with the presence of bricks and stones, are overlapped to those of the inner leaf and those of the plain masonry.

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY 53 10 Monza Pavia

peak stress [MPa]

8 6 4 2 0 0

500

1000 1500 2000 sonic velocity[m/sec]

2500

3000

Figure 2.35: Peak stress of pseudo-creep tests vs. sonic velocity.

1E+001

Δεv /Δt [x106/sec]

Monza Pavia 1E+000

1E-001

1E-002

1E-003 100

1000 10000 Time [sec]

100000

Figure 2.36: Secondary creep strain rate before failure vs. duration of the last load step. Considering the last load step for each specimen tested with pseudo-creep tests, the secondary creep rate, which is the strain rate during the phase of stable damage growth, has been calculated before collapse and then related to the duration of the last load step, which can be regarded as the residual life of the material. In Fig. 2.36 these values for the masonry of Monza and the ruins of the tower of Pavia have been plotted. Though the number of test results is not particularly large, an interesting inverse relationship can be found, which seems to apply to both the materials considered, as well as to other brittle materials subjected to creep and fatigue tests [10, 11]. In this respect a useful comparison with concrete behaviour could be made since the analysed relationship is well known in the case of concrete [12, 13]. A strong correlation exists between creep time to failure and secondary creep rate which,

54


accordingly, can be used as a reliable parameter to predict the residual life of a material subjected to a given sustained stress. In view of preserving the historical heritage, it would be useful to define similar relationships to evaluate, for instance, the results of a monitoring campaign on a massive historic building subjected to persistent load, to judge whether the creep rate indicates a critical condition in terms of safety assessment. Of course, the precocious recognition of a critical state will allow one to design a strengthening intervention to prevent total or partial failure of the construction.

Acknowledgements Architects C. Curallo, M. Garau, P. Garau, L. Giannecchini, M.G. Paccapelo, R. Tassi and S. Sironi are gratefully acknowledged for their assistance in the experimental work and data elaboration; Mr Marco Antico for his technical support in the laboratory. The research has been partially supported by COFIN 2002 MIUR funds.

References [1]

[2]

[3]

[4]

[5]

[6] [7]

[8]

Binda, L., Gatti, G., Mangano, G., Poggi, C. & Sacchi Landriani, G., The collapse of the Civic Tower of Pavia: a survey of the materials and structure. Masonry International, 6(1), pp. 11–20, 1992. Anzani, A., Binda, L. & Taliercio, A., Application of a damage model to the study of the long term behavior of ancient towers. Proc. 1st Canadian Conference on Effectiveness Design of Structures, Hamilton, Ontario 10–13/07/2005, CD ROM. Anzani, A., Binda, L. & Melchiorri, G., Time dependent damage of rubble masonry walls. Proceedings of the British Masonry Society, 2(7), pp. 341–351, 1995. Anzani. A., Mirabella Roberti. G. & Binda, L., Time dependent behaviour of masonry: experimental results and numerical analysis. Structural Repair and Maintenance of Historical Buildings, Vol. III, Bath: STREMA, pp. 415–422, 1993. Anzani, A. & Mirabella Roberti, G., Experimental research on the creep behaviour of historic masonry. Struct. Studies Repairs and Maintenance of Heritage Architecture VIII, ed. C.A. Brebbia, WIT Press: Southampton and Boston, pp. 121–130, 2003. Binda, L. & Anzani, A., The time-dependent behaviour of masonry prisms: an interpretation. The Masonry Society Journal, 11(2), pp. 17–34, 1993. Anzani, A., Binda, L. & Mirabella Roberti, G., The behaviour of ancient masonry towers under long-term and cyclic actions. Proc. Computer Methods in Structural Masonry, 4, pp. 236–243, 1998. Modena, C., Valluzzi, M.R., Tongini Folli, R. & Binda, L., Design choices and intervention techniques for repairing and strengthening of the Monza


[9]

[10]

[11] [12]

[13]

Cathedral bell-tower. Proc. 9th Int. Conf. and Exhibition, Structural Faults + Repair, CD-ROM, 2001. Mirabella Roberti, G., Binda, L. & Anzani, A., Experimental investigation into the effects of persistent and cyclic loads on the masonry of ancient towers. Proc.7th Int. Conf. and Exhibition, Structural Faults + Repair 97, Edinburgh, Vol. 3, pp. 339–347, 1997. Lenczner, D., The effect of strength and geometry on the elastic and creep properties of masonry members. Conf. of North American Masonry, Boulder, CO, 1978, 23-1/23-15. Xiao, X. & Shrive, N.G., Compressive fracture of masonry. Experimental study. 10th Canadian Masonry Symposium, Banff, Alberta, 8–12 June 2005. Taliercio, A. & Gobbi, E., Effect of elevated triaxial cyclic and constant loads on the mechanical properties of plain concrete. Magazine of Concrete Research, 48(176), pp. 157–172, 1996. Taliercio, A. & Gobbi, E., Fatigue life and change in mechanical properties of plain concrete under triaxial deviatoric cyclic stresses, Magazine of Concrete Research, 50(3), pp. 247–256, 1998.


CHAPTER 3 Collapse prediction and creep effects P.B. Lourenço & J. Pina-Henriques Department of Civil Engineering, University of Minho, Portugal.

3.1 Introduction The collapse of the Pavia Civic Tower in 1989 was an event of great concern for the public authorities and for the technical community. The collapse rapidly became a focus of interest among masonry researchers and several masonry blocks were recovered from the ruins for mechanical and physical/chemical laboratory testing [1]. Such tests permitted to identify the time-dependent mechanical damage of the tower walls due to high sustained loading as the possible main cause of collapse. The tower of Pavia is not an isolated case and several other famous examples can be mentioned, such as the collapse of the St. Magdalena bell-tower in Goch, Germany, in 1993, the partial collapse of the Noto Cathedral, Italy, in 1996, and the severe damage exhibited by the bell-tower of the Monza Cathedral, Italy. Masonry creep depends mainly on factors such as the stress level and the temperature/humidity conditions but cyclic actions, such as wind, temperature variations or vibrations induced by traffic or ringing bells, in the case of bell towers, have a synergetic effect, increasing material damage. For these reasons, high towers and heavily stressed columns are the structural elements where severe time-dependent damage can occur [2]. Traditionally, three creep stages can be recognized: a primary stage where the creep rate decreases gradually, a secondary stage where the creep rate remains approximately constant and a tertiary stage where the creep rate increases rapidly towards failure. A sufficiently high stress level must be applied so that the last two stages are initiated. In the secondary stage, diffuse and thin vertical cracking propagates and coalesces into macro-cracks that may lead, possibly, to creep failure of the material. Creep of cementitious materials is generally attributed to crack growth and interparticle bond breakage due to moisture seepage. In fact, under

58


sustained loading, forced moisture redistribution can occur in the pore structure of the material causing debonding and rebonding of the micro-structure particles [3]. In the case of concrete or new masonry, if drying shrinkage is occurring simultaneously to creep, the time-dependent deformation is increased due to a coupled effect known as the Pickett effect [4]. Time-dependent deformation in a constant hygral and thermal environment, and in the absence of cracking, is denominated by basic creep (see, e.g., Neville [5], and the reader is referred to Van Zijl [6] for a comprehensive discussion on the viscous behaviour of masonry). For low stress levels, below 40 to 50% of the compressive strength, only primary creep is present and creep deformation can be assumed proportional to the stress level. References on masonry creep within the elastic range are rather abundant in literature, [7–9]. On the contrary, creep under high stresses, even in the case of concrete, is not a sufficiently debated issue [10–12]. The fact that standard design methods for new structures are based on linear elastic material hypothesis has contributed to the diminished interest of researchers on this topic. However, ancient masonry structures are often functioning under low safety margins according to modern safety regulations. This can be due to inadequate knowledge of mechanics or due to the structural modifications that occurred along centuries, resulting in overweighting of the structure and rendering importance to non-linear creep. Detailed modelling approaches in which units and mortar are individually represented are of great interest in understanding the phenomena occurring at the constituent level. In particular, insight into stress redistribution and damage growth occurring under sustained loading can be provided. However, before introducing long-term effects, knowledge of the short-term behaviour and governing failure mechanisms is of fundamental importance. Nevertheless, numerical prediction of the short-term response of masonry based on the properties of the constituents remains unresolved [13]. In Section 3.2, an attempt to provide reliable predictions of the compressive strength of masonry and a discussion of the observed failure mechanisms are discussed. A standard continuum model, based on plasticity and cracking, and a particle model developed in discrete settings have been considered to represent units and mortar. In Section 3.3, an experimental investigation into the behaviour of ancient masonry under high compressive stresses is described and its results are carefully analysed. Standard uniaxial compression tests, short-term creep tests and long-term creep tests were considered with the aim of presenting a comparative discussion.

3.2 Short-term compression: failure analysis and collapse prediction using numerical simulations 3.2.1 Experimental results Binda et al. [14] carried out deformation controlled tests on masonry prisms with dimensions of 600 × 500 × 250 mm3, built up with nine courses of

Collapse Prediction and Creep Effects

59

Table 3.1: Mechanical properties of the masonry components [14]. Component

E (N/mm2)

v

fc (N/mm2)

ff (N/mm2)

Unit Mortar M1 Mortar M2 Mortar M3

4865 1180 5650 17760

0.09 0.06 0.09 0.12

26.9 3.2 12.7 95.0

4.9 0.9 3.9 15.7

Table 3.2: Mechanical properties of the masonry prisms [14]. Prism type

Mortar type

E (N/mm2)

fc (N/mm2)

M1 M2 M3

1110 2210 2920

11.0 14.5 17.8

P1 P2 P3

250 × 120 × 55 mm3 solid soft mud bricks and 10 mm thick mortar joints. Three different types of mortar, denoted as M1, M2 and M3, have been considered and testing aimed at the evaluation of the compressive properties of the prisms. For each type of mortar, a total of three prisms were tested. The tests were carried out in a uniaxial testing machine MTS® 311.01.00, with non-rotating steel plates and a maximum capacity of 2500 kN. The applied load was measured by a load cell located between the upper plate and the testing machine, while the average vertical displacement was recorded with the machine’s in-built displacement transducer, permitting one to capture the complete stress– strain diagram, including the softening regime. The characteristics of the masonry components in terms of compressive strength fc, flexural tensile strength ff, elastic modulus E and coefficient of Poisson v are given in Table 3.1. The results obtained for the prisms are given in Table 3.2. Prisms P1, P2 and P3 were built with mortars M1, M2 and M3 of increasing strength, respectively. The experimental failure patterns found were rather similar despite the type of mortar used [15]. Figure 3.1 depicts the typical failure pattern. 3.2.2 Continuum model The simulations were carried out resorting to a basic cell, i.e. a periodic pattern associated to a frame of reference (see Fig. 3.2), in which units and mortar were represented by a structured continuum finite element mesh. However, in order to reduce computational effort only a quarter of the basic cell was modelled assuming symmetry conditions for the in-plane boundaries (see Fig. 3.3). The dimensions of the components are equal to the ones used in the experiments. It is emphasized that the adopted approach is only an approximation of the real geometry

60


130

Figure 3.1: Typical experimental failure patterns [15]. The shaded areas indicate spalling of material.

(a)

260 (b)

Figure 3.2: Definition of basic cell: (a) running bond masonry and (b) geometry.

Unit Mortar

Figure 3.3: Continuum model used in the simulations (only the indicated quarter was simulated, assuming symmetry conditions).

and that the obtained numerical response is phenomenological, which means that a comparison in terms of experimental and numerical failure patterns is not possible. In particular, splitting cracks usually observed in prisms tested under compression [16], boundary effects of the specimen and non-symmetric failure modes are not captured by the numerical analysis. Nevertheless, most of these effects control mainly the post-peak response, which is not the key issue in the present contribution. Three different plane approaches have been considered taking into account the out-of-plane boundaries, namely: (a) plane-stress (PS), (b) plane-strain (PE) and (c) an intermediate state, here named enhanced-plane-strain (EPE). This last approach consists in modelling a thin out-of-plane masonry layer with 3D elements, imposing


61

equal displacements in the two faces of the layer. Full 3D analyses with refined meshes and softening behaviour are unwieldy, and were not considered. Moreover, recent research indicated that enhanced-plane-stress analysis provides very similar results [17]. EPE response is always between the extreme responses obtained with PS and PE. For this reason, EPE is accepted as the reference solution for the continuum simulations and only its results are considered in this paper. A complete description of the continuum simulations can be found in Pina-Henriques and Lourenço [18]. Modelling of the cell in EPE was carried out using approximately 900 20-noded brick elements with 6650 nodes, totalling 13,300 degrees of freedom (note that the tying adopted for the out-of-plane degrees of freedom mean that, basically, a 2D model is used). The integration used was 3 × 3 × 3 Gauss. The material behaviour was described using a composite model including a traditional smeared crack model in tension, specified as a combination of tension cut-off (two orthogonal cracks), tension softening and shear retention [19], and a Drucker-Prager plasticity model in compression [20]. The inelastic behaviour exhibits a parabolic hardening/softening diagram in compression and an exponential-type softening diagram in tension. The material behaves elastically up to one-third of the compressive strength and up to the tensile strength. In order to reproduce correctly the elastic stiffness of the masonry prisms, the experimental elastic modulus of the mortar E must be adjusted by inverse fitting. In fact, the mortar experimental stiffness leads to a clear overstiff response of the numerical specimens. This can be explained by the fact that the mechanical properties of mortar inside the composite are different from mortar specimens cast separately. This is due to mortar laying and curing and represents a severe drawback of detailed micro-models. The material properties adopted, including the adjusted mortar stiffness values E* are fully detailed in Table 3.3. Here, c is the cohesion, ft is the tensile strength, f is the friction angle, y is the dilatancy angle, Gft is the tensile fracture energy and Gfc is the compressive fracture energy. The value adopted for the friction angle was 10° (a larger value in plane-stress would implicate an overestimation of the biaxial strength) and, for the dilatancy angle, a value of 5° was assumed [21]. The values assumed for the fracture energy have been based on recommendations supported by experimental evidence [22, 23], and practical requirements to ensure numerical convergence. Table 3.3: Inelastic properties given to masonry components. E* c ft Component (N/mm2) (N/mm2) (N/mm2) sin f sin y Unit Mortar M1 Mortar M2 Mortar M3

4865 355 735 1065

11.3 1.3 5.3 39.9

3.7 0.7 3.0 12.0

0.17 0.17 0.17 0.17

0.09 0.09 0.09 0.09

*In the case of mortars, the values refer to the adjusted stiffness values.

Gft Gfc (N/mm) (N/mm) 0.190 0.350 0.150 0.600

12.5 2.7 10.0 23.0

62


3.2.3 Particle model The 2D particle model supposed to represent the micro-structure of units and mortar consists of a phenomenological discontinuum approach based on the finite element method including interface elements. The discontinuous nature of the masonry components is considered by attributing a fictitious micro-structure to units and mortar, which is composed by linear elastic continuum elements of polygonal shape (hereafter named particles) separated by non-linear interface elements. All inelastic phenomena occur in the interfaces and the process of fracturing consists of progressive bond-breakage. This is, of course, a phenomenological approach, able, nevertheless, to capture the typical failure mechanisms and global behaviour of quasi-brittle materials. For a detailed discussion of the model, including proposals for selection of numerical data, sensitivity studies, fracture processes and failure mechanisms, and size effect studies, the reader is referred to Pina-Henriques and Lourenço [13]. There, it is also shown that the compressive and tensile strength values yielded by the model can be considered as independent from particle size and particle distortion for practical purposes. The constitutive model used for the interface elements was formulated by Lourenço and Rots [24] and is implemented in the finite element code adopted for the analyses [20]. The model includes a tension cut-off for tensile failure (mode I), a Coulomb friction envelope for shear failure (mode II) and a cap mode for compressive failure. Exponential softening is present in all three modes and is preceded by hardening in the case of the cap mode. Micro-structural disorder is considered in the model by the irregular geometry of the particles and by attributing to particles and interfaces randomly generated material properties, according to a Gaussian distribution, for given values of the average and coefficient of variation of the material parameters. The particle model simulations were carried out employing the same basic cell used for the continuum model (see Fig. 3.2). The particle model is composed by approximately 13,000 linear triangular continuum elements, 6000 linear line interface elements and 15,000 nodes (see Fig. 3.4). Macro homogeneous symmetry conditions have been assumed. The material parameters were defined by comparing the experimental and numerical responses of units and mortar considered separately. Each material was modelled

Mortar

Unit

Figure 3.4: Particle model of the masonry cell (only the quarter indicated was simulated, assuming symmetry conditions).


63

resorting to specimens with the same average particle size, mesh distortion and dimensions of the masonry components used in the composite model (basic cell). Given the stochastic nature of the model, five simulations were performed for each masonry component assuming equal average values for the model material parameters. The parameters were obtained, whenever possible, from the experimental tests described in Section 3.2.1, but most of the inelastic parameters were unknown and had to be estimated. For the particles, average elastic modulus E values larger than the experimental ones had to be adopted due to the contribution of the interfaces deformability, characterized by kn and ks, to the overall deformability of the specimen. This correction is necessary despite the high dummy stiffnesses assumed. On the contrary, the values adopted for the interfaces tensile strength ft are slightly lower than the experimental tensile strength of the specimens, given the contribution of the interfaces shear strength due to the irregular fracture plane. The cohesion c was taken, in general, equal to 1.5 ft [25]. However, quite low experimental ratios between the compressive and tensile strengths were reported for the units and mortars considered here, with values ranging between four and eight. Due to this reason, cohesion values lower than 1.5 ft had to be adopted for mortars M1 and M2. The values for the friction coefficient tanf were adopted so that the numerical compressive strength showed a good agreement with the experimental strength. The values assumed for mode I fracture energy GfI have been based on recommendations supported in experimental evidence [23, 26]. For mode II fracture energy GfII, a value equal to 0.5c was assumed, with the exception of the very high strength mortar M3, for which a lower value equal to 0.3c was adopted. The complete material parameters adopted are given in Table 3.4 and, for such input, the response obtained is given in Table 3.5. 3.2.4 Discussion of the results The numerical results obtained for the masonry prisms considering the mortar experimental Num_E and adjusted Num_E* stiffnesses are given in Table 3.6, Table 3.4: Values assumed for the material parameters (in brackets, the coefficient of variation is given in %). Unit Particles Interfaces

(N/mm2)

E* 6000 (30) v 0.09 (0) kn (N/mm3) 1 × 104 (0) ks (N/mm3) 1 × 104 (0) ft (N/mm2) 3.40 (45) GfI (N/mm] 0.170 (45) c (N/mm2) 5.10 (45) GfII (N/mm) 2.55 (45) tan f 0.10 (45)

M1

M2

M3

355 (30) 0.06 (0) 1 × 104 (0) 1 × 104 (0) 0.75 (45) 0.038 (45) 0.30 (45) 0.15 (45) 0.00 (0)

750 (30) 0.09 (0) 1 × 104 (0) 1 × 104 (0) 3.50 (45) 0.175 (45) 0.70 (45) 0.35 (45) 0.00 (0)

1200 (30) 0.12 (0) 1 × 104 (0) 1 × 104 (0) 10.50 (45) 0.525 (45) 15.75 (45) 3.15 (45) 0.10 (45)

*In the case of mortars, the values refer to the adjusted stiffness values.

64


Table 3.5: Numerical response obtained for the masonry components (in brackets, the coefficient of variation is given in %).

fc (N/mm2) ft (N/mm2) E (N/mm2)

Unit

M1

M2

M3

27.2 (2.7) 3.61 (1.4) 4786 (1.9)

3.2 (5.0) 0.64 (4.7) 1309 (1.4)

12.7 (5.4) 2.70 (4.2) 5632 (3.0)

95.8 (4.4) 11.62 (6.6) 17176 (3.1)

Table 3.6: Experimental results (Exp) and numerical results using experimental Num_E and adjusted Num_E* mortar stiffness values. Continuum model Prism type fc (N/mm2) ep (10–3)

Exp Num_E Num_E* Exp Num_E Num_E*

Particle model

P1

P2

P3

P1

P2

P3

11.0 19.8 18.2 10.5 10.6 19.9

14.5 24.2 24.1 7.9 9.7 16.0

17.8 31.0 30.0 6.6 8.4 33.5

11.0 15.5 15.4 10.5 5.4 11.8

14.5 19.3 17.3 7.9 4.6 8.1

17.8 30.8 24.6 6.6 6.2 8.9

where fc is the compressive strength and ep is the peak strain. In addition, the prisms experimental results are shown for a better comparison. It is noted, however, that the reference solution for the numerical simulations is the solution provided by Num_E*. Figure 3.5 depicts the experimental and numerical stress–strain diagrams. From the given results, it is clear that the experimental collapse load is overestimated by the particle and continuum models, and that the predicted strength is affected by the mortar stiffness, especially in the case of the particle model. However, a much better agreement with the experimental strength and peak strain has been achieved with the particle model, when compared to the continuum model. In fact, the numerical over experimental strength ratios ranged between 165 and 170% in the case of the continuum model while in the case of the particle model, strength ratios ranging between 120 and 140% were found. The results obtained also show that the peak strain values are well reproduced by the particle model but large overestimations are obtained with the continuum model. For this last model, experimental over numerical peak strain ratios ranging between 190 and 510% were found. Failure patterns are an important aspect when assessing numerical models. The (incremental) deformed meshes near failure using the continuum and particle models are depicted in Fig. 3.6–3.8 for prisms P1 to P3, respectively. In case of the continuum model, the contour of the minimum principal plastic strains is also given for a better interpretation of the mechanisms governing failure. It is noted that despite the fact that only a quarter of the basic cell has been modelled the results are shown in the entire basic cell to obtain more legible figures.

Collapse Prediction and Creep Effects (a)

20.0 CM

PM

16.0 Stress [N/mm2]

65

12.0 8.0

Exp

4.0 0.0 0.0

5.0

10.0 15.0 Strain [10-3]

20.0

25.0

(b) 30.0 CM Stress [N/mm2]

24.0 PM

18.0 12.0

Exp

6.0 0.0 0.0

4.0

8.0

12.0

16.0

20.0

Strain [10-3]

(c)

35.0

Stress [N/mm2]

28.0

PM

CM

21.0 14.0 Exp

7.0 0.0 0.0

4.0

8.0 12.0 Strain [10-3]

32.0

36.0

Figure 3.5: Numerical and experimental stress–strain diagrams, using adjusted mortar stiffness values, for prisms: (a) P1, (b) P2 and (c) P3. In the diagrams CM stands for continuum model, PM for particle model and Exp for experimental data. The numerical failure patterns obtained are similar for both continuum and particle models. Even if the proposed particle model approach is phenomenological, the failure patterns resemble well typical compression experimental patterns observed in the face of masonry specimens. In the case of prism P1, failure occurs mainly due to the development of vertical cracks in the centre of the units and along the head-joints, being the mortar in the bed-joints severely damaged. Prism P2 fails due to diffuse damage developing in units and mortar in a rather uniform manner. In the case of prism P3, diffuse damage is also present but localized crushing of the units can be clearly observed at one-half and one-sixth of the length of the masonry units.

66


(a)

(b)

(c)

Figure 3.6: Results at failure for prism P1 using the continuum model: (a) deformed (incremental) mesh and (b) minimum principal plastic strains; and using the particle model: (c) deformed incremental mesh.

(a)

(b)

(c)

Figure 3.7: Results at failure for prism P2 using the continuum model: (a) deformed (incremental) mesh and (b) minimum principal plastic strains; and using the particle model: (c) deformed incremental mesh.

3.3 Long-term compression: experimental assessment 3.3.1 Tested specimens The experimental investigation was carried out on ancient masonry prisms due to the difficulty of producing laboratory specimens that correctly represent the


(a)

67

(b)

(c)

Figure 3.8: Results at failure for prism P3 using the continuum model: (a) deformed (incremental) mesh and (b) minimum principal plastic strains; and using the particle model: (c) deformed incremental mesh. Table 3.7: Number of specimens n for each type of test. n Compression Short-term creep Long-term creep

4 4 6

material typically found in historical masonry structures. Major obstacles to fabricate specimens are mortar carbonation, hardening or setting, which have a significant influence on the viscous behaviour of masonry and cannot be adequately reproduced in new specimens. On the other hand, the high cost and very limited number of ancient masonry specimens available for destructive testing are obvious. As previous experience with similar materials in the scientific community is not frequent [2], the current testing program was much relevant as it represents a learning process. In particular, recommendations for testing such specimens could only be given at the end of the testing program. The experimental investigation carried out focuses on regular coursed brick masonry specimens PRe recovered from the ruins of the belfry of the Pavia Civic Tower. The dimensions of the specimens were (200 ± 5) × (200 ± 5) × (330 ± 20) mm3. Before subsequent testing under compression, the loaded faces of the prisms were regularized with a cement based mortar layer approximately 10 mm thick. In all tests, Teflon sheets were introduced between the prisms and the loading plates to minimize restraining frictional stresses. A summary of the tests performed is given in Table 3.7.

68


3.3.2 Standard compression tests Standard compression tests were conducted on four specimens. The tests were partly carried out in University of Minho (specimens PRe_1 and PRe_2) and in Politecnico di Milano (specimens PRe_3 and PRe_4). The specimens had to be tested with different test setups according to the conditions locally available at each laboratory. In this way, the tests performed in University of Minho were carried out in a uniaxial hydraulic testing machine with non-rotating steel plates and a maximum capacity of 2000 kN. The load was monotonically increased under displacement control at the rate of 4 μm/s. The applied load was measured by a load cell located between the upper plate and the testing machine, and displacements in the specimens were recorded by two vertical inductive displacement transducers HBM (10 mm range), positioned at two different faces of the prisms and by two horizontal transducers positioned at the other two faces. The tests performed in Politecnico di Milano were carried out using a uniaxial servo-controlled MTS® 311.01.00 testing machine, with non-rotating steel plates and a maximum capacity of 2500 kN. Loading was applied under displacement control at a rate of 1 μm/s. The applied load was recorded by a load cell and displacements were measured with one vertical and one horizontal displacement transducers GEFRAN PY2-10 (10 mm range) positioned at each face of the prisms. For all tested specimens, longitudinal displacements were measured over approximately 200 mm span and transversal displacements over about 150 mm span. The results obtained are illustrated in Fig. 3.9. Here, the negative sign is adopted for contraction (longitudinal or vertical strains ev) and the positive sign is adopted for elongation (transversal or horizontal strains eh). It is noted that the null horizontal deformations exhibited up to the peak load in the case of specimen PRe_1 can be explained by the fact that only two horizontal transducers per specimen were used. Table 3.8 gives a summary of the test results in terms of the elastic modulus E, compressive strength fc and peak strain ep. The elastic modulus was

9.0

Stress [N/mm2]

7.5 6.0 4.5 3.0 1.5

εh 0.0 12.0 8.0

PRe_1 PRe_2 PRe_3 PRe_4 4.0

εv 0.0 -2.0 -4.0 -6.0 -8.0

Strain [10-3]

Figure 3.9: Stress–strain diagrams obtained from standard compression tests.


69

Table 3.8: Results obtained from standard compression tests (in brackets, the coefficient of variation is given). Specimen

E (N/mm2)

fc (N/mm2)

ep (10–3)

PRe_1 PRe_2 PRe_3 PRe_4 Average

4980 4515 2510 2720 3680 (34%)

8.0 6.3 5.7 6.2 6.6 (15%)

2.7 2.9 2.2 3.0 2.7 (13%)

calculated as the average slope of the stress–strain diagram between 30 and 50% of fc. It is noted that the elastic modulus is the parameter showing the largest coefficient of variation, approximately the double of the values found for the strength and peak strain. 3.3.3 Short-term creep tests Experimental set-up Short-term creep tests were carried out at Politecnico di Milano using, again, the uniaxial servo-controlled MTS® 311.01.00 testing machine. The experimental tests considered in this section are part of an extensive testing program under development at the Politecnico di Milano, which is thoroughly described in Chapter 2. The displacements in the specimens were recorded by a vertical and a horizontal displacement transducer GEFRAN PY2-10 (10 mm range) positioned in each face of the prisms, in a total of eight transducers per specimen. Vertical transducers measured the average longitudinal deformation over approximately 200 mm span and horizontal transducers measured the average transversal deformation over approximately 150 mm span. Testing program A total of four specimens were tested for short-term creep. In standard creep tests, a specimen is subjected to a constant load and strain is recorded at subsequent times. Reproduction of the test with a series of different loads gives a family of creep curves, which characterize the creep behaviour of the material. However, in the case of ancient masonry, this procedure has severe drawbacks due to the high scatter of the material strength and the limited number of specimens available. To overcome these problems and to obtain as much information as possible from each specimen, a stepped load-time diagram has been applied to the specimens. The specimens were tested by applying successive load steps of 0.30 N/mm2 at intervals of eight hours. In this way, failure could occur either during the loading phase (short-term failure) or during sustained loading (tertiary creep). An attempt to obtain creep failure of the specimens was pursued by increasing the duration of the last steps whenever the strain rate was similar to the values observed in previously tested specimens. This issue will be further addressed in Section 3.3.5.

70


Test results Figure 3.10a depicts the average vertical (longitudinal) and horizontal (transversal) strains obtained, respectively ev and eh. Figure 3.10b illustrates, as an example, the time–stress–strain diagram for specimen PRe_5, which provides a detailed description of the results. In addition, Table 3.9 gives a summary of the experimental results in terms of the elastic modulus E, peak stress fc¢ and time to failure T, which corresponds to the duration of the creep test. The values for the elastic modulus E were calculated as an average from the second to fourth load steps (0.30–1.2 N/mm2). The sample is too small to extract any conclusion. Nevertheless, the comparison between the average standard compression strength ( fc = 6.6 N/mm2) and the

(a) -6.0

(b) -6.0

-4.0 -4.5 εv [10-3]

εv [10-3]

PRe_8

PRe_5 PRe_7

PRe_6 -2.0

-3.0 -1.5

0.0 0.0 PRe_6 5.0 εh [10-3]

εh [10-3]

4.0 8.0 PRe_5

12.0

PRe_8

16.0 0.0

2.0

10.0 15.0

PRe_7

4.0 6.0 Time [days]

8.0

20.0 6.0

4.0 2.0 σ [N/mm2]

0.0

3.0 6.0 Time [h]

9.0

Figure 3.10: Results obtained from short-term creep tests: (a) strain–time diagrams for all tested specimens and (b) time–stress–strain diagram for specimen PRe_5.

Table 3.9: Results obtained from short-term creep tests (in brackets, the coefficient of variation is given). Specimen

E (N/mm2)

fc¢ (N/mm2)

T (days)


2700 3185 4075 3815 3445 (18%)

4.50 5.70 5.40 3.90 4.9 (17%)

4.7 7.0 6.1 4.1 5.4


(a)

(b)

(c)

71

(d)

Figure 3.11: Failure pattern for specimen PRe_7. Shaded areas indicate spalling/ loss of material.

average short-term creep strength ( fc¢ = 4.9 N/mm2) seems to indicate that damage growth due to sustained loading influenced the results. In terms of average elastic modulus, the difference is rather small. With respect to crack patterns, thin and diffuse vertical cracks developed in the specimens during testing but large cracks and spalling were observed only at failure. This failure mode is particularly dangerous as it can lead to erroneous conclusions about the safety level of existing structures. Figure 3.11 illustrates, as an example, the failure pattern for specimen PRe_7. 3.3.4 Long-term creep tests Experimental set-up Long-term creep tests require specific testing equipment able to keep the load constant for long periods. In this study, three steel frames were specially designed and built to perform the tests conducted at University of Minho, see Fig. 3.12a and b. Each frame includes two loading steel plates, a hydraulic jack, a pressure gauge and a gas reservoir to stabilize the applied load. The lower steel plate was fixed, while the upper plate was hinged. The equipment was designed to test two prisms simultaneously, separated by a steel plate. Upon failure of one of the specimens, the equipment is unloaded to remove the failed specimen and re-loaded with the remaining specimen. Further references on long-term creep tests can be found in [27]. Longitudinal and transversal deformations were measured on each face of the prisms with a removable strain-gauge Laser electronic TP (see Fig. 3.12c). Longitudinal deformations were measured over three mortar bed-joints with an approximate span of 250 mm, while transversal deformations were measured over one head-joint with an approximate span of 145 mm. In addition, one inductive transducer HBM (10 mm range) per specimen was employed in the longitudinal direction to act as control of the strain-gauge measurements. It is noted that in the face of the specimen where the transducer was placed, the transversal displacement was not measured. In this way, the average longitudinal displacement of each specimen results from four strain-gauge measurements, while the transversal

72


(a)

(b)

(c)

Figure 3.12: Testing apparatus: (a) hydraulic frame, (b) specimens under testing and (c) removable strain gauge and contact seats glued to the specimen.

displacement results from three strain-gauge measurements. The tests were carried out under controlled conditions of temperature (22 ± 2ºC) and humidity (55 ± 10%), which were recorded by a data logger Testostor 175-2. Testing program The tests were conducted on six specimens. As in short-term creep tests, the load was applied by successive steps and kept constant for a given period. Two different load histories have been considered in order to better define future testing programs in similar specimens. A total of two prisms were tested by applying an initial stress of 1.50 N/mm2 and successive steps of 0.65 N/mm2. The initial load step corresponds, approximately, to 25% of the compressive strength fc obtained from the standard compression tests described in Section 3.3.2, while further load steps correspond, approximately, to 10% of fc. The duration of each period under constant load was of three months. The other four specimens were initially loaded at 4.10 N/mm2 (approximately 60% of fc) with subsequent load increases of 0.65 N/mm2 (about 10% of fc), applied at intervals of six months. Both load histories adopted have been defined in order that the estimated duration of the tests would be of about two years. Test results Figure 3.13a illustrates the average vertical (longitudinal) and horizontal (transversal) strains obtained for prisms tested with constant load periods of three months. Table 3.10 gives a summary of the experimental results obtained. For specimens tested with constant load periods of six months, Fig. 3.13b shows the average strain–time diagrams obtained for all tested prisms. In addition, Table 3.11 gives a summary of the results. Figure 3.14 illustrates, as an example, the strain evolution at each face of specimen PRe_12 and, also, the time–stress–strain diagram for the same specimen. From Fig. 3.14a it is possible to observe that the strain evolution is different at each face of the prism. This behaviour is typical of compression tests in quasi-brittle materials but, in the present experiments, such


(b) -4.5

σ?= 1.5 σ?= 2.2 σ?= 2.8 σ?= 3.5 σ?= 4.1 σ?= 4.8

σ?= 4.1

-2.0

-1.0

1.0

2.0

εh [10-3]

εh [10-3]

184 days 187 days 188 days 180 days

0.0

2.0

4.0

PRe_11 PRe_12 PRe_13 PRe_14

PRe_9 PRe_10

100

200 300 Time [days]

400

σ?= 6.1

-1.5

89 days 95 days 91 days 91 days 97 days

0

σ?= 5.4

-3.0

0.0

3.0

σ?= 4.8

σ?= 6.7

εv [10-3]

εv [10-3]

-3.0

73

500

6.0

0

200

400 600 Time [days]

800

Figure 3.13: Strain–time diagrams obtained from long-term creep tests: (a) constant load periods of three months and (b) constant load periods of six months. s stands for applied stress in N/mm2.

Table 3.10: Results obtained from long-term creep tests with constant load periods of three months. Specimen PRe_9 PRe_10 Average

E (N/mm2)

fc¢ (N/mm2)

T (days)

5055 4380 4718

4.75 4.75 4.8

465 464 464

feature is more salient due to the hinged upper loading plate. Another important aspect is that in some specimens cracks suddenly arise during constant load steps, resulting in a strain jump in the strain–time diagram, see, for example, the diagrams of specimen PRe_10 at 325 days or PRe_11 at 450 days shown in Fig. 3.13a and b, respectively. The values obtained for the compressive strength are within the range obtained for the standard compressive strength and short-term creep tests. Displacements recorded with the transducers employed (one per specimen) were found to be in agreement with the strain-gauge measurements. Figure 3.15 depicts the crack pattern evolution for specimen PRe_13 as an example. Again, diffuse vertical cracks developing during testing have been

74


Table 3.11: Results obtained from long-term creep tests with constant load periods of six months (in brackets, the coefficient of variation is given).

(a)

Specimen

E (N/mm2)

fc¢ (N/mm2)

T (days)


3720 5055 4345 3270 4100 (19%)

6.05 6.70 6.70 4.75 6.0 (15%)

559 742 749 184 558

(b)

-8.0

σ = 4.1 σ = 4.8 σ = 5.4 σ = 6.1 σ = 6.7

-4.0 -3.0

-4.0

εv [10-3]

εv [10-3]

-6.0

-2.0 0.0

εh [10-3]

εh [10-3]

-1.0 0.0

2.0 4.0 A B C D

6.0 8.0

-2.0

0

200

1.0 2.0 3.0

400 600 Time [days]

800

4.0 8.0 6.0 4.0 2.0 0.0 40 80 120 160 200 Time [days] σ [N/mm2]

Figure 3.14: Results from long-term creep tests on specimen PRe_12 (constant load periods of six months): (a) strain evolution for each face and (b) time–stress–strain diagram. s stands for applied stress in N/mm2.

observed, with large cracks and spalling occurring near failure. It is noted that the specimens with lower values of fc¢ presented the most diffused crack patterns. Severe non-uniform distribution of damage can be observed along the four faces of the specimens, confirming the results shown in Fig. 3.14a. 3.3.5 Discussion of the results The short-term compressive strength fc of each prism tested in creep is, of course, unknown and can only be estimated. In this section, the peak stress values fc¢


(a)

(b)

(c)

75

(d)

Figure 3.15: Failure pattern for specimen PRe_13. Shaded areas indicate spalling/ loss of material.

(b)

0.20 0.16

Creep coefficient [-]

Creep coefficient [-]

(a)

0.12 0.08 0.04 0.00 0.0

2.0

4.0 Time [h]

6.0

8.0

0.20 0.16 0.12 0.08 0.04 0.00

0

20

40 60 Time [days]

80

100

Figure 3.16: Variation of the creep coefficient with time obtained from: (a) shortterm creep results and (b) long-term creep results (constant load periods of three months).

obtained from the creep tests are considered as a close estimate of the compressive strength fc. Even if, in reality, the compressive strength fc does not correspond to fc¢, such values remain the closest estimate in a material as heterogeneous as the one addressed in this study. Figure 3.16 illustrates the evolution of the creep coefficient, defined as the ratio between the creep strain and the elastic strain, calculated from the short-term and long-term creep tests results. For each specimen, the creep coefficient was calculated considering all creep diagrams at low stress levels (below 45% of fc¢). It is further noted that the creep coefficient obtained from short-term creep tests was calculated from the average of the four tested specimens while the values obtained from long-term creep tests result from the average of the two specimens tested with constant load periods of three months. In the remaining four specimens tested in long-term creep, a first load step of approximately 60% of fc was applied and, thus, such tests cannot be used to calculate creep coefficients. Creep coefficients of approximately 0.10 and 0.15 were found at the end of 8 hours and 90 days of sustained loading, respectively, confirming that most creep

76


strain occurs at an early stage. Another important aspect is that the creep coefficient found at the end of 90 days is significantly lower than the values recommended by EC6 [28] for masonry made with clay units, which range from 0.5 to 1.0. This can be explained by the fact that EC6 values refer to new masonry, where maturation of mortar is in an initial stage and, also, because the specimens tested had already been under service loads for approximately five centuries prior to testing. . . Figure 3.17 shows the strain rate evolution, vertical e v and horizontal e h, versus the applied stress over strength ratio s/fc¢ for specimens tested in short-term creep. Strain-rate values were calculated between the sixth and eighth hour of each constant load step. It is expected that vertical strain rate values would be negative and horizontal strain rate values positive but some exceptions were found. This can be explained by minor variations in the applied load or changes in the environmental conditions. Such values have been considered equal to zero in the strain-rate diagrams shown in the rest of this section. In Fig. 3.17a three phases can be distinguished: for low stress levels (up to 50% of fc¢), the vertical strain rate is approximately constant and rather low; for medium stress levels (between 50 and 80% of fc¢), the vertical strain rate increases at a moderate pace; and, for high stress levels (over 80% of fc¢), a remarkable growth of the strain rate stress can be observed. The existence of three distinct phases had also been reported by Mazzotti and Savoia [29] on short-term creep tests performed on concrete specimens. Figure 3.17b shows that beyond 50% of fc¢, crack growth initiates, influencing the creep behaviour of the material. Figures 3.18 and 3.19 illustrate the strain rate evolution versus stress over strength ratio for long-term creep tests with constant load periods of three and six months, respectively. Strain rates were calculated from the average results over the last 30 days in the case of the tests with constant load periods of three months and over the last 90 days in the case of tests with constant load periods of six months. It is noted that the number of results is scarce and further testing is needed to better fundament the observations made. Nevertheless, the difference between the strain rate values obtained from short-term creep tests and long-term creep tests

(b) -5.0E-001

2.5E+000

-4.0E-001

2.0E+000 εh [year-1]

εv [year-1]

(a)

-3.0E-001 -2.0E-001 -1.0E-001 0.0E+000 0.0

1.5E+000 1.0E+000 0.5E-001

0.2

0.4 0.6 σ/fc' [-]

0.8

1.0

0.0E+000 0.0

0.2

0.4 0.6 σ/fc' [-]

0.8

1.0

Figure 3.17: Strain rate evolution versus applied stress over strength ratio for shortterm creep tests: (a) vertical strain rate and (b) horizontal strain rate.


(b)

-1.5E-003

1.5E-003 1.2E-003

εh [year-1]

εv [year-1]

-1.2E-003 -9.0E-004 -6.0E-004

9.0E-004 6.0E-004 3.0E-004

-3.0E-004 0.0E+000 0.0

77

0.2

0.4 0.6 σ/fc' [-]

0.8

0.0E+000 0.0

1.0

0.2

0.4 0.6 σ/fc' [-]

0.8

1.0

Figure 3.18: Average strain rate over the last 30 days versus applied stress over strength ratio for long-term creep tests (three months steps): (a) vertical strain rate and (b) horizontal strain rate.

(b) -4.0E-004

8.0E-004

-3.0E-004

6.0E-004

-2.0E-004 εv =

εh [year-1]

εv [year-1]

(a)

2.70 . 10-5 – 6.76 . 10-5 σ/fc –1

4.76 . 10-5 + 1.19 . 10-4 1– σ/fc

4.0E-004 2.0E-004

-1.0E-004 0.0E+000 0.4

εh =

0.5

0.6

0.7 0.8 σ/fc' [-]

0.9

1.0

0.0E+000 0.4

0.5

0.6

0.7 0.8 σ/fc' [-]

0.9

1.0

Figure 3.19: Average strain rate over the last 90 days versus applied stress over strength ratio for long-term creep tests (six months steps): (a) vertical strain rate and (b) horizontal strain rate.

is striking. In fact, strain rates ranging from zero to –5.0 × 10–1 year–1 were observed in short-term creep tests while in long-term creep tests, values ranging from zero to –1.0 × 10–3 year–1 were found. The results obtained from the two types of test seem therefore not comparable. Furthermore, primary creep seems not extinguished at the end of 8 h under sustained loading and, thus, secondary creep rates measured from short-term creep tests must be interpreted carefully. Another important aspect is that secondary creep was observed to initiate between 60 and 70% of fc. It is further noted that larger strain rate values were obtained for the prisms tested with constant load periods of three months, stressing the scattered nature of the masonry tested. A hyperbolic least squares fit of the experimental data obtained from the longterm creep tests with constant load periods of six months was computed, which

78 (a)

Learning from Failure (b)

-8.0E-003

2.0E-002 εh [year-1]

εv [year-1]

-6.0E-003 -4.0E-003 -2.0E-003 0.0E+000

2.5E-002 Average values

Average values

1.5E-002 1.0E-002 0.5E-003

0

40

80 120 Time [days]

160

200

0.0E+000

0

40

80 120 Time [days]

160

200

Figure 3.20: Strain-rate evolution in time for applied stresses larger than 60% fc¢: (a) vertical strain rate and (b) horizontal strain rate.

can be quite useful in calibrating non-linear creep models. The hyperbolic curve adopted is in the following form . e =

0.4 a 1 − s fc

+a

(1)

which yields zero for s/fc = 0.6 and has a vertical asymptote for s/fc = 1.0. From the least squares method, a = –6.76 × 10–5 for the vertical strain rate and a = 1.19 × 10–4 for the horizontal strain rate. The striking difference between strain rate values in short-term and long-term creep tests draws attention to what should be the minimum duration of constant load periods when conducting creep tests at high stress levels. A reasonable criterion is believed to be keeping the load constant until only secondary creep is present, i.e. until a fairly constant strain rate is attained. For this purpose, the vertical and horizontal strain rates were calculated for each 15-day period of the total 180 days constant load steps, as illustrated in Fig. 3.20. It is noted that only results corresponding to load levels larger than 60% of fc¢ were considered. The results obtained indicate that the strain rate gets approximately constant after 70–80 days in the case of longitudinal strains and after 30–40 days in the case of transversal strains.

3.4 Conclusions and future work The ability of standard continuum models, based on plasticity and cracking, and of a particle model, consisting in a phenomenological discontinuum approach, to reproduce the experimental compressive behaviour of masonry has been addressed. The comparison between the obtained numerical results and experimental results available in literature allows one to conclude that discontinuum models show clear advantages when compared to standard continuum models in predicting the compressive strength and peak strain of masonry prisms from the properties of


79

the constituents. Further investigation on models able to provide reliable predictions of masonry compressive strength, accounting for the discrete nature of the masonry components, is therefore suggested. The creep behaviour under high stresses of ancient regular masonry specimens recovered from the collapsed Civic Tower of Pavia has also been analysed. Standard compression tests, short-term creep tests and long-term creep tests have been conducted. From experimental practice, it is possible to conclude that creep tests on ancient masonry prisms should be carried out by applying the load in successive steps, at a given time interval, starting from a low stress level. In this way, a thorough description of the viscous behaviour of the material can be obtained. Creep tests in which the load is applied in a single step are inadequate in the case of ancient masonry due to the high scatter in the mechanical properties and to the small number of specimens usually available. The time period between successive load steps should be sufficiently long to extinguish primary creep. In fact, the evolution for different stress levels of the strain rate associated with secondary creep can only be evaluated in such a way. From the results obtained on the regular masonry prisms tested, a minimum time period under sustained loading of 70–80 days should be adopted. For this reason, remarkable differences were observed between secondary creep rates calculated from short-term or long-term creep tests. Short-term creep results should, therefore, be interpreted carefully. Finally, it should be stressed that secondary creep was found to initiate at 60–70% of the compressive strength. A hyperbolic fit to describe the evolution of secondary creep rate with the applied stress-level has been suggested in the present study. Suggestions for future work include further creep tests so that an adequate characterization of the material can be obtained, given the wide scatter associated with ancient masonry. With respect to the masonry constituents, experimental results on the non-linear creep behaviour of units and mortar are nearly absent in literature [30], meaning that further investigation is required. In terms of numerical modelling, the development of suitable 3D models for viscous inelastic behaviour is needed in order to include time-dependent effects in the numerical simulations of failure.

References [1]

[2]

[3]

Binda, L., Gatti, G., Mangano, G., Poggi, C. & Landriani, G.S., The collapse of the Civic Tower of Pavia: a survey of the materials and structure. Masonry Int., 6(1), pp. 11–20, 1992. Anzani, A., Binda, L. & Mirabella Roberti, G., The effect of heavy persistent actions into the behaviour of ancient masonry. Materials and Structures, 33(228), pp. 251–261, 2000. Bazant, Z.P., Material models for structural creep analysis. Mathematical Modelling of Creep and Shrinkage of Concrete, ed. Z.P. Bazant, John Wiley & Sons: New York, pp. 99–215, 1988.

80 [4] [5] [6] [7] [8] [9] [10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19] [20] [21]


Pickett, G., The effect of change in moisture content on the creep of concrete under a sustained load. ACI J., 38, pp. 333–355, 1942. Neville, A.M., Properties of Concrete, John Wiley & Sons: New York, 1997. Van Zijl, G.P., Computational Modelling of Masonry Creep and Shrinkage. Dissertation, Technical University of Delft, Delft, The Netherlands, 2000. Ameny, P., Loov, R.E. & Shrive, N.G., Models for long-term deformation of brick work. Masonry Int., 1, pp. 27–36, 1984. Lenczner, D., Creep and prestress losses in brick masonry. The Structural Engineer, 64B(3), pp. 57–62, 1986. Brooks, J.J., Composite modelling of masonry deformation. Materials and Structures, 23, pp. 241–251, 1990. Bazant, Z.P., Current status and advances in the theory of creep and interaction with fracture. Proc. 5th Int. RILEM Symp. on Creep and Shrinkage of Concrete, Barcelona, Spain, pp. 291–307, 1993. Papa, E., Taliercio, A. & Gobbi, E., Triaxial creep behaviour of plain concrete at high stresses: a survey of theoretical models. Materials and Structures, 31, pp. 487–493, 1998. Mazzotti, C. & Savoia, M., Nonlinear creep damage model for concrete under uniaxial compression. J. Engineering Mechanics, 129(9), pp. 1065– 1075, 2003. Pina-Henriques, J. & Lourenço, P.B., Masonry compression: a numerical investigation at the meso-level. Engineering Computations (accepted for publication). Binda, L., Fontana, A. & Frigerio, G., Mechanical behaviour of brick masonries derived from unit and mortar characteristics. Proc. 8th Int. Brick and Block Masonry Conf., Dublin, Ireland, Vol. 1, pp. 205–216, 1988. Frigerio, G. & Frigerio, P., Influence of the Components and Surrounding Environment in the Mechanical Behaviour of Brick Masonry (in Italian). Graduation thesis, Politecnico di Milano: Milan, Italy, 1985. Mann, W. & Betzler, M., Investigations on the effect of different forms of test samples to test the compressive strength of masonry. Proc. 10th Int. Brick and Block Masonry Conf., Calgary, Canada, pp. 1305–1313, 1994. Berto, L., Saetta, A., Scotta, R. & Vitaliani, R., Failure mechanism of masonry prism loaded in axial compression: computational aspects. Materials and Structures, 38(276), pp. 249–256, 2005. Pina-Henriques, J. & Lourenço, P.B., Testing and modelling of masonry creep and damage in uniaxial compression. Proc. 8th Int. Conf. Structural Studies, Repairs and Maintenance of Heritage Architecture, Halkidiki, Greece, pp. 151–160, 2003. Rots, J.G., Computational Modelling of Concrete Fracture. PhD Dissertation, Delft University of Technology, Delft, The Netherlands, 1988. DIANA Finite Element Code, version 8.1. TNO Building and Construction Research, Delft, The Netherlands. Vermeer, P.A. & de Borst, R., Non-associated plasticity for soils, concrete and rock. Heron, 29(3), pp. 1–64, 1984.


[22]

[23] [24]

[25]

[26]

[27] [28] [29]

[30]

81

Lourenço, P.B., A User/Programmer Guide for the Micro-Modelling of Masonry Structures. Report 03.21.1.31.35, Delft University of Technology, Delft, The Netherlands, 1996. Available from http://www.civil.uminho.pt/ masonry. CEB-FIP Model Code 1990; Bulletin D’Information No. 213/214, Comite Euro-International du Beton, T Telford: London, 1993. Lourenço, P.B. & Rots, J.G., A multi-surface interface model for the analysis of masonry structures. J. Engineering Mechanics, ASCE, 123(7), pp. 660– 668, 1997. Lourenço, P.B., Computational Strategies for Masonry Structures. PhD Dissertation, Delft University of Technology, Delft, The Netherlands, 1996. Available from www.civil.uminho.pt/masonry. van der Pluijm, R., Out-of-plane Bending of Masonry: Behaviour and Strength. PhD Dissertation, Eindhoven University of Technology, Eindhoven, The Netherlands, 1999. Anzani, A., Binda, L. & Melchiorri, G., Time dependent damage of rubble masonry walls. Proc. British Masonry Society, 2(7), pp. 341–351, 1995. Eurocode 6: Design of masonry structures; prEN 1996-1-1:2002, CEN: Brussels, Belgium, 2003. Mazzotti, C. & Savoia, M., Nonlinear creep, Poisson’s ratio, and creepdamage interaction of concrete in compression. ACI Materials J., 99(5), pp. 450–457, 2002. Papa, E., Binda, L. & Nappi, A., Effect of persistent loads in masonry structures. Proc. 3rd Int. Masonry Conf., London, pp. 290–294, 1992.


CHAPTER 4 Effects of creep on new masonry structures N.G. Shrive1 & M.M. Reda Taha2 1Department

of Civil Engineering, University of Calgary, Calgary, Canada. 2Department of Civil Engineering, University of New Mexico, Albuquerque, USA.

4.1 Introduction Creep can affect structures in two ways: deformations typically increase and loads (stresses) can be redistributed among structural components and, within a member, the constituent materials [1]. The effects of creep can be beneficial, neutral, or detrimental for a structure: beneficial, for example through the relief of stress concentrations, detrimental through increasing deformations. The latter can lead to a structure no longer meeting serviceability criteria. Stress redistribution can cause cracking, especially in cases where there is deterioration in strength over time due to environmental factors in that element of the structure which carries increasing load due to creep effects. Sometimes the two effects work together. Creep buckling is one example. An initial lateral imperfection in a column subject to axial load, or an initial eccentric load, causes an initial lateral displacement of the column. Consequently, there are higher compressive stresses on the inner curvature than on the outer curvature of the column. The side of the column under the higher stress creeps more than the other side, under the lower stress. The creep strains result in increasing lateral displacement. In turn, the secondary moment (the axial load times the lateral displacement) increases, increasing the stress on the inner curvature. Creep increases with the higher stress, so the lateral displacement increases more and more rapidly with the end result being a buckling failure of the column. An initial applied load less than the Euler buckling load for the end constraints of the column can thus cause a buckling failure sometime after load application. For some materials, the stress to initiate such failure can be as low as 60% of the failure stress in a monotonic

84


compression test. Binda et al. [2] indicate that for some types of masonry this number may be in the order of 45–50%. Crack growth caused by creep in tension tests has been recognized as ‘damage’ in the same context as that caused by fatigue [3, 4]. Cracks also grow under compression-induced creep, parallel to the direction of compression. The cause is similar to that in creep buckling in that the presence of the crack disturbs the local stress field, with a higher than average compressive stress parallel to the edge of the crack. Increased creep there accentuates the bending component of the stress and deformation beside the crack, increasing the crack width, and thus the tensile stresses at the crack tip. The crack extends when the stress and energy conditions favor such growth [5]. Creep crack propagation and its cracking rate dependence on bond breakage at the fracture process zone were discussed and modeled [6–8]. Binda et al. [9] remark on the existence of such cracks in the civic tower of Pavia at least 20 years prior to its collapse, and the appearance of such cracks in many historic structures at various ages after construction [2]. It is now well established that masonry creeps. The pioneering work of Lenczner [10, 11] has led to the realization that creep can be expected with any masonry units [2, 12–15] perhaps with the exception of some dry stacked stonework. The potential effects of creep therefore need to be considered in new construction and in rehabilitation. In rehabilitation interventions in historic masonry structures, essentially a new structure has been created, in which one component has already undergone some creep and the new component has yet to creep. Some masonry codes of practice now recognize the effect of creep in terms of increased deformation. Such codes advise designers to use the effective modulus technique to estimate long-term displacements [16, 17]. This technique, however, ignores what may happen in the structure between the initial and long-term states.

4.2 The step-by-step in time approach to modeling time-dependent effects We demonstrate here, using a simple step-by-step in time technique, that elements in a structure may see increasing, then decreasing, proportions of load over time: that by calculating only the initial and long-term states, the designer may miss a peak stress occurring at an intermediate time. We recognize that masonry is complex, multi-component material: an outer skin of brickwork or blockwork may be filled with grout or rubble masonry, and may contain reinforcing bars. Modern techniques of rehabilitation may involve use of fiber reinforced polymers (FRPs), some of which are known to creep [18]. Alternatively, the epoxy binding the FRP to the underlying masonry may relax over time under the shear stresses transferring load between the FRP and the masonry: such behavior would cause a redistribution of load between these two components. The step-by-step in time method of creep analysis relies on the applicability of the principle of superposition. In relation to creep, the principle requires that for a material subjected to stresses at different times, the creep strain produced at any

Effects of Creep on New Masonry Structures

85

time due to a previously applied stress is independent of the effects of any other stresses applied before or after that particular stress. The creep response to a set of stresses applied at different times is thus the summation of the creep effects of each stress. We demonstrate the technique and the consequences for load redistribution and increasing deformations in structures through the examples of an axially loaded masonry column and a beam subjected to pure bending. We also demonstrate the effect of damage of masonry on stress redistribution. A wall subjected to both axial and bending loads could be analyzed similarly. The complexity of the analysis can be increased by including plasticity constitutive equations as in [15] or by adopting variable adaptive time-stepping when damage is considered, as recommended by [19]. At the end of the chapter we introduce the concept of using Artificial Neural Networks (ANNs) to predict creep effects, as they can be substantially more accurate than explicit equations that best fit with regression to experimental data.

4.3 Case 1: An axially loaded column 4.3.1 Creep model Consider a concentric axial load P applied to a symmetric column made of two materials A and B each symmetrically distributed about the column axis. Effects due to eccentricity can therefore be neglected. The two materials have different time-dependent properties. The two materials have cross-sectional areas: AA being that of material A and AB that of material B. Equilibrium requires: AAsA + ABsB = P

(4.1)

where P is the applied concentric axial load and sA and sB are the stresses in materials A and B, respectively. Compatibility requires the axial strain ε in the column and each respective material is the same e = eA = eB

(4.2)

Next we assume that each material creeps such that the creep can be expressed as a compliance function in time, where DA and DB are the compliances of materials A and B, respectively. This creep function (eqn (4.3)) is shown in Fig. 4.1. −t ⎛ ⎞ tA eA (t ) = DA (t ) sA = DA fA sA ⎜1 − e ⎟ ⎝ ⎠

(4.3)

The creep strain eA(t) is obtained by simply multiplying the time-dependent creep coefficient, (fA(t)), by the initial strain as in eqn (4.3). fA is the creep coefficient for infinite time. The time constant tA denotes the time when 63% of the creep has occurred. Material B is assumed to creep with a mathematical form

86

Learning from Failure Asymptotic for t = ∞

εA

fA sA DA

sA D A

tA Time (t)

Figure 4.1: The simple creep function. similar to material A, but with DB, fB(t) and tB representing its compliance, creep coefficient, and the 63% creep time, respectively. Other formulations of the creep function as suggested by other researchers [e.g. 11, 12, 20, 21] can be employed in lieu of eqn (4.3) and will have a slight effect in the overall conclusion. Using the equilibrium and compatibility considerations above, the initial stresses in the two materials are: sA =

DB P AB DA + AA DB

(4.4)

sB =

DA P AB DA + AA DB

(4.5)

Since both materials are stressed, both will want to creep. We therefore permit a small increment in time to occur from t = 0 to t = t1. In this first time increment, material A will want to creep an amount of strain ΔecrA as presented in eqn (4.6). − t1 ⎛ ⎞ ΔecrA (1) = sA fA DA ⎜ 1 − e tA ⎟ ⎝ ⎠

(4.6)

Material B will also have a creep increment of similar form. However, the increments in creep strain will be different. Hence, compatibility will be violated. In order to restore compatibility, the material that wants to creep more will have its stress reduced by the one that wants to creep less, while the latter will have its strain increased by the former. Compatibility therefore requires: ΔecrA (1) + ΔsA (1)DA = ΔecrB (1) + ΔsB (1)DB

(4.7)

where the Δss are the incremental changes in stress. Since there is no increase in the overall axial force, equilibrium requires: ΔsA (1)AA + ΔsB (1)AB = 0

(4.8)

87


The incremental stress changes are therefore ΔsA (1) =

− AB ( ΔecrA (1) − ΔecrB (1)) AB DA + AA DB

(4.9)

ΔsB (1) =

AA ( ΔecrA (1) − ΔecrB (1)) AB DA + AA DB

(4.10)

The stress in A (and similarly in B) at the end of the first time step is therefore sA (1) = sA + ΔsA (1)

(4.11)

The materials, however, want to continue to creep. We therefore invoke superposition since we have made the materials linear viscoelastic. The amount of creep strain that material A would like to creep in the second time step can therefore be expressed as: − t2 ⎛ −t t1 ⎞ A ΔecrA (2) = sA fA DA ⎜ e − e tA ⎟ ⎝ ⎠ − ( t2− t1 ) ⎛ ⎞ − + ΔsA (1)fA DA ⎜ 1 − e tA ⎟ ⎝ ⎠

(4.12)

The specific creep (creep strain per unit stress) curves for the different stress increments are the same; they just start at each time step, as shown in Fig. 4.2. Assume c1 is the specific creep that material A would like to creep in time step 1 due to the initial stress. c1 is also the specific creep for the stress increment ΔsA (4.1) between time t1 and t2, whereas the influence of the initial stress in that time interval will be c2. When multiplied by their respective stresses, the influences are simply added. Equilibrium and compatibility can be enforced again and the third step considered. This leads to the formula for the (nth) time step where (n ≥ 2). − tn ⎛ − tn−1 ⎞ ΔecrA (n) = sA fA DA ⎜ e tA − e tA ⎟ ⎝ ⎠ − ( t n − ti −1 ) n ⎛ − − ( tn−t1− ti−1 ) ⎞ − A + ∑ ΔsA (i − 1)fA DA ⎜ e − e tA ⎟ i=2 ⎝ ⎠

(4.13)

with the stress in material A at the end of the nth time step being n

sA (n) = sA + ∑ ΔsA (i )

(4.14)

i =1

With a similar equation for material B, the total strain is n

n

i =1

i =1

eA (n) = eA + ∑ ΔecrAn (i ) + DA ∑ Δsn (i )

(4.15)

88


Figure 4.2: The specific creep for the different stress increments.

Example Consider, for example, a blockwork column (A) filled with grout (B). We consider the following values for the following parameters: AA = 0.6Atotal, AB = 0.4Atotal, DA = 1/15 GPa–1, DB = 1/22 GPa–1, fA = 5.0, fB = 2.5, tA = 500 days and tB = 1000 days. The blockwork is modeled to creep more and in a relatively shorter time than the grout. The results in Fig. 4.3 show the stress changes in both the blockwork and the grout over time. Based on their relative stiffnesses, the initial stress in the blockwork is 12.6 MPa while that in the grout is 18.5 MPa. As the blockwork wants to creep faster than the grout, the blockwork initially offloads to the grout. However, as the grout creeps more than the blockwork at later ages, the blockwork will be re-stressed and the grout stress will be reduced during this phase. The effective modulus method [1, 22] is applied to estimate the final stress in the blockwork using eqn (4.16): s A (∞ ) =

DB (1 + fB ) AB DA (1 + fA ) + AA DB (1 + fB )

(4.16)

The final stress in the grout can be evaluated similarly. Final stresses of 9.3 and 23.5 N/mm2 are determined for the blockwork and grout, respectively. Similar stresses are attained using the step-by-step analysis (Fig. 4.3). However, a designer using the effective modulus method will only detect that creep of the two materials will result in the grout stress rising by 25%, while in reality the grout will be overstressed by 36% from the initial value during an intermediate time period. The model presented here does not include the possibility that the material in which the stress rises (here the grout) might be damaged (degraded) during the overloading period. Typically, as a quasi-brittle material, the grout might be cracked during the overloading, reducing its stiffness. The stress distribution would therefore be


89

Figure 4.3: Stress development in blockwork and grout due to creep (Case 1).

changed from what is shown here and the blockwork re-stressed to a level higher than shown in Fig. 4.3. The example also demonstrates that the initial and final stress states are not the extremes. Higher stresses occur at intermediate stages. 4.3.2 Effect of coupling creep and damage in concentrically loaded columns Another interesting effect that is difficult to correlate is the coupling of creep and damage. As mentioned, models are being developed for tensile creep and fatigue [3, 4], but there are other mechanisms which can induce damage. External deterioration can begin on the surface of masonry from actions like freeze-thaw or weathering. Mirza [23] for example, discussed how the resistance of a member in the context of limit states design can decline with time after construction. Valluzzi et al. [24] and Bažant [25] presented methods to account for this coupling effect in finite element modeling of historical masonry. Various damage models are described in the literature [26–28]. We have chosen a simple model as our objective is to show what can happen, rather than to develop a model for a particular case or material. We consider the analysis above but we also introduce a

90


damage model to account for the effect of damage in one material of the column and couple it with creep. Damage is assumed to accumulate in the form DM(t ) =

⎛ h ⎞ ⎛ −t ⎞ ∑ ⎜ ⎟⎜ ⎟ i = tDstart ⎝ tDM ⎠ ⎝ tDM ⎠ t

n

(4.17)

tD is the damage time constant which refers to the time where most damage would occur. The coefficients are taken here as tD = 800, h = 0.3, and n = 10. DM(t) represents the level of damage accumulated from the time at which damage starts, tDstart, to the time of evaluation t. In the calculations here, damage is assumed to begin at 400 days. The rate of damage accumulation with this model is slow initially, but accelerates over time, as shown in Fig. 4.4. For the sake of showing the trends and effects, quite considerable damage is assumed to occur in a relatively short time in this example. Following [26] and [29], the modulus of the material changes over time with this model as EA(t) = (1 − DM(t))EA(tDstart)

(4.18)

where EA(tDstart) is the material stiffness at the time when the damage begins. When DM is zero, there is no damage and when DM equals 1, the material is unable to bear any load.

Figure 4.4: The damage model showing the non-linear change of damage ratio with time. Here the blockwork will have a damage factor of about 0.33 after 1000 days with the damage starting at 400 days. Damage initially accumulates at a very low rate but then increases rapidly.


91

The effect of combined creep and damage on the Young’s moduli of both materials is shown in Fig. 4.5, while the stresses variations with time are shown in Fig. 4.6. These stresses are different to those in Fig. 4.3 in that they begin to change quite rapidly at later ages, as the damage accumulates in the outer blockwork, causing redistribution to the stiffer, undamaged grout. It thus becomes possible that the grout could now begin to fail, leading to collapse of the whole structure in time. This problem has been analyzed further elsewhere [30], with consideration of several possible combinations of creep and damage. 4.3.3 Examining the effect of rehabilitation Much effort has been spent on rehabilitating and strengthening structures, both of historic and of simply practical value. Fiber reinforced polymers have been used on various occasions as they offer distinct advantages over steel in terms of being light weight and thus adding little mass to a structure, and highly durable if protected from sunlight. Some FRPs creep while others do not, unless the stress is a

Figure 4.5: The change in effective moduli of the two materials with time due to combined creep and damage. Note the change of the slope of stiffness reduction of the blockwork due to the combined effect of creep and damage after 400 days of age while the slope of grout stiffness reduction due to creep only is almost constant after 400 days.

92


Figure 4.6: The change in stress in the two materials over time with creep and damage. very high proportion of ultimate [18, 31]. Thus when an FRP is used to strengthen a structure, the longer term consequences should be evaluated. If the structure is historic, creep may well have substantially run its course for the current loading. However, if the FRP is prestressed or changes the stresses in the structure in some other way then creep will start anew. Essentially a new structure has been created and the consequences of time-dependent effects need to be evaluated. One potential effect that needs to be considered is the reduction in load carried by the FRP from flow of the bonding epoxy from the shear that transfers load between the FRP and the underlying substrate. For example, if an FRP strip is applied to a structure to help carry a dead load, or is applied pretensioned to counteract a dead load, then there is the potential for the bonding epoxy to flow [32]. The FRP strip offloads over time. The effect is demonstrated with the next problem. Rigid mechanical anchorage of the strip would be required to avoid the consequence shown.

4.4 Case 2: Composite structural element subject to bending 4.4.1 Development of model Consider a reinforced concrete beam where a layer of external reinforcement is bonded to the bottom of the beam as shown in Fig. 4.7. The external reinforcement


93

Figure 4.7: Schematic representation of a reinforced concrete beam cross-section with one layer of steel reinforcement and externally applied FRP. is added to the model such that the model is general and the effect of any externally applied strengthening material can be considered. We consider the case of pure bending for simplicity. Prestressing or axial dead load can be included. Again, for simplicity, we have assumed there is no compression reinforcement. Strain compatibility, with plane sections remaining plane, gives ⎛ d − kd ⎞ es = ec ⎜ ⎝ kd ⎟⎠

(4.19)

⎛1− k⎞ es = ec ⎜ ⎝ k ⎟⎠

(4.20)

⎛ h − kd ⎞ ef = ⎜ e ⎝ kd ⎟⎠ c

(4.21)

where kd is the depth of the neutral axis. Force equilibrium requires Tf + Ts − C = 0

(4.22)

1 Af sf + As ss − bkd sc = 0 2

(4.23)

Moment equilibrium requires kd ⎞ kd ⎞ ⎛ ⎛ Ts ⎜ d − ⎟ + Tf ⎜ h − ⎟ = M ⎝ ⎝ 3⎠ 3⎠

(4.24)

kd ⎞ kd ⎞ ⎛ ⎛ As ss ⎜ d − ⎟ = M − Af sf ⎜ h − ⎟ ⎝ ⎝ 3⎠ 3⎠

(4.25)

94


Solving the equations provides ⎛ E ⎞ ⎛1− k⎞ 1 As sc ⎜ s ⎟ ⎜ ⎟ − bkd sc = − Af sf ⎝ Ec ⎠ ⎝ k ⎠ 2 sc =

Af sf ⎡1 ⎛ Es ⎞ ⎛ 1 − k ⎞ ⎤ ⎢ bkd − As ⎜ ⎟ ⎜⎝ ⎟⎥ ⎝ Ec ⎠ k ⎠ ⎦ ⎣2

(4.26) (4.27)

and from the moment equations kd ⎞ ⎛ 3 − k ⎞ ⎛ Es ⎞ ⎛ 1 − k ⎞ ⎛ As d ⎜ s = M − Af sf ⎜ h − ⎟ ⎝ 3 ⎟⎠ ⎜⎝ Ec ⎟⎠ ⎜⎝ k ⎟⎠ c ⎝ 3⎠

(4.28)

Thus at t = 0 (no creep) ⎛ E ⎞ ⎛ h − kd ⎞ sf = sc ⎜ f ⎟ ⎜ ⎟ ⎝ Ec ⎠ ⎝ kd ⎠ sf h − kd Af = = sc kd ⎛ E ⎞ ⎛ 1 − kd ⎞ 1 bkd − As ⎜ s ⎟ ⎜ ⎟ 2 ⎝ Ec ⎠ ⎝ k ⎠

(4.29)

(4.30)

leaving the following equation to be solved for k: ⎛1 2⎞ 2 ⎜⎝ Ec bd ⎟⎠ k + d ( As Es + Af Ef )k − ( Af Ef h + As Es d ) = 0 2

(4.31)

Thus the initial stresses in the concrete, FRP, and steel are sci =

M v

(4.32)

⎛ 3 − k ⎞ ⎛ Es ⎞ ⎛ 1 − k ⎞ v = As d ⎜ ⎝ k ⎟⎠ ⎜⎝ Ec ⎟⎠ ⎜⎝ k ⎟⎠ ⎛ E ⎞ ⎛1− k⎞ ⎤ kd ⎞ ⎡ 1 ⎛ + ⎜ h − ⎟ ⎢ bkd − As ⎜ s ⎟ ⎜ ⎟⎥ ⎝ ⎠ 3 ⎣2 ⎝ Ec ⎠ ⎝ k ⎠ ⎦

(4.33)

⎛ E ⎞ ⎛ h − kd ⎞ sfi = sci ⎜ f ⎟ ⎜ ⎟ ⎝ Ec ⎠ ⎝ kd ⎠

(4.34)

⎛ E ⎞ ⎛1− k⎞ ssi = sci ⎜ s ⎟ ⎜ ⎟ ⎝ Ec ⎠ ⎝ k ⎠

(4.35)

Now, for t > 0, the concrete creeps and E c (t ) =

ei Eci e (t )

(4.36)


95

Further, we need to solve for k as a function of sf as sf will reduce with time ⎛ ⎞ ⎜ ⎟ Af sf ⎛ 3 − k ⎞ ⎛ Es ⎞ ⎛ 1 − k ⎞ ⎜ ⎟ As d ⎜ ⎝ 3 ⎟⎠ ⎝⎜ E c (t ) ⎠⎟ ⎜⎝ k ⎟⎠ ⎜ ⎡ 1 ⎛ Es ⎞ ⎛ 1 − k ⎞ ⎤ ⎟ ⎜ ⎢ bkd − As ⎜ ⎜ ⎟ ⎥⎟ ⎜⎝ 2 ⎝ E c (t ) ⎟⎠ ⎝ k ⎠ ⎦ ⎟⎠ ⎣ kd ⎞ ⎛ = M − Af sf ⎜ h − ⎟ ⎝ 3⎠

(4.37)

⎡⎛ ⎛ E ⎞ ⎛1− k⎞ ⎤ ⎛ Es ⎞ ⎛ 1 − k ⎞ ⎤ kd ⎞ ⎡ 1 Af sf ⎢⎜ h − ⎟ ⎢ bkd − As ⎜ s ⎟ ⎜ ⎥ As d ⎜ ⎟ ⎜ ⎟⎥ 3 ⎠ ⎣2 ⎝ Ec (t ) ⎠ ⎝ k ⎠ ⎦ ⎝ Ec (t ) ⎟⎠ ⎝ k ⎠ ⎦⎥ ⎣⎢⎝ ⎡1 ⎛ E ⎞ ⎛1− k⎞ ⎤ = M ⎢ bkd − As ⎜ s ⎟ ⎜ ⎟⎥ ⎝ E c (t ) ⎠ ⎝ k ⎠ ⎦ ⎣2

(4.38)

⎛ E ⎞ ( Af sf d 2 b)k 3 + 3bd ( M − Af sf h)k 2 + 6 As ⎜ s ⎟ ( M − Af sf (h − d )) − k ⎝ Ec ( t ) ⎠ ⎛ E ⎞ − 6 As ⎜ s ⎟ ( M − Af sf (h − d )) = 0 ⎝ Ec ( t ) ⎠

(4.39)

We let the FRP stress decline with time as the epoxy creeps (flows) under the shear it is transmitting. We consider a simple classical formula to represent FRP stress relaxation due to binding matrix creep [33]. At the end of the first time step, the stress in the FRP is − t1 ⎛ ⎞ sf′ (1) = sfi ⎜ a + (1 − a )e tr ⎟ ⎝ ⎠

Ec (1) =

ei Eci e(t1 )

(4.40)

(4.41)

Equation (4.39) is solved for k′(1) and this value is substituted into eqn (4.27) for sc′(1) ec′ (1) =

sc′ (1) Ec (1)

⎡ h − k ′(1)d ⎤ Δef = ec′ (1) ⎢ ⎥ ⎣ k ′(1)d ⎦ Δsf (1) =

(4.42)

(4.43)

Ef ⎛ h − k ′(1)d ⎞ (sc′ (1) − sci ) ⎜ ⎝ k ′(1)d ⎟⎠ Ec (1)

(4.44)

sf′′(1) = sf′ (1) + Δsf (1)

(4.45)

96


With the increment in concrete stress, force and moment equilibrium are checked. If equilibrium is not obtained, we reiterate the calculation of k. After k has been computed, sc(1) is calculated from eqn (4.27) Δsc1 = sc (1) − sci

(4.46)

Δsf1 = sfi − sf (1)

(4.47)

t ⎛ t −t ⎞ n −1 ⎡ ⎡ − n ⎤ −⎜ n i ⎟ ⎤ sf′ (n) = sfi ⎢a + (1 − a )e tn ⎥ + ∑ Δsfi ⎢a + (1 − a )e ⎝ t ⎠ ⎥ ⎣⎢ ⎦⎥ i =1 ⎣⎢ ⎦⎥

(4.48)

t ⎛ t −t ⎞ n −1 ⎡ ⎛ ⎛ − n ⎞⎤ −⎜ n i ⎟ ⎞ ⎤ Δsci ⎡ ⎢1 + f ⎜ 1 − e ⎝ t ⎠ ⎟ ⎥ ec (n) = e ⎢1 + f ⎜ 1 − e tn ⎟ ⎥ + ∑ ⎝ ⎠ ⎦⎥ i =1 Ec (ti ) ⎣⎢ ⎝ ⎠ ⎦⎥ ⎣⎢

(4.49)

for the nth step

E c (n ) =

ei Eci e (n )

(4.50)

The cracked beam curvature at any section j along the beam at any time t denoted Ψ2j(t) can be computed as Ψ 2j ( t ) =

Mi Ec (t )I tj (t )

(4.51)

where Itj(t) is the transformed cracked moment of inertia at the jth section at time t, computed as b [k (t )d ]

3

I tj (t ) =

3

⎛ E ⎞ + As ⎜ s ⎟ [d − k (t )d ]2 ⎝ E c (t ) ⎠

⎛ E (t ) ⎞ + Af ⎜ f ⎟ [h − k (t )d ]2 ⎝ E c (t ) ⎠

(4.52)

The uncracked beam curvature at any section along the beam at time t denoted Ψ1j(t) can be computed as Ψ1j (t ) =

Mj Ec (t )I gj (t )

(4.53)

Given the effect of tension-stiffening on beam deflection, an effective curvature can be determined by interpolating between the cracked and uncracked section curvatures using the moment-curvature approach recommended by the CEB-FIP [34] and Ghali and Favre [1] as Ψej (t ) = xΨ j 2 (t ) + (1 − x )Ψ j1 (t )

(4.54)

where x is the tension stiffening coefficient that can be determined using the CEBFIP [34] method. Here the tension stiffening coefficient x was determined such


97

that the error between the experimentally measured (Section 4.4.2) and model predicted mid-span deflections is a minimum. The mid-span deflection of the beam Δmid(t) can be predicted by integrating the curvature along the span (S) or estimated approximately by considering the geometrical relation using three sections at the ends and at mid-span as Δ mid (t ) =

S2 (Ψleft (t ) + 10Ψemid (t ) + Ψ right (t )) 96

(4.55)

where Ψleft and Ψright can be assumed to be equal to zero as no end curvature due to restrained shrinkage is expected to occur and Ψemid (t) is the mid-span curvature computed as in eqn (4.54). 4.4.2 Application to a beam The model is now applied to reinforced concrete beams with the dimensions shown in Fig. 4.8 and loaded as shown in Fig. 4.9. The material and load properties, including the concrete creep are taken as listed in Table 4.1. Two beams were tested. Both beams have similar properties (cast from the same concrete batch, at the same time and cured in a similar way) one without FRP strengthening strips and one with FRP strengthening strips. The cross-section of the FRP strengthened beam is shown in Fig. 4.8.

Figure 4.8: Cross-section dimensions of the concrete beam reinforced with one layer of steel reinforcement and externally applied FRP.

Figure 4.9: Schematic representation of the beam loading set-up.

98


For the beam without FRP strengthening, the predicted increase in deflection at the center of the beam is compared with experimental data (presented in [35, 36]) in Fig. 4.10. It can be observed in Fig. 4.10 that the model was capable of predicting the creep deflection of the beam fairly well at early and late times. It is worth mentioning this prediction is achieved using the creep properties listed in Table 4.1 and by adjusting the tension stiffening coefficient to reduce the model error. A tension stiffening coefficient x = 0.9 is needed. This high coefficient indicates that the section will be very close to fully cracked in this case (x = 1.0 indicates fully cracked section). In fact, the beam has numerous flexural cracks. Now, if we consider the beam strengthened with the FRP strips to have similar material properties, and assume that the only time-dependent effect is the concrete creep, we get the result

Table 4.1: Material properties of reinforced concrete beam. Concrete compressive strength (MPa) Concrete initial modulus of elasticity (GPa) Reinforcing steel modulus of elasticity (GPa) CFRP modulus of elasticity (GPa) Concrete creep coefficient f (t, t0) Concrete ultimate creep time tc (days)

34.3 21.1 200 165 4.2 2000

Figure 4.10: Predicted versus experimentally measured deflections of reinforced concrete beam including creep effect (Beam 1: no FRP is used).


99

Figure 4.11: Predicted versus experimentally measured deflections of reinforced concrete beam (Beam 2: FRP is used) including creep effect only. Tension stiffening coefficient similar to that of Beam 1 is used (x = 0.9).

shown in Fig. 4.11. It is obvious that the predicted mid-span deflection does not meet the measured mid-span deflection. The significant difference between the measured and predicted deflections in Fig. 4.11 can be attributed to two factors: the tension-stiffening effect and the effect of the creep of the epoxy binding matrix. As installing the FRP strips increased the cracking capacity of the beam, a lower tension stiffening coefficient (representing a cracked section) is required compared to that used in computing the mid-span deflection of the unstrengthened beam. Changing the tension-stiffening coefficient in the case with FRP we obtain the curve shown in Fig. 4.12. It can be observed that predicted deflection in this curve is closely related to the experimentally measured one. The deflection predicted in Fig. 4.12 assumes no FRP binder creep has occurred (a = 1.0). If relaxation of stress in the FRP strips due to the creep in the epoxy binding the FRP strip to the concrete (a = 0.9 and t = 600 days) is included, we get Fig. 4.13. While higher creep coefficient of epoxy at the concrete– FRP interface might be assumed, recent experimental investigations showed that creep of epoxy at the concrete–FRP interface would result in little but fast stress loss in the FRP sheets [37]. Therefore the reduction of FRP stress in the analysis presented here due to creep of epoxy was limited to 90% of the original stress. Figures 4.12 and 4.13 look very similar, but it is misleading to judge the effect of FRP binder creep from these time-deflection diagrams. This is because the section is close to uncracked and the influence of FRP stress-relaxation on the

100


Figure 4.12: Predicted versus experimentally measured deflections of reinforced concrete beam (Beam 2: FRP is used) including creep effect of concrete and no FRP stress relaxation effect (a = 1.0) and tension stiffening effect (x = 0.27).

Figure 4.13: Predicted versus experimentally measured deflections of reinforced concrete beam (Beam 2: FRP is used) including creep of concrete effect, FRP stress relaxation effect (a = 0.9 and t = 600 days) and tension stiffening effect (x = 0.27). transformed section properties is not reflected in the change in beam deflection. The influence of changing the FRP stress-relaxation coefficient from no relaxation (Case 1: a = 1.0) to significant relaxation (Case 2: a = 0.9) on the transformed inertia is shown in Fig. 4.14.


101

Figure 4.14: Change in transformed cracked moment of inertia of the FRP strengthened beam with two cases: one with no FRP stress relaxation (Case 1: a = 1.0) and the other with FRP stress relaxation (Case 2: a = 0.9). Both cases include tension stiffening effect (x = 0.27).

The results shown in Fig. 4.14 demonstrate the fact that the transformed cracked section inertia reduces due to FRP stress relaxation. This reduction would result in a considerable change in the beam deflection if the beam was cracked, particularly if the beam were cracked prior to the application of the FRP strengthening strips. This change (although happening) did not affect the beam deflection in the case study because the beam was uncracked and thus its deflection is dominated by the uncracked section inertia. The step-by-step in time analysis also allows the change in the stress in the concrete top fibers, the reinforcing steel bars, and the FRP strips to be followed. Exemplar result for the change in the concrete stresses is shown in Fig. 4.15. The stresses shown in the Fig. 4.15 are based on the FRP stress decreasing due to creep of the epoxy at the FRP–concrete interface. With the current model, we force this reduction in stress through our imposition of relaxation in the FRP. However, such a reduction is likely not to be correct over the full time domain if the concrete creeps extensively, as would occur if the concrete were young. Such creep will increase the curvature of the beam resulting in increasing stress in the FRP after the initial decrease. This issue represents a modeling challenge because the concrete and epoxy have different rates of creep. Creep in the epoxy occurs in a considerably shorter time compared with that of creep in concrete. Therefore, the analysis above can be used to model the beam deflection and to give a reasonable estimate of the stresses in the concrete but not in the steel or the FRP. The small

102


Figure 4.15: Change of concrete top fiber stresses with time due to combined concrete creep and FRP stress relaxation (a = 0.9 and t = 600 days).

Figure 4.16: Change of stresses in FRP strips with time due to creep of epoxy at the concrete–FRP interface (a = 0.9 and t = 600 days) while creep of concrete is neglected. effect on the accuracy of the concrete stresses in this example is related to the relatively small change in the FRP stress over the entire analysis time due to stress relaxation (only 3%) given the geometry of the beam analyzed and the relaxation parameters considered (a = 0.9 and t = 600 days). If the creep of concrete is minimal, as would be the case in strengthening an old concrete beam under its own weight, then the FRP stress would be accurately estimated from the above analysis as shown in Fig. 4.16.


103

4.4.3 Masonry walls subject to axial load and bending Masonry walls are typically subject to both axial load (example 1) and bending (example 2). Hence to solve for the effects of creep for such loading, it is necessary to combine the two examples above, invoking the need for equilibrium and compatibility in the process. The equations for this situation are being developed. The consequences are well known, in that out-of-plane deformation of the wall will increase, just as the central deflection of the concrete beam in example 2. The stress on the inside curve of the wall will increase while that on the outside will decrease. Two possible long-term consequences are that failure by cracking or crushing may develop on the inner curve of the wall, or the wall may buckle. The situation which should be carefully analyzed is one where a cracked wall, vault, or beam is strengthened in situ, and the load increased. The FRP is likely to off-load itself over time if not anchored mechanically (The FRP strips in the beam as above were anchored with U-shaped FRP sheets).

4.5 New mathematical approaches to modeling creep The above analysis demonstrated the importance of considering time-dependent analysis in evaluating serviceability of masonry structures. It also showed the importance of predicting creep with a good accuracy. Here we present findings of recent research efforts to enhance the accuracy of predicting creep using means of artificial intelligence. The inspiration for ANNs came from the desire to produce artificial systems capable of performing sophisticated (or perhaps intelligent) computations that mimic the routine performance of the human brain. Artificial neural networks are networks of many simple processors (neurons) operating in parallel, each possibly having a small amount of local memory. Artificial neural networks resemble the brain in two respects: first, knowledge is acquired by the network through a learning process and second, the interneuron connection weights are used to store the knowledge [38, 39]. No closed-form solution for the problem is provided by ANNs. However, ANNs offer a complex, accurate solution based on a representative set of historical examples of the relationship [38]. The units (neurons) are connected by weighted channels which are adjusted on the basis of learning data. Artificial neural networks learn from examples (of known input/output sequences) and exhibit some capability for generalization beyond the training data. Artificial neural networks normally have great potential for parallelism, since the computations of the components are largely independent of each other [39, 40]. The creep deformations of masonry prisms subjected to different stress levels, representing approximately (12, 24, 36, and 48%) of the prisms’ compressive strength, respectively, and exposed to different environmental conditions [12] were used to develop and assess the ANN model. A series of unloaded prisms subjected to environmental conditions similar to their counterparts – loaded prisms – was also measured at the same time intervals to account for shrinkage and

104


(1/MPa)

800

700

Predicted J(t,t 0) x 10

Predicted J(t,t 0) x 10

700 600

-6

600

-6

(1/MPa)

800

500 400 300 200 100 100

200

400 300 200 100 100

300 400 500 600 700 800 Measured J(t,t 0) x 10-6 (1/MPa)

(a)

500

200

300 400 500 600 700 800 -6 Measured J(t,t 0) x 10 (1/MPa)

(b) 15%

RTN1

50%

GERBER

Figure 4.17: Prediction of creep compliance using (a) an ANN model [41] and (b) a regression analysis (modified Burger) model [12]. thermal changes. Test results from fourteen testing groups were included in training of the network. A series of multi-layer ANNs for predicting creep performance of masonry structures was developed [41, 42]. The creep prediction neural network consists of an input layer, one hidden layer, and an output layer. The network utilizes a log-sigmoid transfer function and a linear output function. A backpropagation training algorithm was used as the learning rule for the network. A learning matrix including 47 training samples drawn from the 14 testing groups was used in training the network. The LevenebergMarquardt training criterion [42] was utilized during the learning process of the network with a training goal of achieving a mean square error of 0.0002. The network was then tested against groups of data that had not been used in training the network. The creep compliance was computed by the network and the output of the network was compared to the measured creep compliance. A comparison between the creep compliance prediction using ANN and a classical model based on regression analysis [12] is shown in Fig. 4.17. While the ANN predictions lie within 15% accuracy, regression analysis prediction lies within only 50% accuracy. Research investigations showed that ANN accuracy can be further enhanced by optimizing the network architecture [42] and by considering timedelaying effects in the model [43].

4.6 Discussion The step-by-step in time technique demonstrated here allows stresses at intermediate stages to be calculated. However, creep in masonry is a function of the age at loading and the environment [4], so more complex analyses will be needed to simulate reality. The step-by-step method can be used with the specific creep as the input [44] and aging functions can be expressed in integral form [1, 21]. Shrinkage and thermal effects can also be included. However, the number of factors that affect


105

masonry creep (age of loading, environment, unit type, mortar type, and stress level) suggests that creep for a particular structure will be very difficult to predict. Few data are available, particularly, long-term data. In these circumstances, methods using means of artificial intelligence (e.g. ANNs) which can deal with high levels of stochastic variation may prove useful in predicting both the creep and the range of possible outcomes from time-dependent effects. It becomes obvious that using means of artificial intelligence in modeling creep have two advantages over classical models, first: it allows incorporating a large number of interdependent factors that affect creep without adding further complexity. Second, it provides a systematic approach for model improvement as new data become available.

4.7 Conclusions The step-by-step in time analysis is a powerful tool to investigate the change of the stresses due to creep over a large time range. Stresses in a material can rise and fall due to the effects of creep (or fall then rise). Although the effective modulus method using the final creep coefficient can accurately estimate the final stresses in the components of a composite material (e.g. masonry) due to creep, the method may not predict intermediate peak stresses accurately: one needs to know when they will occur. Rehabilitation with FRPs may introduce additional creep mechanisms with undesirable effects. Particularly, FRP strips may unload a part of any additional dead load applied to a structure after ‘strengthening’. Adequate anchorage must be designed. The use of the step-by-step time-dependent analysis in creep stress redistribution can be made more accurate by incorporating ANNs where all factors affecting creep deformations can be included in the modeling process.

References [1] [2]

[3] [4]

[5]

Ghali, A. & Favre, R., Concrete Structures: Stresses and Deformations, 2nd edn, E&FN Spon: London, 1994. Binda, L., Gatti, G., Mangano, G., Poggi, C. & Sacchi Landriani, G., The collapse of the civic tower of Pavia: a survey of the materials and structure. Masonry International, 6(1), pp. 11–20, 1992. Shenoi, R.A., Allen, H.G. & Clark, S.D., Cyclic creep and creep-fatigue interaction in sandwich beams. Journal of Strain Analysis, 32(1), 1–18, 1997. Oh, Y.J., Nam, S.W. & Hong, J.H., A model for creep-fatigue interaction in terms of crack-tip stress relaxation. Metallurgical and Materials Transactions A, 31(7), pp. 1761–1775, 2000. Wang, E.Z. & Shrive, N.G., Brittle fracture in compression: mechanisms, models and criteria. Engineering Fracture Mechanics, 52(6), pp. 1107– 1126, 1995.

106 [6]

[7]

[8]

[9]

[10]

[11] [12]

[13]

[14]

[15]

[16] [17] [18]

[19]

[20]

[21]


De Borst, Feenstra, P.H., Pamin, J. & Sluys, L.J., Some current issues in computational mechanics of concrete. Computational Modelling of Concrete Structures, eds H. Mang et al., Pineridge Press: Sansea, UK, pp. 283–302, 1994. Wu, Z.S. & Bažant, Z.P., Finite element modelling of rate effect in concrete fracture with influence of creep. Creep and Shrinkage of Concrete, eds Z.P. Bažant et al., E. & FN Spon: London, pp. 427–432, 1993. van Zijl, G.P.A.G., de Brost, R. & Rots, J.G., The role of crack rate dependence in the long-term behaviour of cementitious materials. International Journal of Solids and Structures. 38, pp. 5063–5079, 2001. Binda, L., Saisi, A., Messina, S. & Tringali, S., Mechanical damage due to long term behaviour of multiple leaf pillars in Sicilian churches, Proc. Historical Constructions, eds Lourenco & Roca, Guimaraes, Portugal, pp. 707–718, 2001. Lenczner, D., Creep in model brickwork. Proceedings of Designing Engineering and Construction with Masonry Products, ed. F.B. Johnston, Houston, USA, pp. 1958–1969, 1969. Lenczner, D., Creep in brickwork piers. Structural Engineer, 52(3), pp. 97–101, 1974. Shrive, N.G., Sayed-Ahmed, E.Y. & Tilleman, D., Creep analysis of clay masonry assemblages. Canadian Journal of Civil Engineering, 24(3), pp. 367–379, 1997. Brooks, J.J. & Abdullah, C.S., Composite modelling of the geometry influence on creep and shrinkage of calcium silicate brickwork, Proc. of the British Masonry Society, No. 4, pp. 36–38, 1990. Ameny, P., Jessop, E.L. & Loov, R.E., Strength, elastic and creep properties of concrete masonry. Int. Journal of Masonry Construction, 1(1), pp. 33–39, 1980. Van Zijl, G.P.A.G., A Numerical Formulation for Masonry Creep, Shrinkage and Cracking, Series 11, Engineering Mechanisms 01, Delft Univ. Press: The Netherlands, 1999. CSA, Masonry Code. Masonry Design for buildings (limit states design) – structures (design). CSA-S304.1-94, Canada, Ontario, 1994. SAA, Masonry in Buildings. Revisions of Australian Standard-SAA-AS 3700/1988. Standards Association of Australia, Sydney, Australia, 1995. Scott, D.W., Lai, J.S. & Zureick, A.H., Creep behaviour of fibre reinforced polymer composites: a review of technical literature. Journal of Reinforced Plastics Composites, 1(6), p. 588, 1995. Van den Boogaard, A.H., De Borst, R. & Van den Bogert, P.A.J., An adaptive time-stepping algorithm for quasistatic processes. Communication in Numerical Methods in Engineering, 10, pp. 837–844, 1994. Harvey, R.J. & Hughes, T.G., On the representation of masonry creep by rheological analogy. Proceedings of the ASCE Structural Congress – Restructuring: America and Beyond. 1, pp. 385–396, 1995. Neville, A.M., Dilger, W.H. & Brooks, J.J., Creep of Plain and Structural Concrete, Construction Press: UK, 1983.


[22] [23]

[24]

[25]

[26] [27] [28]

[29] [30]

[31]

[32]

[33] [34]

[35]

[36]

[37]

107

Bažant, Z.P., Prediction of concrete creep effects using age-adjusted effective modulus method. ACI Journal, 69(4), pp. 212–217, 1972. Mirza, S., A framework for durability design infrastructure, Proc. First Canadian Conf. on Effective Design of Structures, Hamilton, Canada, pp. 67–103, 2005. Valluzzi, M.R., Binda, L. & Modena, C., Mechanical behaviour of historic masonry structures strengthened by bed joints structural repointing. Journal of Construction and Building Materials, 19, pp. 63–73, 2005. Bažant, Z.P., Asymptotic temporal and spatial scaling of coupled creep, aging diffusion and fracture process. Creep, Shrinkage and Durability Mechanics of Concrete and Other Quasi-Brittle Materials, eds Ulm et al., pp. 121–145, 2001. Lemaitre, J.A., Course on Damage Mechanics, 2nd edn, Springer Verlag: Berlin, 1996. Sukontasukkul, P., Nimityongskul, P. & Mindess, S., Effect of loading rate on damage of concrete. Cement and Concrete Research, 34, pp. 2127–2134, 2004. Garavaglia, E., Lubelli, B. & Binda, L., Two different stochastic approaches modelling the deterioration process of masonry wall over time. Materials and Structures, RILEM, 35, pp. 246–256, 2002. Løland, K.E., Continuous damage model for load-response estimation of concrete. Cement and Concrete Research, 10, pp. 395–402, 1980. Reda Taha, M.M. & Shrive, N.G., A model of damage and creep interaction in a quasi-brittle composite materials under axial loading. Journal of Mechanics, 22(4), 2006. Saadatmanesh, H. & Tannous, F.E., Relaxation, creep and fatigue behaviour of carbon fibre reinforced plastic tendons. ACI Materials Journal, 96(2), pp. 143–153, 1999. Gauthier, C., Bonnet, A., Gaertner, R. & Sautereau, H., Creep behaviour of polymer blend based in epoxy matrix and intractable high Tg thermoplastic. Polymer International, 53(5), pp. 541–549, 2004. Shackelford, J.F., Introduction to Materials Science for Engineers, 6th edn, Pearson, Prentice Hall: Upper Saddle River, NJ, 2005. CEB-FIP Model Code 90, Model Code for Concrete Structures, Comité Euro-International du Béton (CEB)–Fédération Internationale de la Précontrainte (FIP), Thomas Telford Ltd.: London, UK, 1993. Masia, M.J., Shrive, N.G. & Shrive, P.L., Creep performance of reinforced concrete beams strengthened with externally bonded FRP strips. Proceedings of Int. Conference on Performance of Construction Materials, eds El-Dieb et al., Cairo, Egypt, Vol. 2, pp. 1295–1304, 2003. Masia, M., Reda Taha, M.M. & Shrive, N.G., Investigations of serviceability of reinforced concrete beams strengthened with FRP. Journal of Composites in Construction, 2006 (in preparation). Meshgin, P., Creep of epoxy at the concrete–fiber reinforced polymer (FRP) interface. MSc Thesis, Department of Civil Engineering, University of New Mexico, 2006.

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[38]

Haykin, S., Neural Networks: A Comprehensive Foundation, Prentice Hall: New York, 1999. Luger, G., Artificial Intelligence: Structures and Strategies for Complex Problem Solving, 5th edn, USA: Addison Wesley, 2004. Tsoukalas, L.H. & Uhrig, R.E.. Fuzzy and Neural Approaches in Engineering, Wiley: New York, USA, 1997. Reda Taha, M.M., Noureldin, A., El-Sheimy, N. & Shrive, N.G., Artificial neural networks to predict creep with an example application to structural masonry. Canadian Journal of Civil Engineering, 30(3), pp. 523–532, 2003. Reda Taha, M.M., Noureldin, A., El-Sheimy, N. & Shrive, N.G., Feedforward neural networks for modelling time-dependent creep deformations in masonry structures. Proc. of the Institution of Civil Engineers, Structures in Buildings, UK, 157(SB4), pp. 279–292, 2004. El-Shafie, A., Noureldin, A. & Reda Taha, M.M., On investigating recurrent neural networks for predicting masonry creep, Proceedings of Third International Conference on Construction Materials: (CONMAT 05), Vancouver, Canada, eds Banthia et al., August 2005 [CD-ROM]. Shrive, N.G. & England, G.L., Elastic, creep and shrinkage behaviour of masonry. International Journal of Masonry Construction, 1(3), pp. 103–109, 1981.

[39] [40] [41]

[42]

[43]

[44]

CHAPTER 5 Experimental study on the damaged pillars of the Noto Cathedral A. Saisi, L. Binda, L. Cantini & C. Tedeschi Department of Structural Engineering, Politecnico di Milano, Milan, Italy.

5.1 Introduction The partial collapse of the Noto Cathedral required the choice to repair and reuse it. This seems in contrast with the need for preserving the authenticity of the monument. Nevertheless a number of difficult problems, from social to safety concerns, suggested the reconstruction of the lost parts. This chapter describes the on-site and laboratory investigation carried out on the remaining parts of the Noto Cathedral, in order to verify their state of conservation in view of reconstruction.

5.2 The collapse and the decision for reconstruction On December 1990 an earthquake hit the eastern part of Sicily damaging old and contemporary buildings in different towns. Noto, known as the ‘Baroque city’ was among them and several of its most beautiful buildings were seriously damaged. Also the Church of St. Nicolò, the Cathedral had damages to the vault, the lateral domes and to the pillars, apparently no more than other buildings. Provisional structures and scaffoldings were set up to sustain the damaged parts waiting for the repair and strengthening intervention. The partial sudden collapse occurred on March 13, 1996, fortunately without any casualty, and left the Noto community astonished by the loss of one of its most famous buildings. The church had been built in different phases suffering several casualties from 1764, over a previous smaller church opened in 1703 to the public and demolished in 1769–70 as the new cathedral was growing. The Cathedral was opened in 1776. In 1780 the dome collapsed and the church was reopened in 1818. In 1848 the

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dome collapsed again under an earthquake and then it was rebuilt and the church reopened again in 1862 but the dome was not completely finished until 1872. In 1950, the cathedral was restored with new renderings and paintings and the timber roof substituted with a concrete structure; the work continued until 1959. The losses caused by the collapse were the following: 4 pillars of the right part of the central nave and one of the 4 pillars sustaining the main dome and the transept, the complete roof and vault of the central nave, three quarter of the drum and dome with the lantern, the roof and vault of the right part of the transept and part of the small domes of the right nave (Fig. 5.1) (see Chapter 1). The extensive experimental and numerical investigation carried out after the removal of the ruins by a team of experts together with the designers R. De Benedictis and S. Tringali [1, 2] clearly showed that the collapse started from one of the pillars, due to the damaged condition they were in before the earthquake (see Chapter 1). Taking into account the clear weakness of the collapsed pillars, the designers asked for a further careful investigation on the remaining pillars of the central nave which also were damaged by the collapse. The first idea was to repair and preserve these pillars during the reconstruction of the cathedral. This chapter describes the on-site and laboratory investigations carried out and how the designers had to take the decision of demolishing them. Other cases of similar damages that occurred in Sicily will also be described showing the importance of investigation in order to prevent future failures.

5.3 On-site investigation on the remaining parts of the collapsed pillars After the study of the collapse mechanism, carried out on site during the removal of the ruins [3], the attention of the consultants was focused on a careful study of the peculiar features of the collapsed pillars.

M1B

P1A

P1B

P1C

P1D

P1E

PA

PB

PC

PD

PE

MB

Figure 5.1: Plan of the remains and of the tested elements.

STUDY ON THE DAMAGED PILLARS OF THE NOTO CATHEDRAL 111 5.3.1 Layout of the section and of the masonry morphology The removal by layers of the components of the collapsed pillars allowed one to understand the poor technique of construction used. Layers of large round river stones with thick mortar joints, where the mortar appeared very weak and dusty, were found in the core of the structure, surrounded by an external leaf made with regular blocks of more compact limestone at the base of the pillars (Fig. 5.2). Since only the base had remained after the collapse and the symmetric pillars were still covered by plaster, the hypothesis was made at first that limestone had been used for the external part of the whole pillars. This material, compact but not very strong, came from sedimentary carbonatic depositions, which can be found in the area and are still used as quarries for the building industry [4]. Inside the rubble filling also pieces of a material full of voids were found, which was called travertine; this material is of the same nature as the limestone, but deposited in the presence of turbulent waters and it is rich in voids of various shape and dimensions, which previously contained vegetarian and organic parts that later on dissolved. The height of the blocks varies from 25 to 30 cm and the thickness, small compared to the pillar dimensions, is ranging from 25 (stretcher) to 40 cm (header). No really effective connection was realised between the external leaf and the core. The stones of the pillar strips supporting the arches, vault, and domes have no connection either to the internal masonry or to the other parts of the external leaf (Figs 5.3 and 5.4). The inner part of the pillars represents 55% of the entire section, while in the pillars sustaining the dome it is 58%. This part is a rubble masonry made with irregular stones. It could be seen from the ruins, that it was made with large round river pebbles approximately up to half of the total height. The courses of these stones are rather irregular without any transversal connection or small stones to fill the voids and with thick mortar joints. Nevertheless every two courses of the external leaf (about 50 cm) a course made with small stones and mortar was inserted in order to obtain a certain horizontality (Figs 5.2 and 5.4). Scaffolding holes were left everywhere, some crossing the whole section. 5.3.2 General characterisation of the materials The mortar appeared to be very weak made with lime and a high fraction of very small calcareous aggregates. Also the bond between the mortar and the stones was very weak; in fact it was possible to remove stones and pebbles from the interior of the pillars without any difficulty and with the stones being completely clean. This poor technique of construction and the use of the weak limestone (actually called ‘Noto stone’) typical in the Noto region, was probably the cause of the damages to the pillars of the cathedral, even if a clear crack pattern was reported to have appeared only after the 1990 earthquake. The walls were built similarly; nevertheless, the internal part was made with smaller sharp stones alternated with a slightly stronger mortar, in some ways a better masonry. Some stones were sampled from pillars and walls and mortar samples were taken from horizontal, vertical joints and

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Figure 5.2: A collapsed pillar.

Figure 5.3: Horizontal pillar section. from the interior of the masonry (Fig. 5.2). The samples were sent to the DIS Laboratory in Milan and tested in order to find the material characteristics [1, 5]. The investigation (Fig. 5.5) has shown that the foundations of pillars and walls were sufficiently well constructed; rubble walls but with enough load carrying capacity for the weight of the structures above. The soil was a sort of natural compact silt and thick layer of clay from where also the aggregates of the mortars were taken.

STUDY ON THE DAMAGED PILLARS OF THE NOTO CATHEDRAL 113

Figure 5.4: Reconstruction of a pillar section.

Figure 5.5: Detail of the foundation.

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Up to this point of the investigation, even if the weakness of the material used seemed to be the cause of the high damage suffered from the earthquake it was not still clear why the pillars reached the point of collapse. 5.3.3 Damage description The pillars on the left, still covered with a thick plaster, seemed to have suffered minor damages; only small and diffused vertical cracks were present on the plaster. Nevertheless the doubt that the damage could be deeper inside and perhaps even present before the 1990 earthquake, led one to carry out on these pillars a more accurate survey. As the plaster applied at the end of the repair works in the fifties was partially removed, a series of vertical large cracks was found, some of which were filled with the gypsum mortar used for the plaster (Fig. 5.6). This finding gave the authors the first evidence that the damage was already present in the fifties. The pre-existing crack pattern was clearly damage from compressive stresses, a long-range damage dating probably from a long time before the fifties. The lesson after the collapse of the Civic Tower in Pavia and the subsequent research taught the authors that the damage would probably have progressed even without the earthquake, which only accelerated the collapse. After the recognition of the damages, the removal of the plaster from all the pillars was planned in order to survey the crack pattern. Figure 5.7 shows a reconstruction of the crack pattern of the pillar before removing the plaster from all the pillars. As it is evident, the cracks are diffused and interesting the whole prospect, with a concentration in the corners. 5.3.4 Laboratory testing On the materials sampled on site physical, chemical, petrographic- mineralogical and mechanical tests were carried out in Milan at the DIS Laboratory. The aim was to characterise the materials of a typical (CC’) transversal section (Fig. 5.8) of the cathedral [5].

Figure 5.6: Large crack in a pillar and example of a crack filled with mortar.


Figure 5.7: Prospect of pillar P1B and survey of the crack pattern.

Figure 5.8: Transversal Section CC’.

5.3.4.1 Mortars The chemical and mineralogical analyses were carried out following a procedure set up in [6] on the mortars sampled from all the pillars and walls at different heights. The mortars contain a high percentage of CaCO3 showing that they are based on hydrated lime with a slightly high content of soluble silica but with fine aggregate size distribution. Table 5.1 gives the results on the mortar of pillar P1A together with the crack repair composition. In the last column, the composition and the high percentage of SO3 shows the presence of gypsum. Figure 5.9 gives an example of grain size distribution of aggregates. The soil was also examined and it appears of being composed by more than 87% of calcium carbonate, by 8% of different silicates and for the remaining 5% by alkali, aluminium, iron, gypsum, etc. The grain size distribution of the soil shows that it is composed of clay (8%), silt (72%) and sand (20%), a very fine material. 5.3.4.2 Stones Some compressive tests were carried out on cylindrical samples of the two stones, limestone and travertine; their texture is shown in Fig. 5.10. The tests performed on the limestone show that its strength when saturated at constant mass (11.56 N/mm2) drops dramatically with respect to the strength measured when dried at constant mass (17.98 N/mm2). The compressive strength of the travertine is very low and can vary from 4 to 6 N/mm2 or more.

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Table 5.1: Chemical analysis and bulk density of pillar P1A mortars. Pillar P1A 13CNMP’3 (%) SiO2 Al Fe2O3 CaO MgO Na2O K2O SO3 Loss on ignition CO2 Ins. Res. Soluble Silica Cl Bulk density

Pillar P1A Filling of cracks (%)

4.27 0.70 1.05 50.22 0.41 0.47 0.98 0.64 41.13 40.50 4.20 0.66 0.025 1313.00 kg/m3

2.32 0.77 0.28 41.05 0.14 0.43 1.06 39.02 14.83 11.92 1.73 0.30 0.028 1489.00 kg/m3

100 90 80 70 (%)

60 50 40 30 20

CNMABS1A

10

CNMN51

0 0.01

0.10

1.00 (mm)

10.00

100.00

Figure 5.9: Grain size distribution.

It should be stressed that the overall strength of the pillars, or better of the external regular leaf, was lower due to the influence of the mortar joints. Tests carried out at the Politecnico showed that the strength of a masonry reproducing the external leaves drops by 40–45% when mortar joints are present [7]. Furthermore, it should also be taken into account the reduction due to dimensional ratio when dealing with the real structure.


Figure 5.10: Calcarenite (Stone of Noto) and travertine.

In order to know the response of the two stones to the elastic waves, the ultrasonic velocity was determined by transmission on stone blocks. The two materials show very different behaviour. In fact, in the case of the limestone (calcarenite) the values are almost constant, between 2912 and 3157 m/s with an average of 3068 m/s. The values of the travertine are more scattered, with a measured velocity between 1325 and 3548 m/s, and an average of 1823 m/s. The scattering of the data is due to the presence of large voids, randomly distributed in the material, and confirms the results of the mechanical tests. 5.3.4.3 Injectability tests Injectability tests proposed in [8] were carried out in laboratory on materials sampled from the internal part of the pillars and walls, and from the collapsed pillars of the cathedral [4]. Grout injection was controlled directly on-site as well [4, 9]. Finally it was decided that injection could not help in improving the behaviour of the damaged pillars since it could not penetrate or strengthen the very thick but weak mortar joints. 5.3.5 On-site tests 5.3.5.1 Flat-Jack tests A single flat-jack test was carried out on the pillar P1E in order to know the state of stress simply due to the dead load of the pillar itself and a value of 0.85 N/mm2 was found at a height of 3.00 m. Taking into account the missed weight of arches, vaults and dome in the collapse, it is easy to make the hypothesis that the pillars must have been under a non-negligible state of stress. Double flat-jack tests were also carried out on pillars P1E and P1A and on the external walls of the cathedral.

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Stress [N/mm2]

2.0

σ

1.5

CNJ1d Elastic modulus:1760[N/mm2]

1.0

CNJ2d Elastic modulus:190[N/mm2]

Local stress

0.5

0.0

εl -6.0

εv -4.0

-2.0 0.0 2.0 Strain [μm/mm]

4.0

6.0

Figure 5.11: Double flat-jack test carried out on the external and internal part of P1A.

A double flat-jack test was also carried out on the inner part of pillar P1A in order to check the behaviour of its weakest part. Figure 5.11 shows the difference between the external leaf (CNJ1D) and the core (CNJ2D), which had a much higher deformability and lower strength. 5.3.5.2 Application of sonic pulse velocity test to pillars As a confirmation of the state of damage, and also a calibration of the procedure, sonic pulse velocity tests were carried out on the remains of the collapsed pillars, as well [9]. It is well known that ultrasonic frequencies can not be used on rubble walls due to the high attenuation caused by joints, voids and homogeneities. Nevertheless, travertine and calcarenite being so different the ultrasonic velocities measured in laboratory on single blocks were very useful. Figure 5.12 localises as an example the test position on the pillar P1E and in the correspondent collapsed pillar called PE. Measurements were taken at different heights. It was impossible to position equal levels for all the pillars due to the presence of safety scaffolding. Nevertheless it was clear that the material of the external blocks was changing from the base (calcarenite) to the top of the pillars (travertine). The measurements were also carried out on some parts of the external walls as a comparison. Figure 5.13 shows the average values found for pillars on the leftand for the external pillar and wall called M1B. Low velocity values were systematically recorded for all the tested pillars of the cathedral from about 1.00–1.50 m onwards, i.e. above the limestone base. The values reported in Fig. 5.14 are average values of the measurements carried out in the two orthogonal directions. The pillar P1B shows the lowest values of the sonic velocities recorded at each level compared to the other P1i pillars. The pillar state


Figure 5.12: Geometry of the pillars P1E and PE and localisation of the sonic tests.

Sonic velocity [m/sec]

1800 1400 1200 1000 800 600 400

Figure 5.13: Vertical distribution of the sonic velocity measured on the pillars and the walls.

Figure 5.14: Sonic velocity distribution in the P1A section at 90 cm.

is in fact characterised by very serious damage, as evident from the crack pattern in Fig. 5.7. 5.3.6 Design decisions The accurate and detailed survey carried out by a multidisciplinary team was very helpful for the designers who had to take many difficult decisions. The crack pattern survey revealed large vertical cracks already present and filled with gypsum mortars in the sixties when the timber roof of the cathedral was replaced by a concrete roof. These damages indicate, together with the laboratory results that

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Figure 5.15: State of damage observed after the removal of the plaster.

the material used for the construction was very weak and damaged by long-term effects; the collapse perhaps would have taken place later if the earthquake had not occurred. Figure 5.15 shows, as a confirmation, the state of damage of one of the pillars as observed after the complete removal of the plaster. The pillars on the left could not be preserved due to the high state of damage caused by the weak technique of construction and the weak materials; therefore it was decided to demolish and rebuild them, together with the collapsed ones using better materials and technique of construction, i.e. hydraulic mortars obtained with hydrated lime and pozzolana, calcarenite stones avoiding travertine and good connections between the external leaf of the pillars and the core. The soil and foundation seem to be acceptable everywhere; the only exception can be made for the foundation of the central nave pillars, which can eventually follow a new conception. 5.3.7 The dismantling of the remaining pillars The substitution of the left pillars takes place in alternate order demolishing one pillar at a time and reconstructing it. Before this operation, the vaults of the left nave are supported by a stiff steel structure (Fig. 5.16).


Figure 5.16: Steel structure supporting the vaults.

Figure 5.17: Detail of fractures.

The dismantling of every single pillar is carried out in successive steps, demolishing stone by stone every single course. The use of the local travertine is confirmed, as well as the serious state of damage and the lack of connection between the external stone leaf and the core. The stones showed passing through cracks or deep cracks; when lifted by the workers, the blocks often broke, revealing the internal large voids. Furthermore the fractures in the external surface could be observed also in the internal rubble, even if less readable for the high inhomogeneity of the masonry. They in fact can follow the boundary between the mortar and the pebbles, but also go through every single stone (Fig. 5.17). Figure 5.18 shows as an example of the sequence of demolition of one course of pillar P1B. It can be seen that the vertical and horizontal joints are so weak that the dismantling can be carried out by hands.

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Figure 5.18: Example of a sequence of demolition of one course of pillar P1B.

Furthermore the inside of the stones, which are practically all broken or fissured, is full of voids and very weak. This explains why the pillar did not bear the state of stress for a long time. Creep phenomena have certainly developed during the life of the pillars, lowering their strength. Moreover, the internal filling of the pillars showed very low damage compared to the external leaves. This situation could be recently explained by some compressive tests carried out on three-leaf stimulating model of the section of the Noto pillars [7]. From these tests it is clear that the stress under compression is transferred even at low values to the external leaves when the internal one, free from stresses, is detached from the bearing one and does not suffer damages even at peak stress level.

References [1]

[2]

[3]

Binda, L., Baronio, G., Gavarini, C., De Benedictis, R. & Tringali, S., Investigation on materials and structures for the reconstruction of the partially collapsed Cathedral of Noto (Sicily). Proc. STREMAH 99, Dresden, Germany, pp. 323–332, 1999. Tringali, S., De Benedictis, R., La Rosa, R., Russo, C., Bramante, A., Gavarini, C., Valente, G., Ceradini, V., Tocci, C., Tobriner, S., Maugeri, M., Binda, L. & Baronio G., The reconstruction of the Cathedral of Noto. Proc. Int. Symp. on Earthquake Resistant Engineering Structures (ERES II), Catania, pp. 499–510, 1999. De Benedictis, R., Tringali, S., Gavarini, C., Binda, L. & Baronio G., Methodology applied to the removal of the ruins and to the survey of the remains after the collapse of the Noto Cathedral in Sicily. Proc. STREMAH 99, Dresden, Germany, pp. 529–538, 1999.

STUDY ON THE DAMAGED PILLARS OF THE NOTO CATHEDRAL 123 [4]

[5]

[6]

[7]

[8] [9]

Binda, L., Baronio, G., Tiraboschi, C. & Tedeschi, C., Experimental research for the choice of adequate materials for the reconstruction of the Cathedral of Noto. Construction Building Materials, Special Issue, 17(8), pp. 629–639, 2003. Baronio, G., Binda, L., Tedeschi, C. & Tiraboschi C., Characterization of the materials used in the construction of the Noto Cathedral. Construction Building Materials, Special Issue, 17, pp. 557–571, 2003. Baronio, G. & Binda, L., Experimental approach to a procedure for the investigation of historic mortars. Proc. 9th Int. Brick/Block Masonry Conf., Berlin, pp. 1397–1405, 1991. Binda, L., Anzani, A. & Fontana, A., Mechanical behaviour of multipleleaf stone masonry: experimental research. 10th International Conference Structural Faults and Repair, London, 1–3 July 2003, Engineering Technical Press, Edinburgh, Keynote Lecture, 2003. Binda, L., Modena, C. & Baronio, G., Strengthening of masonries by injection technique. Proc. 6th NaMC, Vol. I, Philadelphia, pp. 1–14, 1993. Binda, L., Saisi, A. & Tiraboschi, C., Application of sonic tests to the diagnosis of damage and repaired structures. NDT&E Int. Journal, 34(2), pp. 123–138, 2001.


CHAPTER 6 Monitoring of long-term damage in long-span masonry constructions P. Roca1, G. Martínez1, F. Casarin2, C. Modena2, P.P. Rossi3, I. Rodríguez4 & A. Garay4 1Universitat

Politècnica de Catalunya, Barcelona, Spain. degli Studi di Padova, Italy. 3R. teknos Srl, Bergamo, Italy. 4Labein, Bilbao, Spain. 2Università

6.1 Introduction Monitoring is a key activity in the study of ancient structures, providing reliable insight into its present condition and the significance and progress of damage. Monitoring can contribute to identifying and evaluating existing damage and help determine which active physical phenomena are involved in its generation. However, which monitoring procedures and strategies are to be considered depends highly on the type of processes experienced by the structure. Four different phenomena – large deformation, tensile damage, compressive damage and largescale fragmentation – are considered and discussed with regard to monitoring possibilities for measuring and characterizing them. Not only the structural effects (rotations, displacements, crack openings, etc.), but also the actions experienced by the construction (wind, earthquake, thermal cycles, soil settlements, etc.) are to be measured together over a sufficiently long period comprising several years. The use of a detailed numerical model may, in most cases, allow accurate physical and quantitative interpretation of the information obtained.

6.2 Monitoring and long-term damage Large deformation and damage are observed in almost all ancient masonry constructions. Structures – and particularly masonry structures – are not fully inert

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and static objects, but living entities which experience active processes throughout their entire life span. Such processes, related to construction effects, material decay, environmental actions and extraordinary actions (such as earthquakes) manifest in deformation and damage which develop in the long term. Monitoring can provide a certain degree of insight into the condition of the structure and the possible presence of active processes associated with incremental damage. However, the results of a monitoring programme are only fully comprehensible when analysed in the light of the historical nature of the construction or, in other words, when its results are interpreted as an evidence of processes which act and evolve over a deep-time or historical scale. Monitoring can be understood as the attempt to open a small window in the domain of time, over a response that develops over centuries or millennia. The challenge, thus, is to develop possible hypotheses or conclusions on the condition of the structure and the phenomena acting upon it, based on just a small, almost infinitesimal, patch or picture of the variation of the structural response in the time domain (Fig. 6.1). Deformation and damage develop as a superimposition of different phenomena, some of which act persistently, some cyclically or periodically, others occurring only on isolated occasions. The effects of these different actions result in the final response of the structure. Obtaining realistic conclusions through a monitoring programme requires the ability to unravel the registered information into its different components, so that they can be related to different actions or phenomena. In particular, the information obtained can include an assortment of reversible (cyclic) components mixed with the long-term accumulation of irreversible components. Obtaining meaningful hints related to long-term damage requires the ability to

amplitude

Damage

Safety

DT

DT

Long term

Figure 6.1: Monitoring as a window over historical time.

Long-Term Damage in Long-Span Masonry Constructions

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(a)

t (b)

t (c)

t (d)

t

Figure 6.2: Breakdown of a captured response into (a) cyclic, (b) circumscribed, (c) monotonic and (d) components. distinguish the unidirectional, accumulative trends from the totality of data registered during the monitored period (Fig. 6.2). Characterizing long-term damage is a challenging task due to the slowness of the processes involved and the fact that they may be masked by more apparent, short-term variations caused by present environmental actions. Both the viability of characterizing long-term damage by monitoring and the possible strategies that can be used to attain it are discussed in the following paragraphs.

6.3 Role of monitoring in the study of ancient constructions Monitoring provides quantitative information on the response of the structure across a short, recent period of time. Monitoring may specifically allow recognition of incremental processes over a term reasonable for engineering purposes, and thus provide information useful for the study and restoration of ancient constructions. Both structural analysis and monitoring deal with quantities and thus allow direct comparison. Monitoring results can be used in combination with a numerical model, provided that not only the parameters associated with the response (deformations, displacements, rotations, vibrations, etc.) are measured, but also those characterizing actions (environmental thermal effects, ground motion, etc.). The role of monitoring in the study of an ancient construction is better understood in the light of the application of scientific methodology based on a multidisciplinary approach. Experts involved in the study of historical structures of the architectural heritage base their research on a combined set of activities, including historical investigation, inspection and structural modelling. Monitoring constitutes

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Learning from Failure PRESENT CONDITION

HISTORY

MONITORING

EMPIRICAL EVIDENCE

STRUCTURAL MODELLING

HYPOTHESES

Figure 6.3: Activities involved in the study of an ancient construction and their role in the application of the scientific method. The structural model is the receptacle of the hypothesis to be validated by the empirical evidence provided by historical research, inspection and monitoring.

a fourth complementary activity intimately related to the rest (Fig. 6.3); used alongside the other activities, monitoring contributes to the successful application of the scientific method in the study of ancient constructions. Applying the scientific method first requires adopting a set of hypotheses and, second, the use of available empirical evidence to prove them. Some of the activities mentioned (specifically, structural modelling) are related to the first stage of the process, namely, the adoption of hypotheses. The structural model is the receptacle of the hypotheses on the physical and mechanical nature of the construction. History, inspection and monitoring are activities intended to provide the empirical evidence needed to validate these hypotheses or to correct or improve them to a satisfactory extent. More specifically, monitoring produces quantitative measurements which allow comparison to the numerical predictions of the structural model. System identification can be undertaken to adjust the material properties or morphological features of the model. An updated or calibrated model, with enhanced predictive capacity, is thus obtained.

6.4 Monitoring: methodology and requirements 6.4.1 Technology Nowadays a variety of sensors and associated equipment is available for measuring structural movements (including absolute or relative displacements, rotations, settlements or accelerations) and environmental parameters such as internal or external temperatures, humidity or wind force and direction. Electronic devices and sophisticated digitizers provide reliable automatic data collection systems and fast and remote recovery of large amounts of data.


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Removable mechanical extensometers or electrical crack gauges are commonly used to measure relative movements between crack surfaces. Not only is it the opening of cracks which is meaningful; attention must also be paid to the relative movements tangent to the crack faces; three different extensometers, placed perpendicularly, can be used to measure possible movements between crack faces. Absolute horizontal movements of vertical members can be registered by means of direct pendulums with measuring systems based on telecoordinometers. Relative horizontal movements can be measured more inexpensively and easily by means of long-base extensometers. Rotations of either vertical or horizontal elements can be measured by fixed or removable clinometers. Differential settlements can be measured by levemetric vessels where the level of the liquid is registered by an electrical transducer. Settlement gauges and piezometers are used to analyse the deformation of the soil foundation in relation to the water table variations. Air temperature and the temperature gradient across the wall thickness can be measured by thermal-gauges fitted inside small diameter boreholes drilled in the walls. A monitoring programme must be laid-out in accordance with a precise definition of its objectives and scope. The design of a monitoring system must bear in mind conditions related to the environment (protection, accessibility, etc.), the necessary accuracy (of instruments and also of the entire system), system reliability (possibility of self-diagnosis, redundancy, etc.), flexibility (easy substitution and recalibration of sensors) and the maintenance needs [1]. More information of the technological alternatives and their application to specific studies can be found in [1–4]. 6.4.2 Distinction between dynamic and static monitoring The monitoring system must be adequately designed to satisfy its intended purpose. Rather than universal, all-purpose systems, more specialized systems aimed at specific targets may be more efficient and also less expensive. In particular, a distinction can be made between static monitoring, aimed at the continuous measurement of gradual, slow-varying parameters over a long period, and dynamic monitoring, aimed at the intensive measurement of sudden variations caused by isolated and short-lived actions (such as micro-tremors or hurricanes), over a brief interval of time (Fig. 6.4). Static monitoring requires the regular measurement of small variations over lengthy periods comprising several years. In principle, there is no need to register measurements at a very high frequency. A few measurements per minute, or even per hour, may be enough to characterize the variations caused by daily climatic cycles or other periodical or gradual effects. Dynamic monitoring is intended to characterize the dynamic or seismic response of the building. It can be carried out by means of dynamic tests measuring the motion of the building caused by forced or natural vibration.

130


t

t

t

Figure 6.4: Continuous static monitoring, circumscribed (threshold) dynamic monitoring and continuous dynamic monitoring.

Another possibility is to install a fixed system capable of self-activating and capturing the motion of the structure at every occurrence of a micro-tremor or any other significant vibration source above a certain threshold. Dynamic monitoring requires the ability to capture a very dense amount of information during a very short interval. Thousands of readings per minute (for instance, 200 readings per second) may be needed to adequately characterize the oscillation of the structure caused by an external source of vibration, and to later carry out the signal processing leading to the determination of significant dynamic properties such as the shapes of the vibration modes, frequencies and damping. High sensitivity sensors are needed when measuring natural vibrations caused by traffic, wind or micro-tremors. Fixed dynamic monitoring may provide valuable information specifically related to the response of the structure during micro-tremors or even significant earthquakes. Long-term variations of damage are also better measured by means of a fixed system left active over a long period. Depending on the chosen threshold, a fixed dynamic system may require significant data storage capacity (or alternatively, frequent information transfer from data-loggers to other storage media). Meaningful information has been recorded using this type of systems for several ancient towers. In the case of the Torrazzo (civic tower) of Cremona, the monitoring system allowed the detection of wind-forced oscillations due to vortex shedding excitation [5]. The continuous capture of dynamic motion over long periods, covering several months or even years, is also possible thanks to more recent technological developments concerning dynamic data acquisition. Modern portable instruments, equipped with large storage capacity (tens or hundreds of Gb), allow the capture of continuous and dense information over long periods of time without having to


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set up an activating threshold. This last possibility, used in the dynamic monitoring of Mallorca Cathedral (Section 6.7.1), is particularly useful when the amplitude of the seismic motion expectable in the short term is very low and similar in magnitude to the effects of wind or traffic; in these cases, it may be difficult or even impossible to set a threshold that would allow the specific capture of seismic motion. Linking the equipment to GPS time, by means of a GPS antenna, allows the information collected to be synchronized with seismic events registered at seismic stations. This specifically enables information related to meaningful seismic episodes to be extracted from the entire volume of data registered over a long period. System identification on data recorded during low-intensity earthquakes has been successfully used to characterize the dynamic. response and the effect of soil structure interaction in the case of Hagia Sophia in Istanbul [6]. Non-linear behaviour was identified even at very low response levels; this non-linearity can be related to existing damage and might become more evident for large intensities. Dynamic monitoring provides the only way to experimentally measure parameters related to the global structural behaviour of the historical construction. However, its real contribution to a clear understanding of structural damage propagation is strongly limited due to several causes. The parameters related to the dynamic response of the structure behave always in the non-linear range (at least those of interest for damage detection) and are highly sensitive to the local or global material properties and the support conditions. Furthermore, the dynamic response of the structure may be highly influenced by the soil–structure interaction. No theoretical or numerical tools are yet available to simulate such effects in an accurate way, and thus to assist in the interpretation of the influence and variation of such parameters. However, dynamic monitoring can be very useful in carrying out model calibration or sensitivity analyses, especially when combined with complementary information on other experimentally measured ‘static’ parameters (local Young modulus, local stresses, via flat-jack measurements). 6.4.3 Requirements Besides the technical challenges posed by the need to acquire information reliably, technicians also face the need to interpret results adequately. In order to ensure the correct interpretation of measurements, a series of requirements should be considered: 1. Before or while undertaking a monitoring programme, detailed characterization of the building is needed. Historical investigation and geometrical and morphological surveys are needed to allow correct interpretation of the monitoring output. Monitoring will normally be accompanied (or preceded) by characterization based on non-destructive or quasi non-destructive tests aimed at determining the internal morphology of the structural members and the mechanical properties of the materials. Damage patterns (particularly major cracks) must also be recognized and carefully documented. The foundation (soil and structure) must be

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characterized carefully since it may significantly influence the motion and deformations to be monitored. Specific and actually monitorable targets should be selected, adequately related to the physical phenomena to be identified or analysed. In particular, long-term damage will require the monitoring of effects such as crack opening and deformation. Characterizing different phenomena (soil settlements, deformations caused by thermal cycles, mechanical deformations caused by loads, etc.) requires specific monitoring strategies. Actions affecting the construction are to be monitored in combination with its structural response. This normally requires monitoring of climatic environmental parameters (temperature and humidity), wind parameters (speed and direction), seismic ground motion and soil settlements, among others. The obvious aim is to correlate causes (actions) and effects (structural response). Furthermore, the varying effect on the structure of different actions can only be extracted accurately from the overall response if the actions themselves have been accurately measured and characterized. Even if climatic actions are not the target they will have to be characterized, since their impact on the structure is normally very prominent and may alter or even mask deformations caused by other possible effects, such as those specifically linked to long-term damage. In this case, characterizing climatic actions is necessary in order to determine and cancel out the climatic component in the monitoring output. In order to characterize incremental, long-term processes, monitoring must be designed to allow a clear distinction between the reversible or cyclic components of the parameters measured, on the one hand, and their irreversible, cumulative components on the other. An accurate numerical model must be available to interpret the results and correlate the causes identified (measurements related to actions) with their effects (deformations or displacements measured at different critical points of the building) in light of hypotheses on the configuration and condition of the structure. Characterizing the action in the time domain will later allow its numerical simulation and comparison between the numerical prediction and the actual response measured. An identification process can then be carried out by adequately modifying such hypotheses until a satisfactory coincidence is attained between the numerical predictions and the measurements. Monitoring must be carried out over a period long enough to cover the entire duration of the cyclic actions at work; since annual variations in temperature must be considered in all cases, the minimum acceptable period is a complete year. Additional years will be of value to confirm the tendencies observed and appraise their possible long-term evolution. In fact, a period of four years is a more reasonable minimum, since it allows confirmation of tendencies and detection of anomalous, local (in time) measurements produced by extraordinary actions or alterations in the monitoring system itself. In order to provide meaningful information with regard to the monitoring target, critical points of the structure must be selected. Prior numerical simulation may help determine the optimal configuration and location points. Normally, the


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most adequate points to install sensors will be those showing comparatively large or even maximum displacement. 8. The global nature of structural response must be taken into account while designing the monitoring strategy or when interpreting its results. Monitoring points should not be chosen individually or based on local considerations, but according to a strategy involving meaningful structural parts or even the entire structure. 9. Moreover, the monitoring system must be designed to allow redundant measurement of related effects, allowing results to be interpreted more consistently and soundly. For instance, displacements or rotations of a façade experiencing a gradual out-of-plumb can be measured in combination with related crack openings experienced at the junction of the façade with other walls.

6.5 Measuring damage and deformation related to historical or long-term processes 6.5.1 Monitoring and long-term damage Long-term processes may cause damage to manifest in different ways. Some of the most significant structural disorders observed are (1) overall large deformations, (2) cracks in elements subject to tension, (3) cracking or crushing in elements subjected to compression and (4) large cracks causing separation between different structural components or significant portions of the building (fragmentation). The following paragraphs consider these types of disorders and how monitoring might contribute to their characterization. 6.5.2 Structural deformation Large deformations affecting piers, buttresses and other structural components are commonly observed in ancient constructions (Fig. 6.5). In most buildings, deformation has been determined by many different actions occurring both during the construction process and the later historical life of the building. Numerical approaches may normally provide fair qualitative simulations of the deformed shape, but they fail at predicting, even roughly, the absolute values of deformations and displacements. In many cases, the real deformation is one or more orders of magnitude superior to those predicted by instantaneous or short-term numerical analysis; this is so even when non-linear material or geometrical effects, or even a conventional treatment of primary creep, are considered. Important effects related to deformation can be ascribed to construction. On the one hand, construction of historical structures spanned large periods of time which, in turn, included lengthy stages during which the structure was subject to provisional support conditions; during these intermediate phases, the structure was forced to develop resisting mechanisms not entirely consistent with its final arrangement and design. Significant deformation could be expected during these phases, due to the

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. Figure 6.5: Küçük Ayasofya Mosque in Istanbul. Example of large deformation of an ancient building. Condition of the real construction and predicted deformed shape (m) [7].

more deformable or mobile character of the incomplete substructures and provisional wooden, iron or masonry buttressing systems. Even after structure completion, creep will tend to partially amplify the deformation acquired at intermediate construction phases, causing both a significant increase of deformation and possible stress redistributions, eventually leading to cracking due to internal deformation incompatibility. Actions occurring after the construction process may have also contributed very significantly to the continuous increase of deformation. Extraordinary actions such as large earthquakes may produce important lesions and irreversible deformations. Low-intensity earthquakes or repeated occurrences of hurricane-force winds may act cumulatively to cause ever-increasing damage and deformation. The individual effect of daily or annual thermal cycles is minimal; however, a certain, irreversible increment of deformation may take place after each cycle, thus contributing to a significant increase in overall deformation over very long periods of time. It must be noted that the effects of cyclic actions do not dissipate with time, but may increase and accelerate as the construction becomes increasingly damaged. Damage affecting the construction, which in normal circumstances always increases due both to the aforementioned and other possible causes, will, in turn, enlarge the sensitivity of the construction towards a variety of actions. This situation contributes to constantly increasing (never-mitigating) stiffness reduction and long-term deformation, or even to an acceleration of long-term deformation, which, in the worst cases, can lead to the collapse of the construction. Since gravity is the most persistent action, it is not strange that such constant increases of flexibility


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and deformation may manifest as a monotonic, non-asymptotic amplification of the initial deformed shape due to dead load. Generally speaking, all historical actions may contribute towards amplifying the initial dead load deformation to a lesser or greater extent. Owing to this, the progress of structure deformation must generally be registered, regardless of the type of damage or physical phenomenon to be characterized. However, the progress of overall deformation of the structure alone can hardly provide enough information to determine the cause or phenomenon generating the progress of damage. Other possible parameters or effects (such as crack opening) must also be measured simultaneously for identification of the involved phenomenon to be more conclusive. 6.5.3 Tensile damage in arches and vaults Tensile damage in arches and vaults will manifest in cracking and deformation. As is well known, the tensile strength of masonry is almost negligible, meaning that a certain amount of cracking may easily develop in members subject to tension effects or eccentric loading. In fact, masonry may initially show significant tensile strength. The presence of a certain amount of tensile strength may help understand the stability for a limited period of time of some intermediate construction configurations. However, tensile strength is easily lost in the medium or the long term due to a variety of effects (settlements, vibrations, deformation cycles, etc.) causing micro-cracking or cracking in the mortar and the stone and the separation of both along their interface. Viable ancient buildings were designed in such a way that equilibrium did not require any tensile strength at their final construction configuration. This type of cracking, which is not normally too meaningful, is not necessarily linked to long-term damaging processes caused by the decay of the material itself. Severe tensile effects – such as severe cracks or large deformation – are likely to be caused by other indirect effects appearing at the buttressing elements or at the foundation. For instance, differential soil settlements, or the decay of the material in piers, buttresses or footings, may produce a loss in the capacity of such elements to properly counter-balance the thrust of arches or vaults, which in turn will experience cracks and openings between voussoirs associated with plastic hinges (Fig. 6.6). Monitoring these cracks, however, will be of use for characterizing the mobility of the structure and the overall progress of damage. Due to the perceptible deformation of the elements and measurable opening of the cracks, this type of effects can be easily monitored. 6.5.4 Damage of compressed members The authors have observed frequent vertical cracking in the piers of long-span buildings. Vertical cracks and related lesions in piers are particularly frequent in Gothic cathedrals and churches. In many cases, severe cracking, spalling or material bursting has appeared in spite of the moderate average compressive stress caused by gravity load (Fig. 6.7a).

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Figure 6.6: Opening between voussoirs in a transverse arch (Tarazona Cathedral).

As is well known, cracks parallel to the direction of applied compression may appear in materials such as concrete or stone, even for stresses significantly lower than the compressive strength. In tests performed at the Laboratory of Structural Technology of the Universitat Politècnica de Catalunya on specimens made of stacked sandstone blocks with 1 cm mortar joints [8], longitudinal cracks appeared for an applied stress ranging from 30 to 60% of the compression strength of the specimen. As expected, specimens made of larger units showed a greater tendency to crack under moderate compression. The lowest ratios between cracking stresses and compression strength (30%) were obtained for specimens made of large blocks (40 × 20 × 20 cm), while the largest ratios (60%) were obtained for specimens with the smallest units (20 × 10 × 10 cm, placed horizontally in both cases). In order to understand the actual existing damage, long-term phenomena leading to progressive deterioration during historical periods must be accounted for. As observed apropos of the study of recent collapses [9, 10], the long-term effect of creep under constant stress may induce significant, cumulative damage in rocklike materials. As mentioned by Binda et al., damage accumulation (eventually leading to collapse) may occur for stress values significantly lower than the normal strength obtained by standard monotonic compression tests. The same authors found that such phenomena could start at 40–50% of normal strength value. Actions other than dead load may also contribute to long-term damage and couple synergistically with the effect of creep. As previously mentioned, the construction process (and the construction techniques used) may induce mid-term or long-term effects. Aspects such as the construction sequence, the duration of the construction, or the use and removal of scaffoldings and other auxiliary elements, may influence the later behaviour of the overall building and even cause deferred lesions or other structural disorders.


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(a)

(b)

(c)

Figure 6.7: Deterioration of piers in Tarazona Cathedral, Spain. (a) Longitudinal cracks and bursting of compressed material at the springing of diagonal arches (b) Artificial thinning of piers. (c) Coupled mechanical and chemical deterioration. A specific aspect could be the use of small wooden wedges as a device to keep stone units in position while the mortar had not yet hardened, which in some cases (for instance, in Mallorca Cathedral, Spain) produced high stress concentrations leading to a deterioration of the external face of the stone (Fig. 6.8a) and causing cracks. Past human actions may be very significant in causing additional damage. In some cases, large operations undertaken during the life of the construction for purposes unrelated to the structure may cause significant alterations in the geometry of the piers or other structural members (such as the ‘thinning’ of piers in Tarazona Cathedral, Spain, to make space for a wooden choir, Fig. 6.7b); in other

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Learning from Failure (a)

(b)

(c)

(d)

Figure 6.8: Effects related to intense compression in the piers of Mallorca Cathedral. (a) Deterioration due to wooden construction wedges. (b) Crack caused after the insertion of a steel rod into a joint. (c) Cracks caused by loss of mortar in the joint. (d) Loose wedge along a corner.

cases, small, apparently inoffensive actions, may reveal to be potentially damaging after some time (such as the insertion of iron or wooden devices in compressed members for ornamental or liturgical purposes, Fig. 6.8b). On the other hand, lack of maintenance or inadequate historical repairs may also contribute to an accelerated deterioration of the building. Initially minor construction or material defects – such as the loss of a portion of mortar, in Fig. 6.8c – may cause cracks to initiate in zones subjected to significant compression. The repeated occurrence of extraordinary actions, such as earthquakes or hurricane-force winds, even if moderate in intensity, also contributes with irreversible,


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cumulative effects. Such actions may cause dramatic increases in the eccentricity of the applied vertical forces at the base of the piers; in turn, this will cause additional vertical cracking or other effects associated with increased maximum compression stresses. Stone or mortar decay due to chemical attack (as observed at the base of the piers of Tarazona Cathedral, Fig. 6.7c), may couple synergistically with mechanical effects related to sustained compression forces and thus cause accelerated deterioration. Cracks in piers or compressed members may be also caused when large blocks accommodate to deformation or irregularities in mortar joints. In this case, such cracks are not necessarily related to actual long-term and cumulative damaging processes. Normally, this type of crack will affect individual blocks and will not propagate causing long discontinuities along the height of the member. Monitoring will allow distinguishing between an already stabilized effect, caused by this type of accommodation, or a more severe, destabilized phenomenon compromising the safety of the construction. Conversely, a truly concerning effect is the development of separated wedges in compressed zones, which in turn produce a reduction of the available resisting section of the members (Fig. 6.8d). This effect usually starts in less-confined parts, in the corners of a rectangular or polygonal pier for example. Measuring variations due to long-term damage in compressed members is intrinsically difficult, due to the very small magnitude of associated movements or crack openings. In fact, such movements may be far smaller than those caused by climatic actions, and thus remain masked. Measuring this type of damage may require very long monitoring periods (much longer than the 4-year minimum previously mentioned) and highly sensitive equipment. A sufficiently long monitoring period may be the only possibility of telling them apart from the entire measurements. Furthermore, certain forms of damage (such as cracks and material losses) may develop suddenly, with almost no previous indication, making anticipated symptomatic detection through monitoring very difficult. 6.5.5 Fragmentation Another common type of damage, not necessarily related to long-term decay, consists of the division (or fragmentation) of the structure into large structural parts or substructures. Similarly, division owing to large cracks affecting the entire contact between structural members or parts of large members is not uncommon in historical constructions. The cause for this type of response can be found in different phenomena (soil settlements, thermal contraction or dilation, construction effects, etc.). In many cases, the safety of the structure is barely affected because the resulting structural parts are self-stable. Soil settlements are a very frequent cause for fragmentation. They can induce the generation of new cracks, enlargement of existing ones or opening of construction joints. The process may stabilize whenever the divided structure becomes cinematically compatible with the settlements.

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(a)

(b)

Figure 6.9: Fragmentation. (a) Separation between the membrane and the transverse arch of a cross-vault in Mallorca Cathedral. (b) Crack developed from a partial construction joint in Girona Cathedral.

Similar effects may be caused by cyclic winter contractions of the structure. In this case cracks or separation planes act as a contraction joint. In Mallorca Cathedral, wide discontinuities can be observed between some of the transverse arches and the vaults of the nave (Fig. 6.9a). Unlike soil settlements, which tend to mitigate with time as the soil consolidates, thermal cycles act continuously and may cause indefinite cumulative damage. Cracks or separation planes, acting as expansion or settlement joints, may easily develop starting at weak planes generated during construction itself. In some ancient buildings, construction joints were finished by interlocking stone units without filling the joints with mortar (Fig. 6.9b).

6.6 Structural modelling and monitoring Structural modelling is of extreme interest to enhancing the possibilities and understanding provided by monitoring. In fact, monitoring fulfils its overall potential when used in combination with a model of the structural response. Structural analysis is useful both when designing a monitoring system and when later interpreting the information collected. On the one hand, a prior structural analysis may contribute to better define significant aspects of the monitoring system. Simulation using a numerical model can help lay out adequate and truly informative monitoring, for instance by casting


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light on the most significant variables to be measured, the expectable ranges of variation (which are meaningful for selecting the type of sensors) or the best location for the sensors. On the other hand, and more importantly, a numerical model will help interpret monitoring results by comparing them with the predictions of a numerical analysis. This comparison may allow, among other aspects, a more quantitative (or absolute) understanding of the variations measured by sensors. For this purpose, it is essential, as mentioned in Section 6.4.3, not only to characterize the structural response but also the main actions that have affected the structure during the period monitored. Wind (force and direction), temperature, humidity and accelerations caused by micro-tremors may be included among the effects which have acted on the structure and generated meaningful measurements. The numerical model can be used to produce a prediction of the response of the structure when subjected to one or more of the actions measured. Comparison with the response actually measured will provide criteria for identifying some of the structural or material properties (in particular, stiffness of materials or structural members) and for improved calibration of the model. In the case of studies addressing long-term phenomena (such as long-term damage), the numerical model needs to have special capabilities in order to allow the simulation of historical processes. Ideally, the numerical model should be capable of simulating most of the present or historical actions that have affected the construction; it should also allow sequential analysis in order to simulate the construction process and the possible structural alterations or repairs that followed. Specific constitutive equations for long-term creep of masonry or stone-like materials, such as the one proposed by Papa and Taliercio [9], are of utmost importance for the purpose here referred. As shown in other chapters of the present book, significant efforts are presently being made for the experimental characterization and numerical modelling of long-term creep-induced damage.

6.7 Case studies 6.7.1 Dynamic monitoring of Mallorca Cathedral The main space of Mallorca Cathedral, built between 1350 and 1601, consists of a three-nave building, 77 m long and 35 m wide, comprising seven bays with central and lateral vaults spanning 19.9 m and 8.75 m respectively (Fig. 6.10). The height of the central vaults at crown reaches 44 m. The central vaults are sustained on octagonal piers with circumscribed diameters of 1.6 and 1.7 m. The remarkable slenderness of the piers, rising up 22.7 m to the springings of the lateral vaults, contributes towards generating the impression of an immense, diaphanous inner space. The construction has reached our days in a satisfactory state of conservation. However, some structural disorders can be observed, including (1) significant deformations affecting the piers; (2) vertical cracks at the base of some of the piers, sometimes forming surface wedges partially expelled from the core of the

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Figure 6.10: Interior of Mallorca Cathedral.

pier (Fig. 6.8d); (3) wide cracks developed throughout the contact lines between transverse arches and vaults (Fig. 6.9a) and (4) significant deformations affecting the flying arches. A detail of the structure, intended to determine the causes and significance of the mentioned lesions and to provide criteria for its future conservation, is now being carried out. The study, funded by the Spanish Ministry of Culture, includes historical research, detailed geometric surveillance, non-destructive testing and structural analysis. Mallorca Cathedral is also one of the case studies considered for the EU–India cooperation project for improving the Seismic Resistance of Cultural Buildings (contract ALA/95/23/2003/077-122) funded by the EC. As part of the activities envisaged within this last project, a monitoring system aimed at characterizing dynamic response has been also implemented. The system consists of a 24-bit resolution dynamic acquisitor connected to two triaxial accelerometers, one of which has been installed on top of a vault of the central nave. The acquisitor’s clock is disciplined to GPS time by means of a GPS antenna (Fig. 6.11). Among the different strategies mentioned in Section 6.4.2, continuous dynamic measurement has been preferred to allow the capture of lowintensity oscillations. The system, with a sensitivity of 10-6g, allows continuous acquisition at 100 sps and 600-plus days of storage. Meaningful seismic episodes are detected thanks to information provided by the nearest seismological station, ETO 8 in Mallorca. Information corresponding to any interval measured in GPS


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Figure 6.11: Triaxial accelerometer (left) and system with GPS antenna used for dynamic monitoring (right) placed over the transverse arches.

time can be then easily extracted from the entire data. The system was installed during April 2005. Preliminary results, which provide some hints as to the dynamic response of the structure, are already available. The effect of the Northern Chile earthquake of 13 June 2005, produced measurable effects on the building. Figure 6.12 shows the variation of accelerations in the time domain and the resulting spectral distribution for two different time intervals (windows) retrieved, for both the ETO 8 seismic station in Mallorca and the accelerometer placed above one of the cathedral vaults. Note that, due to the great distance from the epicentre, the building was mostly subjected to low-frequency oscillations. In spite of this, the building experienced a certain excitation and its fundamental vibration mode can be clearly distinguished in the peak corresponding to 1.68 Hz in the spectral diagrams. Both windows produced similar results. The acceleration referred is that produced in the longitudinal direction of the building, which showed the largest amplitude due to the fragmentation caused by the cracks between transverse arches and vaults (Fig. 6.9a). The mentioned frequency matches the measure previously obtained by means of a dynamic test carried out at the level of the vaults, in April 2005, during which traffic and wind vibrations were measured. In turn, another dynamic test, based on Nakamura’s (or H/V relationship) technique [11] and executed at the ground surface, yielded a soil natural frequency of 2.0 Hz. The corresponding peak can also be recognized in Fig. 6.12d (right). It must be noted that the building is founded over strata composed of quaternary sediments to a depth of about 80 m over the bed rock and that certain concern exists over the possible dynamic amplification effects that could be caused by such strata. The analysis of additional information generated in the occasion of future earthquakes may provide larger and more accurate information on the dynamic response of the building. This information will be used, among other purposes, to calibrate a detailed numerical model of the building.

Learning from Failure Northern Chile Earthquake 13/06/2005 ETOS station EW record (window 1)

6.00E-06 5.00E-06 4.00E-06 3.00E-06 2.00E-06 1.00E-06 0.00E+00 -1.00E-06 -2.00E-06 -3.00E-06 -4.00E-06 637

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Figure 6.12: Effect of a long-distance earthquake on Mallorca Cathedral: (a) accelerogram captured in nearby seismic station and (b) at the vaults of the structure; (c) corresponding spectral diagrams and (d) transference functions. Left and right: windows corresponding to two different time intervals.


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6.7.2 S. Maria Assunta Cathedral, Reggio Emilia, Italy The S. Maria Assunta Cathedral in Reggio Emilia, Italy, is one of the most important religious buildings of the city. Built on a previous roman construction around 857 AD, it underwent several style remodellings during the thirteenth, fifteenth, sixteenth and seventeenth centuries. The Cathedral presents a Latin cross plan with three naves and transept; the crypt is placed below the presbytery. The building ends in three semicircular apses, the central longer than the two lateral ones (Figs 6.13 and 6.14). A static monitoring system was positioned to evaluate a settlement phenomenon affecting one of the pillars sustaining the massive cupola at the crossing between the main nave and the transept. Such settlement, bringing visible deformations on the horizontal structures connected to the pillar (see Fig. 6.15), is a ‘historical’ phenomenon, in the sense that it was noticed since long time, but it seemed to worsen in the last period, so it was decided to control its possible evolution.

Figure 6.13: View of the Cathedral’s façade.

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Figure 6.14: Plan, longitudinal and transverse cross-section.

Figure 6.15: Slope in the access steps to the aisle apse due to the sinking of the pillar, indication of the affected pillar. The acquisition system is composed of 10 long base cable extensometers, 13 electric extensometers, 2 multi-base extensometers equipped with 3 measurement bases each, 2 measurement panels equipped with switch and thermometer (Fig. 6.16). The acquisition is semi-automatic, meaning that the system is able to store the data in the panels’ memory, and at determined time intervals it is necessary to recover the data on-site.


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Figure 6.16: View of a long-base extensometer, of an electric extensometer placed across a fissure and of the extensometers positioning plan, at the crypt’s level.

The system was implemented in a way to have redundant information, from the measurement obtained at specific reference points. In fact, the settlement of the pillar brings deformations also on the surrounding structural elements and determines visible crack patterns, evidently related to the observed phenomenon. Aiming at defining further settlements of the pillar, the different types of extensometers positioned are able to detect the relative displacements of the vertical structures, to measure variations in the openings on the main fissures, to evaluate the settlements of the foundations of the crypt’s pillars with respect to fixed points of the underlying soil, at the depths of 5, 10 and 15 m. The temperature, fundamental parameter for the comprehension of seasonal non-monotone behaviours, is also monitored. A year and a half have passed since the system has been active, hence at least the seasonal effects can be appreciated. Figure 6.17 shows the crack mouths relative displacements, plotted versus the observation date. From the visualized data,

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0.20 28.00

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10.00 DATE

Figure 6.17: Crack mouth opening, extensometers EL1 . . . EL13.

it is possible to notice that the seasonal effect is fully visible (contraction when the temperature is higher), and that the relative displacements are contained within narrow variations (the tenth part of a millimetre/half mm). There still are some sensors that indicate some trends that are not directly related to the temperature; longer observation periods are needed in order to define if such singular relative displacement tendencies are of importance for the studied phenomenon. 6.7.3 Vitoria Cathedral The Cathedral of Santa Maria, also known as the Old Cathedral or Vitoria’s Cathedral, is located on the highest part of the city of Vitoria. The construction of this interesting monument of Gothic Style began in the thirteenth century and finished in the fifteenth. The building, declared Historic-Artistic Monument, has the form of a pronounced Latin cross with three naves in the main hall space and a head wall with ambulatory and radial chapels (Fig. 6.18). Throughout its life, many interventions have taken place in the monument in order to solve different structural problems. The first intervention happened just a few years after the construction was finished. The last intervention stands among the major ones carried out through the ages and took place in 1967. Twenty-six years after that, the temple had to be closed to the general public owing to the appearance of worrying signs of ancient structural problems reactivating.


149

Figure 6.18: Interior of Vitoria Cathedral.

At that time, people in charge of the conservation of the Cathedral opted decisively for embarking on a long study towards the integral understanding of the building before starting new structural interventions. They conceived the Cathedral Refurbishment Programme as a living project open to the public. The restoration of Vitoria Cathedral has deserved the Europa Nostra 2002 Prize, the highest award given by the European Union for the conservation and enhancement of the city’s cultural heritage. The structural studies have demonstrated that the important historical deformations of the cathedral are due to insufficient capacity of the piers to adequately resist the thrust of the vaults. The original structure had no flying arches and all the buttressing capacity depended on the piers. The monitoring of the Cathedral is one of the most important activities in the process of the study and restoration of the structure. In the beginning it provided knowledge on the structural behaviour and its stability, and nowadays it allows detecting states of risk during the restoration works. Likewise, monitoring is used to gauge the repercussion of the consolidation actions on the whole structure.

150


The monitoring began in November 1992 and, at the moment, is intended to continue indefinitely. Since 1998, the Labein Technological Centre is responsible for it. In order to improve monitoring, the equipment installed was complemented in 1999 with new sensors. The monitoring equipment consists of temperature and relative humidity sensors (5), crackmeters (16), clinometers (6), extensometers (load cells and chains, 10) and convergence meters (9). Sensors are located in strategic points to detect the largest and more significant movements. Readings of all sensors are taken automatically every twelve hours and once in a week a computer collects all

(a) 40,00 35,00

TEMPERATURE ºC

30,00 25,00 20,00 15,00 10,00 5,00 0,00 -5,00 -10,00 16/03/00 08/05/00 01/07/00 23/08/00 15/10/00 07/12/00 30/01/01 24/03/01 16/05/01 08/07/01 31/08/01 23/10/01 15/12/01 06/02/02 01/04/02 24/05/02 16/07/02 07/09/02 31/10/02 23/12/02 14/02/03 08/04/03 01/06/03 24/07/03 15/09/03 07/11/03 31/12/03 22/02/04 15/04/04 07/06/04 31/07/04 22/09/04 14/11/04 06/01/05 01/03/05 23/04/05 15/06/05 07/08/05 30/09/05 22/11/05

-15,00

DATE T1

T2

T3

T4

(b) 1178,000 936,000

LOAD (Kg.)

694,000 452,000 210,000 -32,000 -274,000 -516,000 -758,000

16/03/00 08/05/00 01/07/00 23/08/00 15/10/00 07/12/00 30/01/01 24/03/01 16/05/01 08/07/01 31/08/01 23/10/01 15/12/01 06/02/02 01/04/02 24/05/02 16/07/02 07/09/02 31/10/02 23/12/02 14/02/03 08/04/03 01/06/03 24/07/03 15/09/03 07/11/03 31/12/03 22/02/04 15/04/04 07/06/04 31/07/04 22/09/04 14/11/04 07/01/05 01/03/05 23/04/05 15/06/05 08/08/05 30/09/05 22/11/05

-1000,000

DATE PE 1

PE 2

PE 3

PE 4

Figure 6.19: (a) Fluctuation of temperature and (b) movements registered in extensometers from 16 March 2000.


151

readings by telephone from the headquarters of Labein. During special periods experiencing important operations, such as movements of the strengthening structures in the main nave of the temple, readings of all the sensors and the interpretation are done daily. The control carried out to date has given very useful information about the evolution of the movements and damage manifested in the structure. The active movements have been perfectly identified, and it is well known that these movements are cyclical in time and related with the changes of temperature and humidity (Fig. 6.19). The main active movement detected is the opening of the central nave and the transept caused by the expansion of the materials of the vaults as a result of the rise in temperature. The evolution of movements obtained at the same time of two consecutive years shows that the structure seems to be now stable. However, certain changes measured during three years since 2002 indicate that the monitoring system is detecting the effect of the present use of the Cathedral and associated infrastructures, as well as the consolidation works that are being carried out.

6.8 Conclusions In the framework of a global study of an ancient structure, monitoring contributes with quantitative information related to the current response of the structure subjected to a combination of ordinary actions (dead load, thermal environmental actions, micro-tremors, wind, traffic, etc.). This information may provide significant evidence as to the type and progression of damage affecting the structure. However, characterizing long-term damage by means of monitoring is a challenging task that requires specific strategies involving lengthy observation periods. Most damage manifestations – including large deformation, cracking under tension or compression and crushing or bursting under compression – are caused by the combined effect of a variety of physical processes, comprising the longterm creep of the materials, cyclic environmental actions or repeated extraordinary actions. They are also influenced by historical facts related to construction, utilization and maintenance. The measurements obtained (crack openings, displacements, accelerations, etc.) will include all these effects bundled into a single response; interpreting the results requires the mixed responses to be broken down into cyclic and reversible processes and monotonic (or cumulative) ones. A further step consists of breaking measurements into the components associated with different effects acting on the structure (wind, temperature, earthquakes, traffic, etc.). The latter specifically requires monitoring of the actions themselves by means of appropriate equipment (thermometers, hygrometers, anemometers, seismometers, etc.). Accurate numerical simulations of structural response, by means of detailed structural models, are also needed, both for the results to be interpreted and for reliable conclusions to be reached regarding the condition of the building and the actions or processes contributing to its decay or damage.

152


Acknowledgements The assistance of the Chapter of Mallorca Cathedral, Studio Mauro Severi Architetto, Studio Associato di Ingegneria Gasparini, Reggio Emilia, Fundación Catedral de Sta. María de Vitoria and the EC project ALA/95/ 23/2003/077-122 in the development of the studies presented is gratefully acknowledged.

References [1]

[2]

[3]

[4]

[5]

[6]

[7]

[8] [9]

[10]

[11]

Rossi, P.P., The importance of monitoring for structural analysis of monumental buildings. Inspection and Monitoring of the Architectural Heritage, Ferrari Editrice: Bergamo, pp. 253–265, 1997. Rossi, P.P. & Rossi, C., Surveillance and monitoring of ancient structures. Recent developments. Structural Analysis of Historical Constructions II. International Center for Numerical Methods in Engineering: Barcelona, pp. 163–178, 1998. Rossi, C. & Rossi, P.P., A low cost procedure for quick monitoring of monuments and buildings. On site Control and Evaluation of Masonry Structures, eds. L. Binda & R.C. de Vekey, RILEM publications S.A.R.L: Bagneux, pp. 81–94, 2001. Modena, C., Advanced monitoring systems. On site Control and Evaluation of Masonry Structures, eds. L. Binda & R.C. de Vekey, RILEM publications S.A.R.L.: Bagneux, pp. 95–104, 2001. Binda, L., Falco, M., Poggi, C., Zasso, A., Mirabella Roberti, G., Corradi, R. & Tongini Folli, R., Static and dynamic studies of the Torazzo in Cremona (Italy), the highest masonry bell tower in Europe. Bridging Large Spans from Antiquity to Present, Sanayi-i-Nefise Vakfi: Istanbul, pp. 100–110, 2000. Çakmak, A.S., Natsis, M.N. & Mullen, C.L., Foundation effect on the dynamics of Hagia Sophia. Structural Studies of Historical Buildings IV, eds. C.A. Brebbia & B. Leftheris, Computational Mechanics Publications: Boston and Southampton, pp. 3–10, 1995. Massanas, M., Roca, P., Cervera, M. & Arun, G., Structural analysis of Küçük Ayasofya Mosque in Ístanbul. Structural Analysis of Historical Constructions IV, Balkema: Amsterdam, pp. 679–686, 2004. Hernández, P., Ensayo en laboratorio de prismas de obra de fábrica en piedra. Universitat Politècnica de Catalunya (UPC): Barcelona, 1998. Papa, P. & Taliercio A., Prediction of the evolution of damage in ancient masonry towers. Bridging Large Spans from Antiquity to Present, Sanayi-iNefise Vakfi: Istanbul, pp. 135–144, 2000. Binda, L., Saisi, A., Messina, S. & Tringali, S., Mechanical damage due to long term behaviour of multiple leaf pillars in Sicilian Churches. Historical Constructions, University of Minho: Guimaraes, pp. 707–718, 2001. Nakamura, Y., A method for dynamic characteristics estimation of subsurface using microtremor on the ground surface. Report of Railway Technical Research Institute (RTRI), 30(1), pp. 25–33, 1989.

CHAPTER 7 Modelling of the long-term behaviour of historical masonry towers A. Taliercio & E. Papa Department of Structural Engineering, Politecnico di Milano, Milan, Italy.

7.1 Introduction In March 1989 the Civic Tower in Pavia, a Middle-Ages masonry building nearly 58 m high, suddenly collapsed, killing four people and destroying part of the adjacent Cathedral, along with some of the buildings overlooking the surrounding square [1]. No special event, to which the collapse might be attributed, was monitored in the preceding months. Also, no evidence of significant soil settlements was found. The results of a number of accelerated creep tests performed on samples extracted from the debris, along with finite element (FE) analyses of the tower, indicated that a possible origin for the collapse was the cumulation of creep-induced damage in time (see also Section 1.2). Indeed, under sustained loading some of the specimens failed at stress levels (see Section 2.2) comparable to the maximum values yielded by the numerical analyses. This remark was the starting point for an extensive research programme aiming at (1) characterizing the creep behaviour of ancient masonry; (2) developing theoretical models suitable to the description of creep evolution and creep-induced damage; and, finally, (3) assessing the safety of ancient masonry buildings subjected to heavy persistent loads through nonlinear structural analyses. In this chapter, a theoretical model developed by the authors is first described (Section 7.2); the procedure employed to identify the model parameters from results of accelerated creep tests is also outlined in Section 7.2.3. Then, the numerical results of structural analyses of two masonry towers are presented (Section 7.3), with particular emphasis on the description of the damage evolution in time, up to the predicted creep time to failure for the building. Finally, the obtained results are critically reviewed, and future improvements for the theoretical model are pointed out (Section 7.4).

154


7.2 A continuum damage model for masonry creep In this section, a model that is capable of accounting for the material damage under increasing stresses, the damage-induced creep acceleration, and the damage-induced anisotropy is presented. The model is addressed to brittle materials, such as concrete or rubble masonry, which are assumed to be isotropic at their virgin (undamaged) state. More details on the model can be found in [2]. Throughout the section, compressive stresses and strains are assumed to be positive. 7.2.1 Unidimensional viscoelastic model with damage Starting point for the development of the proposed model is the so-called ‘Burger’s rheological model’, which consists of a Kelvin element in series with a Maxwell element (Fig. 7.1). Both elements are composed by a spring and a dashpot: in the first one, the two components are in parallel, whereas the Maxwell element has the two components in series. The spring constants are denoted by EK, EM and the relaxation times of the dashpots by tK, tM; the superscripts K and M stand for Kelvin and Maxwell, respectively. The spring of the Maxwell element accounts for the instantaneous (elastic) response of the material; the Kelvin element describes primary creep, whereas the Maxwell dashpot simulates the steady-state (secondary) creep. A ‘frictional’ (or Bingham) element is inserted between the spring and the dashpot of the Maxwell element to prevent the activation of secondary creep at low stress levels (say, lower than s0 in uniaxial conditions). The classical Burger’s model cannot describe the decay in stiffness experienced by a material element subjected to stresses increasing beyond the elasticity limit, nor allow for the tertiary stage that precedes creep failure. These effects can be reproduced by accommodating some damage variables in the model (see similar proposals for concrete by Bazant and Chern [3], or Cervera et al. [4]). Figure 7.1 shows

primary creep (Kelvin)

EK

secondary and tertiary creep (Maxwell-Bingham) s0

s E M (1−D)

tK

t M (1−D) elastic behaviour (with damage)

Figure 7.1: Modified Burger’s rheological model.

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY TOWERS 155 the rheological model, as modified by the authors. The damage variable, D, reduces the elastic modulus of the Maxwell spring, thus accounting for the decrease in stiffness induced by an increase in stress. D affects also the relaxation time of the Maxwell dashpot, making it possible to capture the tertiary creep phase and creep failure. The value of the damage variable ranges between 0 (virgin state) and 1 (complete failure); this variable is supposed to start increasing as a suitable threshold for the elastic strain is attained. Primary creep is supposed to be unaffected by damage. Assuming infinitesimal deformations, the total strain e(t) of the Burger model is the sum of the strains in the Maxwell and Kelvin elements. The stress–strain (rate) law for the Kelvin element reads K K K K s = E e + h e& .

(7.1a)

The strain rate in the Maxwell element due to any stress increment can be conveniently expressed as the sum of a delayed term: M e& =

s M

h (1 − D )

2

H (s − s0 )

(7.1b)

and an instantaneous term, which is the rate of the elastic strain: s

el

e =

M

E (1 − D )

.

(7.1c)

In eqns (7.1a–c), ha = taEa, a = M or K, and H is the Heaviside function. The form of the damage evolution law has now to be specified. It will be assumed that the variable driving the damage process is a ‘damage force’, Y, which, according to thermodynamical rationales, is given by Y =

1 2

M

el 2

E (e )

(see e.g. Lemaitre and Chaboche [5]). . . s . VThe. sdamage rate will be assumed to be the sum of two contributions: D = D + D . D dominates under increasing stress. It can be obtained by differentiating the following expression, which conforms to a proposal of La Borderie et al. [6] for concrete: S

D = 1−

1 1 + AH (Y − Y0 H ) / E

M BH

,

(7.2)

where Y0H is a threshold value for the damage force, AH and BH are material parameters, and 〈〉 are Macauley brackets. Different parameters define the damage evolution laws, depending on whether strains are compressive (H = C) or tensile (H = T).

156


. DV dominates under sustained stresses: the following expression, borrowed from rock mechanics (see Chan et al. [7]), is proposed for this term: a M a V D& = a1H (Y / E ) 2 H D (– log D) 3 H ,

(7.3)

where aiH (i = 1, 2, 3; H = C or T) are additional material parameters. . . . Eventually, it is possible to integrate the strain rate e = eK + eM to obtain the – with the boundary condition e(0) = damaged creep law at constant stress s, – M s/[E (1 − D(0))]. A detailed parametric study of the model is presented in [8]. For the sake of illustration, here only some creep curves computed according to the proposed model are shown in Fig. 7.2 for a given set of material parameters, at different – values. Provided that creep failure is reached, these curves exhibit the values s classical S-shape corresponding to the sequence of primary, secondary and tertiary creep. Also note that the time to failure decreases as the stress intensity increases, in agreement with experiments. Under any stress history, a numerical procedure has usually to be employed to integrate the strain response of any material element. If the element undergoes a stress increment Δsi = si − si–1 during any (small) time interval Δti = ti − ti–1, the relevant strain increment Δei can be approximately computed assuming the stress to vary linearly during the time step and no increase in damage to occur. This gives: Δei =

Ei

in

+ Δei .

(7.4)

7 MPa

10 8 transversal strain (*1000) axial strain

Δsi

6 MPa

6 4

4 MPa

2

3 MPa

0

3 MPa

-2 -4 -6 7 MPa

-8

6 MPa 4 MPa

-10 0

200000

400000

600000

time (sec)

Figure 7.2: Simulation of uniaxial creep tests at different stresses.

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY TOWERS 157 The first term on the RHS of eqn (7.4) is the (damaged, elastic) strain increment due to the stress increment, where 1 Ei

=

⎛ H (si − s0 ) Δti ⎞ 1 1+ M + K M E (1 − Di −1 ) ⎜⎝ 2 t (1 − Di −1 ) ⎟⎠ E 1

⎛ tK ⎜⎝ 1 − Δt i

⎛ ⎛ Δti ⎞ ⎞ ⎞ ⎜⎝1 − exp ⎜⎝ − t K ⎟⎠ ⎟⎠ ⎟⎠ . (7.5)

The second term is the (inelastic) strain increment due to the stress acting on the material element at the beginning of the step, and is given by in

Δei =

si −1 H (si − s0 ) Δti M

h (1 − Di −1 )

2

⎡

⎛ Δti ⎞ ⎤ K e , ⎝ t K ⎟⎠ ⎥⎦ i −1

+ ⎢1 − exp ⎜ −

⎣

(7.6)

k is given by the recursive formula where ei–1 K

ei −1 =

⎡ ⎛ Δt ⎞ ⎤ ⎛ Δt ⎞ K 1 − exp ⎜ − Ki −1 ⎟ ⎥ + exp ⎜ − Ki −1 ⎟ ei − 2 . ⎢ ⎝ t ⎠⎦ ⎝ t ⎠ Δti −1 E ⎣ Δsi −1t

K

K

(7.7)

This explicit forward Euler integration scheme proposed here is not unconditionally stable, so that sufficiently small time steps have to be taken. This condition also ensures the reliability of the assumption that no increase in damage occurs during Δti. 7.2.2 Three-dimensional viscoelastic model with damage When the proposed constitutive model is extended to 3D solids, it is assumed that the damage variable, D, is a second-order symmetric tensor; its eigenvalues will be denoted by Da (a = I, II, III). Each principal direction of this tensor (xa) is assumed to be aligned with the normal (na) to a plane microcrack that forms and grows at any point in the solid. Because of the choice made for the damage variable these directions are mutually perpendicular, so that the damage-induced local material anisotropy is, in the more general case, orthotropy. This is consistent with the assertion made by Kachanov [9], stating that ‘even for high crack densities with interacting cracks, the effective elastic properties remain orthotropic with good accuracy’. The damage process driving variable in 3D is supposed to be a non-dimensional ‘damage force’, y = ½ eeleel, which is basically an equivalent strain measure. This is a quite common assumption in damage models, where equivalent stresses [7] or equivalent strains [10] are often employed as damage indicators. The first damage direction, xI, is supposed to activate as the maximum eigenvalue of y exceeds a threshold value in tension (y0T) or compression (y0C), according to the sign of the relevant principal strain. From now onwards, the material element is no longer isotropic: this means that, in general, stress tensor and strain tensor are not collinear in the continuation of the load history. An additional damage direction, xII, can activate in the plane orthogonal to xI as the maximum direct component of the damage force tensor, i.e. yaa = na⋅(yna), attains either one of the threshold values in tension

158


or compression. The third possible damage direction, xIII, is then automatically identified, having to be orthogonal to both xI and xII. Note that at any point in the solid the activated damage directions are fixed throughout the subsequent load history, so that the proposed model can be classified as a ‘non-rotating, smeared crack model’. As for the damage evolution law, here it was chosen to employ eqns (7.2) and (7.3) for each one of the principal values of the damage tensor, which is supposed to be related to yaa (a = I, II, III). The time integration scheme presented in the preceding paragraph will be now generalized to the 3D case. In view of the implementation of this scheme into a FE code, from now onwards a matrix notation will be employed. The six independent stress and strain components in any Cartesian reference frame (x1, x2, x3) will be gathered into two arrays:

s = {s11, s22, s33, s12, s23, s31}T; e = {e11, e22, e33, 2e12, 2e23, 2e31}T, where the classical Voigt’s notation for strains was adopted. Let any stress increment Δsi be applied to a material element during any time interval Δti. By generalizing eqn (7.4), the relevant strain increment can be expressed as: Δ ei = Ci Δ si + Δ eiin,

(7.8)

where Ci is the compliance matrix at time ti−1. Similar to eqn (7.5), this matrix can be expressed as the sum of three matrices: Ci = Ciel + CiM + CiK.

(7.9)

Owing to the orthotropic nature of the damaged material, it is expedient to give the expressions of the first two matrices in the reference frame of the principal directions of damage (xI, xII, xIII):

⎡ 1 ⎢ y ⎢ I,I ⎢ ⎢ ⎢ ⎢ 1 ⎢ el Cˆ i = M ⎢ E ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣⎢

−n

−n

yI,II

yI,III

1

−n

yII,II

yII,III 1 yIII,III

symm.

⎤ ⎥ ⎥ 0 0 0 ⎥ ⎥ ⎥ 0 0 0 ⎥ ⎥ ⎥ 2(1 + n ) 0 0 ⎥ yI,II ⎥ ⎥ 2(1 + n ) 0 ⎥ yII,III ⎥ 2(1 + n ) ⎥ ⎥ yI,III ⎦⎥ t =t 0

0

0

,

i −1

(7.10)

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY TOWERS 159

⎡ 1 ⎢ y2 ⎢ I,I ⎢ ⎢ ⎢ ⎢ ⎢ Δ t M i Cˆ i = M ⎢ 2h ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣⎢

−n

−n

2 yI,II

2 yI,III

1

−n

2 yII,II

yII,III

2

1 2 yIII,III

symm.

⎤ ⎥ ⎥ 0 0 0 ⎥ ⎥ ⎥ 0 0 0 ⎥ ⎥ ⎥ 2(1 + n ) 0 0 ⎥ 2 yI,II ⎥ ⎥ 2(1 + n ) ⎥ 0 2 yII,III ⎥ 2(1 + n ) ⎥ ⎥ 2 yI,III ⎦⎥ t =t 0

0

0

,

i −1

(7.11) with yjk = [(1−Dj)(1−Dk)]1/2, j, k = I, II, III. These matrices can be rotated in any ^ Cartesian reference frame using the classical transformation rule Ci = T Ci TT, where the transformation matrix T depends on the direction cosines of the angles defining the orientation of (x1, x2, x3) to (xI, xII, xIII) (see e.g. [11]). Note that damage affects the off-diagonal terms in the compliance matrices in eqns (7.10) and (7.11) through geometric averages of the relevant components: this is in accordance with proposals found in the literature for ductile [12] and brittle materials [13, 14]. The Heaviside function that affects the term Δti /tM in eqn (7.5) was omitted for brevity; it will be implicitly assumed that secondary creep activates along any direction when a certain threshold (in terms of damage forces) is exceeded. The third matrix in eqn (7.9) is unaffected by damage and can be expressed, in any reference frame, as CiK = CKs (1−Δli), where CKs is the flexibility matrix for an isotropic material with Young’s modulus EK and Poisson’s ratio n and Δli =

⎛ ⎛ Δt ⎞ ⎞ 1 − exp ⎜ − Ki ⎟ ⎟ . ⎜ ⎝ t ⎠⎠ Δti ⎝ t

K

(7.12)

Finally, the inelastic strain increment Δeiin in eqn (7.8) can be obtained by generalizing eqn (7.6):

in

Δ ei

⎛ ⎛ Δt ⎞ ⎞ = ⎜ 1 − exp ⎜ − Ki ⎟ ⎟ e iK−1 +2 CiM s i −1 , ⎝ t ⎠⎠ ⎝

(7.13)

160


where K

Ks

⎛ Δti −1 ⎞ K e . ⎝ t K ⎟⎠ i − 2

e i −1 = −Δli −1C Δs i −1 + exp ⎜ −

(7.14)

7.2.3 Identification of the model parameters and comparisons with experimental results In this section the procedure to identify the model parameters is briefly outlined, referring to tests on masonry samples, subjected to uniaxial compressive stresses either monotonic or constant in time. On the whole, 17 constitutive parameters are required to characterize the mechanical response of masonry according to the proposed model. Two parameters (EM,n) are associated with the elastic behaviour of the virgin (undamaged) material, which is supposed to be isotropic; three more (EK, tK and tM) define the viscoelastic behaviour in the absence of damage. The damage effects that characterize the material behaviour under monotonic or sustained stress are separately taken into account by introducing six different parameters for each kind of damage contribution (namely, AH, BH, y0H for the static damage contribution, eqn (7.2); a1H, a2H, a3H for the viscous damage contribution, eqn (7.3)). The threshold stress s0 above which secondary creep activates is supposed to correspond to the damage threshold y0H. The model parameters have to be identified both in tension (H = T) and in compression (H = C). As direct tension tests are not easy to perform, the model parameters defining the tensile behaviour of the material can be approximately estimated according to the evolution of the transversal strains during simple compression tests. In the continuation, attention is mainly focused on the identification of the parameters defining the damage evolution in compression. The elastic modulus EM can be evaluated by best fitting the first sensibly linear part of the axial stress–strain plots relative to monotonic tests (usually between 30 and 60% of the peak stress; segment 0–1 in Fig. 7.3) and by averaging the computed experimental slopes. The elasticity limit furnishes the threshold values for the (normalized) damage forces (y0C). The model parameters that define the static damage evolution law in compression (AC, BC) can be derived by best fitting the nonlinear part of the stress–strain plot in uniaxial compression (1–2–3 in Fig. 7.3). In particular, AC mainly affects the strength value, whereas BC is related to the shape of the softening branch [6]. The parameters associated with the viscoelastic behaviour of the material (EK, K t ) are determined according to the primary creep phase in creep tests at relatively low stresses, so that the strain evolution in time is unaffected by damage. Starting from the time evolution of the axial strain at constant stress above the elasticity limit, s0, it is possible to estimate the relaxation time tM of the Maxwell dashpot of the rheological model in Fig. 7.1, which is related to the secondary (or steady-state) creep rate, dein/dt (phase 1–2 in Fig. 7.4). The parameters defining the viscous damage law, eqn (7.3), could be evaluated by computing the decrease in elastic stiffness during the reloading phases between

50 2

2

40 1

1

5 4

30

3

20 10 0

0

0 -15

-10 -5 0 5 10 transversal strain (*1000) axial strain

Figure 7.3: Stress–strain plot relative to a monotonic test on a concrete specimen.

strain (*1000)

3

stress (MPa)


3 2

3 1

2 1 0

0 0

50000 100000 150000 200000 250000 time (sec)

Figure 7.4: Axial strain versus time for a uniaxial creep test on a concrete specimen.

two subsequent steps at constant stress. The relevant increase in damage, divided by the time spent between the two reloading phases, gives an estimate of the average damage rate, which can be used to identify a1C, a2C and a3C. If unloading– reloading cycles are not performed, a1C, a2C, a3C can be derived by best fitting the tertiary phase of the creep curves (2–3 in Fig. 7.4) for tests performed at higher stress levels. In particular, the creep time to failure of the material at different stress levels defines the values of a1C and a3C; a2C controls the rate of the viscous damage (see also [8]). As true creep tests at constant stress are extremely time-demanding, it may be expedient to identify the model parameters according to the results of pseudo- (or accelerated) creep tests, of the type described in Chapter 2. Figures 7.5 and 7.6 show the results of two tests on rubble masonry samples, taken from the ruins of the Civic Tower of Pavia, together with their numerical simulation according to the proposed model; the viscous parameters were basically identified by best fitting the axial strain creep curve. The experimental plot of Fig. 7.5 was obtained testing a 200 mm × 200 mm × 350 mm prism, coming from the external layers of the masonry constituting the tower (Section 2.2.6), whereas the data in Fig. 7.6 refer to a test carried out on a 300 mm × 300 mm × 510 mm prism taken from the internal part of the walls (Section 2.2.4). Tests were performed in controlled thermo-hygrometric conditions (20°C and 50% RH) using a hydraulic machine capable of applying a maximum constant load of 1000 kN. Further details on the characteristics of the tested sample and the experimental procedure are reported in Section 2.2. In the test to which Fig. 7.5 refers, the compressive stress applied to the specimen was progressively increased at a rate of 2.5 × 10−3 MPa/s; at the end of each step of 0.25 MPa, the load was stopped and kept constant for about three hours. On the contrary, Fig. 7.6 refers to a test characterized by phases at constant stress of a


9 experimental test numerical simulation

6 3 0 -3 -6 -9 0

50000 100000 150000 200000 250000 time (sec)

Figure 7.5: Strain–time plots for a uniaxial test on a rubble masonry sample with load steps of a duration of 3 hours each; experimental data and numerical simulation.

transversal strain (*1000) axial strain (*1000)

transversal strain (*1000) axial strain (*1000)

162

4

experimental test numerical simulation

2

0

-2

-4 0

200

400 600 time (days)

800

1000

Figure 7.6: Strain–time plots for a uniaxial test on a rubble masonry sample with load steps of variable duration; experimental data and numerical simulation.

duration that ranges between 15 and 200 days. Accordingly, the global duration of the former test is equal to less than three days, whereas the duration of the latter one is of about three years. In Table 7.1 the values of the model parameters used in the numerical simulations are reported. It can be noted that the two tested materials are similar as far as the damage evolution laws (both static and viscous) are concerned. The two materials essentially differ in terms of creep behaviour: indeed, the relaxation times (tK and tM) employed in the simulation of the two tests differ of some orders of magnitude. Upon the whole, the agreement between test data and theoretical predictions shown in the two figures is satisfactory. The main difference lies in the prediction of the transversal strains when failure is approached, which are underestimated by the model. According to Herrmann and Kestin [15], this problem could be circumvented by introducing additional inelastic (permanent) strains related to the damage variables: this was successfully done, for example, by Papa and Taliercio [16], with reference to uniaxial creep tests in a previously developed model; a similar extension will be considered in future developments of the present research. The model was also used to simulate creep tests performed on masonry samples taken from the crypt of Monza Cathedral (see Section 2.3). All the (prismatic) specimens were subjected to uniaxial compression applied by subsequent steps of 0.25 MPa, at a rate of 1.25 × 10–3 MPa/s. The stress is then kept constant for one hour and half, before the following stress increment is applied. Table 7.2 reports the specimen sizes and the main results of three of the tests performed (see also Table 2.9). Readers are referred to Section 2.3 for a detailed description of the specimens and the experimental results.

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY TOWERS 163 Table 7.1: Tests on samples taken from Pavia Civic Tower: model parameters used in the numerical simulations shown in Figs 7.5 and 7.6. Model parameter EM (MPa) tM EK (MPa) tK n AC BC AT BT y0C y0T a1C a2C a3C a1T a2T a3T

Test of Fig. 7.5

Test of Fig. 7.6 3500

690000 (s) 30000 7500 (s) 0.2

1228 (days) 3400 5 (days) 0.25 14.3 × 106 1.2 47.4 × 106 1.05 5.7 × 10–7 5.7 × 10–9

2.2 (s–1)

2.2 (days–1) 0.45 1.45

7.7 (s–1)

7.7 (days–1) 0.35 1.13

Table 7.2: Samples taken from the crypt of Monza Cathedral: main experimental results. Test CDM I p4 CDM II p4 CDM II p11

Size (mm)

Failure stress (MPa)

Time to failure (s)

Failure strain (μm/mm)

200 × 200 × 314 200 × 200 × 314 200 × 200 × 316

4.25 2.75 5.30

55736 21974 109772

8.87 7.57 4.98

Some of the model parameters (EM, EK, n, y0C, y0T, tM) were identified according to the previously outlined procedure. The remaining parameters were initially given the same values as the samples extracted from the ruins of Pavia Civic Tower. In this way, the axial strain versus time plot identified by triangles in Fig. 7.7 was obtained. To increase the predicted time to failure, three numerical tests were made, either by decreasing AC (from 800 × (EM)1.2 to 380 × (EM)1.2), or by increasing a2C (from 0.45 to 0.55); in the latter case, it was found that better results are obtained if, at the same time, a2T is reduced (from 0.35 to 0.25). The results of these tests are shown in Fig. 7.7 (plots identified by circles and diamonds). Decreasing AC slackens the evolution of damage in accelerated creep tests between two subsequent load steps. Changing a2C and a2T makes the transversal viscous damage variable to

164


axial strain (*1000)

8

6

experimental tests

4

AC=380 a2C=0.55a2T=0.25 AC=800 a2C=0.55a2T=0.25 AC=380 a2C=0.45a2T=0.35

2

0 0

20000

40000 60000 time (sec)

80000 100000

Figure 7.7: Comparison between the results of accelerated creep tests on samples taken from the crypt of the Monza Cathedral and the predictions of the theoretical model. evolve more quickly than the axial one, so that the phenomenon of dilatancy when approaching failure can be captured (which is not the case with the original choice for the parameter values). For further analyses, it was decided to take AC = 380 × (EM)1.2 = 56.3 × 106, a2C = 0.55, a2T = 0.25: these values approximately give the same time to failure as the experimental test of intermediate duration. The final set of identified values is reported in the third column of Table 7.3 and compared with the homologous set of values for Pavia Tower (second column). In Fig. 7.8, the predicted axial, transversal and volumetric strains are plotted versus time for a material element subjected to a sustained compressive stress of 1.23 MPa (which is the average vertical stress computed at the base of the bell-tower of Monza Cathedral). Note that the volumetric strain turns from positive (compaction) to negative (dilatancy) when creep failure is approached: this is a feature peculiar to the failure of brittle materials, which can be captured thanks to the anisotropic nature of the damage model employed, allowing for a faster increase in transversal strain than in axial strain as the creep-induced damage process evolves. Finally, a problem that rose in the structural analyses presented in the following Section had to be tackled. Using the value for tM identified according to accelerated creep tests led to the prediction of unrealistically short times to failure of the analysed structures. Thus, in the applications presented hereafter, it was decided to set tM equal to a very high value (1000 years), so as to make the estimate for the time to failure of the structures unaffected by the choice made for the value of this parameter. In Fig. 7.9 the numerical results obtained with

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY TOWERS 165 Table 7.3: Comparison between the values of the model parameters for specimens taken from Pavia Tower and Monza Cathedral. Value

Model parameter

Pavia

EM

(MPa) tM (s) EK (MPa) tK (s) n AC BC AT BT y0C y0T a1C (s−1) a2C a3C a1T (s−1) a2T a3T

Monza

3500 690000 30000

2800 110000 20000 7500

0.2 14.3 × 106 1.2 47.4 × 106

0.15 56.3 × 106 1.5 37.5 × 106 1.05

5.7 × 10−7 5.7 × 10−9 2.2 0.45 1.45

3.6 × 10−9 3.6 × 10−11 8 0.55 1.13

7.7 0.35

0.25 1.13

4

vertical strain horizontal strain volumetric strain

3 2

strain (*1000)

1 0 -1 -2 -3 -4 0

500

1000 1500 time (years)

2000

2500

Figure 7.8: Vertical, horizontal and volumetric strain versus time for a material element subjected to a uniaxial compressive stress of 1.23 MPa.

166


axial strain (*1000)

experimental tests 6

numerical simulation (110000 sec) numerical simulation (1000 years)

4

2

transversal strain (*1000)

8

-2

-4 experimental tests numerical simulation (110000 sec) numerical simulation (1000 years)

-6

-8

0 0

20000 40000 60000 80000 100000 time (sec) (a)

0

20000 40000 60000 80000 100000 time (sec) (b)

Figure 7.9: Accelerated creep tests on samples taken from the crypt of Monza Cathedral: experimental results and theoretical predictions with different values for the relaxation time of Maxwell’s spring: (a) axial strain versus time; (b) transversal strain versus time.

two values for tM in the simulation of the tests performed on samples taken from Monza Cathedral are shown: note that, although the secondary creep rate is in general underestimated, the time to failure of the material is not very sensitive to the choice made for tM.

7.3 Structural analyses of two masonry towers The theoretical model described in Section 7.2 was implemented into a commercial FE code, suitable for nonlinear structural analyses and endowed with a user-oriented interface (ABAQUS®). This code was used to predict the time behaviour of two massive Middle-Ages masonry towers in Italy: the Civic Tower of Pavia (Section 1.2) collapsed in March 1989, and the bell-tower of the Cathedral of Monza (Section 1.4.2), which has recently been restored. 7.3.1 The Civic Tower of Pavia More details on the research programme carried out on this building can be found in Sections 1.2.2, 1.2.3, 2.2.2 and in [17]. The lower part of the tower (22 m high) was discretized using three-dimensional FEs of different shapes (see Fig. 7.10). The total number of d.o.f.s of the FE model is about 11000. The loads acting on the model are the dead weight of the discretized part (unit weight: g = 18 kN/m3) and the weight of the upper part of the tower, including the belfry, which was assumed to be evenly distributed at the top of the discretized part, with an intensity q = 675 kN/m2. These loads are supposed to grow ‘quickly’ (in about ten years), up to their final value; afterwards, they remain constant throughout the rest of the analysis. The model parameters employed in the analysis are listed in the second column of Table 7.3 (except for tM = 1000 years).

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY TOWERS 167 q = 675 kN/m2

g = 18 kN/m3

22 m

(a)

(b)

Figure 7.10: (a) Civic Tower of Pavia; (b) FE model of the lower part. Figure 7.11 shows the evolution in time of the vertical displacement of a corner at the top of the FE model. It is important to note that failure is reached in about 400 years: this value matches the experimental collapse time (1989 AD) reasonably well, if computed from the end of sixteenth century when the construction of the belfry ended. The time evolution of damage is represented in Fig. 7.12 in the form of contour plots of the trace of the damage tensor. Note that damage is negligible at the end of construction (Fig. 7.12a). At this time, it was found that the maximum vertical (compressive) stress is of the order of 1.8 MPa at the corner of the base of the tower located near the entrance: although this stress is compatible with the short-term strength of the masonry forming the tower, it was found to be able to bring the material to failure if acting for a long time (see Section 2.2). Damage evolves slowly for about 200 years (Fig. 7.12b and c); then, it starts growing quickly leading the tower to failure for loss of bearing capacity in the region near the most stressed base corner (Fig. 7.12d). The numerically identified ‘failure mechanism’ of the tower, that is, the deformed shape at incipient failure, is shown in Fig. 7.12e: the tower seems to collapse by crushing the corner near the entrance. It is interesting to note that this failure mechanism agrees both with the survey of the tower ruins (see Section 1.2) and verbal evidences of some witnesses. 7.3.2 The bell-tower of Monza Cathedral The second masonry structure analysed is the bell tower of Monza Cathedral (Fig. 7.13a). This tower is presently under restoration, as it showed evidence of diffused cracking (Fig. 7.13b): more details on the research programme carried

168

Learning from Failure -7

displacement (cm)

-6 -5 -4 -3 -2 -1 0

0

5

10

15

20 25 30 time (years *10)

35

40

45

50

Figure 7.11: FE analysis of Pavia tower: vertical displacement of a node at the top of the model versus time.

(c)

(a)

(b)

(d)

(e)

Figure 7.12: FE analysis of Pavia Tower: damage contour plots different times: (a) end of the construction; (b) 100 years; (c) 210 years; (d) numerical collapse (417 years); (e) failure mode.


2 3

1 (a)

(b)

(c)

Figure 7.13: Cathedral of Monza and bell-tower; (b) crack pattern before restoration; (c) FE mesh of the lower part of the bell-tower. out on this building can be found in Section 1.4.2 and in [18]. Only the lower part of the tower was discretized by FEs, for a height of 35 m (see Fig. 7.13c). The FE model employed to analyse the Monza tower consists of isoparametric eight-noded 3D FEs; the total number of d.o.f.s of the mesh is around 18000. In the analysis, the tower was supposed to be loaded only by its self-weight, with a unit weight of the material equal to 18 kN/m3. The upper part of the tower, which was not discretized by FEs, enters the analysis only as an evenly distributed load of 50.7 kN/m2 at the top of the FE model: this load was estimated according to the volume of the upper part and the belfry (which is about 1500 m3) and the area of the cross-section of the tower at 35 m (which is 53.54 m2). The values of the parameters employed in the analysis are listed in Table 7.3, third column, except for tM = 1000 years. In Fig. 7.14 the results of the FE analysis are presented in the form of contour plots of the maximum eigenvalue of the damage tensor at different times. t = 0 corresponds to the end of the construction phase of the tower: it can be seen that damage is nearly negligible, meaning that the tower would be deemed to be safe according to a short-term analysis. A maximum vertical stress of the order of 1.23 MPa was computed at the base of the tower, which is nearly twice the average vertical stress computed as the ratio of the tower weight to the base area. Figure 7.14c refers to the estimated damage distribution at the end of the current century (around 2100 AD): it is interesting to note that damage evolves in time mainly in the vicinity of the openings located in the western and eastern sides of the tower, thus matching the monitored experimental cracks (see Fig. 7.13b). The diffusion of damage is relatively slow up to 300 years, whereas it accelerates after this time (corresponding to the end of nineteenth century) leading the tower to

170


(a)

(c)

(b)

(d)

(e)

Figure 7.14: Contour plots of one of the principal components of the viscous damage tensor at (a) 150 years, (b) 300 years, (c) 500 years and (d) 650 years (estimated failure); (e) deformed FE mesh at failure.

LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY TOWERS 171 1.6

0.8

displacement (mm)

displacement (mm)

0.4 u1 u3

0 -0.4 -0.8 -1.2

u1 u3

1.2

0.8

0.4

0 0

200


800

0

200


800

Figure 7.15: Horizontal displacement components versus time for two nodes of the FE mesh located at a height of about 9 m. failure after about 650 years. Fig. 7.14e shows the deformed FE model at the predicted time to failure: note that the ‘barreling’ of the lower part is matched by the spalling of the corners of the tower observed in reality (Section 1.4.2). To emphasize the potentially catastrophic increase in damage with time, in Fig. 7.15 the horizontal displacement components of a couple of nodes located at the level of the most damaged zone are plotted versus time; the sign of the displacements is immaterial, as it depends on the choice made for the reference frame (see Fig. 7.13c). Note how in these plots the three stages typical of the creep behaviour of materials experiencing damage effects are visible, namely primary, secondary (or steady-state) and tertiary creep; the latter phase precedes structural failure. Note that the predicted time to failure of the tower is much shorter than the time to failure of a material element subjected to a uniaxial compressive stress of 1.23 MPa (see Fig. 7.8): this is attributable to the stress concentrations originated by the diffusion of damage throughout the tower.

7.4 Remarks and future perspectives The numerical model developed to analyse damage effects induced by heavy persistent loads in existing masonry buildings is potentially an effective tool to assess the safety of these structures. Both the predicted time to failure of Pavia Civic Tower and the predicted crack pattern in the bell-tower of Monza Cathedral were found to match experimental evidences fairly well. In particular, the predicted failure mechanisms for the analysed structures may give indications regarding the effectiveness of possible strengthening techniques. Pavia Civic Tower was found to collapse for a sort of rotation about one of the corners, which got apparently crushed whereas the rest of the building did not significantly participate in the failure mechanism (Fig. 7.12e). Thus, hooping the tower would not likely make it safer against collapse, as this technique would not hinder the predicted mode of failure.

172


On the contrary, hooping Monza bell-tower might actually contrast ‘barrelling’ at the base of the building, the deformation mode that precedes failure according to numerical analyses (see Fig. 7.14e): this restoration technique is currently being employed to strengthen the tower (see Section 8.3.3, or [19]). Regarding the evaluation of the model parameters, the relaxation time of the Maxwell’s dashpot, tM, was found to play a crucial role in the prediction of the residual life of the analysed structures. An open problem is how this parameter can be realistically estimated according to accelerated creep tests rather than true creep tests. This is strictly related to the detection of the actual exhaustion of the primary creep phase (related to tK) in tests of a given, finite duration. This problem should be addressed in the continuation of this research. On the side of the accuracy of the FE model, there is a point that should have to be tackled in future researches, regarding the mesh-sensitivity of the numerical solution. It is well known that, in the presence of a strain-softening constitutive law, strains localize in narrower bands as the FE mesh is refined. A ‘non-local’ version of the presented damage model will be formulated, according to proposals of other researchers (see e.g. Saetta et al. [20]), to overcome this limitation of the present model and make numerical predictions unaffected by the mesh size. Other problems that will be tackled in continuation of the present research to improve the numerical model are (1) the distinction between “cracks” activated in tension or compression and (2) the so-called unilateral effect. Indeed, in the present version the model makes no distinction between damage directions associated to tensile strains and to compressive strains, assuming that both are aligned with the direct strain which induces the damage process. A more realistic modelization of the damage process should account for the experimentally observed inclination of cracks with respect to the compressive strains by which they are induced. The unilateral effect consists in a recovery in stiffness when an opened crack heals, for instance, as a consequence of a stress reversal from tension to compression. This effect could be described by introducing two independent second-order damage tensors, say DC and DT, that separately allow for damage induced by compressive and tensile strains, rather than a single damage tensor that evolves differently, according to the sign of the principal strains.

References [1]

[2]

[3] [4]

Binda, L., Gatti, G., Mangano, G., Poggi, C. & Sacchi-Landriani, G., The collapse of the civic tower of Pavia: a survey of the materials and structure. Masonry International, 6(1), pp. 11–20, 1992. Papa, E. & Taliercio, A., A damage model for brittle materials under non-proportional monotonic and sustained stresses. Int. J. Numer. Analyt. Methods in Geomechanics, 29, pp. 287–310, 2005. Bažant, Z.P. & Chern, J.C., Strain softening with creep and exponential algorithm. J. Engng. Mech., ASCE, 111, pp. 391–415, 1985. Cervera, M., Oliver, S., Oller, S. & Galindo, M., ‘Pathological behaviour’ of large concrete dams analysed via isotropic damage models. Proc. 2nd Int.


[5] [6]

[7]

[8]

[9] [10] [11] [12] [13] [14] [15]

[16]

[17]

[18]

[19]

[20]

Conf. on Computer Aided Analysis and Design of Concrete Structures, Zell am See (A), pp. 633–644, 1990. Lemaitre, J. & Chaboche, J.L., Mechanics of Solid Materials. Cambridge Univ. Press: Cambridge (UK), 1990. La Borderie, C., Berthaud, Y. & Pijaudier-Cabot G., Crack closure effect in continuum damage mechanics: numerical implementation. Proc. 2nd Int. Conf. on Computer Aided Analysis and Design of Concrete Structures, Zell am See (A), pp. 975–986, 1990. Chan, K.S., Bodner, S.R., Fossum, A.F. & Munson D.E., A constitutive model for inelastic flow and damage evolution in solids under triaxial compression. Mechanics of Materials, 14, pp. 1–14, 1992. Papa, E., Taliercio, A. & Binda, L., Creep failure of ancient masonry: experimental investigation and numerical modelling. Structural Studies, Repairs and Maintenance of Historical Buildings VII, ed. C.A. Brebbia, WIT Press: Southampton (UK), pp. 285–294, 2001. Kachanov, L.M., Elastic solids with many cracks: a simple method of analysis. Int. J. Solids Structures, 23, pp. 23–43, 1987. Mazars, J., A description of micro- and macro-scale damage for concrete structures. Engng. Frac. Mech., 25, pp. 729–737, 1986. Lekhnitskii, S.G., Theory of Elasticity of an Anisotropic Body. Holden-Day: San Francisco (USA), 1963. Cordebois, J.P. & Sidoroff F., Anisotropic damage in elasticity and plasticity. J. Méc. Th. Appl. (Special issue), pp. 45–60 (in French), 1985. Ortiz, M., A constitutive theory for the inelastic behaviour of concrete. Mech. of Materials, 4, pp. 67–93, 1985. Suaris, W., Ouyang, Ch. & Fernando, V.M., Damage model for cyclic loading of concrete. J. Engng. Mech., ASCE, 116(5), pp. 1020–1035, 1990. Herrmann, G. & Kestin, J., On the thermodynamic foundations of a damage theory in elastic solids. Strain Localization and Size Effects due to Damage and Cracking, eds J. Mazars & Z.P. Bazant, Elsevier: London, pp. 228–232, 1998. Papa, E. & Taliercio, A., Anisotropic damage model for the multiaxial static and fatigue behaviour of plain concrete. Engng Frac. Mech., 55(2), pp. 163–179, 1996. Papa, E. & Taliercio, A., Creep modelling of masonry historic towers. Structural Studies, Repairs and Maintenance of Heritage Architecture VIII, ed. C.A. Brebbia, WIT Press: Southampton, pp. 131–140, 2003. Papa, E., Taliercio, A. & Binda, L., Safety assessment of ancient masonry towers. Proc. 2nd Int. Congress ‘Studies in Ancient Structures’, eds G. Arun & N. Seçkin, Istanbul, 1, pp. 345–354, 2001. Modena, C., Valluzzi, M.R., Tongini Folli, R. & Binda, L., Design choices and intervention techniques for repairing and strengthening of the Monza cathedral bell-tower. Construction and Building Materials, Special Issue, Elsevier Science Ltd., 16(7), pp. 385–395, 2002. Saetta, A., Scotta, R. & Vitaliani, R., Mechanical behaviour of concrete under physical-chemical attacks. J. Engng. Mech., ASCE, 124(10), pp. 1100–1109, 1998.


CHAPTER 8 Repair techniques and long-term damage of massive structures C. Modena & M.R. Valluzzi Dipartimento di Costruzioni e Trasporti, University of Padua, Italy.

8.1 Introduction Brick-masonry load bearing elements of heavy historic structures such as towers, heavily loaded pillars, and large masonry walls (i.e. curtains) frequently exhibit very typical mechanical deterioration phenomena like (a) formation of vertical or sub-vertical, thin but very diffused cracks and (b) more or less local detachment of the outer leaf in multiple leaf walls [1, 2]. Such a particular crack pattern is often not attributable to common causes of damage like seismic events, foundation settlements, instantaneous increase of external loads (e.g. for added storey or building changes) or to chemical, physical and mechanical degradation of the basic materials. On the contrary, it is due to the prevalent effect of the dead load and to the connected time dependent phenomena, often combined with cyclic loads, like wind actions, thermal and hygroscopic excursions, or bell ring oscillations (in bell-towers) [3, 4]. Because of the large weight of this sort of structures, wind and temperature loads do not cause substantial increase of stresses (shear and flexure) at the bottom. On the contrary, they can act in combination with the previously mentioned condition and contribute to worsening the crack situation in the heaviest portions of the structure with their cyclic trend. In fact, close to the ultimate strength of the material, alternate cycles of loading and unloading can lead to fatigue damage, which can increase the failure hazard of the structure. As it is well known, cracks appear very thin until the failure, which happens suddenly, without any apparent warning (such as large cracks or spalling), even in close proximity of the collapse. In the past, such problems were disregarded in comparison with other more evident critical conditions (large cracks, out-of-plumb, relevant deformations, etc.),

176


because the presence of the above-mentioned cracking pattern was considered as a steady state of the structure. The sudden collapse of some of them induced researchers to deepen the study in order to find specific solutions of repair and strengthening. Experimental investigations performed in collaboration between the University of Padova and the Polytechnic of Milan [5, 6] demonstrated that the creep damage can be effectively counteracted by the ‘bed joint reinforcement’ technique (known later also as ‘structural repointing’). It requires the insertion of minimal reinforcement of the superficial layer of the masonry, and a correct execution and selection of compatible materials. This chapter describes the most significant experimental researches that contributed to validate the above-mentioned technique for specific application on real case studies. Stainless steel bars were first adopted, then FRP (fibre reinforced polymer) bars and thin plates have been more recently considered; the use of different types of embedding materials (lime-based or additivated mortars, resins) is also discussed. Finally, some applications of the proposed technique on masonry structures are briefly illustrated [7, 8].

8.2 The bed reinforcement technique The reinforcement of the mortar bed joint in brick masonry structures has been recently considered for the strengthening and repair of massive brick masonry structures like towers, pillars and heavy loaded walls. The technique is performed by the insertion of small diameter reinforcing elements (stainless steel or FRP bars or plates) in the mortar bed joints previously excavated (up to about 6–8 cm) and then filled by a repointing material (compatible mortars should generally be used, also possibly with additives for particular requirements). The intervention can be executed at one or both sides of the wall, depending of the in situ conditions (accessibility, thickness, type of masonry, etc.). Transversal ties, inserted into drilled holes successively sealed, can improve the confining action of the bars, both in the longitudinal and in the transversal directions, especially in the case of multi-leaf masonry, where out-of-plane phenomena, as the detachment of the external leaf can occur (Fig. 8.1). Such a technique is particularly suitable to brick walls having regular courses of mortar. Moreover, the technique can be successfully applied when the control of cracking due to different settlements and thermal and moisture movements is required. It exploits the bond actions among bars and mortar to counteract the dilation caused by the compression loads. It is clearly a surface intervention but a combination of this technique with rebuilding (where bricks are particularly damaged) and/ or injections (especially for multi-leaf masonry walls with internal core having a high percentage of voids), can improve the strength of the damaged compressed wall and consequently reduce the cracking. The application of the technique involves many aspects as follows: (1) the preliminary preparation of the joints, (2) the choice of the reinforcement in terms of

Repair Techniques for Massive Structures

(a)

(b)

177

(c)

Figure 8.1: Examples of different techniques in different types of brick masonry walls: (a) single-leaf bearing wall; (b) multi-leaf wall with external bearing walls; (c) multi-leaf wall with external veneer leaf.

material (steel bars or plates, or FRP laminates) and in terms of spacing and amount to obtain the best performances, (3) the type of repointing material (mortar or resins) and (4) the aesthetic of the wall face. The intervention is characterized by the following operative phases: 1. Possible removal of plaster or finishing from the surface, to check the masonry condition. 2. Cutting of the bed mortar joints by using suitable (very common) tools; the recesses should be at least 10 mm high and 50–70 mm deep, so that the reinforcement can be inserted and the remaining mortar in the masonry can bear the applied loads. 3. Accurate inspection of the masonry: it should be appropriate to inject some large voids or replace some bricks. 4. Removal of powder or rubble through compressed air, or water, or particular solvents, depending on both the existent and the repointing materials. In particular, water can be used if a mortar is adopted for repointing, such that excessive absorption from the mortar to the bricks can be avoided, whereas the groove should be kept dry in case of the synthetic mortars (additivated with resins). 5. Placing of a first layer of repointing material, which should be accurately compacted; a proper embedding material should be used. Mortars are usually made of hydraulic lime for a better compatibility (chemical, physical and mechanical) with the existent ones, and can contain special additives (e.g. with expansive properties to compensate the shrinkage during the hydration phase). Synthetic resins (epoxy, acrylic or polyester) may be used for particular cases, for example, when the achievement of the strength is needed in a shorter time. 6. Placing of the reinforcing material: steel bars or plates (stainless, in general) or FRP laminates can be used. To increase the friction between reinforcement and

178


Figure 8.2: Detail of embedding phase in strengthened joint.

mortar rough surfaces should be preferred, as reinforced steel bars. To the same purpose, steel bars or plates can be previously sandblasted in order to clean their surface and to improve the adhesion with the repointing material. Moreover, the placing of spacers can be appropriate to separate the reinforcement from the surface of the bricks. Finally, the use of more bars with smaller diameter rather than a single bar with larger diameter should be preferred. Moreover, due to the small dimension of the bed joints (usually around 10–15 mm) only reduced sizes of reinforcement (4–6 mm in diameter for rods) can be inserted. 7. A second layer of embedding material has to be applied over the bars to cover them accurately; further bars or other reinforcement type can be put in if necessary. 8. A final layer of repointing material should be placed in the last 15–20 mm available, to seal the horizontal joints and for aesthetic and homogeneity purpose; special sands or pigments can be used to obtain particular effects. The proposed technique does not show particular difficulty of application; some care is required in some operative phases (cutting of the bed joint, cleaning, repointing, etc.) but it can be performed quite easily and quickly (Figs 8.2 and 8.3).

8.3 The experimental campaigns First experimental investigations [5–7, 9] with applications of low diameter (5 or 6 mm) stainless steel reinforced bars showed the efficiency of the intervention in reducing the transverse dilation of walls. Later on, investigations were focused on verifying the possible application of FRP materials. Monotonic, cyclic and creep simulating tests were performed first on panels strengthened with circular section carbon bars (CFRP) (5 mm in diameter) [10]


179

Figure 8.3: Arrangement of bar and tie into an excavated joint before final sealing of hole. and then, more recently, with thin rectangular section CFRP strips (1.5 × 5 mm) (Fig. 8.21) [9, 11, 12]. The advantages of the use of carbon fibres instead of steel reinforcement are mainly related to their complete corrosion immunity, but many aspects still need to be deeply investigated. Despite their high strength, FRP’s are very brittle; thus, even though the tensile stresses able to provoke rupture are not practically achievable in the moderate stress conditions detectable in the masonry structures, FRP’s inductility to bending and folding (e.g. for anchorage) does not allow low-cost solutions. Moreover, they are sensitive to high temperatures [13] and constitutive laws able to describe the interface behaviour among reinforcement–mortar–brick are so far not comprehensively known in masonry [8]. More advantages may be gained with the use of thin strips in comparison to circular bars, due to their higher adaptability to the unevenness of the joints and better behaviour against splitting failures [11], which may enable more superficial and less obtrusive interventions, but further research both at global and local level are required for the proper validation of this reinforcement system. Finally, the correct application of the techniques requires that compatible embedding mortars should be properly selected to avoid further undesirable problems to the original masonry. 8.3.1 Laboratory tests on the use of stainless steel bars Experimental work carried out on 1999–2001 by the Polytechnic of Milan and the University of Padua on brick panels having dimensions of about 25 × 50 × 110 cm primarily showed that the bars are able to contribute in bearing the tensile stresses acting into the bricks and, consequently, to reduce the dilation of the wall. A preliminary finite element model (FEM) study calibrated on the basis of the materials’ characterization contributed to quantify the stresses borne by the bars

180


and the bricks and to optimize the geometrical distribution of the bars into the panels (Fig. 8.4). This can provide information for the choice of the reinforcement in the design phase. By using two 6 mm diameter bars every three joints, the migration of the tensile stresses from the bricks to the reinforcing material was estimated to be approximately 40% of the total. The same analysis demonstrated that higher reduction of the tension (over 50%) can be obtained by using smaller bars (e.g. one bar of 5 mm in diameter, see Fig. 8.5) in every bed joint, but such condition can be inapplicable in practice (more damaging of the masonry during execution and consequent higher costs of intervention). On the contrary, higher diameter bars, always total amount of reinforcement being equal (e.g. 3 bars of 8 mm in diameter every 9 joints), can lead to a reduction of the tensile stresses only by 20%. Therefore, in the experimental campaign, two stainless steel bars of 6 mm diameter (2∅6) were used for every three bed joints of mortars. Different configurations (either both sides or just one side reinforced) and different types of repointing material (hydraulic mortar or resins) were considered. Mechanical characteristics (compressive strength and elastic modulus) of basic materials were as follows: fc = 5.4 MPa and E = 3890 MPa for the hydraulic mortar, fc = 50–90 MPa for resin type 1, and E = 6–9 GPa and fc = 55–65 MPa for resin type 2. Two series of laboratory tests were performed (see Table 8.1 and Fig. 8.6): (1) monotonic compressive tests on six masonry prisms repaired at one side, after

Figure 8.4: Reduction of principal tensile stress in bricks (the model concerns the upper-left portion of a panel) before (left) and after (right) insertion of steel bars every three joints (stresses are in MPa).


(a) 3∅8

(b) 2∅6

181

(c) 1∅5

Figure 8.5: Optimization of bed joint reinforcement in brick masonry panel (the same amount of steel is distributed): the support of a numerical analysis showed a reduction of tensile stresses in bricks of 20, 40 and 50%, for the cases (a) (3∅8), (b) (2∅6) and (c) (1∅5), respectively. The positioning of two bars every three joints optimizes structural performance with minimal obtrusiveness.

damaging caused by previous compressive tests and, (2) creep simulating tests on six prisms strengthened (i.e. without any previous damage) on both sides. Such latter actions can be performed by progressive increments of compressive loads, kept constant for a fixed time (e.g. three hours) up to collapse, which occurs for excessive deformations (tertiary creep phase). As regards the monotonic series of tests, the repaired panels reached only about 50% of the original strength and were characterized by a stiffness ranging between 43% for the consolidated sides and 29% for the non-consolidated side compared to the original stiffness (see Fig. 8.7). Due to the limited dimension of the samples in comparison with a whole existing wall, the damage caused by the cutting of the joints in the post-compression phase was probably in most cases excessive. Anyway, it is important to notice that the main results have been obtained in terms of reduction of the dilation and of the vertical cracking of the masonry. In particular, all the prisms showed a reduced cracks pattern in the repaired sides, whereas in the nonrepaired side the damage increased both in number and in the depth of fissures. As for the accelerated creep series of tests, the scheme of loading was able to show a crack pattern very similar to the typical observations in the real structures, with lower transversal deformation obtained for the strengthened walls, especially in the main sides (see Fig. 8.8). Figure 8.9 shows the vertical and the horizontal deformation versus stress diagrams of the creep tests. It can be noticed that in the proposed configuration

182

Series

Sample

Loading test

0-SS (unreinforced) 1-SS (one side reinforced)

M01 M03 MU6H1

Creep Creep Monotonic

MU6H2 MU6H3 MU6H4 MU6H5 MU6H6 M02

2-SS (two sides reinforced)

Reinforcing material

Reinforcing case

– – Repair

– – 2Ø6

– – A

– – Hydraulic lime mortar

Creep

Repair Repair Repair Repair Strengthening Strengthening

2Ø6 2Ø6 2Ø6 2Ø6 2Ø6 2Ø6

A B C B A E

Hydraulic lime mortar Resin type 1 Resin type 2 Resin type 1 Hydraulic lime mortar Hydrated lime and pozzolana mortar

M04 M05

Monotonic Monotonic

Strengthening Strengthening

2Ø6 2Ø6

D E

M06

Creep

Strengthening

26

D

Hydraulic lime mortar with resin Hydrated lime and pozzolana mortar Hydraulic lime mortar with resin

Intervention

Repointing material


Table 8.1: Experimental programme: stainless steel bars reinforcement (1999–2001).


original mortar

original mortar A

A Case D

Case E

A hydraulic lime mortar with resin

183

A hydraulic lime and pozzolana

Figure 8.6: Panels configuration investigated during experimental campaign.

(Fig. 8.10) the reinforcement does not have great influence on the strength and the vertical deformations, whereas it has a great role in the control of the horizontal deformations. In particular, the reinforcement was able to reach the tertiary creep conditions at deformations around 70% of the original case; moreover, in such ultimate phase, the prisms reinforced by technique D, showed an increment of more than 25% in strength. Reduction of lateral deformation was around 37–39% (Fig. 8.11), even though the increase in strengthening is between 5 and 28%. 8.3.2 Laboratory tests on the use of CFRP bars and thin strips As for CFRP rods, laboratory tests were performed both at local and global level, to characterize the mechanical properties of the basic materials and their mutual

184


7.00 6.00 5.00 stress [MPa]

MU6H1

ε volumetric εv - BCD sides (repaired) εl - BCD sides (repaired) εv - A side (plain) εl - A side (plain) before-repair curves εl, εv volLVDT

4.00 3.00 2.00 1.00 0.00 -40.0

-35.0

-30.0

-25.0

-20.0 -15.0 -10.0 strain [μm/mm]

-5.0

0.0

5.0

10.0

Figure 8.7: Typical stress–strain diagram before and after repair for first series of panels (Case A).

Side B

Side A

(a)

Side B

Side A

(b)

Figure 8.8: Crack pattern detected in second series of panels: (a) unreinforced prism MO1; (b) MO6 (Case D).


185

(a) 5.0 Case D (M06) 4.0 σ [MPa]

Plain panel (M01) 3.0 Case E (M02) 2.0 1.0 0.0 1.0

(b)

5.0

2.0

3.0

4.0 5.0 6.0 εv [×10-3]

7.0

8.0

9.0

Case D (M06) Case E (M02)

σ [MPa]

4.0 3.0

Unreinforced prism (M01)

2.0 1.0 0.0 0.5

1.0

1.5 2.0 2.5 3.0 εl sides AB [×10-3]

3.5

4.0

Figure 8.9: Creep test results: (a) vertical and (b) horizontal deformations of panels.

interaction, and of full-scale masonry panels. Pull-out and sliding tests on triplets were performed to characterize respectively the bar and the brick interfaces with the mortar and the embedding materials. Solid clay bricks having dimensions 50 × 120 × 250 mm were used. Their average compressive strength is around 16.55 MPa, whereas the flexural and the tensile strength (from Brazilian test) are 4.75 and 2.30 MPa, respectively. The parent mortar was a premixed product based on a natural hydraulic lime binder (1.35 and 4.80 MPa for flexural and compressive strength respectively, and 4.500 MPa for elastic modulus, after 28 days of curing). As repointing materials an epoxy resin (having 40.10 and 81.50 MPa for flexural and compressive strength) and a premixed fibre-reinforced hydrated lime and pozzolana mortar (having 3.80 and 16.70 MPa for flexural and compressive strength and 16.000 MPa) were adopted. Pultruded CFRP bars 5 mm in diameter, twisted and sand-coated in order to improve

186


Figure 8.10: General scheme of reinforcement technique with steel bars.

Figure 8.11: Maximum transversal deformation measured during creep tests carried out on steel reinforced panels [12].

their bond properties, were characterized by high tensile strength (2300 MPa), a modulus of elasticity of 130 GPa, and an ultimate strain of 1.8%. Results at local level demonstrated a higher sliding strength developed at the interface between resin and brick (4.60 MPa against the 3.40 MPa for the mortar case), but related to a more brittle failure mechanism, characterized by a sudden detachment of the elements, which involved the surface layers of the bricks also. Cohesion and friction coefficients were 0.88 and 40.45°, and 1.34 and 47.37° for the fibre reinforced mortar and the resin, respectively. To check the bond between the bars and the embedding materials pull-off tests were performed. Under a transverse compressive stress equal to the maximum value utilized in the triplet tests (3.00 MPa) resins were able to develop bond strength higher than twice that of


187

mortar (20.60 MPa against 9.45 MPa) but, similar to the triplet test results, the failure was more brittle and involved also the splitting of the bricks. At overall level, ten panels of 110 × 52 × 25 cm were subjected to strengthening by CFRP bars and subsequent uniaxial compression, under monotonic or cyclic loads. Cycles were executed at load levels corresponding approximately to 1/2 or 1/3 of the monotonic strength (for 2-cycle and 3-cycle cases respectively). To make up for the current unavailability of foldable FRP bars or of special corner reinforcing elements, the bars were anchored in the short sides of the samples by using sleeves composed by a metal tube filled by resin laid on a square plate, whose reliability was tested by a preliminary experimental phase [10]. The whole experimental programme is given in Table 8.2. Results confirmed that the best results are obtained for symmetric reinforcement (both sides) and for the use of lime-based mortar (Fig. 8.12). The maximum increase in strength was around 40% (2S.M panels, embedded with lime-based mortar), with a slight increase in the modulus of elasticity too. A great reduction Table 8.2: Experimental programme: CFRP bars reinforcement (2003). Intervention

Reinforcing material

Repointing material

UR.1 Monotonic UR.2 2 cycles 1S.M.1 Monotonic

– – Strengthening

– – 1Ø5

1S.M.2

2 cycles

Strengthening

1Ø5

1S.R.1 1S.R.2 2S.M.1

2 cycles 3 cycles 2 cycles

Strengthening Strengthening Strengthening

1Ø5 1Ø5 1Ø5

2S.M.2

3 cycles

Strengthening

1Ø5

2S.R.1 2S.R.2

2 cycles 3 cycles

Strengthening Strengthening

1Ø5 1Ø5

– – Fibre-reinforced hydrated lime & pozzolana mortar Fibre-reinforced hydrated lime & pozzolana mortar Resin type 3 Resin type 3 Fibre-reinforced hydrated lime & pozzolana mortar Fibre-reinforced hydrated lime & pozzolana mortar Resin type 3 Resin type 3

Series

Sample

0-CFRPb (unreinforced) 1-CFRPb (one side reinforced)

2-CFRPb (two sides reinforced)

Loading test

188


8.00

Unreinforced (UR.2) Mortar (1S.M.1) Resin (1S.R.1)

Stress (MPa)

6.00

4.00

2.00 Strain (‰) 0.00 -8.00

-6.00

-4.00

-2.00

10.00

0.00

2.00

4.00

6.00

8.00

Stress (MPa)

8.00 6.00 Unreinforced (UR.2) 4.00

Mortar (2S.M.1) Resin (2S.R.1)

2.00 Strain (‰) 0.00 -8.00

-6.00

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

Figure 8.12: Stress–strain diagrams for 1-CFRP series (a, one side strengthening) and for 2-CFRP series (b, two sides strengthening). of the crack pattern was detected at the end of the tests on the reinforced sides of the strengthened panels in comparison with the plain ones (decrease of the Poisson ratio of about 50%) (Figs 8.13 and 8.14). Panels repointed with epoxy resins also gave good results, but their behaviour is characterized by a brittle failure mechanism and by the presence of higher opening of cracks in the longitudinal side at the ultimate load (Fig. 8.12). The strength values obtained on the tested panels in both the first cracking and the ultimate phases are depicted in Fig. 8.15. Cyclic tests performed in two or three steps showed that after the first loading phase (up to 30% of the stress peak) the increment in strength is still possible, due to the elastic properties of the materials and the possible settling of the panel. On the contrary, after the second cycle (up to 60% of the stress peak), the internal damage is progressively increasing, thus the retrieval of the previous strength is not possible anymore. Compared to the strengthened masonry, first cracks appears very close to the ultimate stress in the


189

Figure 8.13: Crack pattern of the 1S.R.1 panel (side A is the strengthened one).

Figure 8.14: Details of one-side (left) and two-sides (right) strengthened panels after failure. unstrengthened masonry (Fig. 8.16); this confirms that the capacity to slowdown the failure process by the progressive plasticization of the masonry is particularly significant for symmetric configurations of strengthening. In comparison to rebars, CFRP thin strips (having a rectangular section and thickness around 1.5 mm), have a higher potential, possibly due to more superficial placements and higher flexibility (Figs 8.17 and 8.18). Pultruded CFRP strips are

190


s (MPa)

8.00 6.00 4.00 2.00 0.00

UR.1

UR.2

1S.M.

First crack

5.96

6.15

6.67

1S.M. 1S.R.1 1S.R.2 2S.M. 2S.M. 2S.R.1 2S.R.2 6.94

6.19

5.32

8.02

7.36

7.67

6.11

Failure

6.17

6.68

7.25

7.42

6.99

7.48

9.67

8.18

8.79

8.43

Figure 8.15: Compression strength values detected on panels.

Figure 8.16: Detail of the cracking of the UR.2 panel. externally sanded to improve adhesion with embedding materials; measured ultimate tensile strength was 1334 MPa at a corresponding strain of 1.8%, with a Young’s modulus of 73.20 GPa. Behaviour at interface and overall levels was extensively investigated experimentally. A first step of the research was carried out at the University of Padua, including the selection and characterization of the materials, the CFRP positioning configuration and a series of monotonic tests on wall samples [10, 14]. Clay bricks had a compressive and flexural strength of 17.24 and 6.40 MPa, respectively. Ordinary hydraulic lime mortar used for the laying of the bed joints had compressive and flexural strength after 28 days of curing of 10.32 and 0.63 MPa, respectively. To exploit the high performances of the FRP a high-strength hydraulic lime mortar was selected for the repointing phase; it had corresponding values of 15.61 and 0.83 MPa. The preliminary monotonic tests carried out on these panels showed the weakness of the corner layout of the reinforcement, which led to premature failure


191

Figure 8.17: Configuration of a plain panel subjected to laboratory test and detail of reinforcement with thin CFRP strips.

Figure 8.18: Experimental study of the interface behaviour of CFRP strips and numerical simulation showing the stress migration along the anchoring length and the influence of the rectangular section in limiting the splitting of the mortar, due to the elliptical stress distribution around the strip [11].

192


mainly concentrated at the top of the panels, as strips were not overlapped at the corners (Fig. 8.19). This was due to the unavailability of special anchorage devices, as L-shaped strips or bars, which may counteract such a brittle mechanism. The second step of the research, carried out at the Polytechnic of Milan, was focused on the evaluation of the creep behaviour of the reinforced masonry [8, 12]. Monotonic and creep tests were carried out on plain and strengthened samples, with CFRP strip inserted at every horizontal joint on the four sides (basic configuration, type A) or with CFRP sheets applied around the corners and the lateral sides of the specimen (configuration B) (Fig. 8.20). This was to prevent the premature failure at corners, as described above. The experimental programme executed on panels in different configurations is reported in Table 8.3. As for monotonic tests, as expected, ultimate axial load of the panels were quite similar, for both reference and reinforced panels. After cracking a relevant

Figure 8.19: Failure mode of unreinforced and reinforced panels.

Figure 8.20: Configuration B for creep tests: CFRP thin strips at every joint and CFRP sheets around corners.

Table 8.3: Experimental programme: CFRP thin strips reinforcement (2003–05). Series

Sample label Loading test

Intervention

Reinforcing configuration

Monotonic

Repair

Monotonic Creep Monotonic

– – Strengthening

– – Strips at each joint on sides A,B,D + sleeves on A

Monotonic

Repair

2-CFRPs (two sides reinforced)

2SA1

Monotonic

Strengthening

2SA2

Monotonic

Strengthening

2SB1

Monotonic

Strengthening

Strips at each joint on sides Each joint A,B,D on side C Strips at each joint on sides – A,B,C,D Strips at each joint on sides – A,B,C,D + FRP sheets Strips at each joint on sides – B,D and every second joint on sides A,C Strips at each joint on sides – A,B,C,D Strips at each joint on sides – A,B,C,D + FRP sheets

Strengthening

2SA4C Creep

Strengthening

Each joint in all sides – –

Repointing material – – – High-strength hydrated lime mortar High-strength hydrated lime mortar High-strength hydrated lime mortar High-strength hydrated lime mortar High-strength hydrated lime mortar High-strength hydrated lime mortar High-strength hydrated lime mortar


0-CFRPs UR1 (unreinforced) UR2 UR3C 1-CFRPs 1SAS1 (one side reinforced) 1SA1

2SA3C Creep

–

Repair case

193

194


improvement in the reduction of the horizontal deformation is obtained with both configurations of strengthening (A = each joint, B = every second joint, for monotonic tests). Both strengthened specimens (2SB1 and 2SA2), at a stress level equal to the UR2 ultimate stress, showed an average horizontal strain more than five times lower than the reference panel (Fig. 8.21a). The strip insertion in every second joint was particularly effective, as the maximum horizontal strain reached by configuration B, corresponding to 13 MPa of compression stress, was almost the same as the one of configuration A. The only difference among the two configurations’ performances consists in higher ultimate stress and strain reached by specimen 2SA2, which was obviously due to the damage concentration located across the nonstrengthened bed joints. As for the effect of repair after preliminary compression, unexpectedly, both repaired specimens revealed a noticeable performance, as the first cracking stress was reached again with a reasonable horizontal strain.

(a)

16.0 14.0 12.0

Stress [MPa]

10.0 8.0 6.0 UR.2 AV 4.0 2S.B.1 AV 2.0 -5.0

-4.0

-3.0

-2.0

0.0 1.0 -1.0 0.0 -2.0 strain [mm/m]

(b)

2S.A.2 AV 2.0

3.0

4.0

5.0

16.0 14.0 12.0

Stress [MPa]

10.0 8.0 6.0

UR.2 AV 1S.A.1 AV* UR.2.R AV 1S.A.1.R AV

4.0 2.0 -5.0

-4.0

-3.0

-2.0

-1.0

0.0 0.0 -2.0

1.0

strain [mm/m]

2.0

3.0

4.0

5.0

* instrumentation removed at first cracking

Figure 8.21: Axial stress versus strain curves of plain and strengthened specimens (a) before and (b) after repairing (AV means strain is average of sides A and C; horizontal strain – negative values).


195

This means that cracks which occurred after the first test could not freely propagate, as would happen, even at negligible axial stress levels, when loading failed plain masonry. Moreover, the repaired specimens were able to bear load up to the former cracking stress (around 9 MPa). At that point, due to the presence of the FRP strips, new cracks could not appear in the central areas of the main sides, but appeared close to the corners, where anchoring of the strips is lower. Panel 1SA1, after first damage and subsequent repairing (1SA1R) showed a coefficient of Poisson passing from 0.37 to 1.19 in the repaired face (side C) (Fig. 8.21b). This consistency demonstrates that CFRP repointing is an effective technique to limit lateral dilation of masonry members in both damaged and undamaged conditions. Also for creep tests, as expected, the strength is not affected by the reinforcement application; in particular, panels strengthened by FRP, despite different fibre configuration and materials that have been used, showed a lower lateral dilation (Fig. 8.22) than unreinforced ones.

(a)

(b)

Figure 8.22: (a) Peak stresses and (b) maximum horizontal deformations measured for creep tests (in test 2SA4C detachment of sheet at corners affected the experimental measures of deformation) [12].

196


A typical diagram which resulted from creep simulating test is shown in Fig. 8.23. The prevalent failure mechanisms are similar to the failure detected during the monotonic tests, and reinforced panel appears cracked with wider expulsions and delamination of the external parts of the bricks (Fig. 8.24). In the 16.0

Stress [N/mm2]

14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0

εv average between the plates (×103) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

Time [sec]

5000 10000 15000 20000 25000 30000

Figure 8.23: Creep simulation on masonry prisms strengthened with FRP strips (Polytechnic of Milan) [12]

Figure 8.24: Crack pattern of the panel 2SA3C.


197

case of application of the CFRP reinforcement at the corners, the detachment of the adhesion system from the masonry at the end of the test was observed.

8.4 Case studies The experimental validation of the performances of the bed reinforcement technique allowed proposing it for the consolidation of several historic constructions and monuments at risk in Italy, in order to counteract the dilation under high compressive stresses by improving the material toughness. It is worth to remark that, in real cases, more damage typologies can coexist, thus the proper selection and combination of different intervention techniques should be considered. In many cases, both injections and limited rebuilding (the traditional ‘scuci-cuci’) may be used, to reduce the stress concentration and to replace the most damaged resistant parts, respectively. Those techniques act locally on improving the mechanical behaviour of the material for the rehabilitation of the proper load bearing capacity of the structure. Despite a number of researches and efforts devoted to FRP materials, until now real applications have been performed only with stainless steel bars in combination with lime-based repointing mortars, as they can assure more guarantees of effectiveness and durability, even in exceptional conditions not easy to predict. In the following, some representative case studies of towers and structural components of churches in Italy are described [6, 8, 9]. 8.4.1 The bell-tower of the Basilica of S. Giustina in Padua The bell-tower of S. Giustina Basilica in Padua is a three-leaf masonry structure 70 m tall, built during the thirteenth century up to 40 m and raised up to the current height in the seventeenth century (Fig. 8.25). This event was responsible for the overloading conditions of the lowest, and poorer, part of the structure, characterized by a serious crack pattern, mainly concentrated at the corners. Some spalling in the internal bricks of the bell-tower was also noticed, possibly due to a worse quality of the structural elements used on the inside. There are signs of rebuilding of at least one whole corner performed in the past (also other similar interventions are visible in other towers still standing) which proves the effectiveness of that solution in preventing the structure from collapse. The point under consideration is why this solution works, notwithstanding the fact that during the operation the local overstress is to increase substantially. The damage in fact involves basically in its first phase the external leaf, where masonry is stiffer, and due to the availability of a large resisting area on the usual thick sections (which allowed one to execute the intervention for safety considerations), the structure is able to ‘accept’ during time a stress re-distribution both for damage and rebuilding operations. In the most deteriorated portions (corner and basement) diffused intervention of injections, partial rebuilding and bed reinforcement technique [5] were

198


(a)

(b)

(c)

Figure 8.25: S. Giustina bell-tower (Padova, Italy): (a) general view, (b) typical cracking due to creep, (c) cracking and spalling of brick elements. executed (Fig. 8.26). In particular, local rebuilding (‘scuci-cuci’) was extensively used during the works aimed at improving the safety conditions of the tower, especially in the lower, less visible parts of the construction, combined with injections, that contribute by reducing stress concentrations, whereas in the more visible parts steel injections are combined with the introduction of small diameter bars into the bed joints [15].


(a)

(b)

199

(c)

Figure 8.26: S. Giustina bell-tower interventions: (a) application of injections, (b) partial rebuilding (‘scuci-cuci’) and (c) phases of the bed joint reinforcement (insertion of bar and situation before injecting the pin hole).

8.4.2 The pillars of S. Sofia church in Padua Similar conditions have been found in some pillars in the S. Sofia church, also located in Padua. Several cracks have been detected and, some traditional repair techniques as steel ties (see Fig. 8.27), injections and rebuilding have been applied in several parts of the structure. 8.4.3 The bell-tower of S. Giovanni Battista Cathedral in Monza (Milan) It is the bell-tower of the Cathedral of Monza, a sixteenth-century building made of solid brick masonry walls, which show passing-through large vertical potentially dangerous cracks on some particularly weak portions of the western and eastern sides [9]. They are slowly but continuously opening as given by a monitoring roughly active since 1927. Wide cracks are also present in the corners of the tower up top 30 m (Fig. 8.28a). Furthermore, a damaged zone at a height of 11 to 25 m with a multitude of very thin and diffused vertical cracks is present (Figs 8.28b,c and 8.29). Design of intervention was mainly aimed at providing an overall confining action of masonry walls, limiting the dilation of the material [16]. In the specific case, due to the large diffusion of the crack pattern (11 × 9.5 m) and to its extension in the wall depth (45 cm over 140 cm), to reconstruct a wall or the use of floor tie roads in order to reduce the lateral deformation of the structure was inapplicable. Therefore, repair and retrofitting of masonry was extensively performed by grout injection, to re-establish homogeneity, uniformity of strength and continuity of masonry walls, and by bed joint reinforcement technique by insertion into a groove (6–8 cm deep) of one or two small diameter reinforcing bars connected to the inner leaf by transversal short pins (Fig. 8.29). Both excavated joints and drilled holes for pins insertion are successively sealed by mortar and grout, respectively (Fig. 8.30).

200


(a)

(b)

(c)

Figure 8.27: S. Sofia church pillars (Padova): (a) general view of the church, (b) provisional measures on a cracked pillar, (c) application of the technique.


(a)

201

(b)

(c)

Figure 8.28: S. Giovanni Battista bell-tower: (a) detachment of the corner; (b and c) thin cracks on the wall [6, 15].

8.5 Final remarks The counteraction of creep damage in massive structures is a topical subject, as many historical constructions, mainly towers or large columns and walls, are in hazardous conditions. The bed joint reinforcement technique revealed its potential in preserving those structures from collapse, as it has been widely experimentally investigated with small diameter reinforced steel bars applications and use

202


Figure 8.29: Crack pattern detected in the western and eastern sides of the belltower of Monza and scheme of the combination of the interventions in the mostly damaged portions.

Figure 8.30: On-site insertion of reinforced bars into the joints [6].


203

of compatible embedding materials. The possible introduction of FRP materials, especially for small rectangular section bars, seems to be promising in similar contexts, even if in some peculiar aspects it needs deeper investigation (local behaviour at interface levels, anchorage systems, sensitivity to high temperatures, use of resins with low compatibility with original materials, etc.). The technique is pretty easy to be performed in-situ and does not require particular skills or special tools. The proper selection of strengthening material is a crucial point of the intervention, especially for the possible application on existing historic masonry buildings. The use of high-strength products as embedding material can be inappropriate, especially in the case of epoxy resins, due to the more brittle behaviour both at local (interfaces with bricks and with the reinforcing bar) and global level. Finally, symmetric interventions are recommended, in order to optimize the global performances of the strengthened walls.

References [1] [2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

Binda, L. & Anzani A., The time-dependent behaviour of masonry prisms: an interpretation. The Masonry Society Journal, 11(2), pp. 17–34, 1993. Anzani A., Binda, L. & Mirabella Roberti, G., The effect of heavy persistent actions into the behaviour of ancient masonry. Materials and Structures, 33(228), pp. 251–261, 2000. Binda, L., Anzani, A. & Gioda, G., An analysis of the time-dependent behaviour of masonry walls. 9th International Brick/Block Masonry Conference, Berlin, 1991, Vol. 2, pp. 1058–1067, 1991. Binda, L., Gatti, G., Mangano, G., Poggi, C. & Sacchi Landriani, G., The collapse of the Civic Tower of Pavia: a survey of the materials and structure. Masonry International, 6(1), pp. 11–20, 1992. Binda, L., Modena, C., Valluzzi, M.R. & Zago, R., Mechanical effects of bed joint steel reinforcement in historic brick masonry structures. Structural Faults + Repair – 99, 8th International Conference and Exhibition, London, England, 13–15 July 1999 (CD-ROM). Binda, L., Modena, C., Saisi, A., Tongini Folli, R. & Valluzzi, M.R., Bed joints structural repointing of historic masonry structures. 9th Canadian Masonry Symposium ‘Spanning the Centuries’, Fredericton, New Brunswick, Canada, 4–6 June 2001 (CD-ROM). Valluzzi, M.R., Binda, L. & Modena, C., Mechanical behavior of historic masonry structures strengthened by bed joints structural repointing. Construction and Building Materials, 19(1), pp. 63–73, 2004. Valluzzi, M.R., Tinazzi, D. & Modena, C., Strengthening of masonry structures under compressive loads by FRP strips: local-global mechanical behaviour. Science and Engineering of Composite Materials, Special Issue, 12(3), pp. 203–218, 2005. Modena, C., Valluzzi, M.R., Tongini Folli, R. & Binda, L., Design choices and intervention techniques for repairing and strengthening of the Monza

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[10]

[11]

[12]

[13]

[14]

[15]

[16]


cathedral bell-tower. Construction and Building Materials, Special Issue, 16(7), pp. 385–395, 2002. Valluzzi, M.R., Disarò, M. & Modena, C., Bed joints reinforcement of masonry panels with CFRP bars. Proc. of the International Conference on Composites in Construction, Rende (CS), Italy, September 2003, eds D. Bruno, G. Spadea & N. Swamy, pp. 427–432, 2003. Valluzzi, M.R., Tinazzi, D., Garbin, E. & Modena, C., FEM modelling of CFRP strips bond behaviour for bed joints reinforcement technique. Proc. of STRUMAS VI, ‘Computer Methods in Structural Masonry 6’, September 2003, Rome, Italy, eds T.G. Hughes & G.N. Pande, Computers & Geotechnics Ltd: Swansea, pp. 149–155, 2003. Saisi, A., Valluzzi, M.R., Binda, L. & Modena, C., Creep behavior of brick masonry panels strengthened by the bed joints reinforcement technique using CFRP thin strips. Proc. of SAHC2004: IV Int. Seminar on Structural Analysis of Historical Constructions – Possibilities of Experimental and Numerical Techniques, Padova, Italy, November 2004, pp. 837–846, 2004. Garbin, E., Moro, L., Valluzzi, M.R. & Modena, C., Influence of high temperature on the bed joint reinforcement of brick masonry by CFRP bars. Proc. of CCC2005 – Composites in Constructions International Conference, Lyon, France, July 2005 (CD-ROM). Tinazzi, D., Valluzzi, M.R., Bianculli, N., Lucchin, F., Modena, C. & Gottardo, R., FRP strengthening and repairing of masonry under compressive load. Proc. 10th International Conference on Structural Faults and Repair, London, 1–3 July 2003, (CD-ROM), Engineering Technical Press: Edinburgh, 2003. Valluzzi, M.R., Casarin, F., Garbin, E., da Porto, F. & Modena, C., Long-term damage on masonry towers: case studies and intervention strategies. 11th International Conference on Fracture, Turin (Italy), 20–25 March 2005 (CD-ROM). Binda, L., Modena, C. & Valluzzi, M.R., Il restauro del campanile del Duomo di Monza: scelte di progetto e tecniche d’intervento. Arkos – Scienza e Restauro dell’Architettura, 1, Genn./Marzo 2003, pp. 44–53, 2003.

CHAPTER 9 Simple checks to prevent the collapse of heavy historical structures and residual life prevision through a probabilistic model L. Binda, A. Anzani & E. Garavaglia Department of Structural Engineering, Politecnico di Milano, Milan, Italy.

9.1 Introduction A survey on approximately 60 Italian ancient towers, carried out to collect information on the most common symptoms of structural decay, particularly on the crack patterns, is described in this chapter. A simple procedure, aimed at achieving a pre-diagnosis of the tower structures and at identifying the cases where more detailed investigations are to be designed for defining the safety of the structure, is proposed, which local institutions might adopt. The vulnerability assessment of historic buildings towards the effects of persistent loading and the achievement of a reliable lifetime estimate on a deterministic basis is often very complex. Therefore, an attempt has been made at solving the problem through a probabilistic approach.

9.2 The safety of ancient towers Masonry towers are largely diffused in Italy and Europe and constitute an important part of our heritage which requires suitable protection. The problem of their safety, which became particularly evident after the collapses of monumental buildings mentioned in previous chapters [1, 2], has to be tackled by local public institutions, which not always can afford very costly diagnostic techniques. On the other hand, before large investments are made for monitoring and/or designing a repair intervention, a preliminary screening should be carried out to qualify the buildings depending on the estimated degree of damage. For this purpose,

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some help might come if guidelines were provided by local authorities, so that a classification of the state of the towers based on direct observation could be routinely performed. As an example, the results of an investigation carried out on some Italian towers are presented and a simple procedure to analyse masonry towers is tentatively proposed. 9.2.1 A survey on Italian cases A survey of about 60 ancient Italian towers has been carried out, to collect information on the most common symptoms of structural decay, particularly on the crack patterns. The analysed towers present various degrees of damage from an almost complete integrity to a very serious situation; therefore a classification has been necessary to categorize some classes with similar characteristics [3]. Different types of towers have been observed, which are qualified by different functions and show specific features that are typical of their group: family-towers, bell-towers, boundary wall-towers, house-towers. A data base has been built with charts and forms, where the information collected for any single tower has been recorded. In particular, geometric data and notes on the material and texture characteristics of the masonry have been gathered. An accurate photographic survey has been performed so as to report on the main cracks in the building facades, indicating, when possible, the ones which cross the wall thickness. Historical information on the buildings has been collected to know their load history and any particular event which could have modified it. In some cases, experimental data on the state of stress were available because some towers are being monitored by private or public research organizations. In the other cases, when the geometry was known, the vertical stress at ground level was estimated assuming a density of 18 and 20 kN/m3, respectively, for brick and stone masonry. To get information on possible instability risks, the critical load has been calculated as a percentage of the acting dead load, assuming a Young modulus of 200 N/mm2 according to the values previously detected on several masonries by use of flat jacks. Two calculations have been done assuming two limit conditions depending on the assumed mutual constraints between orthogonal walls: on the one hand perfect continuity has been assumed, on the other hand any single wall has been considered as isolated. Of course this hypothesis is far more pessimistic but it is also on the safe side. 9.2.2 Comments on the observed crack patterns Different kinds of crack patterns have been observed on the examined towers which might be due to different causes. Of course only a direct experimental investigation with a complete non-destructive and/or destructive evaluation could provide

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207

a satisfying diagnosis but such very costly survey can not always be afforded. Nevertheless, some interesting considerations can be made based on the available information, which have more easily been obtained, and a comparison between similar cases can be done given also some experience which has been gained by previous investigations. Examples of two kinds of damages will be presented trying to connect, when possible, the observed cracks to the experimental knowledge on long-term behaviour of masonry. In Figs 9.1–9.4 two leaning towers are shown: the Garisenda family-tower (Bologna, twelfth century) and the S. Maria del Pero bell-tower (Monastier [Treviso] tenth century), both made by brick masonry. The first one is 47.5 m high, with a base of 8 × 8 m and three-leaf walls 2.35 m thick at ground level. The second one is 45 m high, with a base of 12.9 × 12.9 m and solid walls 3.5 m thick at ground level. In both cases all four fronts of the tower are badly cracked: it is interesting to note that the sloping face is the most damaged one, with a concentration of flaws at the base level and at mid-height in the case of the Garisenda and a multitude of vertical cracks in the case of S. Maria del Pero. The walls orthogonal to the direction of the slope are also cracked vertically, as if the wall had split into two parts which sheared mutually: the crack path always follows a preferential way, which runs along a line of openings.

Figure 9.1: Garisenda family-tower (Bologna, twelfth century), north, west, south and east fronts.

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Figure 9.2: Bell-tower of S. Maria del Pero (Monastier, tenth century).

In Figs 9.5–9.8 two towers damaged by compression effects are shown: the belltower of the Duomo of Monza (sixteenth century) [4] (see also Chapter 1) and the Coronata family-tower (Bologna, thirteenth century) both of them made again by brick masonry. The first one is 78.5 m high, with a base of 9.8 × 10.3 m and solid walls 2.1 m thick at ground level and at present is subjected to a reinforcing intervention. The second one is 61 m high, with a base of 9 × 9 m and three-leaf walls 2.8 m thick at ground level. In both cases vertical cracks are visible. In the case of Monza cracks positioned at the corner indicate that the wall thickness is possibly split. Many cracks are also present in the lower part for a height of about 30 m; the most damaged face is the western one, where cracks crossing the wall thickness rise up to about 15 m also cutting the bricks. In the case of the Coronata Tower, the most damaged face is the southern one where a concentration of cracks is visible just above the stone basement and a single long crack runs up for about 12 m along a line of openings. In general, vertical cracks are always present whenever a compressive stress concentration takes place, the path of which is greatly influenced by the masonry texture.


Figure 9.3: Garisenda family-tower (Bologna, twelfth century): detail of a crack.

209

Figure 9.4: Bell-tower of S. Maria del Pero (Monastier, tenth century): detail of a crack.

9.2.3 Elaboration of the collected data After the calculations described above, a comparison between the obtained values and those corresponding to the collapsed Tower of Pavia has been made. In Fig. 9.9 the distribution of average vertical stress at ground level is shown, where it appears that in most cases the stress level varies between 0.25 and 0.75 MPa, but in some cases it is higher than that of Pavia. In Fig. 9.10 the vertical stress is shown as a function of the tower height. Of course a linear relationship appears, with house-towers and boundary wall-towers showing the lowest values of the considered parameters. The stress value of the Tower of Pavia is shown again. In Fig. 9.11 the average stress value is related to the ratio between the tower height and the wall thickness where again, despite some scatter in the data, a linear relationship can be observed. In Fig. 9.12 the critical loads, calculated according to the two assumptions previously mentioned, are plotted as a percentage of the dead load versus the tower heights. Again the levels corresponding to the Tower of Pavia are indicated. It is interesting to notice that in the case of Pavia very low values of this ratio have been

210


Figure 9.5: Bell-tower of the Duomo of Monza (sixteenth century): west and east fronts.

Figure 9.6: Coronata family-tower (Bologna, thirteenth century): east and south fronts.

obtained, even in the case of the more optimistic assumption when a value not much greater than 1 has been obtained. As far as the other towers are concerned, it has to be observed that unfortunately for many of them (the tallest ones) the analysed ratio lies below the Pavia level and also below 1. Of course this is not equal to a statement of a critical situation for these towers, but certainly it might be enough to recommend that a deeper evaluation be carried out.

9.3 A probabilistic model for the assessment of historic buildings The results of the creep and pseudo-creep tests described in Chapter 2 have been interpreted by means of a probabilistic model, based on the definition of a random


Figure 9.7: Bell-tower of the Duomo of Monza (sixteenth century): detail on a crack.

Pavia Tower

40 30 20

4

10 0 -0.5

Figure 9.8: Coronata family-tower (Bologna, thirteenth century): detail on a crack.

σv [MPa]

Frequency [%]

50

Bell-Towers Family-Towers

3

Boundary Wall-Towers House-Towers

2 1

0.0

0.5

1.0

1.5

2.0

σv [MPa]

Figure 9.9: Bar chart of the average vertical stress at ground level.

2.5

211

0

Pavia Tower

0

20

40

60 80 H [m]

100

120

Figure 9.10: Average stress value at ground level versus tower height.

variable as a significant index of vulnerability, and on the solution of the classic problem of reliability in stochastic conditions. A comparison between vertical and horizontal strain-rate is put forward and the application of the proposed procedure to the Tower of Monza is attempted. Aim of the research is to provide a

212


3 2

1E+1

Pavia Tower

1 0

1E+2

Bell-Towers Family-Towers Boundary wall-Towers House-Towers

Pcr /P

σv [MPa]

4

10

20

30

40

50

H/S

Figure 9.11: Average stress value at ground level versus the ratio between tower height and the wall thickness.

Pavia Tower

0.1 1E-2

0

c) Pavia Tower

1

i)

0

40

80

120

H [m]

Figure 9.12: Critical load over acting dead load versus tower height: ‘c’ represents collaborating walls and ‘i’ represents isolated walls.

mathematical model able to predict possible failures of heavy masonry structures due to long-term damage, allowing preventive repair interventions. By experimental evidence, the strain evolution connected with a given stress history of a viscous material such as a historic masonry can be described through . . the parameters ev and eh, respectively, defined as the vertical and horizontal strainrate taken on the linear branches of the strain versus time diagrams shown by the specimen at the stress level s, remaining constant for a certain time interval. For each s the high randomness connected with the changing of strain-rate, due . to the high non-homogeneity of the masonry here tested, brings to consider e as a random variable with a certain distribution of values (Fig. 9.13). The diagrams, referred to the horizontal strain components, show an initial pseudo-constant branch with low values of the strain-rate, followed by a clearly increasing part that ends with the collapse [5]. Following this way, the deformation process can be interpreted as a stochastic . process of the random variable e. The strain-rate also depends on the stress level s corresponding to which the deformation is recorded. Therefore, for each stress . level s the strain-rate e (measured in e/s) can be modelled with a probability den. . sity function (PDF) fE (e, s) that results to be dependent on the stress s and on the . strain-rate e. The experimental measurements are taken at discrete stress values . . . s*, the PDF fE. (e, s) becomes fE. (e, s*) and is dependent on the strain-rate e and on s* which is constant at every step. Therefore the modelling of the strain-rate . . behaviour depends only on the random variable e. In order to model fE. (e, s*), at every stress level s* a family of theoretical distributions has to be chosen. No doubt that, in the choice of a distribution modelling a given phenomenon has to be connected not only to the physical aspects of the phenomenon itself but also to the characteristics of the distribution function in its tail, where often no experimental data can be collected. This last aspect of the matter can be investigated by analysing . the behaviour of the immediate occurrence rate function fE. (e, s*) connected with the chosen distribution function. On this subject more details are described in [6] and [7].


213

0.005 0.0045 0.004

0.003

. f . ( ε, σ∗)

0.0025

_. ε h = 0.002

Ε

. ε h [(ε h ×10 3 )/sec]

0.0035

0.002 0.0015

_. ε h = 0.001

0.001

_. ε h = 0.0005

0.0005 0 1

1.2

1.4

1.6 σ*

1.8

2

2.2

2.4

2.6 2.8 σv [N/mm2]

3

Figure 9.13: Interpolation of the horizontal strain-rate versus applied stress and the . modelling of fE. (e, s*).

The physical knowledge of the phenomenon has shown a relationship between the secondary creep strain-rate and the residual life of the material [8, 9]. In view of the preservation of historic buildings from major damage or even failure, it would be very convenient to indicate a critical value of the strain-rate under which the residual life of the building is conveniently greater than the required service . life. Here a conventional value of e may be assumed as a critical value indicating a safety limit. Consequently, for a given stress level s* the probability to record the critical strain-rate connected with the secondary creep safety limit increases . if the strain-rate e increases. Therefore, it seems correct to assume that, at a given stress level s* the higher is the strain-rate, the higher that the . . is the . probability . secondary creep strain-rate falls in the interval {E < e ≤ E + dE}. The assumed hypothesis, as a satisfied (but not unique) physical interpretation of the decay . process, leads to model the strain-rate e at the stress level s* with a Weibull distribution (Fig. 9.13). This family of distributions presents an. immediate occurrence rate function . . fE. (e, s*) which increases if the value of E increases and tends to ∞ if E → ∞; this fact seems to respect the physical interpretation of the strain-rate behaviour previously commented. For a correct probabilistic modelling of the process, the parameters involved in the chosen PDF of the considered random variable need to be estimated. For a

214


. probabilistic modelling of e, the maximum likelihood method, applicable through a computer code, is preferable to the least squares method. It is furthermore interesting to evaluate the probability for the system of reach–. ing or exceeding a given strain-rate level e over a stress history. This probability –. can be seen as the shadowed area above e as shown in Fig. 9.14 and [5, 8–10]. This . . area can be calculated by using the survive function ℑE. (e, s*) = 1 − FE. (e, s*) . where FE. (e, s*) is the cumulative distribution function of the density chosen. The . calculation of ℑE. (e, s*) is possible with the use of any kind of computer code for –. numerical integration. For different strain-rate levels e h, the survive function has been evaluated for all stress levels s*. The calculated values allow the plotting of an experimental fragility curve connected to each chosen strain-rate levels (see Fig. 9.15, Section 9.4.1 and [7, 10]). Since the experimentally measured strainrates only refer to a discrete number of stress levels, it would be quite convenient to have a suitable tool capable to predict, though in probabilistic terms, the system behaviour at any stress level. Following this approach the deterioration process can be treated as a reliability problem [11, 12]. Indeed the reliability R(t) concerns the performance of a system over time and it is defined as the probability that the – system does not fail during the time t. Here this definition is extended and R(s) is assumed as the probability that a system exceeds a given significant strain-rate –. – e with a stress s. The random variable that is used to quantify reliability is Σ which

0.005 0.0045 0.004

0.003

. f . ( ε, σ∗)

0.0025

Ε

. ε h [(ε h ×10 3 )/sec]

0.0035

0.002 0.0015 0.001

_. ε h = 0.0005

0.0005 0 1

1.2

1.4

1.6 σ*

1.8

2

2.2

2.4

2.6 σv

2.8

[N/mm2]

–. Figure 9.14: Exceedance probability to cross the threshold e .

3


215

–. is just the stress to exceed strain-rate e . Thus, from this point of view, the reliability function is given by [11, 13] R (s ) = Pr( Σ > s ) = 1 − FΣ (s ),

(9.1)

– where FΣ– (s) is the distribution function for Σ and represents the theoretical modelling of the experimental fragility curves. In order to model the experimental fragility curves and to evaluate FΣ– (s), a Weibull distribution has been chosen [5, 10, 13]. In fact, this distribution seems to be a good interpretation of the physical phenomenon: the larger the stress level, the higher the probability that a critical strain–. rate e , connected with the creep phenomenon, will happen for s value included in – – the next (Σ + dΣ) interval. Therefore, distributions with the function φ Σ– (s) increasing with s and tending to ∞ as s → ∞ are needed. Also this time the Weibull distributions satisfy this requirement. The fitting of the experimental fragility curves with the Weibull distribution has been made using an optimization procedure for the parameters estimation through a computer code involving the least squares method. Since in this case the parameters estimation is made on cumulative distributions the least squares method is preferable to the maximum likelihood method.

9.4 Fragility curves from the experimental data . 9.4.1 Fragility curve e versus s applied to creep tests Referring to the creep tests described in Chapter 2 and considering the strain versus time evolution, the interpolation of the strain-rate versus stress and the model. ling of fE.(e, s*) have been plotted as shown in Fig. 9.13. On it, as possible critical –. strain-rate values, three different e h have been identified connected to the initiation of the secondary creep phase [14]. In Fig. 9.15 the experimental and theoretical fragility curves connected with horizontal strain-rate thresholds are reported. They describe the probability to exceed the critical thresholds as a function of the reached stress level sv. If applied to real cases, this type of prediction allows to evaluate, for instance, the results of a monitoring campaign on a massive historic building subjected to persistent load and to judge whether the creep strain indicates a critical condition in term of safety assessment (see Section 9.5). Of course, the precocious recognition of a critical state will allow designing a strengthening intervention to prevent total or partial failure of the construction. 9.4.2 Comparison between vertical and horizontal strain-rate Referring to a previous research that analysed the experimental results obtained in the vertical direction [5], possible critical values of the vertical strain-rate, connected

216


F σ (σv)

0.9

–•

ε h = 0.0005

0.8 0.7

–•

0.6

ε h = 0.001

0.5 0.4

–•

0.3

ε h = 0.002

0.2 0.1 0 1

1.2

1.4

1.6

1.8

2 2.2 σv [N/mm2]

2.4

2.6

2.8

3

Figure 9.15: Horizontal strain-rate: experimental (•) and theoretical (⎯⎯) fragility curves. to the initiation of the secondary creep may also be indicated. Therefore, to compare the experimental results obtained in the horizontal and vertical directions, the same vertical and horizontal strain-rates thresholds have been chosen. In Fig. 9.16 the experimental and theoretical fragility curves connected with the previous thresholds are reported for the vertical strain-rates. In Tables 9.1 and 9.2 a comparison between vertical and horizontal strain-rate in term of exceedance probability is reported. Comparing these results it can be observed that always the exceedance of the chosen threshold strain-rate is performed at a lower stress level in the case of horizontal strain. This is quite in agreement with the dilatant behaviour of ancient masonry when approaching failure, as shown by Fig. 2.13a, where the horizontal strain appears to be higher and developing at a higher rate than the vertical ones. This is also confirmed by Fig. 2.15b where the crack pattern of a prism at the end of the test is shown: having loaded the specimen vertically in compression, the cracks follow a mainly vertical path, therefore giving an apparent horizontal dilation. However, from a probabilistic point of view caution must be offered to tails of distribution where usually not much data are present and where the prediction becomes critical.

. 9.4.3 Fragility curve e versus s applied to pseudo-creep tests Also in the case of pseudo-creep tests as those shown in Fig. 2.17, possible critical strain-rate values, connected to the initiation of the secondary creep phase,


217

F (σv) σ

1 0.9 0.8 0.7 0.6 0.5

_. ε v = 0.001

0.4 0.3

_. ε v = 0.002

_. ε v = 0.0005

0.2 0.1 0 1

1.2

1.4

1.6 σv

1.8

2

2.2

2.4

[N/mm2]

Figure 9.16: Vertical strain-rate: experimental (•) and theoretical (⎯⎯) fragility curves. –. Table 9.1: Probability to exceed ev = 0.0005 for different sv. Exceedance probability –. of ev (%) 10 63 90

sv (N/mm2) 1.40 1.81 2.00

–. Table 9.2: Probability to exceed eh = 0.0005 for different sv. Exceedance probability –. of eh (%) 10 63 90

sv (N/mm2) 1.38 1.75 1.90

were found. In Fig. 9.17 the experimental and theoretical fragility curves con–. nected with the threshold e h = 1.00e – 005 are reported. Table 9.3 shows that for sv = 4.22 N/mm2 63% of population (samples) could be already failed. The same observation made in the previous paragraph can apply here.

218


F σ (σv)

0.9 0.8 0.7 _. ε h = 1.00e-005

0.6 0.5 0.4 0.3 0.2 0.1 0 0

1

2

3

4 5 6 σv [N/mm2]

7

8

9

10

Figure 9.17: Experimental (▲) and theoretical (⎯⎯) fragility curves. –. Table 9.3: Probability to exceed eh for different sv. –. Exceedance probability of eh(%) sv (N/mm2) 10 63 90

2.37 4.22 5.25

9.4.4 Comparison between vertical and horizontal strain-rate In Fig. 9.18 the experimental and theoretical fragility curves connected with the –. threshold e h = 1.25e – 005 are reported for both vertical (Fig. 9.18a) and horizontal (Fig. 9.18b) strain-rates. Comparing these results with those reported in Tables 9.4 and 9.5, a tendency similar to that shown by the creep test is confirmed, but here some additional comments have to be made. It can be observed that in 10% of the cases the exceedance of the chosen threshold strain-rate is performed at a lower stress level in the case of vertical strain. On the contrary, in 63 and 90% of the cases the exceedance of the chosen threshold strain-rate is performed at a lower stress level in the case of horizontal strain, exactly like in the creep test. In fact, at low stress values the material response is still viscoelastic; therefore, the higher strain is shown in the loading direction. This was not evident in the case of creep tests because the load history of the different prisms was not the same and less regular data were available, therefore

Checks to Prevent the Collapse of Heavy Historical Structures (a)

219

(b) _. ε v = 1.25e-005

F σ (σv)

1 0.9

F σ (σv)

1 0.9

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

_. ε h = 1.25e-005

0

0 0

1

2

3

4 5 6 7 σv [N/mm2]

8

9 10

0

1

2

3

4 5 6 7 σv [N/mm2]

8

9 10

Figure 9.18: Experimental (•, ) and theoretical (⎯⎯) fragility curves: (a) vertical strain; (b) horizontal strain. –. Table 9.4: Probability to exceed ev = 1.25e – 005 for different sv. Exceedance probability –. of ev(%) 10 63 90

sv (N/mm2) 2.35 4.30 5.40

–. Table 9.5: Probability to exceed eh = 1.25e – 005 for different sv. Exceedance probability –. of eh(%) 10 63 90

sv (N/mm2) 3.00 4.23 4.75

on a statistical basis the phenomenon was not evident. At higher stress level, approaching failure, the tendency is inverted: the material response turns into viscoplasticity with visible crack appearance corresponding to dilatant behaviour, as shown by Fig. 2.17. Again, this is confirmed also by the crack patterns (Fig. 2.19).

9.5 Application to the bell-tower of Monza The proposed probabilistic approach has been applied for the first time to a real case trying to evaluate the results of the monitoring of a massive historic building

220


subjected to persistent load. The bell-tower of Monza, a sixteenth-century structure built in solid brickwork masonry, had suffered major and diffused cracks due to high compression (Fig. 9.5). After the constitution of a Technical Committee in 1976 the building, together with the Cathedral, was subjected to a systematic control, setting up 31 fixed bases, 7 of which were on the Tower corresponding to the major cracks. The bases had a length of about 400 mm, and the measurements were taken, starting in January 1978, every month during the first three years and every three months subsequently. The instrument used was a millesimal deformometer. After the recorded increase of the cracks aperture on the tower and an anomalous geometry recorded in the Cathedral, in 1992 a new committee was constituted by Politecnico di Milano which installed a static control system that included the continuation of the geometric evaluation of the cracks. Each of the previous bases was substituted by a couple of new bases placed above and below the other ones, having a length of 200 mm, the readings being taken at the same periodicity. Considering the data collected until 1999 (Fig. 9.19), the influence of thermal variation on the crack opening can clearly be observed. Nevertheless, tracing a regression line between the data, a neat increase of the aperture in time is visible; in the case of the base shown in Fig. 9.19 a rate of 6.48 μm/year can be measured until 1986 and a higher rate of 24.94 μm/year can be measured subsequently, clearly indicating a worsening of the Tower static conditions. After the static survey, a consolidation intervention on the Tower was required, which is still in progress. In order to compare the rate of crack opening of the Tower with the strain-rate measured in the laboratory, the monitoring readings were divided by the base length and the rate in μm/mm over seconds was calculated. 400

aperture variation [μm]

300 200 100 0 -100 -200 6.48 μm/year 24.94 μm/year

-300

19 7 19 8 7 19 9 8 19 0 8 19 1 8 19 2 8 19 3 84 19 8 19 5 8 19 6 8 19 7 8 19 8 8 19 9 9 19 0 9 19 1 9 19 2 9 19 3 9 19 4 9 19 5 9 19 6 9 19 7 9 19 8 9 20 9 00

-400

years

Figure 9.19: Monitoring of the bell-tower of Monza: opening variation of a crack versus time.

Checks to Prevent the Collapse of Heavy Historical Structures 1

221

F σ (σv)

0.9

_. ε = 1e-9

0.8 0.7 0.6 0.5

_. ε = 2e-9

0.4 0.3 0.2 0.1 0 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

σ [N/mm2]

Figure 9.20: Experimental (•, ▲) and theoretical (⎯⎯) fragility curves.

Relating this calculated rate with the values of the vertical stress, locally measured by flat-jack tests at the same height of the crack monitoring, the fragility curves shown in Fig. 9.20 were built for the Tower cracks for two different thresh–. olds e In this case the strain-rate recorded is lower than the strain-rate obtained by creep and pseudo-creep laboratory tests. Here the modelling appears a hazard, but on the basis of the results obtained by laboratory tests it is possible to suppose the same distribution (Weibull distribution) for modelling the probability of exceedance of the thresholds chosen. Although two data are not sufficient to investigate the Weibull shape, the results obtained look like an interesting example of possible application of the procedure to real cases, where more suitable data were available.

9.6 Conclusions An accurate visual survey based on experimental and analytical experience has been shown to give important information on the state of damage of massive buildings like towers. Typical major or diffused cracks were found capable of giving preliminary information on the state of damage of these buildings. The collapse of a badly damaged structure happens generally very rapidly, but it may be avoided if the damage symptoms as cracks, deformations, etc. are carefully taken into

222


account as early as possible. To this purpose the following procedure is suggested as a preliminary investigation, which public institutions may adopt: • Geometrical survey and preparation of drawings of the building using simple tools like photography and the subsequent restitution by software for image elaboration; • Representation of the crack pattern visually detected over the geometrical restitution; measure of the wall thickness. • Interpretation of the crack pattern and recognition of its causes: tilting, effect of dead load, others; • Rough calculation, based on geometrical data, density of the material and the assumption of homogeneous and elastic material, of the maximum stress value; • Rough calculation of the critical load value under the same hypothesis. These preliminary results can indicate the possible need of a more detailed investigation and/or of periodically repeated surveys. A probabilistic model has also been applied to the study of the long-term behaviour of masonry specimens subjected in laboratory to creep and pseudo-creep. The chosen model seems to appropriately interpret the experimental results also capturing the passage between viscoelastic and viscoplastic behaviour. An attempt of applying the procedure to the results of long-term monitoring of displacements, particularly of crack opening, was carried out. The research will continue with the aim of providing a tool for preventing the masonry failure under particular states of stress.

Acknowledgements Architects E. Bertocchi and D. Trussardi are gratefully acknowledged for creating the database on Italian towers. Dr. G. Cardani is gratefully acknowledged for the data elaboration. Thanks are given also to ISMES for providing information on the towers. The research was carried out with the support of MIUR Cofin 2000.

References [1]

[2]

[3]

[4]

Binda, L., Gatti, G., Mangano, G., Poggi, C. & Sacchi Landriani, G., The collapse of the Civic Tower of Pavia: a survey of the materials and structure. Masonry International, 6(1), pp. 11–20, 1992. Binda, L., Anzani, A. & Mirabella Roberti, G., The failure of ancient towers: problems for their safety assessment. Conf. on Composite Construct. – Conventional and Innovative, IABSE, Insbruck, pp. 699–704, 1997. Binda, L. & Anzani, A., The safety of ancient masonry towers: a survey on the effects of heavy dead loads. Int. Conf. on Studies in Ancient Structures, Istanbul, Turkey, pp. 207–216, 1997. Modena, C., Valluzzi, M.R., Tongini Folli, R. & Binda L., Design choices and intervention techniques for repairing and strengthening of the Monza


[5]

[6]

[7]

[8]

[9]

[10]

[11] [12] [13] [14]

223

Cathedral Bell-Tower. Construction & Building Materials, 16(7), pp. 385– 395, 2002. Anzani, A., Binda, L. & Garavaglia, E., The vulnerability of ancient buildings under permanent loading: a probabilistic approach. Proc. of 2nd Int. Symp. ILCDES 2003, Integrated Life-Cycle Design of Materials and Structures, Kuopio, Finland, 1–3 December 2003, ISSN 0356-9403, ISBN 951758-436-9 Helsinki, Finland, UE., I, pp. 263–268, 2003. Garavaglia, E., Lubelli, B. & Binda, L., Service life modelling of stone and bricks masonry walls subject to salt decay. Proc. of Integrated Life-Cycle Design of Materials and Structures, ed. A. Sarja, RILEM/CIB/ISO, Pro 14, Technical Research Center of Finland (VTT); Helsinki, 1, pp. 367–371, 2000. Binda, L., Garavaglia, E. & Molina, C., Physical and mathematical modelling of masonry deterioration due to salt crystallisation. Proc. of 8th Int. Conf. on Durability of Building Materials and Components, eds M.A. Lacasse & D.J. Vanier, NRC-CNRC: Ottawa, I, pp. 527–537, 1999. Taliercio, A.L.F. & Gobbi, E., Experimental investigation on the triaxial fatigue behaviour of plain concrete. Magazine of Concrete Research, 48(176), pp. 157–172, 1996. Anzani, A., Binda, L. & Mirabella Roberti, G., The effect of heavy persistent actions into the behaviour of ancient masonry. Materials and Structures, 33, pp. 251–261, 2000. Garavaglia, E., Lubelli, B. & Binda, L., Two different stochastic approaches modeling the deterioration process of masonry wall over time. Materials and Structures, 35, pp. 246–256, 2002. Evans, D.H., Probability and Its Applications for Engineers, Marcel Dekker, Inc.: New York, NJ, USA, 1992. Melchers, R.E., Structural Reliability – Analysis and Prediction, Ellis Horwood Ltd: Chichester, West Sussex, England, 1987. Bekker, P.C.F., Durability testing of masonry: statistical models and methods. Masonry International, 13(1), pp. 32–38, 1999. Garavaglia, E., Anzani, A. & Binda, L., Probabilistic model for the assessment of historic buildings under permanent loading. J. of Materials in Civil Engineering, ASCE, USA, 18(6), pp. 858–867, 2006.


Conclusions This book is probably the first one completely dedicated to the study of long-term behaviour of massive historic buildings. Although the creep behaviour of materials such as rocks, concrete and steel has been well known for a long time, very little research has been carried out on the behaviour of masonry. The fact that historic masonry walls are usually characterized by very thick sections, to better diffuse the dead load and hence reduce the stresses due to compression, has caused a lack of interest in the long-term behaviour of masonry structures. Collapses, such as the one of the S.Marco bell-tower in Venice and others that occured previously, were never interpreted as caused by long-term progressive damage, but rather by high stress or some other cause – never connected to time. Only after the collapse of the Civic Tower in Pavia, and the following experimental research, was the phenomenon of continuous damage due to heavy loads taken into account (Chapter 1). The importance of persistent loads in the damage of historic masonry has been studied experimentally and their effects on the mechanical properties of the material have been shown. Constant load step (pseudo-creep) tests turned out to be a suitable procedure for analysing creep behaviour, having the advantage of being carried out more easily than long-term tests. Primary, secondary and tertiary creep phases have been clearly observed, together with their relationship with the stress level, a damage development being associated with an increase in the stress level. Considering the last load step for each specimen tested with pseudo-creep tests, the secondary creep rate, which is the strain rate during the phase of stable damage growth, has been calculated before collapse and then related to the duration of the last load step, which can be regarded as the residual life of the material. A strong correlation exists between creep time to failure and secondary creep rate which, accordingly, can be used as a reliable parameter to predict the residual life of a material element subjected to a given sustained stress. In view of preserving the historical heritage, it would be useful to define similar relationships to evaluate, for instance, the results of a monitoring campaign on a massive historic building subjected to persistent load, to judge whether the creep rate indicates a critical condition in terms of safety assessment. Of course, the precocious recognition of a critical state will allow one to design a strengthening intervention to prevent total or partial failure of the construction.

226

LEARNING FROM FAILURE

The action of cyclic and persistent loads has proved to cause severe damage to the mechanical properties of ancient masonry. The fatigue life of masonry under uni-axial cyclic compression was also related to the secondary creep strain rate, which is the strain rate during the phase of stable cyclic damage growth (Chapter 2). Concerning the possibility of carrying out creep tests in the long-term, it can be concluded that creep tests on ancient masonry prisms should be performed by applying the load in successive steps, at a given time interval, starting from a low stress level. In this way, a thorough description of the viscous behaviour of the material can be obtained. Creep tests in which the load is applied in a single step are inadequate in the case of ancient masonry due to the high scatter in the mechanical properties and to the small number of specimens usually available. The time period between successive load steps should be sufficiently long to extinguish primary creep. In fact, the evolution of different stress levels of the strain rate associated with secondary creep can only be evaluated in such a way. From the results obtained on regular masonry prisms tested, a minimum time period under sustained loading of 70 to 80 days should be adopted (Chapter 3). Finally, it should be stressed that secondary creep was found to initiate at 60 to 70% of the compressive strength. In the case of soft-stone masonry the secondary creep can initiate even at 40% of their compressive strength (Chapter 5). Much more complicated is the modelling of the phenomenon, even if the approach by fracture mechanics is suggested by some authors. Authors such as N. Shrive et al. suggest that the step-by-step in time analysis is a powerful tool to investigate the change of stresses due to creep over a large time range. Stresses in a material can rise and fall due to the effects of creep (or fall and then rise). Although the effective modulus method using the final creep coefficient can accurately estimate the final stresses in the components of a composite material (e.g. masonry) due to creep, the method may not predict intermediate peak stresses accurately: one needs to know when they will occur (Chapter 4). The numerical model developed by E. Papa and A. Taliercio to analyzse damage effects induced by heavy persistent loads in existing masonry buildings is to be considered as an effective tool to assess the safety of these structures. Both the predicted time to failure of Pavia Civic Tower and the predicted crack pattern in the bell-tower of Monza Cathedral were found to match experimental evidences fairly well. In particular, the predicted failure mechanisms for the analyzsed structures may give indications regarding the effectiveness of possible strengthening techniques. On the accuracy of the finite element (FE) model, there is a point that will have to be tackled in future researches, regarding the mesh-sensitivity of the numerical solution. It is well known that, in the presence of a strain-softening constitutive law, strains localize in narrower bands as the FE mesh is refined. A ‘non-local’ version of the presented damage model will be formulated, according to proposals of other researchers, to overcome this limitation of the present model and make numerical predictions unaffected by the mesh size. Other problems that will be tackled in the continuation of the research to improve the numerical model are (1) the distinction between ‘cracks’ activated in tension or compression and (2) the so-called ‘unilateral’ effect (see Chapter 7).


227

A probabilistic model has also been applied by E. Garavaglia, A. Anzani and L. Binda to the study of the long-term behaviour of masonry specimens subjected in laboratory to creep and pseudo-creep. The chosen model seems to appropriately interpret the experimental results also capturing the passage between visco-elastic and visco-plastic behaviour. An attempt at applying the procedure to the results of long-term monitoring of displacements, particularly of crack opening, was carried out. The research will continue with the aim of providing a tool for preventing masonry failure under particular states of stress (Chapter 9). One of the most difficult tasks is to understand when the damaged structure can reach such a level of risk so that a deep investigation or intervention is needed. An accurate visual survey based on experimental and analytical experience has been shown to give important information on the state of damage of massive buildings like towers. Typical major or diffused cracks were shown to be capable of giving preliminary information on the state of damage of these buildings. The collapse of a badly damaged structure happens generally very rapidly, but it may be avoided if the damage symptoms such as cracks, deformations, etc. are carefully taken into account as early as possible. To this purpose the following procedure is suggested as a preliminary investigation which public institutions may adopt: • • • • •

Geometrical survey and preparation of drawings of the building using simple tools like photography and the subsequent restitution by software for image elaboration; Representation of the crack pattern visually detected over the geometrical restitution; measure of the wall thickness. Interpretation of the crack pattern and recognition of its causes: tilting, effect of dead load, etc.; Rough calculation, based on geometrical data, density of the material and the assumption of homogeneous and elastic material, of the maximum stress value; Rough calculation of the critical load value under the same hypothesis.

These preliminary results can indicate the possible need for a more detailed investigation and/or for periodically repeated surveys. In this case an exhaustive investigation on site and in laboratory as the one described in Chapter 1 should be carried out, after which a decision can be made as to start a monitoring of the structure (Chapter 6), or in case of short-term risk, to provide an intervention design. In case of monitoring, the measurements obtained (crack openings, displacements, accelerations etc.) will include all the effects caused by static, cyclic, dynamic loads, soil settlements, etc. bundled into a single response; interpreting the results requires the mixed responses to be broken down into cyclic and reversible processes and monotonic (or cumulative) ones. A further step consists of breaking measurements down into the components associated with different effects acting on the structure (wind, temperature, earthquakes, traffic, etc.). The latter specifically requires monitoring of the actions themselves by means of appropriate equipment (thermometers, hygrometers, anemometers, seismometers etc.).

228


The techniques to be applied in the case of long-term or fatigue damages are well described in Chapter 8. No heavy interventions are needed; the aim is to confine the dilation of the masonry; therefore steel tie rods at different heights can tackle instability of the walls. Bed joint reinforcements in the most damaged areas have high potential in preserving those parts from collapse. The technique is pretty easy to be applied on site and does not require special skill or special tools and it is not so far destructive. The proper selection of strengthening materials is a crucial point of intervention. The research on long- term behaviour of masonry structures will still continue, particularly on the experimental and modelling procedures. Nevertheless, it is worthwhile to inform the professionals and Cultural Heritage curators of a phenomenon which can affect in a serious way, and particularly in seismic areas, the life of our massive structures.

...for scientists by scientists

Structural Studies, Repairs and Maintenance of Heritage Architecture X Edited by: C.A. BREBBIA, Wessex Institute of Technology, UK The importance of architectural heritage for the historical identity of a region, town or nation is now widely recognized throughout the world. In order to take care of our heritage we need to look beyond borders and continents to benefit from the experience of others and to gain a better understanding of our cultural background. Featuring contributions from the Tenth International Conference on Structural Studies, Repairs and Maintenance of Heritage Architecture, this book covers a broad spectrum of topics including: Heritage Architecture and Historical Aspects; Regional Architecture; Structural Issues; Seismic Vulnerability Analysis of Historic Sites; Maintenance; Seismic Behaviour and Vibrations; Surveying and Monitoring; Material Characterization; Material Problems; Protection and Prevention; Simulation Modeling; Environmental Damage; Assessment and Retrofitting; Preservation and Prevention; Historical Dockyards, Shipyards and Buildings; Underwater Heritage; Surveying Techniques; Rivers, Lakes, and Canals Heritage; Site Protection, Oral Traditions and Stories. WIT Transactions on The Built Environment, Vol 95 ISBN: 978-1-84564-085-9 2007 736pp

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The Great Structures in Architecture From Antiquity to Baroque F.P. ESCRIG, Universidad de Sevilla, Spain Starting in antiquity and finishing in the Baroque, this book provides a complete analysis of significant works of architecture from a structural viewpoint. A distinguished architect and academic, the author’s highly illustrated exploration will allow readers to better understand the monuments, get closer to them and to explore whether they should be conserved or modified. Contents: Stones Resting on Empty Space; The Invention of the Dome; The Hanging Dome; The Ribbed Dome; A Planified Revenge – Under the Shadow of Brunelleschi; The Century of the Great Architects; The Omnipresent Sinan; Even Further; Scenographical Architecture of the 18th Century; The Virtual Architecture of the Renaissance and the Baroque. Series: Advances in Architecture, Vol 22 ISBN: 1-84564-039-X 2006

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The Revival of Dresden Edited by: W. JÄGER, Technical University of Dresden, Germany and C.A. BREBBIA, Wessex Institute of Technology, UK In 1945 the ancient City of Dresden was destroyed by massive bombardments and much of its rich architectural heritage appeared to have been obliterated forever. Over the last half-century, however, Dresden has been lovingly reconstructed with the active collaboration of its citizens. This process, now culminating in the rebuilding of the Frauenkirche (the Church of Our Lady) is documented in this unique book. Partial Contents: THE REVIVAL OF THE CITY: The Contribution of Preservationists to the Reconstruction of the Semper Opera House; Restoration of the Castle in Dresden; The Reconstruction of Taschenberg Palace; The Conservation of the Neustadt District as Part of the Cultural Cityscape. THE FRAUENKIRCHE: The Citizens’ Initiative to Promote the Rebuilding; A Construction of Stone and Iron – Structural Concept for Reconstruction of the Dresden Frauenkirche; Structural Proof-Checking Using a Complete 3D FE-Model. Series: Advances in Architecture, Vol 7 ISBN: 1-85312-787-6 2000 272pp

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Environmental Deterioration of Materials Edited by: A. MONCMANOVA, Slovak Technical University, Slovakia This book deals with the fundamental principles underlying the environmental degradation of widely used and economically important construction materials. The invited contributions cover aspects such as the deterioration mechanisms of materials and metal corrosion, environmental pollutants, micro- and macro-climatic factors affecting degradation, the economic impact of damaging processes, and fundamental protection techniques for buildings, industrial and agricultural facilities, monuments, and culturally important objects. Basic details of ISO standards relating to the classification of atmospheric corrosivity and low corrosivity of indoor atmospheres are also included. Designed for use by materials, corrosion, civil and environmental engineers, designers, architects and restoration staff, this book will also be a useful tool for managers from different industrial sectors and auditors of environmental management systems. It will also be a suitable complementary course book for university students in all of the above disciplines. Series: Advances in Architecture, Vol 21 ISBN: 978-1-84564-032-3

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The Conservation and Structural Restoration of Architectural Heritage G. CROCI, University of Rome ‘La Sapienza’, Italy “The book should be seen and known about by all engineers and architects who are developing their work in the field.” THE STRUCTURAL ENGINEER “...instructive and fascinating.... The excitement and challenges of preserving and stabilizing historic buildings is captured by this very readable book.” JOURNAL OF ARCHITECTURAL CONSERVATION Designed for use by all professionals involved or interested in the preservation of monuments, the purpose of this book is to contribute to the development of new approaches in the area. Many of the examples examined, including the Colosseum, the Tower of Pisa and the Pyramid of Chephren, are the result of work carried out during Giorgio Croci’s distinguished career. Featuring numerous black and white photographs and illustrations by the author, the text is divided into two main sections entitled The Scientific Approach to the Study of Architectural Heritage and Structural Analysis of Masonry Buildings. Series: Advances in Architecture, Vol 1 ISBN: 1-85312-482-6 1998 272pp

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Structures Under Shock and Impact IX Edited by: N. JONES, The University of Liverpool, UK and C.A. BREBBIA, Wessex Institute of Technology, UK This book contains the papers presented at the Ninth International Conference on Structures Under Shock and Impact. The shock and impact behaviour of structures is a challenging area, not only because of the obvious time-dependent aspects, but also because of the difficulties in specifying the external dynamic loading characteristics for structural designs and hazard assessments and in obtaining the dynamic properties of materials. Thus, it is important to recognise and utilise fully the contributions and understanding emerging from theoretical, numerical and experimental studies on structures, as well as investigations into the material properties under dynamic loading conditions. Featured topics include: Impact and Blast Loading Characteristics; Material Response to High Rate Loading; Missile Penetration and Explosion; Protection of Structures from Blast Tools; Behaviour of Structural Concrete; Structural Behaviour of Composites; Interaction between Computational and Experimental Results; Energy Absorbing Issues; Structural Crashworthiness; Structural Serviceability Under Impact Loading; Seismic Engineering Applications. WIT Transactions on The Built Environment, Vol 87 ISBN: 1-84564-175-2 2006

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Computational Mechanics for Heritage Structures B. LEFTHERIS, Technical University of Crete, Greece, M.E. STAVROULAKI, Technical University of Crete, Greece, A.C. SAPOUNAKI, Greece and G.E. STAVROULAKIS, University of Ioannina, Greece This book deals with applications of advanced computational-mechanics techniques for structural analysis, strength rehabilitation and aseismic design of monuments, historical buildings and related structures. The authors have extensive experience working with complicated structural analysis problems in civil and mechanical engineering in Europe and North America and have worked together with architects, archaeologists and students of engineering. The book is divided into five chapters under the following headings: Architectural Form and Structural System; Static and Dynamic Analysis; Computational Techniques; Case Studies of Selected Heritage Structures; Restoration Modeling and Analysis. Series: High Performance Structures and Materials, Vol 9 ISBN: 1-84564-034-9 2006

288pp+CD-ROM

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