EARTHQUAKE GEOTECHNICAL ENGINEERING VOLUME 3
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PROCEEDINGS OF THE SECOND INTERNATIONAL CONFERENCE ON EARTHQUAKE JUNE 1999 GEOTECHNICALENGINEERING/LISBOA/PORTUGAL/21-25
Edited by
Pedro S. Sec0 e Pinto Portuguese Societyfor Ge'otechnique(SPG),Lisboa, Portugal National Laboratory of Civil Engineering (LNEC),Lisboa, Portugal
VOLUME 3 Keynote lecture I Theme lectures1General reports1PanelistS contributions
U
A.A. BALKEMA./ROTTERDA.M/BROOKFIELDI1999
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0 1999 A.A.Balkema, Rotterdam Printed in the Netherlands
Earthquake Geotechnical Engineering,S6co e Pinto (ed.)0 1999Balkema, Rotterdam, ISBN 90 5809 1 163
Table of contents
Keynote lecture Performances of storage tanks during the 1995 Kobe earthquake K.Ishihara & K. Furukawazono
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Dynamic characterizationof soils: - Theme lecture - General report - Panelist’s contributions Dynamic soil properties: Laboratory, field and correlation studies K. H. Stokoe, II, M,B,Darendeli, R. D.Andrus & L.I:Brown
811
On the dynamic characterizationof soils J. D. Bray, M. I;:Riemer & W B. Gookin
847
Visualization of soil behavior from dynamic centrifuge model tests B. L. Kutter & A. Balakrishnun
857
Dynamic characterisation of soils from laboratory tests
863
M.Maugeri & A. Cavallaro Soil characterization by shear wave velocity
869
M.Hatanaka Strong motions and site ampljjication: Theme lecture - Panelist’s contributions -
Strong ground motions and site amplification A.M.Ansal
879
Modeling of liquefaction-induced shear deformation A. Elgamal, Z Yang, E. Parra & R. Dobry
895
Site effects: Recent considerations and design provisions K. D. Pitilakis, D. G Raptakis & K.A. Makru
90 1
Effect of nonlinear soil properties on seismic amplification in surface layers Kokusho
913
Site amplification J. L.Just0 & R. Carrasco
919
Soil-structure interaction and retaining structures: Theme lecture - General report - Panelist’s contributions -
Soil-structureinteraction studies through shalung table tests S.Iai & TSugano
927
Soil-structureinteraction and retaining structures G. Gazetas
941
Dynamic soil-structureinteraction of adjacent structures SA.Savidis & R. Hirschauer
943
Seismic soil-structure interaction of rigid and flexible retaining walls R. S. Steedman
949
Performance of pile foundations in laterally spreading soils K.Tokimatsu
957
Seismic soil-pile-structureinteraction in soft clay CJ.Curras, R.WBoulanger,B. L. Kutter & D.WWilson
965
Underground and buried systems: Theme lecture - General report - Panelist’s contributions -
Responses of large-diameterburied pipes to earthquakes J. I? Bardet & CA.Davis
973
Underground and buried structures h? Yoshida
987
Dynamic analysis of tunnel-shaft-soil systems using FEM and ANN
993
M.R Romo, S. R.Garcia & J. Merlos Design and technologies for improvement of tunnels in seismic areas
999
h? h?Fotieva Super-dense real-time disaster mitigation system Y Shimizu, K. Koganemaru, ? Nakuyama I? & S.Yasuda
VI
1005
Liquefaction - General report - Panelist’s contributions Liquefaction and deformation of silty and fine-grained soils T.L.Youd & S. D.Gilstrap
1013
Estimation of minimum undrained shear strength for flow liquefaction using the CPT
1021
I?K. Robertson Constitutive modeling of cyclic mobility and implications for site response S,L. Kramer & l? Arduino
1029
Soil liquefaction in Peru J. E.Alva-Hurtado
1035
Slopes and embankments Theme lecture - General report - Panelist’s contributions
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Effect of subsurface liquefaction on stability of embankment resting upon surface I. Towhata & T.Mizutani
1045
Slopes and embankments R S. Stco e Pinto
1059
Assessment of residual strength for embankments R M. Byrne & M. H. Beaty
1069
Seismic slope stability - The critical acceleration S. K. Sarma
1077
A review of experimental studies of seismic behavior of reinforced soil structures N. Sitar & L. Nova-Roessig
1083
Codes, standards and safety evaluation Theme lecture - General report - Panelist’s contributions -
Codes, standards and seismic safety evaluation of earth structures U!D. L. Finn
1091
Session: Codes, standards and safety evaluation A. Pecker
1107
Recent advances in US codes and policy with regard to seismic geotechnics R.B. Seed & R. E. S. Moss
1111
Seismic design codes for liquefaction in Asia S.Yasuda
1117
VI I
Geotechnicalearthquake engineering design practice in New Zealand M.J. Pender
1123
Codes and standards for Europe VCue'llar
1129
Author index
1135
Vlll
Keynote lecture
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Earthquake Geotechnical Engineering,SBco e Pinto (ed.) 0 1999 Balkema, Rotterdam, ISBN 90 5809 1 163
Performances of storage tanks during the 1995 Kobe earthquake Kenji Ishihara & Kenro Furukawazono Department of Civil Engineering, Science University of Tokyo,Japan
SYNOPSIS: Following the 1995 earthquake in Kobe district, survey was conducted on the tilt of oil storage tanks in the severely shaken area. The survey consisted in measuring elevations of several points along the periphery of each tank. Some parameters indicative of levels of soundness or risk for continued operation were defined to properly analyze the vast amount of available data. Thus, the parameter “overall tilt” and “local tilt” were considered most appropriate to reflect the level of damage due to liquefaction of the ground. Features of the tanks in each farm regarding the size, scale and amount of oil contained at the time of the earthquake were introduced and summary of the damage to the tanks is presented in term of the above parameters for each group of tanks classified according to the scale and the kind of seismic regulation used in the design. Brief description is given concerning the soil conditions in the severely shaken areas and rough correlations are introduced between the extent of damage and the thickness of at-depth soil deposits likely to have developed liquefaction at the time of the earthquake. SEISMIC DESIGN OF STORAGE TANKS IN JAPAN
INTRODUCTION At the time of the January 17, 1995 earthquake in Kobe, Japan, liquefaction developed extensively in the man-made deposits which were reclaimed with gravel-containing silty sands. In several islands consisting of such deposits there were many farms for oil storage tanks where deleterious effects of liquefaction were noted for safe operation of the tanks. Fortunately, no fire broke out in any of the oil tanks though there were many injuries such as elephant-shoe buckling and tilting of the tanks due to liquefaction of the ground. Inasmuch as the earthquake occurred on Monday following the New Year’s period, oil had been consumed exhaustively for domestic use leaving relatively a small amount of reserve in the tanks. Hence, the majority of the oil tanks contained oil at a level less than half of the full capacity and this is deemed as one of the reasons for not having had fire breakout. The other types of damage to the oil tanks were striking, however, including the injury to tank body, the concrete-made mounds, pipelines, and appurtenances for the tank facilities. Following the earthquake, detailed investigations were conducted on these injuries, but most systematic was the survey made for identifying tilting of tanks. The results of such survey will be introduced in the following pages of this paper.
During the period of 1960 - 1980, there has been a remarkable growth in the energy and chemical industries in Japan and a number of tanks for storage of oil, LPG and chemical materials have been constructed on alluvial and reclaimed deposits in the lowland areas particularly near the sea. Since ground conditions are generally poor in these areas, it has been recognized of prime importance to pay due attention to the risk of damage to these tanks during large earthquakes in future. Overall regulation was put into effect in 1959 by Fire Department of the Japanese Government regarding design and construction of large tanks having a storage capacity greater than 1OOOkl. Of particular importance was the consideration of seismic effects on the safe operation of the tanks. Some guidelines were put forward in this regulation regarding the seismic design of tank body. This regulation was modified and revised into the new regulation in 1977. The regulation which was effective prior to 1977 is referred to as the old regulation. Upon experiencing liquefaction-induced damage during the major earthquakes in 1960’s and 1970’s, the importance of considering effects of liquefaction was recognized and some items related with it were incorporated in the revised new version of the design regulation in 1977.
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- for the ground in the periphery of tanks for the ground in the center of tanks
2 $
15
5
o_
Q
T 01 0
I
I
5
10
I
I
I
I
11
15
20
25
30
35
Fines content (%)
Fig. 1 Chart for identifying soils with liquefaction susceptibility stipulated in the regulation on hazardous materials (Fire Department, 1978)
In this new regulation, it was stipulated that the ground conditions be diagnosed to identify whether or not a sandy deposit in question is liable to liquefaction in future earthquakes. This diagnosis was stipulated to be made by way of a simple chart shown in Fig. 1 where the threshold SPT N-value differentiating between liquefaction and non-liquefaction is indicated as a function of fines content of the sandy deposit under consideration. It was assumed tacitly that the rule of identification as indicated in Fig. 1 is applicable for the intensity of seismic shaking which is similar to that experienced in Niigata at the time of the 1969 earthquake, namely, for the level of the horizontal ground acceleration of the order of 200 to 250 gals. It is to be noticed that both the old and new seismic design regulations were stipulated to be applicable for large-scale tanks having a storage capacity in excess of 1000M. Therefore, small scale tanks with a lesser amount of storage capacity have been left out of restriction by any regulation. The large tanks to be designed under any regulation as above are referred to as “specified tank”, whereas those not subject to any regulation is called “unspecified tank”. Thus, the large-scale tanks with a storage capacity greater than lOOOkl is called “specified tank” and those with lesser capacity are referred to as “unspecified tank” in the following. TYPES OF SEmLEMENTS AND DEFINITIONS Oil storage tanks made of steel plates are generally placed on the flattened surface of gravely soil fills. Since the steel-made bottom plate is deformable under the weight of oil, the load is deemed to be distributed uniformly over the entire area of the bottom plate. If
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Fig. 2 Types of settlements of tanks the underlying soil deposit develops uneven settlements, the tank body is deformed accordingly and this is deemed as sources of breakage and sometimes leakage of oil. The settlements of the oil storage tank may be classified into three types as illustrated in Fig. 2. If the settlement is uniform, there would be no problem for maintaining integrity of the tank body itself. If the settlement is combined with a uniform tdt as illustrated in Fig. 2(b), some degree of inconvenience would be encountered in the annexed structure and pipeline system attached to the tank. Non-uniform tilt as illustrated in Fig. 2(c) would involve local deflection of the steel plate and if it becomes large enough in excess of an allowable limit, partial breakage of the tank body will take place. In order to assess the level of soundness, it is a usual practice to monitor the elevation of the tank along its periphery at various stages of the tank operation including the check-up tests at the completion of construction, initial water-filling tests, and periodical tests conducted at a certain interval of time. If the tank is inclined with a uniform tilt, the elevation measured at points along the periphery can be expressed in terms of cosine function as follows,
Fig. 3 Representation of uniform tilt Fig. 4 y - y a = (&= -6,,)COS(-X)
71:
D
....**
Representation of non-uniform tilt and definition of local tilt
(1) deviatric portion that is associated with distortion and hence the damage of the tank body. There would be several methods of approach for assessing the level of injury to the tank based on the data as arranged in Fig. 4(c). In evaluating the integrity of a tank, it has been customary to determine what may be called “overall tilt”. This is defined as the difference between the maximum, am,, and minimum elevation, 6min, divided by the diameter, D, of the tank,
As illustrated in Fig. 2, 6,, and 6 ,” denote maximum and minimum settlements, respectively, and D is the diameter of a tank. y, denotes the elevation at the point of the minimum settlement and y is the elevation at any point along the periphery of the tank. The coordinate x is measured around the tank starting from its origin which is fixed at a point of the maximum elevation. If the relation of Eq.(l) is displayed in a diagram, it is represented by a cosine curve as shown in Fig. 3(b). When the tank body is deformed as a result of nonuniform tilt, measured elevations along the tank periphery may be plotted versus the distance, x, from a datum point, as schematically illustrated in Fig. 4(b). It is to be noted that the points indicating the elevations plotted in the diagram do deviate from the cosine curve of Eq. (1) representing the uniform tilt. To examine features of the non-uniform settlement, it would be preferable to read off the deviation of the measured elevation from that corresponding to the uniform tilt. Such deviatric portion of the elevation may be plotted versus the distance, x, as schematically illustrated in Fig. 4(c). It is this
According to the stipulation by the Japanese Government, the overall tilt of a tank needs to be less than 1% at any stage of operation during the life span of a tank. This limit is not a value derived from any rational background data, but a conservative value based on empiricism for safe operation of a tank. An other factor which might be related with the injury to the tank body would be the gradient of the settlement difference between two successive measuring points as indicated in Fig. 4(c). For a tank in question, the spacing between two nighbouring points of 797
Fig. 5 Processing of settlement data for a tank. 798
elevations are replotted in Fig. 5(b). Superimposed in Fig. 5(b) is the plot of values for the case of the uniform tilt which are calculated via Eq. (1) using 6 = 43.8cm. It is to be noticed that the theoretical curve in Fig. 5(b) was constructed so that it passes through the point 15, and for this reason overall coincidence does not appear good between the measured values and those corresponding to the uniform tilt as calculated by Eq. (1). Then, an attempt was made to shift the theoretical curve rightwards so that the best degree of coincidence is achieved. The curve thus shifted is shown in Fig. 5(c), together with the plot of the measured values. In this adjustment, the theoretical curve was shifted. so that it coincided with the measured values at point 16 and 8, as indicated in Fig. 5(c). After making the above adjustment, the difference between the measured and theoretical values was obtained at each point of the elevation measurement. The differential settlement thus obtained is displayed in Fig. 5(d). In this diagram, the maximum value of the local tilt is calculated as 0.39% as accordingly indicated in the figure. Thus, for the tank 66 studied, the overall tilt was 2.51% with the local tilt amounting to 0.39%. More exact account on the design and damage feature of t h s tank will be described in the later section.
measurement is generally set at an equal interval. Therefore, the maximum value of the settlement difference at any two neighbouring points divided by the corresponding peripherical distance may be taken as a measure of local distortion of the tank body. This value will be referred to as the “local tilt” and denoted by AS,. ARRANGEMENTS OF MEASURED DATA Actual data of elevation survey are somewhat complicated and even erratic. Thus, some additional procedures are required in the data processing in order to single out values of the local tilt, AS,. This process will be explained by referring to actually measured data shown in Fig. 5(a). This example is quoted from the elevation survey performed on a 17.43m in-diameter tank No. 66 in Wagehama Island, Kobe, which was severely affected by the earthquake in 1995. Location of this island is show in Fig. 6 and the exact location of the tank is shown in Fig. 7. It is seen in Fig. 5(a) that the tank had tilted southwards with the maximum differential settlement of 6 , - 6,,=S =43.8cm. Thus the overall tilt is calculated as 6/D=2.5 1% as indicated in the figure. By choosing the point 15 on the southeast side as a datum point, all measured
Fig 6. Locations of the major tank farms in the severely shaken area 799
Fig. 7 Layout of the tanks at MC-site
GENERAL FEATURES OF TANK DAMAGE IN KOBE AREA
varies widely with its maximum of 32m at one particular tank. Generally, the tanks are flat in shape with the height smaller than the diameter. For smaller tanks pertaining to the unspecified type with a storage capacity less than 1000k1, it may be seen in Fig. 8 that the tanks are slender with the heightto-diameter ratio greater than 1.O. The conditions of oil storage tanks at MC-site at the time of the earthquake are demonstrated in Fig. 9 in which the height of oil filling, h, is plotted versus the diameter of the tanks. It may be seen that for the large-capacity tanks, the majority was less than onequarter filled, whereas about half of the smallercapacity tanks were filled to a level greater than half of the height. From records of the survey over all the tanks at MC-site, the overall tilt AS was evaluated and plotted in Fig. 10 versus the height-to-diameter ratio of the tanks. It may be seen that there is no tendency for the overall tilt either to increase or decrease with change in the height-to-diameter ratio, but as many as half of the tanks had developed the overall tilt in excess of 1%.
In the coastal area of Kobe, there are a number of tank farms constructed on reclaimed or alluvial sandy deposits. A majority of these farms suffered liquefaction at the time of the 1995 earthquake resulting in more or less damage to tanks constructed on such deposits. The sites of major tank farms in the severely shaken area are indicated in Fig. 6.
Tanks at MC-site The layout of the oil tanks at MC-site is shown in Fig. 7. In this farm, about half,of the tanks were of the specified type with a storage capacity greater than 1000k1, but most of them were constructed before 1977 in accordance with the old regulation. The dimension of each tank is shown in Fig. 8 in terms of the height H plotted versus the diameter D of the tanks. It may be seen that the height of these relatively large tanks is 13m - 17m, but the diameter 800
Tanks at S-site In the tank farm at S-site, practically all the tanks were constructed in the period between 1954 and 1973 and hence designed based on the old regulation. The layout of the tanks in this farm is shown in Fig. 11. The tanks in this premise have a height which is more or less equal to the diameter as shown in Fig. 12. However, for the small-tanks with a storage capacity less than IOOOM, the height is larger than the diameter. Regarding storage conditions at the time of the earthquake, Fig. 13 shows that in a majority of tanks, the amount of oil was less than half of their capacity. The lesser amount of oil storage is considered due to the fact that the earthquake took place in the early period of New Year, January 17, 1995, when domestic consumption of energy had been exhaustive in the New Year period. The feature of the settlements in the tanks is demonstrated in Fig. 14 in terms of the overall tilt plotted versus the height-to-diameter ratio where it may be seen that the overall tilt is generally less than 1% for the large specified tanks. For the unspecified small-scale tanks the overall tilt is shown in Fig. 14 to be generally in excess of 1%. These small tanks were constructed directly on the man-made fills without improvement of underlying loose deposits of sandy soils.
Fig.8 Height and diameter of the tanks at MC-site
Fig.9 Height of oil storage at the time of the 1995 quake plotted versus the diameter of the tanks at MC-site
Fig. 10 Overall tilt versus the height-to-diameter ratio of the tanks at MC-site Fig. 11 Layout of the tanks at S-site
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tilt of individual tanks is plotted versus the heightto-diameter ratio. Practically all the tanks developed tilting in excess of 1% With the maximum reaching a the tilt Of the value as large as 20%. slender tanks in this lot were visible from far away after the earthquake.
Tanks at G-site At G-site located west of &be city district(Fig.6), the tilting of rather slender tanks was striking because of poor soil conditions in this farm. The layout of various tanks is shown in Fig. 15. The dimensions of the tanks in this premise is shown in Fig. 16 in terms of the height plotted versus the diameter of the tanks. It may be seen that the majority of the tanks have a height which is about 1.5 times larger than the diameter. All the tanks are used not for oil but for storage of various kinds of chemicals for industrial use. Since the tanks have an equivalent storage capacity less than 1000k1, they are classified as being of unspecified type and hence were not designed based on any design code.
Fig. 14 Overall tilt versus the height-to-diameter ratio of the tanks at S-site
Fig.12 Height and diameter of the tanks at S-site
Fig.13 Height of oil storage at the time of the 1995 quake plotted versus the diameter of the tanks at S-site At the time of the earthquake, the tanks in this premise had a storage of chemical materials to varying levels as indicated in Fig. 17. The level of the damage may be seen in Fig. 18 where the overall
Fig.15 Layout of the tanks at G-site 802
EXAMPLES OF TANK DAMAGE Since the damage were investigated more thoroughly for the tanks in Mikage-hama Island, somewhat detailed account will be given for the feature of the damage there. Detailed arrangements of the tank group at MC-site in the island of Mikagehamaare shown in Fig. 7. In this premise, the triangular section in the southeast is the lot where storage tanks with liquefied propane gas (LPG) are installed for which detailed account is given elsewhere (Ishihara, 1979). The remaining part of the premise in the northwest is occupied by steel-made oil-storage tanks of various sizes. Fig. 16 Height and diameter of the tanks at G-site
Fig.17 Height of storage of chemical at the time of the 1995 quake plotted versus the diameter of the tanks at G-site
Fig. 19 Feature of overall tilt of the tanks at MC-site The group of tanks installed in the premise of MC-site have suffered more or less damage resulting mainly from the differential settlements due to liquefaction of the reclaimed fills in the Mikagehama Island. The feature of the tilt in each tank is demonstrated in Fig. 19 in terms of vectors oriented towards the direction of tilting. The length of the vectors indicates the amount of tilt. It may be seen in Fig. 19 that the tilt is almost randomly directed PhCUlarlY for the tanks inland, but oriented by and large towards the waterfront
Fig. 18 Overall tilt versus the height-to-diameter ratio of the tanks at G-site
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Fig. 20 Side and plan view of the 3000kl tank 66 at MC-site for the tanks located close to the quaywall. There are two pile-supported tanks, denoted by 71 and 72, in the northwest corner which had been designed by the new regulation authorized in 1977. These tanks suffered some damage to the footing-pile connection accompanied by the overall tilt of 0.5 and 0.4%. All other tanks rest on the mound about 50cm high enclosed by reinforced concrete ring. The gravelly sand was filled inside the ring and compacted as dense as possible to provide a sound base for the flat bottom of the tank. In some, of the large-capacity tanks, the gravel-containing man-made fill deposits underneath the mound were compacted by means of the vibroflotation technique, but in a majority of small tanks, the soil deposits underneath the mound were left uncompacted and intact. There are two tanks TA65 and TA66 with a storage capacity of 3000kl located 30m from the quaywall in the southwest corner as shown in Figs.7 and 19. The
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details of the damage will be described below for these tanks. They were constructed in 1967 and basically the same in design as that shown in Fig. 20. The soil deposits were compacted by means of the vibroflotation to a depth of 6m. The diameter of the sand piles was 23cm and the spacing was 1.2m as accordingly indicated in Fig. 20. As shown in the figure, the tanks of roof-type were 13.66m high and 17.63m in diameter. Compacted sand fill was lad inside the concrete ring and asphalt motor 50mm thick was put on top of it to provide a sound base for the bottom plate of the tank. It is to be noted that the stabilization by the sand pile extends 2.5m outward from the side of the tank. At the time qf the earthquake, the tank 65 contained oil to a height of only 1.83111 and there was no oil in the tank 66. The tank 65 sustained a uniform tilt of 0.55% which is well below the allowable limit of 1% stipulated by the Japanese Government. The tank 66 suffered a
uniform tilt as much as 2.5% which is in excess of the allowable limit. Thus, somewhat detailed account will be given below for the damage feature of the tank 66. A set of figures showing the settlement characteristics of the tank 66 were demonstrated already in Fig. 5 where a local tilt of 0.39% is noted between the measuring points 15 and 16. In fact, a cave about 30cm deep was observed at this location following the earthquake under the concrete ring as illustrated in Fig. 21. Minor cracks were observed having developed in the concrete ring at the portion of the caving. The concrete ring tilted slightly as a whole towards the waterfront. It is highly likely that, as compared to the largely displaced soil deposit beneath the tank, the tank body was unable to move equally to catch up and left somewhat behind, and consequently a large tension crack about 5m long developed along the toe of the circular mound as shown in Fig. 21(a). This tension crack was left in a form of a long caving as illustrated in Fig. 2 1.
Fig. 22 Soil Profile near the tank 66 at MC-site
Fig. 21 Partial caving in the, south portion on the Tank 66 at MC-site The soil condition at this site may be represented by the soil profile data shown in Fig. 22. The profile at Point G2 was obtained by boring at a Place Just south of the Tank 66(Fig.7). It may be seen that the SIT N-value for the reclaimed deposit shows values 805
Fig. 23 Settlements of outdoor tanks for different storage capacities ( 6 farms in Kobe area )
ranging from 10 to 15. Although the compaction was performed to a depth of 6m as described above, there is no discernible stiff layer in the soil profile in Fig. 22 corresponding to the compact portion near the surface. Thus, the point G2 is likely to be outside the compacted zone and represent as-deposited soil condition in the vicinity of the tank 66. The repair work for the tank 66 was conducted by removing the tank body and by adjusting the elevation of the concrete ring. The sandy gravel inside the ring was compacted and the surface was levelled off. The same tank body was placed on the smoothed surface. The tank 65 suffered practically no damage as envisioned by a small amount of overall tilt of 0.55%. There was no need for retrofit for this tank.
than 1.5% accompanied also by the local tilt less than 0.4%.
PERFORMANCES OF STORAGE TANKS IN GENERAL Following the earthquake, in-situ survey was conducted for all the tanks in the strongly shaken area to diagnose the integnty of each tank. The outcome of the survey of damage for various size ranges of the tank was compiled and expressed in terms of the overall tilt as defined above. For the specified tanks designed by the old regulation, Fig. 23 indicates that the number of tanks surveyed was 67. Out of these, 18 tanks showed the overall tilt in excess of 1%. For the small tanks less than lOOkl storage capacity, 68% of the tanks surveyed showed the overall tilt greater than 1%. It is to be noted in Fig. 23 that for the relatively large tanks with the capacity of 700 1000kl, as many as 94% of the tanks surveyed indicated the overall tilt which is greater than 1%. Reflecting on the fact that these tanks had not been designed liquefaction-resistant, needs were addressed for including this size range of tanks in the realm of the seismic design code if it is to be revised again in the future. Other aspects of the damage would be the local tilt as defined above. The surveyed data were Drocessed in the manner described above to obtain values of overall tilt and the local tilt. The data processed in this fashion are shown in Fig. 24 for the unspecified tanks with the storage capacity less than 10Cklkl. It may be seen that for this category of tanks constructed without specifically considering seismic effects, the uniform tilt as much as 2.7% indeed occurred with the AS,-value of 1.2%. The majority of data points is shown to fall in the range of 0.5 2.0% for the uniform tilt and in,the range of 0.1 - 1% for the local differential tilt. Similar data plotting is made in Fig. 25 for the specified tanks with the capacity greater than lOOOkl designed based on the old regulation which was effective until 1997. Also shown in Fig. 25 are the data pertaining to the specified tanks with the capacity greater than 1OOOkl constructed acting upon the new regulation. AU of these tanks shows a small amount of uniform tilt less 806
Fig.24 ~ o c a tilt l plotted versus the overall tilt for unspecified tanks in Kobe district
the Overall tilt for Fig*25 Local tilt plotted specified tanks in Kobe district
SOIL CONDITIONS RELATED WITH DAMAGE
In the majority of the tank farms, the ground consists of man-made deposits reclaimed by gravel-containing silt sands which were derived from weathered granite. The materials were obtained from mountain areas just north of Kobe city and transported to the site for filling. The reclamation work was conducted mainly in 1960 and tanks were constructed over the period of 1960 - 1980. The soil conditions in the reclaimed deposits in Kobe are represented by a typical example of soil profile shown in Fig. 26. This is the soil
profile at point No.2 at G-site in the west of Kobe (Fig. 15). It may be seen that there exists a deposit reclaimed by the disintegrated granite called “Masado” to a depth of 12m which is underlain by a silt deposit of marine origin. It is believed that the loose deposit of the reclaimed Masado did developed liquefaction at the time of the earthquake. Although not clear exactly, it may be assumed with reasons that the reclaimed deposit with NI-values less than 15 had developed liquefaction, where N, indicated the SPT N-value normalized to an overburden pressure of 1.O kgf/cm2. Entering in the soil profile in Fig. 26 with the above definition, one may assume that the thickness of unliquefied layer H I near the surface is H1=2.5m and the thickness of underlying liquefied layer is H2=9.5m for this particular soil profile.
indicated by solid circles. It may be seen in Fig. 27 that the tanks designed by the new regulation suffered only a small amount of overall tilt less than 0.2 % without any damage whatsoever. The small-scale tanks unspecified suffered relatively large overall tilt amounting to values of the order of 10%. These tanks were located mostly in the farm at G-site, where the thickness of the liquefied layer was as large as 1520m below the surface layer having a thickness of 23m.
Fig. 27 Overall tilt plotted versus the thickness underlying liquefied deposit
It is apparent that the observed values of the overall tilt 6/D of the tanks tends to increase with increasing thickness of the at-depth deposit which is likely to have developed liquefaction with SPT N,-values less than 15.
CONCLUSIVE REMARKS Fig. 26 Typical soil profile at G-site It is likely that the tanks resting on the reclaimed deposit with larger thickness of liquefied layer were more susceptible to damage than that on the deposit with smaller thickness of liquefied layer. In order to examine this feature, the over41 tilt 6/D surveyed after the earthquake was compiled and plotted in Fig. 27 versus the thickness H, of the liquefied deposit for each of the tanks surveyed. In this figure, the data on the specified tanks with more than lOOOkl capacity designed by the new and old regulations are indicated, respectively, by open circles and open rectangles. The data on the unspecified tanks having smaller sizes constructed without considering earthquake effects are 807
To evaluate the integrity of an oil tank for its safe operation, it has been customary to measure the elevation of the base along the periphery of the tank. The data obtained in this way for the tanks affected by the Kobe earthquake of 1995 was used to evaluate the overall tilt which is defined as the difference in elevation between its maximum and minimum points divided by the diameter of the tank. The definition as above was examined from a broader perspective and a new parameter called “local tilt” was introduced which may be related with the injury of the tank body. The procedure for evaluating these parameters on the diagrams were described by quoting an example of the damage of a tank. The features of the damage to many tanks at the time of the 1995 Kobe earthquake were introduced by compiling and processing the surveyed data in the
above manner. The outcome of such data processing showed that the local tilt tends to generally increase with increasing overall tilt for the tanks affected by the Kobe earthquake. The maximum value of the overall tilt observed was of the order of 2.5% and the maximum value of the local tilt was of the order of 1.0 %. ACKNOWLEDGMENTS The data presented here were offered by the Fire Department of the Japanese Government. The authors wish to acknowledge the cooperation of Chief Officer Mr. T. Yanagisawa. REFERENCES Fire Department, 1978, “Regulation on Hazardous Materials”. (in Japanese) Ishihara, K., 1977, “Geotechnical Aspects of the 1995 Kobe Earthquake”, ‘Terzaghi Oration”, Proc. of the International Conference on Soil Mechanics and Foundation Engineering, Hamburg, Vol. 4 Japanese Geotechnical Society, 1996, Report of the Hanshin-Awaji Earthquake, pp.253-257 (in Japanese) Sakemi, T., 1996, “Settlements of Oil Storage Tanks Caused by Liquefaction”,Proc. 31st Annual Convention of the Japanese Geotechnical Society, pp.1231 -1232 (in Japanese)
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Dynamic characterization of soils: - Theme lecture - General report - Panelist’s contributions
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Earthquake Geotechnical Engineering, Sec0 e Pinto (ed.) 0 1999Balkema, Rotterdam, ISBN 90 5809 1 163
Dynamic soil properties: Laboratory, field and correlation studies K. H. Stokoe, I1 & M. B. Darendeli University of Texas,Austin, Tex., USA
R.D.Andrus National Institute of Standards and Technology,Gaithersburg, Md., USA
L.T. Brown Geovision Geophysical Services, Corona, CaliJ:, USA
ABSTRACT: Laboratory and field studies of dynamic soil properties for geotechnical earthquake engineering analyses are presented. The dynamic properties are expressed in terms of shear wave velocity, V,, shear modulus, G, and material damping ratio, D. The effects of various parameters on these properties are studied in the laboratory using combined resonant column and torsional shear equipment. Intact specimens were tested over shearing strains, y, where the soil response ranged from linear (y < 0.001 %) to highly nonlinear (y > 0.1 %). The results are compared with generic nonlinear modulus and damping curves, and strong correlations with plasticity index and effective confining pressure are shown. Recent developments in correlating field measurements of V, with the liquefaction resistance of granular soils are presented. Field studies involving surface wave measurements to evaluate profiles of V, and small-strain material damping ratio are also discussed. Results from a study in which Vs profiles evaluated independently by downhole, surface wave, and suspension-logging tests are compared. the difference between traditional D - log y relationships (families of curves) and observed soil behavior, and 3. the importance of effective confining pressure on the nonlinear modulus and damping relationships. All of these issues can be quite important in evaluating dynamic site response, especially if generic degradation curves are used in place of site-specific measurements. The second section of the paper deals with recent studies involving the use of shear wave velocity to predict the liquefaction resistance of sands. Although there is another theme lecture dealing with liquefaction in this conference, this particular information is presented because it deals with a dynamic soil property; that is, the smallstrain shear wave velocity, V,, which is measured in the field Finally, the third section of the paper deals with field measurements of dynamic soil properties at small strains. In this case, advances and improvements in field seismic testing are presented. These include Spectral-Analysis-of-Surface-Waves (SASW) and suspension-logging techniques for Vs profiling and the use of SASW testing to estimate small-strain material damping, D ~ n .
1 INTRODUCTION The topic of this Theme Paper is dynamic soil properties. This topic has been studied extensively over the past 40 years. It is very broad, and the words “dynamic soil properties” have a multitude of meanings. A sense for the breadth of the topic can be obtained simply by reviewing recent proceedings such as Shibuya et al. (1994), Ebelhar et al. (1994), Ishihara (1995), and Dakoulas et al. (1 998) and recent textbooks such as Ishihara (1996) and Gamer (1996). In the context of this conference, the topic is narrowed to cover the dynamic response of soils to earthquake shaking in the free field. The properties of concern are the shear wave velocity, V,, shear modulus, G, and material damping ratio, D, over strains which range from low-amplitude shaking where soils respond linearly to high-amplitude shaking where nonlinear, degradable behavior is exhibited. The main text in this paper is divided into three sections. The first section deals with evaluation of dynamic soil properties in the laboratory using intact specimens. Key issues addressed herein are: 1. the importance of excitation frequency on D, 2 .
811
2
EFFECTS OF VARIOUS PARAMETERS ON G AND D OF INTACT SPECIMENS
same piece of equipment. Switching from one type of test to the other is simply done outside the confining chamber by changing: 1. the input excitation frequency used to drive the specimen and 2. the motion monitoring devices used to record the specimen response. As a result, variability due to testing different specimens is eliminated so that results from both tests can be compared effectively. Second, the loading frequency in the torsional shear test can be easily changed from 0.01 to about 10 Hz. Therefore, the effect of frequency and number of loading cycles on the deformational characteristics of intact specimens can be conveniently investigated. The basic operational principle in the RC test is to vibrate the cylindrical specimen in first-mode torsional resonance. At the University of Texas (UT), this process is completely automated so that first-mode resonance can be quickly and accurately established as illustrated in Fig. 2a. (Ni, 1987). Determinations of resonant frequency and amplitude of vibration are made from the response curve. These values are then combined with equipment characteristics and specimen size to calculate shear wave velocity, V,, shear modulus, G, and shearing strain amplitude, y. Material damping in the RC test is evaluated from the dynamic soil response using either the free-vibration decay curve or the half-power bandwidth method. The free-vibration decay curve is recorded by shutting off the driving force after the specimen is vibrating in steady-state motion at the resonant frequency. Figure 3 shows an example of this process. The logarithmic decrement, 6, is defined from the decay curve as:
About one third of the papers contributed to this technical session deal with evaluation of shear modulus and material damping of soils in the laboratory. These papers highlight the importance of time and magnitude of confining pressure on small-strain shear modulus and material damping ratio. They also show the effects of soil type, particle size, plasticity, confining pressure, number of loading cycles, and shearing strain amplitude on G and D in the nonlinear range. Understanding the effects of these parameters is important in predicting and analyzing the response of geotechnical sites during earthquake shaking. As a complement to the laboratory results presented in the other papers and as an extension in the evaluation of some of the parameters, the results from a comprehensive set of combined resonant column and torsional shear (RCTS) tests on three intact soil specimens are shown. Test parameters include: effective isotropic confining pressure, oo’ , loading frequency, f, shearing strain amplitude, y, and number of loading cycles, N . The soil specimens have been selected to cover a range in material type, going from nonplastic silty sand to moderate plasticity clay with a plasticity index, PI, of 36 %. To elaborate further on the effect of some of the test parameters, selected results from additional specimens have also been included. Emphasis is placed in this study on material damping because it is more difficult to measure and more sensitive to many of the parameters than shear modulus. Finally the effects of various parameters on the dynamic soil response are compared with behavior estimated from generic curves, with limitations of several of the generic curves shown through the comparisons.
6 = ln(zl/z2) (1) where zl and z2 are the amplitudes of two successive cycles. Material damping ratio, D, can then be determined from 6 by:
2.1 Background on Combined RCTS Equipment
D = [62/(4~2+62)]1/2 (2) The half-power bandwidth method is based on measurement of the width of the dynamic response curve around the resonance peak. For small values of material damping, one can approximate damping
The effects of various parameters on G and D are conveniently evaluated in the laboratory with combined RCTS equipment as discussed by Stokoe et al., 1994a. This equipment is of the fixed-free type, with the bottom of the specimen fixed and torsional excitation applied to the top as illustrated in Fig. 1. The equipment has two important attributes. First, both resonant column (RC) and torsional shear (TS) tests can be performed with the
as: D G (f2 - fl)/2fr (3) where fl and f2 are the two frequencies at which the amplitude is 0.707 times the amplitude at the resonant frequency ,f,, as illustrated in Fig. 4.
812
Figure 1 Simplified Diagram of a Combined Resonant Column (RC) and Torsional Shear (TS) Device (Confining Chamber not Shown)
Figure 3 Material Damping Measurement in the RC Test Using the Free-Vibration Decay Curve
Figure 4 Material Damping Measurement in the RC Test Using the Half-Power Bandwidth (Same Specimen as Shown in Fig. 3) Figure 2 Examples of Measurements Performed in the RC and TS Tests
813
For measurements at small strains (y 0.002 % but more correctly represents the strain associated with damping measurements from the free vibration decay curve. In the TS test, shear modulus and material damping are measured using the same RCTS equipment, but the equipment is operated in slow cyclic torsional loading at a given frequency. Instead of determining the resonant frequency, the stress-strain hysteresis loop is determined from measuring the torque-twist response of the specimen as shown in Fig. 2b. Proximitors are used to measure the angle of twist while the voltage applied to the coil is calibrated to yield torque. Shear modulus is calculated from the slope of a line through the end points of the hysteresis loop. Material damping is determined from the hysteresis loop as the ratio of the energy dissipated in one cycle of loading (AL) to the peak strain energy stored during the cycle (AT) times a factor of 4n: as shown in Fig. 2b. As discussed by Stokoe et al., (1994a), the RCTS equipment at UT is calibrated so that equipment-generated damping can be subtracted from the measurements. Equipment-generated damping, D,,, is measured along with material damping of the specimen when the damping measurements are performed following the procedures outlined in Figs. 2 through 4. Equipment-generated damping results from the back-electromagnetic force generated by the magnets moving through the drive coils. It is important to calibrate the drive system of each RCTS device over the entire range of frequencies used in testing so that equipment-generated damping can be determined before testing any
Figure 5 Example of Equipment-Generated Damping Measured in the Resonant Column Device Using Metal Specimens (from Hwang, 1997) specimens. Typical results for D,, in RC testing are shown in Fig. 5 (Hwang, 1997). This damping is then subtracted from the combined measurement to yield material damping of the specimen. In all results where material damping ratios of soil specimens are presented, these values have been corrected by subtracting Dq from the combined measurement of D. 2.2 Effects on Small-Strain Shear Modulus and Material Damping Ratio The effects of various state, material, and ground shaking parameters on the small-strain shear modulus, Gm,,, and material damping ratio, Dmin, are shown in Figs. 6 through 8. The state parameters are presented in terms of the effective isotropic confining pressure, o0’, and the overconsolidation ratio, OCR. The material parameters are soil type and plasticity index, PI, as listed in Table 1. (The first three specimens in Table 1 are used throughout this section. Also, in Table 1, the liquid limit, LL, natural water content, w,, dry unit weight, y d , void ratio, e, and degree of saturation, S,, are listed.) The only ground shaking parameter is excitation frequency because all dynamic measurements were performed at small shearing strains (y around 0.001%), where the effects of strain amplitude and number of loading cycles are insignificant.
814
It should be noted that time of confinement at a constant o0 also affects the values of Gmax and Dminmeasured in the laboratory. The general effect is that Gmax increases and Dmin decreases with confinement time. All reported values of Gmax and Dminwere measured approximately 1000 minutes after each confining pressure was applied. The 1000-minuteconfinement time is well past the time for primary consolidation in these specimens. However, no effect of long-term confinement was considered herein. The influence of effective isotropic confining pressure, o0’ on Gmax and void-ratio adjusted G m a x of the intact specimens is shown in Figs. 6a and 6b, respectively. The void-ratio adjusted Gmax is simply Gmax multiplied by the Hardin (1978) void ratio term, F(e), which is: F(e) = 0.3 + 0.7e
2
(4)
where e is the void ratio at each confinement state. (Other void-ratio-adjustment terms, such as ones proposed by Jamiolkowski et al. (1995), Shibuya and Tanaka (1996), and Vrettos and Savidis (1999) could also be used.) The log Gmax - log 0, ‘ and log Gmax F(e) - log o0’ relationships are composed of two linear segments, with the intersection occurring near the maximum previous in situ mean effective stress, Omp’ . For each of these three specimens, the value of O m p ‘ approximated the present value of the estimated in situ mean effective stress, 0,‘ based on a coefficient of earth pressure at rest of 0.5. Therefore, each specimen was essentially normally consolidated in situ. The solid symbols and lines in Figs. 6a and 6b represent values and relationships determined with the resonant column (RC) test. The open symbols in each figure were measured in the torsional shear (TS) test after 10 cycles of loading at a frequency of 1 Hz. The small differences in Gmax values between the RC and TS measurements are due to loading frequency as discussed below. By comparing Figs. 6a and 6b, it can be seen that the void-ratio adjustment factor brings the small-strain modulus relationships closer together. This general aggregating of the curves usually occurs, but it never results in a unique curve when a range in soil types are compared. Furthermore, use of the F(e) adjustment term by itself (as done in Fig. 6b) was intended by Hardin (1978) for only
Figure 6 Variation in Small-Strain Shear Modulus (a), Void-Ratio Adjusted G,, (b), and Small-Strain Material Damping Ratio (c) of Intact Specimens with oo from RC and TS Tests
815
Figure 7 Variation in Small-Strain Shear Modulus (a) and Normalized Small-Strain Shear Modulus (b) with Loading Frequency at ci, '
Soil Type Silty Sand (SM) Sandy Lean Clay (CL) Fat Clay (CH) Sandy Lean Clay (CL) Fat Clay (CH) Peat
(W
Figure 8 Variation in Small-Strain Material Damping Ratio (a) and Normalized Small-Strain Material Damping Ratio (b) with Loading Frequency at ci,
VoidRatio,
S,*
e
(%)
1.70
0.58
99
21
1.67
0.6 1
93
36
50
1.14
1.38
98
37
15
20
1.59
0.70
77
122
79
84
0.82
2.3 1
98
285
0.28
4.45
96
Depth (m) 7.9
cim'
LL
PI
Wn
(kPa)
(%I
(%)
(%)
(g/cm
110
NP
NP
22
4.9
62
33
10
8.4
48
63
3.1
55
11.0
41
9.1
76
*Based on assumed values of specific gravity.
816
yd
1
Table 2 Values of Dimensionless Constants A and n from Least-Squares Fits of Resonant Column
the normally consolidated range. The Hardin equation, adopted from Hardin and Dmevich ( 1972), has an additional overconsolidation term which is used in conjunction with the F(e) term when normalizing the overconsolidated range, if desired. This equation is:
where: A = dimensionless stiffness coefficient, OCR = overconsolidation ratio, k = exponent dependent on PI, P, = atmospheric pressure (100 kPa) n = exponent related to isotropic stress state. The values of A and n are presented in Table 2 for separate fits to the normally consolidated and overconsolidated portions of the relationships. The influence of oo’ on Dminis shown in Fig. 6c. The solid symbols and lines represent values and relationships determined with the RC test. The open symbols and dashed lines represent measurements in the TS test after 10 cycles of loading at a frequency of 1 Hz. It is clear from Fig. 6c that: 1. D,in decreases with increasing oo’ and 2. lower values of Dminare measured in the TS test The when compared with the RC results. difference between D,in values from TS and RC testing is related to excitation frequency as discussed below. The decrease in Dmin with confining pressure can be expressed in a general form as:
Fatclay (CH) * Based on G,,
289
0.40
317
F(e) = A oc P(’-”oc) a
0.56
ohno,
Table 3 Values of Constants B and m from LeastSquares Fits to the log Dmin - log oo’ Relationships Measured in the Resonant Column Over-
SiltySand (SM) SandyLean Clay (CL) Fatclay (CH)
Normally
1.9
0.17
1.8
0.20
4.0
0.04
3.8
0.18
2.4
0.05
2.4
0.06
overconsolidated range Table 4 Values of Constants B and m from LeastSquares Fits to the log Dmin - log oo‘ Relationships Measured in the Torsional Shear Test
The values of B and m are presented in Tables 3 and 4 for separate fits to the normally consolidated and overconsolidated portions of the relationships. The effect of excitation frequency on Gmax and Dminis shown in Figs. 7 and 8, respectively. It should be noted that these results are only for testing performed at the estimated in situ mean effective stress, q,,’ , for each specimen. In these figures, G, and Dminmeasured at all frequencies have been normalized by dividing by the respective value measured at 1 Hz. The effect of excitation frequency on Gmaxis small, averaging only about 10 % as frequency changes from 1 Hz to 50 Hz. On the other hand, the effect of excitation frequency on D d n is very significant in the range of 1Hz to 50 Hz, with Dmin increasing by about
*Based on a linear fit to Eq. 6 in the overconsolidated range
817
100 % over this frequency range. This effect is clearly shown in Fig. 6c, where nearly all values of Dmin measured in the RC test plot above values measured in the TS test at I Hz. It is interesting to observe the effect of excitation frequency on Gma, and Dminshown in Figs. 7b and 8b, respectively. First the effect o f f on Gmax increases as the plasticity of the soil increases for frequencies greater than about 10 Hz. The relationship with PI is a general trend and not a perfect correlation when a wide range in soils are tested. Second, the effect of frequency on Dmin follows this general trend with soil type, but the highest PI material does not exhibit the largest change for these three specimens. In the writers’ experience, significant variability with soil type is typically seen in the effect of excitation frequency on Dmin. Often soils composed of both sands and clays exhibit a very strong frequency effect. Finally, the results in Fig. 8 clearly show that a frequency-independent model does not represent small-strain material damping in these undisturbed soil specimens as frequency increases above about 10 Hz. 2.3 Efsects on G in the Nonlinear Range The effects of y, o O rand N on G are shown in Fig. 9. The solid symbols represent values determined in the RC test, the open symbols represent values determined in the first cycle in the TS test, and the symbols with an “X’ in them represent values determined in the tenth cycle in the TS test. (In this figure and in Fig. 10, TS testing was performed at 1 Hz.) There are two sets of combined RCTS measurements in each figure. The lower set of measurements was performed at a confining pressure approximately equal to the estimated in situ mean effective stress, CTm ’ , and the second set (the upper set) was performed at four times Gm ’ . For each soil type shown in Fig. 9, Om’ is approximately 0.5 atmosphere. Also, the results from the silty sand (shown in Fig. 9a) were adjusted from a somewhat higher pressure to be representative of Om ’ 0.5 atm. First consider the linear and nonlinear behavior shown in Fig. 9. The shear modulus is constant and equal to Gmax below an elastic threshold strain, 74, which is nominally in the range of 0.001 % to 0.01 %. The value of yf generally increases with
-
Figure 9 Variation in Shear Modulus of Intact Specimens with Shearing Strain, Confining Pressure and Number of Loading Cycles as Determined by RC and TS Tests
818
increasing PI and increasing confining pressure as shown in Table 5. The value of Gmax determined in the RC test is slightly above the value of Gmax determined in the TS test at a frequency of 1 Hz because of the effect of frequency. The response of soil at shearing strains below yf is commonly termed linear or “elastic.” The word “elastic” is used even though soils exhibit material damping at such low strains. The term yf is also called the nonlinearity threshold by Vucetic and Dobry, 1991, and Ishihara, 1996. As shearing strain increases above yf, G decreases nonlinearly with increasing y. Shear modulus decreases in a similar manner in both the RC and TS tests. Number of loading cycles has no effect on G (at least for N I 1000 cycles) until a cyclic threshold strain, yt, is exceeded. Above y:, G varies with y and N. This threshold strain also varies with PI and confining pressure as shown in Table 5. The value of y: is nominally in the range of 0.01 % and 0.1 %. If the specimens were saturated and if volume change were measured, then the threshold denoting the onset of volume change is also presumed to be at or slightly below y:. Above y:, G decreases somewhat with increasing N at a constant y as shown in Fig. 9 for all three specimens. This effect of N on G can be influenced by void ratio, confining pressure and degree of saturation. The term y: is called the degradation threshold by Vucetic and Dobry, 1991, and Ishihara, 1996. The effect of plasticity on yf and y: has been studied by these researchers as well as Vucetic, 1994. The variation in normalized shear modulus, G/Gmax, with the logarithm of shearing strain is shown in Fig. 10 for each intact specimen tested at its estimated in situ mean effective stress, CTm .
The elastic and cyclic threshold strains are more easily seen in Fig.10 than in Fig. 9. There is a clear trend for each of the threshold strains to increase with increasing plasticity index as shown in Table 5. It is not unusual for an unsaturated nonplastic soil with fines to exhibit a cyclic threshold strain on the order of that found with a low PI material. The general relationship between the G/Gmax log y curves for these soil types is shown in Fig. 11. The nonplastic and low PI soils show a similar relationship while the general relationship shifts to higher strains as PI increases. This trend agrees with the generic curves presented by Sun et al. (1988) and Vucetic and Dobry (1991) which show the effect of PI on normalized shear modulus. The effect of effective confining pressure on the G/Gmax - log y relationships is presented in Fig. 12. The relationships were determined from the RC results shown in Fig. 9. (The same trend is observed in the TS results.) The general trend shows the G/ Gmax - log y relationship shifting to higher strains as ooI increases. In this case, the largest shift is shown by the nonplastic material, with the effect decreasing with increasing PI. The effect of 0,’ is not taken into account in many generic G/Gmax - log y curves as discussed in Section 2.5. However, Kokusho (1980), Ni (1987), Sun et al. (1988) and Ishihara (1996) present studies showing similar trends in the G/Gmax - log y relationship with o0 . Each curve in Fig. 12 has been fitted with a hyperbolic relationship in the form: G/Gmax = 1/(1 +y/yr)
(7)
in which reference strain, yr, is simply a curve fitting parameter and is equal to y when G/Gmax
Table 5 Values of Elastic Threshold Strain ( yf ) and Cyclic Threshold Strain ( y:) from Figs. 9, 10 and 14 Confining Pressure = Om
,
Silty Sand (SM) SandyLean Clay (CL) FatClay (CH)
*
Confining Pressure = 4 x o m
PI
Y::
(%)
(0.001 %)
yffor G (0.001 %)
$for D (0.001 %)
(0.001 %)
y:for G (0.001 %)
yf for D (0.001 %)
NP
0.7
10
6.0
1.o
**
**
1o
1.o
15
8.0
1.5
22
10
36
3.0
35
25
5.0
60
40
819
Yf
,
Figure 11 Effect of Soil Type on the G/Gmaxlog y Relationship at a Constant o0’
Table 6 Reference Strain, yr, Values for the G/Gmax - log y Curves Based on Eq. 7 at
*
y,estirnated to be > 1 %
Table 7 Reference Strain, yr, Values for the G/GmaX- log y Curves Based on Eq. 7 at 4 x
Figure 10 Variation in Normalized Shear Modulus of Intact Specimens with Shearing Strain and Number of Loading Cycles from RC and TS Tests
820
equals 0.5. (Improved fits can be obtained using a modified hyperbolic relationship with the term, ( ~ / y ~However, )~. the original hyperbolic model is used herein for simplicity.) The resulting yr values are given in Tables 6 and 7. The trend of increasing yr with increasing PI is clearly shown in Table 6. The trend of increasing yr with increasing oo is shown by comparing Tables 6 and 7. To illustrate further the effects of confining pressure and PI on the G/G,,, - log y relationships, the results of a study involving 40 intact samples recovered from sites shaken by the 1994 Northridge earthquake in the Los Angeles, California area are presented in Fig. 13. (This work is part of a joint project called ROSRINE, Resolution of Site Response Issues in the Northridge Earthquake.) The curves can be subdivided according to plasticity and effective confining pressure. In this case, oo is presented in terms of sample depth. In Fig. 13a, the effect of PI is shown for soils in the depth range of 7.5 to 100 m. (This depth range was one of three categories based on depth.) As noted earlier, natural nonplastic soils with fines and soils with low plasticity (in this case PI 5 5 %) exhibit very similar relationships. This result is clearly shown in Fig. 13a. Figures 13b and 13c illustrate the effect of confining pressure on plastic and non-plastic soils, respectively. Comparison of these two figures also shows that the effect of oo' decreases somewhat with increasing PI as indicated in Fig. 12. The values of yr associated with the curves in Fig. 13 are presented in Table 8. I
I
Table 8 Reference Strain, yr, Values for the
7.5 - 100
I
I Figure 12 Effect of Effective Confining Pressure on the G/G,,, - log y Relationship for Each Soil Type
821
7.5 - 100 7.5- 100 c 7.5 13b 7.5- 100 100 - 250 1 3 ~ 7.5- 100 100 - 250
I
4.72E-02
1
15-36 2 - 20 6 - 14 5 - 36 NP NP
I
1.01E-01 5.04E-02 7.18E-02 1.77E-01 4.72E-02 1.57E-01
I
2.4 Efsects on D in the Nonlinear Range The effects of y, ool and N on D are shown in Fig. 14. As in Fig. 9, the solid symbols represent values from RC testing, the open symbols represent values from the first TS cycle, and the symbols with an “X’ represent values from the tenth TS cycle. Only results from testing at O m l are presented in Fig. 14. The results from testing at 4 x CTm have not been included in Fig. 14 (as they were in Fig. 9) because oo has a smaller effect on D than G. Therefore, material damping results determined by combined RCTS testing at multiple confining pressures can become quite challenging to study if data from several pressures are presented in the same figure. It is seen in Fig. 14 that material damping is constant and equal to Dmin at strains less than or equal to an elastic threshold strain, yf, which is nominally the same as that found for G (see Table 5). As with Gmax, there is a difference between Dmin values determined in the RC and TS tests because of different loading frequencies in the two tests as shown in Section 2.2. The value of yf is affected by PI and increases as PI increases. As y increases above y f , D increases significantly. A cyclic threshold strain, y:, is also found for D which ranges from about 0.006% to 0.025% in these tests. It is interesting to note that y: for D is somewhat smaller than that found for G (see Table 5). Above y:, D decreases as N increases. The importance of N increases as y increases further above yt. This effect is most easily seen in Figs. 14a and 14b. Much of the decrease in D with increasing N occurs in the first 10 cycles as shown in Fig. 14. It is also interesting to note that: 1. N has a greater influence on D than G in the unsaturated nonplastic specimen, and 2. excitation frequency still has an important effect over the strain range in these tests, strains as high as 0.1%. The variation in D with log y for each specimen as determined in the RC tests is shown in Fig. 15a. The variations in D with log y as determined for the first and tenth cycles in the TS test are shown in Figs. 1% and 15c, respectively. The general trends in Fig. 15 are: 1. the nonplastic soil exhibits the lowest Dminvalue, 2. the nonplastic soil exhibit the highest value of D at y = 0.1 %, 3. Dminvalues increase with increasing PI, and 4. values of D
Figure 13 Trends in the Average G/G,,, - log y Relationships with Confining Pressure (Depth) and Plasticity Index Determined from RCTS Tests of Soils Subjected to the 1994 Northridge Earthquake
822
Figure 15 Effect of Soil Type on the D - log y Relationship at a Constant o0’ as Determined by RC test (a), first cycle of TS test (b) and tenth cycle of TS test (c)
Figure 14 Variation in Material Damping Ratio of Intact Specimens with Shearing Strain and Number of Loading Cycles as Determined by RC and TS Tests
823
decrease at y = 0.1 ‘XOas PI increases. This rather complex relationship between the D - log y curves for different soils is generally not shown in any generic model curves as discussed in Section 2.5. It has been presented in a general sense in Electric Power Research Institute, EPRI, (1993a and b) based on RCTS tests of intact soil specimens tested at UT. This behavior has also been observed by Vucetic et al., 1998. Also, the general switching in the relative positions of the curves for the different soil types is best shown in the TS tests at an excitation frequency of 1 Hz. (Figs. 15b and 15c). The relative positions are changed and less ordered when the effect of excitation frequency impacts the measurements as shown in Fig. 15a in the RC measurements. The effect of oo‘ on the D - log y relationship is also shown in Figs. 16 and 17 for RC and TS results, respectively. The general trend shows the D - log y relationship shifting to higher strains while simultaneously shifting downward. As a result, D decreases slightly at a given y as oo’ increases. In general terms, the largest shift is shown by the nonplastic material, with the effect decreasing with increasing PI. This behavior is similar to that evaluated for shear modulus, except that Dmin of the nonplastic soil exhibited little change with increasing oo‘ . Sun et al., 1988 have noted the same overall effect. The effect of o0’ is not taken into account in many generic D - log y curves as discussed in Section 2.5 The effect of loading frequency at small strains, on G,, and Dmin,is discussed earlier (Figs. 7 and 8). The effect o f f on shear modulus and material damping at strains above yf, and sometimes at strains exceeding yt, is shown in Figs. 18a and 18b, respectively. The effect of f on G is small and decreases even more as cyclic strain increases above yf. This effect is shown in Fig. 18a by the G50Hz/G1 Hz - log y relationship. For these intact specimens, shear modulus increased slightly with increasing f at y > yt, presumably because of cyclic stiffening which becomes more important with increasing y. In terms of D, the effect of f on D is significant at small strains but decreases as y increases above yf . It is interesting to note at these strains and in these soils, the importance of cycling above yf on D seems to have been minor compared to the effect of frequency.
Figure 16 Effect of Effective Confining Pressure on the D - log y Relationship for Each Soil Type as Determined by RC Tests
824
Figure 18 Variation in G (a) and D (b) with Frequency over a Range in Shearing Strains for Each Soil Type 2.5 Additional Results and Comparisons with Generic Curves The G/G,,, - log y and D - log y relationships from additional specimens are presented in Fig. 19 along with the previous results from Figs. 11 and 15. Three additional specimens (see Table 1) have been included: 1. a sandy lean clay (PI=15%), 2. a fat clay (PI 79%), and 3. a peat. The general shifting of the G/G,,, - log y relationships to higher strains as PI increases in clays is further shown. The more complex shifting of the D - log y relationships (upward shifting of Dmin and downward shifting of D at y = 0.1% with increasing PI in clays) is also confirmed. For interest, the extreme linearity exhibited by peat is shown.
Figure 17 Effect of Effective Confining Pressure on the D - log y Relationship for Each Soil Type as Determined in the tenth cycle of the TS Test
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Additional results from testing performed as part of the ROSFUNE project are presented in Figs. 20 and 21. The double-specimen direct simple shear, DSDSS, (Doroudian and Vucetic, 1995) tests were performed by Prof. Vucetic and students at the University of California at Los Angeles (UCLA). These results are shown by the solid symbols in Figs. 20 and 21. Each UCLA and UT companion specimen was recovered from the same undisturbed sample, and each companion specimen was tested at equivalent effective stresses based on an effective coefficient of earth pressure at rest of about 0.5. (It is important to note that the RC and DSDSS confinement states are isotropic and anisotropic, respectively.) The main difference between the results exists in shear modulus. The GIG,,, - log y relationships are nearly identical as are the D - log y relationships from TS and DSDSS testing. As usually happens, the in situ seismic values of G,, (Figs. 20a and 21a) are above those determined in the laboratory. In this case, they are about 50% greater than the values determined in the RC test. Generic curves of G/G,,, - log y and D log y proposed for sands by Seed at al. (1986) and for sands and clays by Idriss, (1990) are presented in Fig. 22. Similar generic curves proposed by Vucetic and Dobry (1991) showing the effect of PI on the relationships are presented in Fig. 23. The results presented by Ni (1987) showing the importance of effective confining - log y and D - log y pressure on the G/G,,, relationships of clean sand are presented in Fig. 24. The G/G,,, - log y results in Fig. 24 are similar to those presented by Kokusho (1980) for Toyoura sand. The D - log y relationships presented by Ni (1987) show the effect of oo on D at all strains which is not readily apparent in other studies. These generic studies show good agreement with the G/G,,, - log y relationships shown earlier for different soil types. The main variable not included is the effect of o0’ on the modulus degradation relationship. The impact of oOf is shown through comparison with the generic curves in Fig. 25a for clay with an average PI of about 15%. The Same COmpariSOn for sandy Soils with no Plasticity is shown in Fig. 2%. In terms of Yr (Eq. 7) which can be used to represent the G/G,,, - log yrelationship, the curve proposed by Vucetic and Dobry (1991) is a good representation of the
Figure 19 Additional Results Comparing the Nonlinear Response of Clayey Soils and Peat with Results Shown in Figs. 11, 15a and 15c
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Figure 20 Comparison of the Dynamic Response of Companion Specimens of Sandy Lean Clay Tested at UT and UCLA on the ROSRINE Project
Figure 21 Comparison of the Dynamic Response of Companion Specimens of Silty Sand Tested at UT and UCLA on the ROSRINE Project
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Figure 23 Generic Curves Proposed by Vucetic and Dobry (1991) Showing the Effect of Plasticity Index
Figure 22 Generic Curves Proposed by Seed et al (1986) for Sands and by Idriss (1990) for Sands and for Clays
Figure 24
Effect of o0' on Nonlinear G and D of Clean Sand (from Ni, 1987)
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(1993a and b) for other RCTS test results from UT and by Vucetic et al. (1998). The curves by Ni (1987) show the effect oo' on the D - log y relationship of clean sand which is reconstituted in the laboratory. However, when intact field specimens are tested and sandy soils with some fines are included, no generic curve shows the effect of N and f on the D - log y relationship. Therefore, behavior of sandy soil with some fines can not be modeled accurately with these generic curves.
3 LIQUEFACTION RESISTANCE BASED ON IN SITUVS In this section, a procedure for evaluating the liquefaction resistance of granular soil based on in situ Vs measurements is briefly discussed. This topic is included because the dynamic response of soil at small-strains, expressed in terms of in situ V,, is the key soil parameter. In addition, nearly half of the papers contributed to this technical session deal either with pore pressure generation and liquefaction of granular soils or in situ techniques to measure V,. The evaluation procedure originally developed for this purpose, termed the simplified procedure, was developed by Seed and Idriss (1971). The simplified procedure uses blow count from the Standard Penetration Test (SPT) correlated with a parameter representing the seismic loading on the soil, called the cyclic stress ratio. Small-strain shear wave velocity measurements provide a promising alternative, or supplement, to the penetration-based approach. The use of V, as an index of liquefaction resistance is soundly based, since both Vs and liquefaction resistance are similarly influenced by many of the same factors (e.g., void ratio, state of stress, stress history, and geologic age). Furthermore, the strong theoretical basis underlying stress wave propagation offers the opportunity for additional advances in the approach. During the past two decades, a number of simplified procedures for evaluating liquefaction resistance based on Vs have been proposed (Dobry et al., 1981; Dobry et al., 1982; Seed et al., 1983; Bierschwale and Stokoe, 1984; de Alba et al., 1984; Hynes, 1988; Stokoe et al., 1988; Tokimatsu
Figure25 Comparison of Generic Curves for Lower PI Clay (a) and Non-Plastic Sandy Soil (b) with the Average ROSRINE Relationships average ROSRINE results for depth categories of: 1 . less than 7.5 my and 2. 7.5 m to 100 m. However, clay specimens from the third depth category of 100 m to 250 m exhibited an average yr about two times the value of the generic curve. This general correspondence is also found for the nonplastic sandy soil specimens, with yr for the average ROSRINE results for the depth category of 7.5 m to 100 m closely approximated by the generic curves but yr for the third (deepest) category of 100 m to 250 m ranging from about 2.5 to 5 times the value of yr from the three generic curves as shown in Fig. 25b. The complexity in the shifting of the D - log y relationships with PI and oo' as shown in Figs. 15, 16 and 17 results in none of the generic curves predicting the behavior of clayey soils properly. This complex behavior has been illustrated in EPRI 829
and Uchida, 1990; Tokimatsu et al., 1991; Robertson et al., 1992; Kayen et al., 1992; Andrus, 1994; Lodge, 1994; Rashidian, 1995; Kayabali, 1996; Rollins et al., 1998; Andrus and Stokoe, 1997; and Andrus, Stokoe and Chung, 1999). Several of these procedures follow the general format of the Seed-Idriss simplified procedure, with V, corrected to a reference overburden stress and correlated with the cyclic stress ratio. However, nearly all of the simplified procedures have been developed with limited or no field performance data. Outlined below is the procedure originally proposed by Andrus and Stokoe (1997) and subsequently updated by Andrus, Stokoe and Chung (1999). The updated procedure uses an expanded database consisting of field performance data from 26 earthquakes and in situ V , measurements at over 70 sites. Much of the new data are from the 1995 Hyogoken-Nanbu (Kobe), Japan earthquake (moment magnitude, M, = 6.9).
3. I .2 Stress-Corrected Shear Wave VelocityFollowing the traditional procedures for correcting SPT blow count to account for overburden stress, one can correct V, to a reference overburden stress by (Sykora, 1987; Robertson et al., 1992):
3.1.3 Cyclic Resistance Ratio (CRR)- The value of the cyclic stress ratio, CSR, separating liquefaction and non-liquefaction occurrences for a given V,, (or corrected blow count in the SPT procedure) is called the cyclic resistance ratio, CSR. Andrus and Stokoe (1997) proposed the following relationship between cyclic resistance ratio, CRR, and Vsl:
Three parameters are required to evaluate the liquefaction resistance of soil. These parameters are: 1. the level of cyclic loading of the soil, expressed as a cyclic stress ratio; 2. the stiffness of the soil, expressed as an overburden-stresscorrected shear wave velocity; and 3. the boundary separating liquefaction and non-liquefaction occurrences, expressed as a cyclic resistance ratio. Each parameter is discussed below.
+b[
3.1.1 Cyclic Stress Ratio (CSR)- The cyclic stressratio, T ~ , , / C T 'at ~ , a particular depth in a level soil deposit can be expressed as (Seed and Idriss, 1971): V
[
* 1
-I)JMSF
VSl - VSl V,*l where V i l is the limiting upper value of V,, for liquefaction occurrence, a and b are curve fitting parameters, and MSF is the magnitude scaling factor. The first term of Eq. 10 is based on a modified relationship between V,, and CSR for constant average cyclic shear strain suggested by R. Dobry (personal communication to R. D. Andrus, 1996). The second term is a hyperbola with a small value at low values of V,,, and a very large value as V,, approaches Vgl. The magnitude scaling factor, which accounts for the effect of earthquake magnitude on the CRR, can be expressed by:
IL,) CTV
g rd (*) where T, is the average equivalent uniform cyclic shear stress caused by the earthquake and is assumed to be 0.65 of the maximum induced stress, amax is the peak horizontal ground surface acceleration, g is the acceleration of gravity, (T', is the initial effective vertical (overburden) stress at the depth in question, (T, is the total vertical (overburden) stress at the same depth, and rd is a shear stress reduction coefficient to adjust for flexibility of the soil profile. d
(9)
where V,, is the overburden-stress-corrected shear wave velocity, P, is a reference stress of 100 kPa or about atmospheric pressure, and 0'"is the initial effective overburden stress in kPa. In using Eq. 9, it is implicitly assumed that the initial effective horizontal stress, o'h, is a constant factor of the effective vertical stress. The factor, generally referred to as K t 0 , is assumed to be approximately 0.5 at sites where liquefaction has occurred. Also, in applying Eq. 9, it is implicitly assumed that Vs is measured with both the directions of particle motion and wave propagation polarized along principal stress directions and one of these directions is vertical (Stokoe et al., 1985).
3.1 Evaluation Procedure
Tav = 0.65 amax -
[?)
0.25
vs,=vs
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where n is an exponent. The lower bound for the range of magnitude scaling factors recommended by the 1996 National Center for Earthquake Engineering Research (NCEER) Workshop on Evaluation of Liquefaction Resistance of Soils (Youd et al., 1997) is defined by Eq. 11 with n = -2.56 (Idriss, personal communication to T. L. Youd, 1995). More recently, Idriss (1999) proposed revised magnitude scaling factors that can be reasonably approximated by Eq. 11 with n = 1.75. The difference in the two proposed MSF relationships is not significant for earthquake with magnitudes of about 7 to 7.5, the range of the majority of the liquefactioncase histories. 3.2
Liquefaction Evaluation Charts Figure 26 Curves Proposed by Andrus, Stokoe and Chung (1999) for Calculation of CRR from V, Measurements Along with Case History Data Based on Lower Bound Values of MSF for the Range Recommended by the 1996 NCEER Workshop (Youd et al., 1997) and Average rd Values Developed by Seed and Idriss (1971).
The case history data for magnitude 5.9 to 8.3 earthquakes adjusted using Eq. 11 with n = -2.56 are presented in Fig. 26. Also presented in the figure are the proposed CRR-V,, curves. The curves are defined by Eq. 10 with a = 0.022, b = 2.8, and VE1 = 200 m/s for a fines content (FC) 2 35 %, VEl = 208 m/s for FC = 20 % and Vgl = 215 m / s for FC I 5 %. The case history data, and CRR-Vsl curves, are limited to relatively level ground sites with average depths less than 10 m, uncemented soils of Holocene age, ground water table depths between 0.5 m and 6 m, and V, measurements performed below the water table. Of the 90 liquefaction case histories shown in Fig. 26, only two incorrectly lie in the noliquefaction region. The two liquefaction cases that lie in the no-liquefaction region are for sites at Treasure Island, California. These sites are located along the perimeter of the island where liquefaction was marginal during the 1989 Loma Prieta earthquake (M, = 7.0). To illustrate the effect of using different magnitude scaling factors on the case history data, the data have been recalculated using the MSF proposed by Idriss (1999). The recalculated case history data are presented in Fig. 27. Also shown in Fig. 27 are the same three liquefaction resistance curves from Fig. 26. Many of the case history data in Fig. 27 plot at higher CSR values than in Fig. 26 since the earthquake magnitude is 57.5 for most of the data. The upward shifting in the liquefaction
Figure 27 Curves Recommended for Calculation of CRR from Shear Wave Velocity Measurements Along with Case History Data Based on Revised Values of MSF and rd Proposed by Idriss (1999).
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Liquefaction is predicted to occur when FS I1. Liquefaction is predicted not to occur when FS > 1. The acceptable value of FS will depend on several factors, including the acceptable level of risk for the project, the extent and accuracy of seismic measurements, the availability of other site information, and the conservatism in determining the design earthquake magnitude and the expected value of amm.
data points near the curves at CRR of about 0.08 is less than 0.01. This difference is not significant and is within the accuracy of the plotted case history data. The three CRR- V,, curves shown in Figs. 26 and 27 exhibit V,, values of 195 m l s and 210 m/s at CRR near 0.6 for FC 2 35 % and FC I 5 %, respectively. These Vsl values are considered equivalent to corrected blow counts, (N,),,, of 21 for FC 2 35 % and 30 for FC I 5 % commonly assumed in the SPT-based procedure as the limiting upper values for cyclic liquefaction Occurrence in the respective soils.
3.4
Case Study
Figure 28 presents the liquefaction evaluation from crosshole seismic testing at the Treasure Island Fire Station site and the 1989 Loma Prieta earthquake. Values of Vsl and CSR are shown in Figs. 28a and 28d, respectively. These values were calculated 3 assuming densities of 1.76 g/cm above the water 3 table and 1.92 g/cm below the water table. Based on amax of 0.16 g and 0.11 g recorded in two horizontal directions at the fire station during
3.3 Factor of Safety A common way to quantify the potential or hazard for liquefaction is in terms of a factor of safety. The factor of safety, FS, against liquefaction can be defined by: CRR FS=CSR
Figure 28 Application of the Recommended Procedure for Evaluating Liquefaction Resistance - Treasure Island Fire Station Site and 1989 Loma Prieta Earthquake
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technique has undergone considerable development (Stokoe et al., 1994b). More recently, suspension logging (Kitsunezaki, 1980 and Toksoz and Cheng, 1991) has received active use. The SASW method is discussed below, and comparisons with suspension logging and downhole seismic testing at two strong-motion sites are shown. In addition, some recent measurements of Dmin with an adaptation of the SASW method are discussed, and comparisons with crosshole and laboratory results are presented.
the 1989 earthquake (Brady and Schakal, 1994), a geometric mean value of 0.13 g is used to calculate CSR. The value of MSF used was 1.19, the lower bound value recommended by the 1996 NCEER Workshop. Values of FS shown in Fig. 28e are less than 1 for the depths of 4 m to 9 m. Between the depths of 4 m and 7 m, the sand contains non-plastic fines and is considered liquefiable. Between the depths of 7 m and 9 m, the soil exhibits plasticity characteristics and may be non-liquefiable by the so-called Chinese criteria. According to the Chinese criteria, non-liquefiable clayey soils have clay contents (particles smaller than 5 pm) 2 15 %, liquid limits 2 35 %, or moisture contents I 90 % of the liquid limit (Seed and Idriss, 1982). Thus, the layer most likely to liquefy, or the critical layer, lies between the depths of 4 m and 7 m as depicted in Fig. 28a. Although, no sand boils or ground cracks occurred at the site during the 1989 earthquake, there is a sudden drop in the fire station strong ground motion recording at about 15 seconds and small motions afterwards (Idriss, 1990). This behavior is unlike behavior observed in recordings at other seismograph stations located on soft soil sites in the San Francisco Bay area. De Alba et al (1994) attributed this behavior to liquefaction of an underlying sand. It is possible that the 5-m thick layer capping the site, predicted not to liquefy in Figs. 28d and 28e, prevented the formation of sand boils at the ground surface (Ishihara, 1985).
4
4.1 Background on SASW Method
Spectral-analysis-of-surface-waves testing is an in situ seismic method for determining shear wave velocity profiles at geotechnical and pavement sites. The test is non-invasive and non-destructive, with testing performed on the ground surface at strain levels in the elastic range (y < 0.00 1%). From the modeled shear wave velocity (V,) profile, a smallprofile can be strain shear modulus, G, determined using an estimated material density, p, as : 2 (13) Gmax = P * VS SASW testing has been used for a variety of engineering applications requiring shear stiffness data, including studies of earthquake site response, liquefaction susceptibility analyses, soil compaction control and evaluation, and pavement testing (Nazarian and Stokoe, 1986; Stokoe et al., 1988; Rix and Stokoe, 1989; Andrus, 1994; Stokoe, et al., 1997; and Bueno, 1998). The basis of the SASW method is the dispersive characteristic of Rayleigh waves when propagating in a layered system. The phase velocity, V,, depends primarily on the material properties (shear wave velocity, mass density, and Poisson’s ratio or compression wave velocity) over a depth of approximately one wavelength. Waves of different wavelengths, h, (or frequencies, f) sample different depths as illustrated in Fig. 29. As a result of the varying shear stiffnesses of the layers, waves with different wavelengths travel at different phase velocities. A surface wave dispersion curve, or dispersion curve for short, is the variation of V, with h or f, and it is the key characteristic of the site evaluated in the field for stiffness profiling.
IN SITU SEISMIC MEASUREMENTS OF VS AND Dmin
The third and final section of the paper deals with measurement of dynamic soil properties in the field by seismic methods. Several papers on this topic have been contributed to this session. Traditionally, shear wave velocity has been the dynamic soil property evaluated by seismic testing. Prior to the early 1980s, the crosshole and downhole methods were the dominant methods for geotechnical engineering purposes. The seismic cone penetration test (SCPT) has been actively used since the early 1980s (Campanella and Robertson, 1984 and Lunne et al., 1997). During this period, the spectral-analysis-of-surface-waves (SASW)
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Figure 29 Approximate Distribution of Vertical Particle Motion with Depth for Two Surface Waves with Different Wavelengths The test method involves actively exciting surface wave energy at one point and measuring the resulting vertical surface motions at various distances (receiver points) away from the source. Figure 30a shows the typical field testing arrangement. Measurements are performed along a linear array placed on the exposed surface. Fourier transforms are performed on the recorded time records of two (or more) vertical receivers. The phase difference relationship between the receivers as a function of frequency (4, vs. f) is found from the cross power spectrum G12(f) , defined by: G 12(f)=S1(f) S*2(f)
Figure 30 Typical SASW Field Arrangement: and Associated Spectral Measurement from One Source-Receivers Set-Up The bulldozer simply moved back and forth over a distance of about 3 m. The bulldozer motion generated random noise which contained significant surface wave energy from about 4 Hz to above 30 Hz as shown in Fig. 30b by the continuity in the pattern of the wrapped phase. The SASW test procedure is repeated with many receiver spacings which cover a broad range of wavelengths. For testing illustrated in this example, receiver spacings of 0.9, 1.8, 3.8, 7.6, 15.25, 30.5 and 61 m were employed. A sledge hammer was used at source spacings up to 3.8 m. The bulldozer was used as the source for the larger spacings. The process of collecting dispersion data at multiple receiver spacings is followed so that wavelengths are measured which cover the complete profile, ranging from shallow materials (high frequencies) to deep materials (low frequencies). Results from three receiver spacings with the bulldozer source are shown in Fig. 32. An important consideration in SASW data collection is that the spacing between the source and first receiver, d in Fig. 30a, is a significant fraction of the longest wavelength, A,, collected at that spacing for use in modeling the data.
(14)
where Sl(f) is the Fourier transform of receiver 1 and S*2(f) is the complex conjugate of the Fourier transform of receiver 2. A typical 4, vs. f result is shown in Fig. 30b. The @ vs. f plot in Fig. 30b is called a wrapped phase plot because of the “jumps” present in the plot. These “jumps” represent 360degree phase shifts or full cycles of the wave. By properly counting these jumps, the phase plot can be unwrapped, as illustrated in Figs. 31a and 31b. From the unwrapped phase and frequency values, the phase velocity can be found from: VR = f
* (360/@)*d
(15)
where VR is the phase velocity, f is the frequency, @ is the unwrapped phase angle and d is the receiver spacing. Therefore, a plot of phase velocity vs. wavelength can be determined as shown in Fig. 31c. In this particular test, the receiver spacing was 30.5 m, the source was a moving bulldozer, and the source was positioned slightly more than 30.5 m from the first receiver.
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never be located closer to the first receiver than d, a distance equal to the receiver spacing. A composite dispersion curve is created from measurements at all receiver spacings, as illustrated in Fig. 33a. Due to the large number of data points in the composite curve, an average dispersion curve with fewer points is calculated for the inversion process, as shown in Fig. 33b. Through an iterative inversion process of matching a theoretical dispersion curve with the average experimental dispersion curve, the shear stiffness profile can be evaluated (Joh, 1997). A final match is shown in Fig. 33c, and the resulting stiffness profile, typically the final product of the SASW test, is shown in Fig. 34.
4.2 Examples of V, Profiles at Strong-Motion Sites A study investigating the utility of the SASW method for V, profiling at strong-motion stations used to record earthquake shaking was undertaken in cooperation with the United States Geological Survey (USGS) (Brown, 1998). As part of the study, SASW testing was performed at various sites in Southern California. Downhole seismic measurements had been performed earlier at several of the sites by USGS personnel. In-hole suspension logging results were also available at a few sites. The results of the SASW tests were analyzed independently of the borehole results. The V, profile from the three methods were then compared. Comparisons from two of these sites are discussed below. The sites are the Rinaldi Receiving Station, RIN, and the Sepulveda Veterans Administration Hospital, SVA. Both sites are located in the Los Angeles, California region, and both sites recorded strong ground motions during the 1994 Northridge earthquake. The analytical model used to compute the theoretical dispersion curves for given stiffness profiles is based on the dynamic stiffness matrix method described by Kausel and Roesset, 1981 and Roesset et al., 1991. The analytical model is called the 3-D global model herein. This model simulates body wave effects and higher modes of propagation as well as the fundamental Raleigh-wave mode. The computer program WinSASW (Joh, 1992 and 1997) incorporates the 3-D global model in it, and this program was used in modeling the RIN and SVA field data presented below.
Figure 3 1 Unwrapped Phase Spectrum and Associated Dispersion Curve from Testing at One Receiver Spacing as Shown in Fig. 30a In general, h,,
can be expressed as:
,A
I 2d
In terms of unwrapped phase (or wrapped phase for that matter), Eq. 16 represents @ = 180" in Figs. 31a and 31b, and all data at longer wavelengths are deleted as shown by the darken zones in the figures. This criterion is used in an attempt to perform all data collection in the far field because forward modeling or inversion of the dispersion curve is based on wave propagation in the far field. In fact, whenever possible, it is preferable to use the criterion h,,, I d in constructing the dispersion curve from each receiver spacing. In all cases, the source should 835
Figure 32 Typical Receiver Arrangements and Associated Dispersion Curves shown in Fig. 36. This was relatively easy to do because of the general increase in shear wave velocity with depth. Since the SASW profiles represent the average material properties across the array, specific features such as layer interfaces and velocity inversion layers that are not laterally extensive cannot be resolved. As seen in Fig. 37, there is good general agreement between the shear wave velocity profiles from the SASW method and the USGS downhole seismic testing. This agreement occurred even though there is considerable scatter in the SASW dispersion data. This good agreement exists from the surface to a depth of about 53 m (175 ft) as shown in Fig. 37. From 53 m (175 ft) to approximately 73 m (240 ft), the shear wave velocity in the 3-D global solution is about 25% higher than the USGS profile. This could be due to the decreasing resolution in the SASW test with depth and also due to assumptions about Poisson’s ratio and lateral uniformity in the modeling process (Brown, 1998). The OYO suspension log exhibits a lot of variability in the profile, especially at depths below about 15 m (50 ft). The general trend in the OYO logger profile is consistent with the other
4.2.I Rinaldi Receiving Station Site SASW testing was conducted along a linear array near the USGS borehole at Rinaldi Receiving Station. To illustrate the test results, the field data and the compacted dispersion curve are presented in logarithmic and linear distributions in the wavelength domain in Figs. 35a and 35b, respectively. A logarithmically distributed compacted dispersion curve gives more weight to the shorter wavelengths, and a linearly distributed compacted dispersion curve emphasizes the longer wavelengths as shown in Fig. 35. Both distributions are useful in interpreting the dispersion curve; the logarithmic distribution is used first in modeling the shallow layers and the linear distribution is used for the deeper layers. The amount of scatter in the dispersion curve for the Rinaldi Receiving Station site in Fig. 35 shows that there is considerable variability in the subsurface. This is consistent with the site geology; the borehole is near the mouth of a small canyon below the Van Norman Dam, where the depth to bedrock presumably changes across the SASW array. The theoretical dispersion curve was fit through the middle of the experimental curve as
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Figure 34 Shear Wave Velocity Profile Determined from the Inversion Process Shown in Fig. 33c
b. Linearly Distributed Field and Compacted Dispersion Curves Figure 33 Developing the Field Dispersion Curve and Matching a Theoretical Curve to It.
Figure 35 Surface Wave Dispersion Curve Determined at the Rinaldi Receiving Station Site
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b. Comparison of the Match in the Linear Wavelength Domain
a. Comparison of the Match in the Logarithmic Wavelength Domain
Figure36 Comparison of the Match Between the Theoretical Dispersion Curve and the Compacted Experimental Curve - FUN Site phase velocity by 10% to represent V, and representing the sampling depth by h 12 or h 13 (Heisey et al., 1982). In Fig. 37 (and in Fig. 38), U3 (lambdd3) is used to approximate the depth. The velocity profile from this interpretational method compares well with the other profiles. In fact, Brown (1998) found this approximation to be a very good starting point in the SASW analytical modeling process with the 3-D global solution. 4.2.2 Sepulveda Veterans Administration Hospital (SVA) Site The SVA site exhibited significant variability andor scatter in the field dispersion data. This variability was considered to be a measure of the lateral variability at the site and indicated that the shallow subsurface is quite nonuniform while the deeper subsurface is fairly uniform. In the forward modeling process, the theoretical curve was simply fit thorough the middle of the band of the experimental data, resulting in a smooth, global profile for the site. Comparison of the SASW, Lambdd3 approximation, USGS downhole, and OYO suspension log profiles is shown in Fig. 38. The match is good except in the top 2 m. The velocity inversion in the USGS downhole profile between 40 m and 47 m is supported by the OYO suspension log, although the high values of Vs in the OYO log from 21 m to 33 m are not consistent with the other profiles. Given the amount of scatter in the composite dispersion curve and the extensive area over which the SASW data were collected at the SVA site, it is to be expected that the SASW
Figure37 Comparison of Shear Wave Velocity Profiles from SASW, USGS Downhole, and Suspension (OYO) In-Hole Logger Tests at the Rinaldi Receiving Station Site
data, except near the surface, where the values are well below the others. Since the OYO data were collected in a borehole about 15 m from the USGS borehole, some difference is to be expected. The V, profile from an empirical Rayleigh wave analysis is also shown in Fig. 37. The empirical analysis procedure simply involves increasing the
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Figure 39 Determination Attenuation Coefficient
of
Rayleigh
Wave
Figure 38 Comparison of Theoretical Shear Wave Velocity Profiles from SASW, USGS Downhole, and Suspension (OYO) In-Hole Logger Tests at the Sepulveda Veterans Administration Hospital Site solutions do not resolve all of the details shown in the borehole measurements. However, the overall good comparison between the profiles shows that the V, profile from the SASW tests correctly represents the global characteristics of the site. 4.3 Field Measurement of Dmin
The SASW method may be extended to permit in situ measurements of material damping ratio in addition to shear wave velocity (Lai and Rix, 1998; Rix et al., 1999). Rayleigh wave attenuation coefficients, a,(o), are obtained from measurements of the vertical particle displacement amplitudes I w (r, o)I at several receiver offsets over a specified range of frequencies using a nonlinear regression based on: Iw(r,o)l = Fz +G(r,w).e-"R(m)'r
Figure40 Comparison of Shear Damping Ratio Measurements at Treasure Island Site near the Fire Station
An inverse analysis is required to evaluate the shear damping ratio of individual soil layers using the frequency-dependent attenuation coefficients. Figure 40 shows the results of the inversion performed using data from the Treasure Island National Geotechnical Engineering Site, NGES, where independent measurements of material damping ratio from field crosshole and laboratory tests are available for comparison. These measurements were conducted by UT personnel
(17)
where F, is the magnitude of the source and G (r, o)is the geometric spreading function. Figure 39 shows an example of the regression for f = 30 Hz.
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6. number of loading cycles, N. The importance of excitation frequency on material damping ratio, D, the difference between traditional D - log y relationships and measured behavior, and the importance of o r o on nonlinear modulus and damping relationships are highlighted in the text. Many of these parametric effects are not captured in present-day generic models. In Section 3, a procedure is outlined for evaluating liquefaction resistance through V, measurements. The proposed procedure follows the general format of the Seed-Idriss (1971) simplified procedure. The procedure has been validated with case history data from soils ranging from fine sand to sandy gravel with cobbles to profiles including silty clay layers. Caution should be exercised when applying the procedure to sites where conditions are different from the database. Additional well-documented case histories with all types of soil that have and have not liquefied during earthquakes are needed, particularly from denser soils (Vsl > 200 d s ) shaken by stronger ground motions (ha,> 0.4 g), to further validate the procedure. Finally some recent developments in field measurements to evaluate V, and Dminprofiles are briefly presented in Section 4. The field techniques include surface wave (SASW) measurements and suspension (OYO) logging. Comparisons of V, profiles from independent USGS downhole tests, and OYO suspension logs show the validity and strengths of the field methods. Adaptation of the SASW method to field measurement of Dmin is shown through comparisons with independent crosshole seismic and laboratory measurements.
(Fuhriman, 1993 and Hwang, 1997) and are presented in EPRI, 1993c along with a discussion of the data collection and analysis procedures. The material damping ratios from surface wave measurements are generally less than those from crosshole testing possibly due to: 1. different amounts of apparent attenuation, 2. different attenuation mechanisms which control at higher frequencies and produce frequency-dependent damping ratios, 3. different volumes of soil sampled by the methods, and 4. uncoupled analyses of V, and Dmin. On the other hand, values of damping ratio from surface wave tests agree well with values from resonant column and torsional shear laboratory tests. Lai and Rix (1998) also describe a method in which measurements of surface wave velocity and attenuation are used to simultaneously determine the shear wave velocity and shear damping ratio profiles. The method takes advantage of the coupling between velocity and material damping in a linear, viscoelastic medium to achieve a more robust inversion of the data. This approach should be considered for analysis of crosshole data in the future.
5 SUMMARY AND CONCLUSIONS One of the goals in geotechnical earthquake engineering is predicting the response of soil sites during earthquake shaking. The sites can range from shallow (a few meters) to very deep (300 m or more) deposits composed of quite soft (V, - 80 d s ) to very stiff (V, > 500 d s ) soils. Characterization of the dynamic properties of these soils is an important aspect in predicting the site response. This work often involves both laboratory and field studies, particularly at important or critical sites. Some recent studies in the measurement and analysis of dynamic soil properties are discussed in this paper The effects of various parameters on dynamic soil properties are discussed in Section 2. Laboratory measurements of intact specimens are presented to illustrate the importance and impact of each parameter. Key parameters discussed herein are: 1. soil type 2. plasticity index, 3. mean effective confining pressure, ci 4. excitation frequency, f, 5. shearing strain amplitude, y, and
6 ACKNOWLEDGEMENT The writers very much appreciate the opportunity given by the organizers of this symposium to present these results. The patience and understanding of Prof. Pedro Sec0 e Pinto is especially appreciated. Support from the California Department of Transportation, the National Science Foundation, the National Institute of Standards and Technology, the United States Geological Survey, and the ROSRINE project is gratefully acknowledged. Earlier support from the Electric Power Research Institute and the Westinghouse
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Earthquake of Oct. 17, 1989--Strong Ground Motion, U.S. Geological Survey Professional Paper 1551-A, R. D. Borcherdt, Ed., U.S. Gov. Printing Office, Washington, D.C., pp. A9-A38. Brown, L.T. (1998). “Comparison of V, Profiles from SASW and Borehole Measurements at Strong Motion Sites in Southern California,” M.S. Thesis, University of Texas at Austin. Bueno, J.L. (1998). “A Study On The Feasibility of Compacting Unbound Graded Aggregate Base Courses in Thicker Lifts Than Presently Allowed by State Departments of Transportation.,” M.S. Thesis, University of Texas at Austin. Campanella, R.G. and Robertson, P.K. (1984). “A Seismic Cone Penetrometer to Measure Engineering Properties of Soil,” Proceedings of the Fify-forth Annual Meeting of the Society of Exploration Geophysicists, Atlanta, Georgia. Dakoulas, P., Yegian, M., and Holtz R. D., Eds. ( 1998). “Geotechnical Earthquake Engineering and Soil Dynamics 111,” Proceedings, ASCE Geotechnical Special Publication No. 75, Vol. 1, Seattle, WA, August, 81 1 pp. de Alba, P. and Faris, J. R. (1996). “Workshop on Future Research Deep Instrumentation Array, Treasure Island NGES, July 27, 1996: Rep. to the Workshop Current State of Site Characterization and Instrumentation,” Univ. of New Hampshire at Durham, 45 p. de Alba, P., Baldwin, K., Janoo , V., Roe, G., and Celikkol, ( 1984). “Elastic-Wave Velocities and Liquefaction Potential,” Geotechnical Testing Journal, Vol. 7 No. 2, ASTM, West Conshohocken, PA, pp. 77-87. de Alba, P., Benoit, J., Pass, D.G., Carter, J.J., Youd, T.L., and Shakal, A.F. (1994). “Deep Instrumentation Array at the Treasure Island Naval Station,” The Loma Prieta, California, Earthquake of October 127, 1989-Strong Ground Motion, U.S. Geological Survey Professional Paper 1551-A, R.D. Bocherdt, Ed., U.S. Gov. Printing Office, Washington, D.C., pp. A155-Al68. Dobry, R., Ladd, R.S., Yokel, F.Y., Chung, R.M., Powell, D. (1982). “Prediction of Pore Water Pressure Buildup and Liquefaction of Sands During Earthquakes by the Cyclic Strain
Savannah River Corporation are also acknowledged. Encouragement and guidance from Dr. Clifford Roblee, Dr. John Schneider, Dr. Walter Silva, Dr. Robert Pyke, Dr. Robert Nigbor, Dr. Donald Anderson, Dr. David Boore, Prof. I.M. Idriss, Prof. T. Leslie Youd, Prof. Mladen Vucetic and Dr. Richard Lee of those organizations are appreciated, and their interactions have made the activities stimulating and enjoyable. The assistance of Prof. Glenn Rix in contributing the material in Section 4.3 on field measurement of Dmin is sincerely appreciated. Finally, the assistance of the many graduate students at the University of Texas who worked on the research projects or on associated projects is also sincerely appreciated. In particular, Mr. Brent Rosenblad, Dr. Seon-Keun Hwang, Dr. James Bay and Dr. Sung-Ho Joh made significant contributions in support of this work. 7 REFERENCES Andrus, R.D. (1994). “In Situ Characterization of Gravelly Soils That Liquefied in the 1983 Borah Peak Earthquake,” Ph.D. Dissertation, Univ. of Texas at Austin, 533 p. Andrus, R.D. and Stokoe, K.H., I1 (1997). “Liquefaction Resistance Based on Shear Wave Velocity,” NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Technical Rep. NCEER-97-0022, T. L. Youd and I. M. Idriss, Eds., held 4-5 Jan. 1996, Nat. Ctr. for Earthquake Engrg. Res., Buffalo, NY, pp. 89128. Andrus, R.D., Stokoe, K. H., 11, and Chung, R. M. (1999). “Draft Guidelines for Evaluating Liquefaction Resistance Using Shear Wave Velocity Measurements and Simplified Procedures,” NISTIR 6277, Nat. Institute of Standard and Technology, Gaithersburg, MD, 121 p. Bierschwale, J.G. and Stokoe, K.H., I1 (1984). “Analytical Evaluation of Lique-faction Potential of Sands Subjected to the 1981 Westmorland Earthquake,” Geotech. Engrg. Rep. GR-84-15, Univ. of Texas at Austin, 231 P. Brady, A.G., and Shakal, A. F. (1994). “StrongMotion Recordings,” The Loma Prieta, Calg,
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Shear Wave Velocities From Spectral-AnalysisOf-Surface-Waves,” Research Report No. 256-2, Center for Transportation Research, University of Texas at Austin. Hwang, S. K. (1997). “Investigation of the Dynamic Properties of Natural Soils,” Ph.D. Dissertation,University of Texas at Austin, 394 PP. Hynes, M. E. (1988). “Pore Pressure Generation Characteristics of Gravel Under Undrainded Cyclic Loading,” Ph.D. Dissertation, Univ. of California, Berkeley. Idriss, I. M. (1990), “Response of Soft Soil Sites during Earthquakes,” Proceedings, H. Bolton Seed Memorial Symposium, Vol. 2, May, pp. 273-289. Idriss, I.M. (1999). Presentation Notes, Transportation Research Board Workshop on Recent Advances in Liquefaction Evaluations, 1999 TRB Meeting, Washington, D.C. Ishihara, K. (1985). “Stability of Natural Deposits During Earthquake,” Proceedings, 1lth International Conference on Soil Mechanics and Foundation Engineering, San Francisco, Vol. 1, pp. 321-376. Ishihara, K. (1996). Soil Behavior in Earthquake Geotechnics, Oxford University Press, Walton Street, Oxford, 350 pp. Ishihara, K., Editor (1995). “First International Conference on Earthquake Geotechnical Engineering,” Proceedings, Japanese Geotechnical Society, Vol. 3, Tokyo, November, pp. 1 189-1517. Jamiolkowski, M., Lo Presti, D. C. and Pallara, 0. (1995). “Role of In-Situ Testing in Geotechnical Earthquake Engineering,” Proceedings, Third International Conference on Recent Advances in Geotechnical Engineering and Soil Dynamics, State-of-theArt Paper, Vol. 3, pp. 1523-1546. Joh, S.-H. (1992). User’s Guide to WinSASW, a Program for Data Reduction and Analysis of SASW Measurements, University of Texas at Austin. Joh, S.-H. (1997). “Advances in Interpretation and Analysis Techniques for Spectral-Analysis-ofSurface-Waves (SASW) Measurements,” Ph.D. Dissertation, University of Texas at Austin.
Method,” NBS Building Science Series 138, Nat. Bureau of Standards, Gaithersburg, MD, 152 p. Dobry, R., Stokoe, K.H., 11, Ladd, R.S., and Youd, T.L. (1981). “Liquefaction Susceptibility from S-Wave Velocity,” Proceedings, In Situ Tests to Evaluate Liquefaction Susceptibility, ASCE Nat. Convention, held 27 Oct., St. Louis, MO. Doroudian, M. and Vucetic, M. (1995). “A Direct Simple Shear Device for Measuring SmallStrain Behavior,” ASTM Geotechnical Testing Journal, Vol. 18, No. 1, pp 69-85. Ebelhar, R. J., Dmevich, V. P., and Kutter B. L., Editors (1994). “Dynamic Geotechnical Testing 11,” Proceedings, ASTM, San Francisco, CA, June, 427 pp. Electric Power Research Institute (1993a). “Guidlines for Determining Design Basis Ground Motions,” Vol. 4; Appendices for Laboratory Investigations, EPRI TR- 102293, Final Report, Pal0 Alto, CA, November. Electric Power Research Institute (1993b). “Guidlines for Determining Design Basis Ground Motions,” Summary Report, EPRI TR102293, Final Report, Pal0 Alto, CA, November. Electric Power Research Institute (1993c). “Guidlines for Determining Design Basis Ground Motions,” Vol. 3; Appendices for Field Investigations, EPRI TR- 102293, Final Report, Pal0 Alto, CA, November. Fuhriman, Mark, D. ( I 993). “Crosshole Seismic Tests at Two Northern California Sites Affected by the 1989 Loma Prieta Earthquake,” M.S. Thesis, The University of Texas at Austin, 516 PHardin, B. O. (1978). “The Nature of Stress-Strain Behavior of Soils,” Proceedings, Geotech. Eng. Div. Specialty Conference on Earthquake Eng. and Soil Dynamics, Vol. 1 ASCE, Pasadena, June, pp. 3-90. Hardin, B. 0. and Drnevich, V.P. (1972). “Shear Modulus and Damping in Soils: Measurement and Parameter Effects,” Journal of Soil Mechanics and Foundation Engineering Div., ASCE, Vol. 98 No. SM6, June, pp 603624. Heisey, J.S., Stokoe, K.H. 11, Hudson, W.R. and Meyer. A. H. (1982). “Description Of In Situ
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Transportation Research Record 1070, pp. 132-144 Ni, S.-H. (1987). “Dynamic Properties of Sand Under True Triaxial Stress States from Resonant Columflorsional Shear Tests,” Ph.D. Dissertation, University of Texas at Austin, 421 pp. Rashidian, M. (1995). “Undrained Shearing Behavior of Gravelly Sands and its Relation with Shear Wave Velocity,” M.S. Thesis, Geotech. Engrg. Lab., Dept. of Civil Engrg., Univ. of Tokyo, Japan, 343 p. Rix, G.J. and Stokoe, K.H. 11. (1989). “Stiffness profiling of pavement Subgrades,” Paper read at Transportation Research Board Annual Meeting, Washington D.C. Rix, G.J., Lai, C.G., and Spang, A.W., Jr. (1999). “In Situ Measurements of Damping Ratio Using Surface Waves,” Accepted for publication in Journal of Geotechnical and Geoenvironmental Engineering, ASCE. Robertson, P.K., Woeller, D.J., and Finn, W.D. L. (1992). “Seismic Cone Penetration Test for Evaluating Liquefaction Potential Under Cyclic Loading,” Canadian Geotech. Journal, Vol. 29, pp. 686-695. Roesset, J. M., D.-W. Chang, and K. H. Stokoe, 11. (1991). Comparison of 2-D and 3-D Models for Analysis of Surface Wave Tests,” Proceedings, 5th International Conference on Soil Dynamics and Earthquake Engineering, pp. 111-126. Rollins, K.M., Diehl, N.B., and Weaver, T.J. (1998). “Implications of V,-BPT Correlations for Liquefaction Assessment in Gravels,” Geotech. Earth-quake Engrg. and Soil Dyn. ZZI, Geotech. Special Pub. No. 75, P. Dakoulas, M. Yegian, and B. Holtz, Eds., ASCE, Vol. I, pp. 506-517. Seed, H. B. and Idriss, I. M. (1971). “Simplified Procedure for Evaluating Soil Liquefaction Potential,” Journal of the Soil Mechanics and Foundations Div., ASCE, Vol. 97, SM9, pp. 1249-1273. Seed, H.B. and Idriss, I.M. (1982). “Ground Motions and Soil Liquefaction During Earthquakes,” Report, Earthquake Engrg. Res. Institute, Berkeley, CA, 134 p. Seed, H. B., Idriss, I. M., and Arango, I. (1983). “Evaluation of Liquefaction Potential Using
Kausel, E. and Roesset, J. M. (1981). Stiffness Matrices for Layered Soils,” Bulletin of the Seismological Soc. of America 71 pp. 1743-1761. Kayabali, K. (1996). Soil Liquefaction Evaluation Using Shear Wave Velocity, Engrg. Geology, Elsevier Publisher, New York, NY, Vol. 44, NO. 4, pp. 121-127. Kayen, R. E., Mitchell, J. K., Seed, R. B., Lodge, A., Nishio, S., and Coutinho, R. (1992). “Evaluation of SPT-, CPT-, and Shear Wave-Based Methods for Liquefaction Potential Assessment Using Loma Prieta Data,” Proceedings, Fourth Japan-U.S. Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures for Soil Liquefaction, Technical Rep. NCEER-92-00 19, M. Hamada and T. D. O’Rourke, Eds., held 27-29 May, Honolulu, Hawaii, Nat. Ctr. for Earthquake Engrg. Res., Buffalo, NY, Vol. 1, pp. 177-204. Kitsunezaki, C. (1980). “A New Method for Shear Wave Logging,” Geophysics, Vol. 45, pp. 1489-1506. Kokusho, T. (1980). “Cyclic Triaxial Test of Dynamic Soil Properties for Wide Strain Range,” Soils and Foundations, Vol. 20, No. 2, pp. 45-60. Kramer, S.L. (1996). Geotechnical Earthquake Engineering, Prentice-Hall, Inc., Upper Saddle River, NJ, 653 pp. Lai, C.G. and Rix, G.J. (1998). “Simultaneous Inversion of Rayleigh Phase Velocity and Attenuation for Near-Surface Site Characterization,” Georgia Institute of Technology, School of Civil and Environmental Engineering, Report No. GIT-CEE/GEO-98-2, July, 258 pp. Lodge, A. L. (1994). “Shear Wave Velocity Measurements for Subsurface Characterization,” Ph.D. Dissertation, University of California at Berkeley. Lunne, T., Robertson, P.K., and Powell, J.M. (1 997), Cone Penetrometer Testin? in Geotechnical Practice, 1st Edition, London, NY, Blackie Academic & Professional Press, 312 pp . Nazarian, S. and Stokoe, K.H., 11, (1986). “Use of Surface Waves in Pavement Evaluation,”
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Field Performance Data,” Journal of Geotech. Engrg., ASCE, Vol. 109, No. 3, pp. 458-482. Seed, H.B., Wong, R.T., Idriss, I.M. and Tokimatsu, K. (1986). “Moduli and Damping Factors for Dynamic Analyses of Cohesionless Soils,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 112, No. SM11, pp. 1016-1032. Shibuya, S., Mitachi, T., and Miura, S . , Editors ( 1994). “Prefailure Deformation of Geomaterials,” Proceedings, International Symposium on Prefailure Deformation Characteristics of Geomaterials , Vol. 1, Japanese Society of Soil Mechanics and Foundation Engineering, Sapporo, Japan, September, 698 pp. Shibuya, S. and Tanaka, H. (1996). “Estimate of Elastic Shear Modulus in Holocene Soil Deposits,” Soils and Foundations, Vol. 36, NO. 4, pp 45-55. Stokoe, K. H., 11, Hwang, S. K., Lee, J. N.-K. and Andrus, R.D. (1994a). “Effects of Various Parameters on the Stiffness and Damping of Soils at Small to Medium Strains,” Proceedings, International Symposium on Prefailure Deformation Characteristics of Geomaterials, Vol. 2, Japanese Society of Soil Mechanics and Foundation Engineering, Sapporo, Japan, September, pp. 785-8 16. Stokoe, K.H., 11, Roesset, J.M., Bierschwale, J.G., and Aouad, M. (1988). “Liquefaction Potential of Sands from Shear Wave Velocity,” Proc., Ninth World Conf. on Earthquake Engrg., Tokyo, Japan, Vol. 111, pp. 213-218. Stokoe, K.H., 11, Joh S.-H., and Bay, J.A. (1997). “In Situ V, Profiles from SASW Testing at Geotechnical Sites Shaken by the 1994 Northridge Earthquake,” Presented to CUREie at the Northridge Research Conference, Los Angeles, California. Stokoe, K.H., 11, Lee, S.H.H and Chu, H.Y.F., (1985). “Effects of Stress State on Velocities of Low-Amplitude Compression and Shear Waves in Dry Sand,” Proceedings, Second Symposium on the Interaction of Non-Nuclear Munitions with Structures, p. 358. Stokoe, K.H., 11, Wright, S.G., Bay, J.A. and Roesset, J.M. (1994b). “Characterization of Geotechnical Sites by SASW Method,” Geophvsical Characterization of Sites,
Technical Committee I0 for XIII ICMFE, A.A. Balkema Publishers/Rotterdam, Netherlands, pp. 785-816. Sun, J.I., Golesorkhi, R., and Seed, H.B. (1988). “Dynamic Moduli and Damping Ratios for Cohesive Soils,” Report, UCB/EERC-88/15, Univ. of California at Berkeley, 48 pp. Sykora, D.W. (1987). “Creation of a Data Base of Seismic Shear Wave Velocities for Correlation Analysis,” Geotechnical Laboratory Miscellaneous Paper GL-87-26, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS. Tokimatsu, K. and Uchida, A. (1990). “Correlation Between Liquefaction Resistance and Shear Wave Velocity,” Soils and Foundations, Japanese Society of Soil Mechanics and Foundation Engrg., Vol. 30, NO. 2, pp. 33-42. Tokimatsu, K., Kuwayama, S., and Tamura, S . (199 1). “Liquefaction Potential Evaluation Based on Rayleigh Wave Investigation and Its Comparison with Field Behavior,” Proceedings, Second Int. Conf. on Recent Advances in Geotech. Earth-quake Engrg. and Soil Dyn., March 11-15, St. Louis, MO, Univ. of Missouri at Rolla, Vol. I, pp. 357-364. Toksoz, M.N. and Cheng, C.H. (1991). Wave Propagation in a Borehole, in J.M. Hovem, M.D. Richardson, and R.D. Stoll (eds.), Shear Waves in Marine Sediments, Kluwer Academic Publishers, Dordrecht, The Netherlands. Vrettos, C. and Savidis, S. (1999). “Shear Modulus and Damping for Mediterranean Sea Clays of Medium Plasticity,” Proceedings, Second International Conference, Lisbon Portugal, June 21-25. Vucetic, M. (1994). “CyclicThreshold Shear Strains in Soils,” ASCE, Journal of Geotechnical Engineering, Vol. 120, No. 12, pp. 2208-2228. Vucetic, M. and Dobry, R. (1991). “Effect of Soil Plasticity on Cyclic Response,” ASCE, Journal of Geotechnical Engineering, Vol. 117, No. 1, pp. 89-107. Vucetic, M., Lanzo, G., and Doroudian, M. (1998). “Damping at Small Strains in Cyclic Simple Shear Test,” ASCE. Journal of
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Geotechnical and Geoenvironmental Engineering, Vol. 124, No. 7, pp 585-594. Youd, T.L., Idriss, I.M., Andrus, R.D., Arango, I., Castro, G., Christian, J.T., Dobry, R., Finn, W. D.L., Harder, L.F., Jr., Hynes, M.E., Ishihara, K., Koester, J.P., Liao, S.S.C., Marcuson, W.F., 111, Martin, G. R., Mitchell, J.K., Moriwaki, Y., Power, M.S., Robertson, P.K., Seed, R.B., and Stokoe, K.H., I1 (1997). “Summary Report,” NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Technical Rep. NCEER97-0022, T. L. Youd and I. M. Idriss, Eds., January 4-5, Nat. Ctr. for Earthquake Engrg. Res., Buffalo, NY, pp. 1-40.
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Earthquake Geotechnical Engineering,S&coe Pinto (ed.) 0 1999 Balkema, Rotterdam, ISBN 90 5809 1 16 3
On the dynamic characterization of soils J. D. Bray & M. E Riemer University of California, Berkeley, CaliJL:,USA
W. B.Gookin URS Greiner Woodward Clyde, Santa Ana, CaliJL:,USA
ABSTRACT: Selected topics relevant to the dynamic characterization of soils are discussed. Some recent state of the art papers in this area are reviewed. Two topics that the authors have explored are discussed in greater detail, namely, issues involved in bender element testing, and load frequency effects in dynamic testing of soils. Sample disturbance represents a major limitation to advances in characterizing small strain dynamic properties of soil, and additional research in this area is warranted.
1 INTRODUCTION Considerable effort has been devoted toward developing analytical techniques for evaluating the seismic response of soil deposits. Practicing engineers often employ these analytical procedures in the evaluation of potential seismic hazards at project sites. Yet, the accuracy and reliability of seismic response analyses are highly dependent on the characterization of the subsurface conditions and the evaluation of the dynamic properties of the critical soil strata. Specifically, the results of dynamic analyses are often quite sensitive to the shear modulus and material damping ratio versus shear strain relationships employed by the engineer. Tremendous recent advances in field and laboratory testing techmques provide the opportunity to improve significantly an engineer's ability to characterize the dynamic properties of soil. Recent papers, including those presented at this conference, describe some of these advanced testing techniques and the implications of the resulting test data. A thorough review of all relevant topics cannot be presented in this discussion paper, so only a few recent state-of-the-art papers are discussed. In addition, two topics, wluch have been investigated by the authors as well as by others, are discussed. These topics are: issues involved in bender element testing, and load frequency effects in dynamic testing of soils. In the end, with the recent advances
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in testing capabilities, sample disturbance remains a significant obstacle to improved characterization of small strain properties of soil.
2 RECENT ADVANCES IN TESTING The development of sophisticated data measurement and acquisition techniques now allows engineers to make precise and reliable measurements of soil properties across a wide range of strains. In particular, small strain measurements can be made reliably in the laboratory allowing for good characterization of small strain dynamic properties of soil. It is now commonly recognized that interpreting load-deformation of soil specimens with measurement devices that are external to the testing chamber are inadequate, especially with regard to small strain dynamic stiffness and material damping. Thorough reviews of potential testing errors and the capabilities of state-of-the-art small strain laboratory measurement devices are presented in Tatsuoka (1988) and Scholey et al. (1995). Measurement devices are separated into three broad classes based on their placement location. External measurement devices such as linear variable differential transducers (LVDT) and load transducers are located outside of the testing chamber, and hence prone to potentially significant errors due to piston friction and connection compliance. Internal
measurement devices, which are located inside the testing chamber, may include LVDTs and load cells in addition to noncontacting proximity transducers. By locating these devices on the top or bottom platens adjacent to the test specimen, most measurement errors can be avoided or minimized. However, interfaces between the platen, porous stone (if used), and specimen can lead to measurements of deformation larger than those experienced by the soil, while at the same time, the boundary conditions at the ends of the specimen may inhibit soil deformations near the platens. Hence, local deformation measurement devices that are attached to the specimen itself in an attempt to measure deformation across a part of the specimen only were developed to avoid these troublesome interfaces. LVDTs and noncontacting proximity transducers may be used to measure the relative deformation of targets mounted directly on the membrane surrounding the test specimen. Recently, new devices, such as the Hall effect gage (Clayton et al. 1989) and the local deformation transducer (LDT; Tatsuoka 1988), allow local deformations across a part of the test specimen to be measured relatively inexpensively with high resolution and accuracy. Attachment of all of these local deformation measurement devices to the test specimen, as well as sensitivity to background electrical noise, etc. does make these devices more difficult to use than internal devices. However, if the platen-specimen interfaces are greased to reduce deleterious boundary effects and to promote more uniform specimen deformation, the local devices are necessary. Both internal and local measurement devices require water proofing for most soil testing applications, and although potentially an initial cost and maintenance issue, these devices can generally be adapted to work immersed in water. Obviously, all measurement t e c h q u e s eventually assume that deformation occurs uniformly across some part of the specimen, and this is a limitation to all of these devices. A micro-mechanical examination of the internal deformation of a test specimen composed of particulate media clearly shows that this assumption of uniform straining across the specimen breaks down at some level. A number of investigators have employed these measurement techniques with advanced instrumentation in their laboratories to provide an improved picture of small strain dynamic properties of soil. Works by Goto et al. (1991), Jamiolkowski et al. (1994a&b), Kim and Stokoe (1994), Tatsuoka
et al. (1994), Lo Presti et al. (1995), Shibuya et al. (1995), Gookin et al. (1996), Boulanger et al. (1998), and Vucetic et al. (1998), to name a few, have provided important insights regarding the small strain stiffness and damping of a variety of soils. Properties at shear strain levels on the order of 0.001% are reliably measured, with some devices often able to attain reliable measurements at the commonly accepted "small strain" level of 0.0001%. These studies, as well as others, represent a significant advancement of the profession's ability to characterize a soil specimen's dynamic properties over a wide range of strain.
3. BENDER ELEMENTS Dynamic StifJitess Since the mid-1970'~~ a technology for measuring shear wave velocities on laboratory soil samples has developed using pairs of polarized piezoceramic wafers described as "bender elements" (e.g. Shirley and Hampton, 1978; De Alba et al., 1984; Dyvik and Madshus, 1985). These elements can be incorporated directly into the top and bottom caps of standard testing devices, and thereby permit direct measurement of shear wave velocity (V,) on the same specimen used for measuring the shear modulus at larger strains (e.g., Gookin et al. 1996). This approach removes errors arising from specimen variability when developing an individual modulus degradation curve. The magnitudes of the shear strains associated with the measured shear waves are difficult to measure, but are estimated to be approximately 10 -'% (Dyvik and Madshus, 1985), and so are believed to provide a measure of the elastic maximum shear modulus, G,, = pV;, where p is the mass density of the medium. However, local strains induced by bender elements may be larger than this for soft soils (on the order of 0.001% for some cases; Arulnathan et al., 1998). While commonly used procedures for bender element testing are straightforward and the instrumented caps are relatively easy to construct, precise interpretation of the data obtained is difficult due to a number of factors. Bender element measurements of shear wave velocity require only knowledge of the travel path length and the travel time, yet the precision of these measurements has been limited primarily by uncertainties in identifying the appropriate travel time. A precise measure of V, is important because any errors in its measurement 848
are amplified when the data is converted to shear modulus, as velocity is squared in that process. Because the bender elements protrude into the soil from the surface of the end caps, it is not intuitively apparent whether the travel path length is the full specimen height, the distance between the tips of the bender elements, or some intermediate "effective" length. Dyvik and Madshus (1985) showed that using the distance between the tips of the bender elements as the travel path length of the shear wave gave the best agreement with the other measurements of modulus. Viggiani and Atkinson (1995) performed a series of bender element tests on specimens of varying heights, and reached the same conclusion. As a result of these studies, it is standard practice to adopt the tip-to-tip distance between the elements as the effective length of the travel path. Researchers have faced considerably greater difficulty in establishing a procedure for accurately evaluating the travel time of the shear wave. The shape of the arriving wave can vary substantially depending on the geometry and fabrication of the apparatus, the specimen properties, and the nature of the transmitted pulse, making a precise interpretation of the travel time difficult. The earlier arrival of compression waves or other "near field effects" (Viggiani and Atkinson 1995) can make the first arrival of the shear wave difficult to detect, as illustrated in Fig. 1, which shows the trace of a wave arrival in medium dense sand created by a step wave pulse (also shown). Such low-frequency step waves., have been widely used as triggering pulses (Thomann and Hryciw, 1990; Dyvik and Olsen, 1989; Jovicic et al., 1996). The nearly square corners and abrupt rise of a step wave pulse seem to provide a distinct measure
Figure 1. Transmitted pulse and received wave in a bender element test on sand. 849
of the appropriate time of triggering, but also produce a transmitted wave that is rich in many frequencies. This is part of the problem in interpreting shear wave data such as that shown in Fig. 1. Viggiani and Atkinson (1995) demonstrated that the form of the arriving wave is much "cleaner" (that is, composed of a single frequency response) if the transmitted wave is sinusoidal, as shown in Fig. 2. They proposed an alternative method of interpretation using the elapsed time between the first peak of the transmitted signal (B) and the first peak of the received signal (B') as the travel time, demonstrating that it produced modulus values in good agreement (within 12%) with those from sophisticated cross-correlation analyses of the step wave signals. Other investigators (e.g. Lohani et al. 1999) have developed alternative interpretation techniques for bender element tests. Although such use of "characteristic peaks" bypasses the near field distortions of the first arrival, it raises questions about the timing and form of the created pulse: the signal displayed by the oscilloscope is the voltage sent to the transmitting element, which is not necessarily the form of the transmitted wave. Delays between the electrical pulse and the physical deformation of the element, which can result from soinender element interaction effects, are not accounted for at either end of the specimen, nor are distortions of the resulting wave due to reflections off the transmitting cap. Analytical studies and numerical simulations of such tests by Arulnathan et al. (1998) have shown that sent waves with long periods will systematically
Figure 2. Typical oscilloscope signals from a bender element test with a sine pulse excitation (after Viggiani and Atkinson 1995).
overestimate V,, while the bender elements are incapable of producing those with very short wavelengths. For these reasons, there is a question as to whether the peak of a received signal actually corresponds to the transmitted peak, and no way of determining at what time the deflection of the transmitting element reaches its peak value (point B) in a test such as that in Fig. 2, both of which are necessary if the method of characteristic peaks is to be used. A new procedure for measuring shear wave velocities, bypassing the difficulties described above, was proposed by the authors (Riemer et al. 1998). The technique, which is based on the generation and interpretation of multiple reflections of the transmitted waves, uses the same basic bender elements, function generators and high resolution oscilloscope used for the standard method, but relies solely on data obtained by the receiving element. As recently noted by Fratta and Santamarina (1996) and Nakagawa et al. (1996) using different transmission and reception techniques, compression and shear waves generated in soil specimens reflect off the end caps of the specimen, and the reflections
Figure 3. Reflected "tuned" sine pulse bender element technique proposed by Riemer et al. (1998)
of a given pulse can be detected. The clarity of the reflected waves and their attenuation with each reflection depends not only on the specimen, but also on the shape and frequency of the transmitted pulse. The authors have found that if a shear wave pulse consisting of a half or full sine wave is properly "tuned" (i.e., the duration is appropriately adjusted), the transmitted wave is sufficiently strong to reflect off the end caps of the specimen multiple times while maintaining its characteristic shape. Each time the reflected wave passes the receiving bender element, a similarly shaped wave trace is recorded, as shown in Fig. 3a ( results from a medium dense sand). The velocity of this reflected wave can then be calculated as two times the full specimen height divided by the elapsed time between similar peaks in the respective waves (e.g., points B and B', or points C' and C" in Fig. 3a). As only the received signal is used in this method, any time delays between the deformation and recorded electrical signal are bypassed and no assumptions regarding first arrival or synchronization of the pulse and the generated wave are required. Simple averaging of the received signals from multiple identical pulses can be used to reduce effects of low frequency noise, but no conditioning, signal processing, spectral analyses or cross-correlation methods are necessary to obtain V, by this method. There is no need to assume an effective length between the two bender elements, because the full height of the specimen is traversed twice by the wave between recorded reflections. To obtain useful data, it is important not only to generate a sufficiently strong wave to detect the reflections, but the shapes of subsequent reflections must be sufficiently similar to identify equivalent points on them. Fig. 3b shows the results of a test performed on the same specimen, under the same conditions, as that shown in Fig. 3a; the primary difference between the two is the duration of the transmitted half-sine pulse, which is much shorter in Fig. 3b. While the short transmitted pulse is still sufficiently strong to generate a detectable reflection, there is no way to identify corresponding points on the reflections, and therefore no way to utilize the reflected wave to calculate V,. Having observed that pulse duration is an important factor in the clarity of the received reflected waves, it is desirable to identify what the optimum pulse duration would be for a particular soil specimen. The clarity of the signal depends both on the properties of the specimen (stiffhess and height) and the properties of the bender elementlcap
850
system, which includes the stifhess of the bender element embedded in the cap. This is not surprising, because the physical response of the transmitting bender element embedded in the soil will have soiVstructure interaction effects. Recent analytical work on these effects (Arulnathan et al., 1998) suggests that using a pulse with a wavelength between 5 and 10 times the cantilevered length of the bender element produces shear waves with strong amplitudes and clear peaks. Finding the best pulse duration for the generation of clear reflected peaks still requires some trial and error for a specific soil. However, because individual shear wave velocity tests are simple and require only a few minutes to conduct and to interpret once the specimen is prepared, it is easy to search for an optimum pulse duration around this target range by altering the pulse duration until a distinct received signal is obtained with at least one geometrically similar reflection.
Damping The attenuation of the amplitude of successive reflected pulses should be related to the degree of damping in the specimen. Clearly, finding a reliable means to obtain material damping from these measurements is desirable, as it would provide data at strain levels for which there is presently little information. However, the soil-cap-bendersystem is not perfectly analogous to that of successive oscillations of a freely resonating specimen, because the amplitude detected by the bender elements will be affected by the efficiency of the reflection off the caps. Other inevitable losses of energy in the system associated with imperfect reflection, dispersion and scattering should not be included with the energy dissipated by the soil when calculating the level of soil damping. However, the tuning process of testing at an optimum pulse duration is essentially an attempt to find a "resonant" response, and one can still calculate the degree of damping in the overall system, thereby identifying an upper limit of material damping. The simplest approach to estimating this upper limit to the damping ratio (1)is to apply the principles used for interpreting general system vibrations, as used for resonant column tests, obtaining an equation of the form:
h = (1/2nn)*ln(Vi/Vi)
85 1
where viand 5 are the full amplitude voltage values from successive reflections of the received signal, and n is the number of wavelengths traveled by the shear wave between those traces. Voltages can be used directly because the voltage output is essentially linear with deformation at very small strains. Applying this simple method to the multiple reflections plotted in Fig. 3a for dry sand yields values of h ranging from 0.35% to 0.6 %, which are reasonable for the small strains involved. Similar analysis for a soft clay yields values of h between 1.0 and 1.5 %. While the above formulation for estimating damping is simple and preliminary, it should be recognized as a true upper limit: there are no assumptions made to ''correct for" machine damping. Any energy losses caused by imperfect reflection as well as other factors imply an actual value of soil damping less than the value calculated. It may also be important to note the relatively h g h frequency of this technique (around 1 kHz), if frequency effects are considered important.
4.FREQUENCY EFFECTS Results presented in the landmark paper by Hardin and Drnevich (1972) indicated that loading frequency (from 0.1 Hz to 260 Hz) had no significant effect on the modulus of both cohesionless and cohesive soils at shear strains lower than 0.001%. However, results presented by Richart (1977) suggested that strain rate or loading frequency effects were not significant for sand, but were potentially significant for clays. Cyclic torsional shear tests performed by Isenhower and Stokoe (1981) clearly indicated that strain rate affects the measured modulus of San Francisco Bay Mud, a medium plasticity silty clay, with higher applied strain rates leading to higher measured modulus values. These test results question the internal consistency of resonant column test results due to the variable loading frequencies or strain rates used to measure the shear modulus at each strain level (see Fig. 4 developed by Isenhower and Stokoe,1981). Dynamic testing of cohesive soils by others, such as Aggour et al. (1987), Georgiannou et al. (1991), Kramer et al. (1992), Shibuya et al. (1995), and Vucetic et al. (1998), also provided results suggesting that loading frequency systematically affected the measured shear modulus and damping ratio in cohesive soils.
TORSWL SHEAR TES
I
I
I
I
I
I
Figure 5. Shear modulus reduction and damping ratio curves for kaolinite specimens isotropically consolidated at 202.3 kPa (OCR=l).
10-4 IO-~ IO-‘ 10” I SINGLE- AMPLtTUDE SHEARING STRAIN,. %
IO-~
Figure 4. Comparison of resonant column data with torsional shear test data at different strain rates (after Isenhower and Stokoe 1981).
It is widely accepted that the dynamic strength of cohesive soils is strain rate dependent, and there is no reason to suspect that the small and intermediate strain dynamic stiffness and damping properties of cohesive soils are not also strain rate dependent. The authors recently re-examined the loading frequency issue using a hydraulic cyclic triaxial testing system capable of imposing a wide range of loading frequencies across a wide range of shear strains (Gookin et al. 1999). Both clean sand and clays of various mineralogies (i.e. kaolinite, illite, and montmorillonite) and plasticity (PI = 0, 10, 75, and 500) were tested. As expected and consistent with previous studies, significant loading frequency effects on sandy soils were not observed. However, loading frequency effects were found to be significant for clay soils under a number of conditions. Representative results from Gookin et al. (1999) are shown in Fig. 5. At each strain level, the measured shear modulus systematically increases and the measured material damping ratio systematically decreases with increasing loading frequency. The offset in the damping ratio measured at 0.1 Hz, 1 Hz, and 10 Hz is evident in Fig. 5. However, the shear modulus curves appear to converge at higher strain levels. This is an artifact due to the smaller shear modulus measured at each load frequency at higher strain levels. In fact, as shown in Fig. 6, if the strain dependent shear modulus curve obtained at each loading frequency is normalized by their respective maximum shear
852
Figure 6. Normalized shear modulus reduction curves for kaolinite specimens of Figure 5 with each normalized by their respective value of G,,,.
modulus, the normalized shear modulus reduction curves for these soils are insensitive to loading frequency. Hence, if the shear modulus values are measured at the same loading frequency and normalized by the small strain shear modulus measured at that same loading frequency, the strain dependent normalized shear modulus reduction curves will be independent of loading frequency. It may be inferred that a similar normalization procedure could be used for testing conducted at the same strain rate. In using these normalized modulus reduction curves for seismic analysis, the appropriate small strain modulus must be used and this parameter will be a function of loading frequency or strain rate. Additional representative results from Gookin et al. (1999) for the illite specimens zire shown in Figs.
Figure 7. Shear modulus reduction and damping ratio curves for illite specimens anisotropically consolidated at 202.3 kPa, with K=0.6 (OCR=l).
Figure 8. Normalized shear modulus reduction curves for illite specimens of Figure 7 with each normalized by their respective value of G,.
7 and 8. Trends similar to those for the kaolinite specimens are observed for these results from the illite tests. However, loading frequency effects are seen to be more significant for the higher plasticity illite clay soil. In an attempt to measure the dynamic properties of soil across a wide range of strain (i.e. from 0.0001% to 10%), bender elements were incorporated into the top and bottom caps of this triaxial testing device to obtain V, and hence G,,,. This procedure was successful for sand specimens (Gookin et al. 1996), but not for these plastic clay specimens (Gookin et al. 1999). For the kaolinite and illite clay specimens, the maximum shear 853
modulus measured using the bender elements were generally lower than that measured in the cyclic triaxial deformation mode at a loading frequency of 0.1 Hz, with G, underestimated by 5% to 15% (see Figs. 5 & 7). Bender element estimates of G, were even lower when compared to G, measured in the cyclic triaxial deformation mode at higher loading frequencies, due to rate effects. The greatest differences between bender element estimates of G, and triaxial measurements of G,,, were for anisotropically consolidated test specimens. For the montmorillinite clay specimens, the bender element estimate of G,, was generally higher than that measured in a triaxial deformation mode. The vertical propagation of shear waves in a test specimen produces a mode of deformation that is significantly different than that produced in the cyclic triaxial device undergoing axial displacement. Hence, in retrospect, it is not surprising that these techniques obtain different values of G,,,, especially for anisotropically consolidated specimens that are stiffer in axial compression than in a pure shear deformation. In addition, as the strain rate induced by bender elements in soft soil are nonuniform (higher in the vicinity of the element and relatively lower away from the element, Arulnathan et al. 1998) and inconsistent with that induced in the triaxial deformation mode, bender elements cannot be used to develop an internally consistent normalized shear modulus reduction curve. It is imperative that a consistent test type and loading frequency (or strain rate) be used to develop a shear modulus versus shear strain curve from 0.0001% strain to higher strain levels. A normalized modulus reduction curve derived from this consistent data can then be used in a dynamic analysis as long as the appropriate strain rate dependent value of G, is used with the normalized modulus reduction curve. Currently, normalized shear modulus reduction curves obtained in the laboratory are combined with a value of G,, obtained from shear wave velocity measurements performed in the field. This approach is acceptable only if the normalized modulus reduction curve is obtained from a consistent data set, as described previously, and if G,, is insensitive to loading frequency and strain rate. Whereas G, is relatively insensitive to loading frequency in cohesionless soils, this is not the case for cohesive soils. Cohesive soils consolidated anisotropically showed an increasing effect of loading frequency on shear modulus and damping ratio with increasing plasticity index (Gookin et al. 1999). This is consistent with the prevailing view of the increasing
importance of rate effects on the dynamic shear strength evaluation of clay soils of increasing plasticity. Hence, for clay soils, the field estimate of G, derived fi-om the in situ shear wave velocity measurement should be adjusted to represent the small strain shear modulus at strain rates appropriate for the dynamic loading in the field. As shown previously in Figs. 5 and 7, tests performed at higher loading frequencies tend to have lower material damping ratios than tests performed at comparable strain levels at lower loading frequencies for a given soil. The separation between the damping ratio values between tests at different loading frequencies appears to be a constant value independent of shear strain. Unlike shear modulus curves that are normalized so that the normalized curves are frequency independent, material damping curves are not normalized. Thus, the effect of loading frequency may be an important consideration in selecting a strain dependent damping curve for a seismic analysis.
5. SAMPLE DISTURBANCE Investigators as early as Seed and Idriss (1970) have recognized that sample disturbance affects the dynamic soil properties measured in the laboratory. For example, the small strain shear moduli measured from laboratory dynamic testing are typically lower than those measured in situ. This is especially true when comparing the in situ dynamic stiffbess of deep deposits of Pleistocene soils with that measured on a laboratory specimen retrieved fiom the field by conventional sampling (e.g. Guha et al. 1997). Factors that influence the laboratory measurement of shear moduli include confining pressure (both magnitude and duration), stress history, shearing strain amplitude, number of cycles of loading, degree of saturation, and drainage conditions (Anderson and Stokoe 1978). Among these, the factors that cause underestimation in laboratory measurements are stress history (i.e. the permanent changes that take place in a soil's structure due to the removal of the soil from its in situ stress environment) and duration of confinement (a factor that takes secondary compression and the aging process into account). Although investigators have found that by reconsolidating high quality soil specimens to the in situ stress state, the laboratory G,,, value is often close to its in situ value, this is often due to the laboratory specimen having a lower void ratio at the end of the reconsolidation process
(Jamiolkowski et al. 1994a). Thus, it is compensating errors that are difficult to quantify independently which leads to the fortuitous agreement between laboratory and field G, measurements on occasions. Investigators have explored some of these issues (e.g. Tatsuoka and Shibuya 1992, Jamiolkowski et al. 1994a, Hight and Georgiannou 1995, Guha et al. 1997), however, additional research is needed to quantity sample disturbance effects due to issues such as stress, state, and fabric differences.
6. CONCLUSIONS Recent advances in laboratory testing equipment and techniques offer engineers the opportunity to develop more accurate characterizations of the dynamic soil properties. These improved characterizations will be necessary to support advanced soil constitutive modeling and numerical analysis in geotechnical earthquake engineering. Whereas the length of this paper does not allow all critical issues regarding the evaluation of dynamic soil properties to be discussed, some key papers in this area have been referenced for the interested reader. Two topics, bender elements and loading frequency effects, were emphasized to promote discussion during this conference. The use of a halfsine or sine wave as the transmitted signal in bender element testing is recommended with the use of reflected wave arrivals at the receiving bender element to estimate shear wave velocity. This technique does not require an assumed travel distance, nor sophisticated techniques to interpret the received signal to estimate travel time. Loading frequency has been shown to shift material damping curves, with higher loading fi-equencies leading to lower measurements of damping ratio at a given strain level. Strain dependent shear modulus reduction curves, normalized by maximum shear modulus measurements made at the same loading frequency, are independent of loading frequency. The small strain shear modulus value used in conjunction with the normalized modulus reduction curve, however, is a function of loading frequency or strain rate. Consequently, bender elements cannot necessarily be used to measure G, in the laboratory, and the same testing device and procedure should be used to measure shear modulus at all strains, so that the normalized modulus reduction curves are internally consistent. These 854
normalized curves should be used with an appropriate value of G,, for the field loading. A major limitation to continued advancement in the profession's ability to characterize soil properties is sample disturbance. Thus, minimization and evaluation of disturbance effects in both field and laboratory testing represent important research needs.
ACKNOWLEDGEMENTS Financial support was provided by the California Department of Transportation under Award No. RTA-59A130, the David and Lucile Packard Foundation, and the National Science Foundation (BCS-9157083). This support is gratefully acknowledged.
REFERENCES Aggour, M., Tawfiq, K. and Amini, F. (1987) "Effect of frequency content on dynamic properties of cohesive soils," Soil Dynamics and Liquefaction, No. 42, Devel. In Geotech. Engrg., Cakmak, A., Ed., pp. 31-39. Anderson, D.G. and Stokoe, K.H. (1978) "Shear modulus: a time dependent soil property," Dynamic Geotech. Testing, ASTM STP 654, ASTM, West Conshohocken, PAYpp. 66-90. Arulnathan, R., Boulanger, R.W., and Riemer, M.F. (1998), "Analysis of bender element tests," Accepted for publication in ASTM Geotechnical Testing Journal, Vol. 21 No. 3. Boulanger, R.W., Arulnathan, R., Harder, L. F., Torres, R. A., and Driller, M. W. (1998) "Dynamic Properties of Sherman Island Peat," Geotech. And Geoenvir. J., ASCE, Vol. 124, No. 1, pp.12-20. Clayton, C.R.1, Khatrush, S.A., Bica, A.V.D., and Siddique, A. (1989) "The use of Hall effect semiconductors in geotechnical engineering," Geotech. Testing J., ASTM, Vol. 12, No. 1, pp. 6976. De Alba, P., Baldwin, K, Janoo, V., Roe, G. and Celikkol, B. (1984), "Elastic-wave velocities and liquefaction potential," ASTM Geotechnical Testing Journal, Vol. 7, No. 2. Dyvik, R., and Madshus, C. (1985), "Laboratory measurements of G,, using bender elements", Proceedings ASCE Convention, Detroit. Dyvik, R., and Olsen, T.S. (1989), "G,,, measured in oedometer and DSS tests using bender a55
elements," Vol. 1 of Proceedings from 12th International Conference on Soil Mechanics and Foundation Engineering, Rio de Janeiro, Brazil. Fratta, D., and Santamarina, J.C. (1996), "Wave Propagation in soils: wide-band testing in a waveguide device," ASTM Geotechnical Testing Journal, Vol 19, No. 2. Georgiannou, V., Rampello, S, and Silvestri, F. (1991) "Static and dynamic measurements of undrained stiffness on natural overconsolidated clays," Proc., 10th European Reg. Conf. On SMFE, Vol. 1, pp. 91-94. Gookin, W., Riemer, M., Boulanger, R., Bray, J. (1996), "Development of a cyclic triaxial apparatus with broad frequency and strain ranges," TRB No. 1548, National Research Council, pp. 1-8. Gookin, W., Bray, J. and Riemer, M. (1999), "The Combined Effects of Loading Frequency and Other Parameters on Dynamic Properties of Reconstituted Cohesive Soils," Geotech. Engrg. Report, Univ. of Calif., Berkeley, 93 pp. Goto, S., Tatsuoka, F., Shibuya, S., Kim, Y-S, and Sato, T. (1991) "A Simple Gage for Local Small Strain Measurements in the Laboratory," Soils and Foundations, Vol. 3 1,No. 1,pp. 169-180. Guha, S., Dmevich, V.P., and Bray, J.D. (1997) "Dynamic characteristics of Old Bay Clay," Geotech. Testing J., ASTM, 20(4), 383-393. Hardin, B. and Drnevich, V. (1972) "Shear modulus and damping in soils: measurement and parameter effects," J. of SMFE, ASCE, Vol. 98, No. 7, pp. 667-691. Hight, D.W. and Georgiannou, V.N. (1995) "Effects of sampling on the undrained behavior of clayey sands," Geotechnique, 45(2), 237-247. Isenhower, W. M. and Stokoe, K. H. (198 1) "Strain-rate dependent shear modulus of San Francisco Bay Mud," Proc., Intl. Conf. On Rec. Adv. In Geotech. EQ. Engrg., Univ. of Missouri., Rolla, Vol. 2, pp. 597-602. Jamiolkowski, M., Lancellotta, R., and Lo Presti, D. C. F. (1994a) "Remarks on the stiffness at small strains of six Italian clays," Proc., Intl. Sym. On Pre-Failure Deformation Characteristics of Geomaterials, IS-HOKKAIDO, Sapparo. Jamiolkowski, M., Lancellotta, R., Lo Presti, D. C. F., and Pallara, 0. (1994b) "Stiffness of Toyoura Sand at Small and Intermediate Strains," Proc. 13th Intl. Conf. On SMFE, New Delhi. Jovicic, V., Koop, M.R., and Simic, M. (1996), "Objective criteria for determining G, from bender element tests," Geotechnique, Vol. 46, No. 2.
Tatsuoka, F. and Shibuya, S. (1992) "Deformation characteristics of soils and rocks from field and laboratory tests," Proc. 9th Asian Reg. Conf. Soil Mech., Bangkok, V. 2, 101-170. Tatsuoka, F., Teachavorasinskun, S., Dong, J. Kohata, Y. and Sato, T. (1994) "Importance of measuring local strains in cyclic triaxial tests on granular soil," Dynamic Geotech. Testing 11, ASTM STP 1213, West Conshohocken, PAYpp. 288-302. Thomann, T.G, and Hryciw, R.D. (1990), "Laboratory measurement of small strain shear modulus under ,&I conditions," ASTM Geotechnical Testing Journal, Vol 13, No. 2. Viggiani, G. and Atkinson, J. (1995), "Interpretation of bender element tests," Geotechnique, Vol. 45, No. 1. Vucetic, M. & Dobry, R. (1991) "Effect of Soil Plasticity on Cyclic Response", J. of Geotech. Eng., ASCE, 117( l), pp. 89- 107. Vucetic, M., Lanzo, G., and Doroudian, M. (1998) "Damping at Small Strains in Cyclic Simple Shear Test," J. of Geotech. Eng., ASCE, 124(7), 585-594.
Kim, D.S. and Stokoe, K.H. (1994) "Torsional motion monitoring system for small-strain (1OW5to 10-') soil testing," Geotech. Testing J., ASTM, Vol. 17,No. 1,pp. 17-26. Kramer, S. L., von Laun, F.Y., and Sivaneswaran, N. (1992) "Strain-controlled, variable frequency cyclic loading system of soft soils," Geotech. Testing J., Vol. 15, No. 3, pp. 264-270. Lo Presti, D. C. F., Pallara, 0. and Puci, I. (1995) "A modified commercial triaxial testing system for small strain measurements: preliminary results on Pisa Clay," Geotech. Testing J., ASTM, Vol. 18, NO. 1, pp. 15-31. Lohani, T.N., Imai, G. and Shibuya, S. (1999) "Determination of shear wave velocity in bender element test," Proc., 2nd Intl. Conf. On Earthquake Geotech. Engrg. Nakagawa, K., Soga, K., and Mitchell, J.K. (1996), "Pulse Transmission System for Measuring Wave Propagation in Soils," Journal of Geotechnical Engineering, ASCE, Vol 122, No. 4. Richart, Jr. (1997) "Field and laboratory measurements of dynamic soil properties," Proc. DMSR 77, Vol. 1. Riemer, M. F., Gookin, W. B., Bray, J. D., and Wartman, J. "Using Reflected Shear Waves to Measure Small Strain Dynamic Properties," Proc., The 5" Caltrans Seismic Research Workshop, Caltrans, Sacramento, CA, June 16-18, 1998. Scholey, G.K., Frost, J.D., Lo Presti, D.C.F., and Jamiolkowski, M. (1995) "A Review of Instrumentation for Measuring Small Strains During Triaxial Testing of Soil Specimens," Geotech. Testing J., Vol. 18, No. 2, pp. 137-156. Seed, H.B. and Idriss, I.M. (1970) "Soil moduli and damping factors for dynamic response analyses," Report No. UCB/EERC-70/10, Univ. of Calif., Berkeley. Shibuya, S., Toshiyuki, T., Fukuda, F. and Degoshi, T. (1995) "Strain rate effects on shear modulus and damping of normally consolidated clay," Geotech. Testing J., ASTM, Vol. 18, No. 3, pp. 365-375. Shirley, D., and Hampton, L. (1978), "Shear wave measurements in laboratory sediments," Journal of the Acoustical Society of America, Vol. 63, NO.2, pp. 607-613. Tatsuoka, F. (1990) "Some Recent Developments in Triaxial Testing Systems for Cohesionless Soils," Advanced Triaxial Testing of Soil and Rock, ASTM STP 977, R. Donaghue, R. Chaney, and M. Silver, Eds., ASTM, Philadelphia, pp. 7-67. 856
Earthquake GeotechnicalEngineering, SBco e Pinto (ed.)0 1999 Balkema, Rotterdam, ISBN 90 5809 1 16 3
Visualization of soil behavior from dynamic centrifuge model tests B. L. Kutter & A. Balakrishnan University of California, Davis, Gal$, USA
ABSTRACT: Due to the increase in complexity and the amount of data and instrumentation obtained in large scale centrifuge model tests, it is important to improve our techniques for processing and presenting the data. This paper attempts to present a large amount of complex model test data involving liquefaction and lateral spreading in formats that allow intuitive understanding of mechanisms involved. Evidence of shear shock waves in liquefying/de-liquefying soil is presented, and time and spatial relationships between acceleration, displacement and pore water pressure are presented using snapshots from data animations. 1. INTRODUCTION Engineers and scientists are becoming more and more burdened by large quantities of information. As our ability to generate and collect data expands, we need to develop better ways to process, present and understand the data. Geotechnical centrifuge modeling has continued to grow in usage and sophistication. The acceptance of usefulness by the engineering profession has contributed to a steady growth and productivity of centrifuge facilities. The quality and quantity of data have made major improvements over the last decade. With the improvements, we see more and more information and detail in the experimental results. The extraction of knowledge (as opposed to data) from complex nonlinear tests, however, takes a tremendous time and effort. Beyond the knowledge gained by the researchers conducting the tests, it is also important to transfer this knowledge to engineers that might find it useful for practice. The large size of the centrifuge at UC Davis has led to a tendency to include increasingly complex models with more detailed structures, and increasing numbers of instruments. For example, in one large container full of soil, we have placed more than one single pile and more than one pile group in one container. Containers have included multiple soil layers and pile groups with more than 30 piles.
Each model is typically subjected to between 5 and 30 shaking events. During each shaking event, 60 to 80 instruments are recorded dynamically. Researchers spend a large fraction of their time organizing data before they get a chance to study the results. As a standard practice, one data report is produced for each container tested on the centrifuge. The electronic data and reports are available for anyone to use; some of these data reports can be directly downloaded from the internet: (http ://cgm. engr.ucdavis. edu) . It is important to make the data available because so much time is spent gathering it. It is just not possible for one or two individuals to completely analyze the test results. So, analysis by outside researchers is encouraged. It is recognized, however, that outside researchers must also invest a major amount of time to understand the motivation, design and intricacies of large-scale complex experiments. This paper presents examples of how centrifuge model test data can be presented in understandable formats. Another goal of this paper is to convey the richness of the available centrifuge data. Finally, it is intended that the reader will gain some new perspectives on mechanisms of liquefaction and lateral spreading. Among other phenomena, the data presented illustrate: the importance of density and soil layering on liquefaction mechanisms, cyclic liquefaction and de-liquefaction (caused by contraction and dilation), the propagation of a slow 857
Figure 1. Configuration of model U50; (a) plan view, and (b) cross-section.
Figure 2. Acceleration and pore pressure time histories for model U50 (south vertical array).
shear shock wave due to nonlinear wave propagation in liquefying soil.
sand had a relative density (Dr = 50%). The top soil layer, made from remolded San Francisco Bay Mud, was preconsolidated in the laboratory and sloped toward a "river" channel which ran across the width of the model. The base of the models was tilted down from South to North with about a 3% slope. This paper also presents some results from model C80, which was identical except that the sand with 50% relative density was replaced by sand with 80% relative density.
2. MODEL TEST DESCRIPTION The liquefaction and lateral spreading of sloping ground was studied in a series of seven model tests. One goal of this study is to investigate the effectiveness and extent of ground improvement required to mitigate effects of liquefaction. Results from just two of the seven model tests is presented here. The models were constructed in a flexible shear beam (FSBl) container (1.72 m long, 0.7 m deep, and 0.69 m wide). The container consists of six rings made from structural aluminum tubing separated by soft neoprene rubber. Wilson et al. (1997) documents aspects of the performance of the FSBl container. The models were tested at a centrifugal acceleration of 30 g on the 9 m radius centrifuge at UC Davis, which accommodates perhaps the largest centrifuge based shaker in the world. The centrifuge, shaker and container are described in more detail by Kutter et al. (1994) and on the internet (http://cgm.engr .ucdavis.edu). The models included two Nevada sand layers, covered by a sloping clay layer as depicted in Figure 1. In test U50, the bottom sand layer was a dense (Dr = 80%) 6 m thick layer. All dimensions presented in this paper are given at the prototype scale unless otherwise indicated. The top 9 m of
3. TEST RESULTS Figure 1 shows the configuration and instrument locations for model U50. Figure 2 shows time histories of acceleration and pore pressure obtained from the vertical array of numbered instruments at the south side of the model. The time histories show a nonlinear transformation of the motion between the base and the ground surface. The plots also show a clear relationship between the downward spikes of pore water pressure and the large spikes of acceleration. Base input motions of U50 and C80 were obtained by scaling recorded motions at Port Island in the 1995 Kobe Earthquake. Similar to the procedure described by Zeghal et al. (1995), it is possible to multiply the horizontal accelerations by tributary layer masses to get estimates of cyclic shear stresses at selected depths. The cyclic shear displacements can be obtained by subtracting displacements computed from two
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Figure 3. Stress-displacement loops computed at interface between sand and clay at the south vertical array of instruments. Model U50 had contains 50% relative density sand. In model C80 the looser sand was replaced by 80% relative density sand. accelerometers. Displacements were computed by double integration of the accelerations with respect to time. Figure 3 shows computed shear stressdisplacement curves at the interface between the clay and sand determined from entries 46 and 50 (see locations on Figure 1). The legend in Figure 3 gives the initial effective stress at the interface and the prototype spacing between the accelerometers; an average shear strain could be computed by dividing the displacement by the spacing. Presentation of the data in the form of stressdisplacement or stress-strain relationships is a useful way to characterize dynamic soil behavior in a region of the model. Here, we prefer to present displacement instead of strain because the strains are clearly non-uniform owing to the interface between
sand and clay. Stress-displacement loops allow an engineer to visualize the soil behavior more directly than is possible by viewing of time histories alone. In Figure 3, we may make a few observations: “banana” shaped stress-displacement relationships are obtained; hysteresis loops for loose sand (U50) are smaller than for dense sand ((280); and, a slack range of strains over which the shear stresses are small seems to evolve. Beyond the slack range, the material stiffens due to increases in effective stress associated with dilatancy (negative pore pressures seen in Fig. 2). Figure 4 shows cross sections of models U50 and C80 obtained from photographs and measurements of black sand columns exposed during post-test dissection of the models. It is apparent that the sand in the looser model deformed much more than that in the dense model. Increasing the density of the 9m thick layer from 50% to 80% was found to reduce settlements and lateral displacements of the sand by a factor of approximately three. The magnitude of lateral clay displacement, however was approximately the same for both models. It appears that densification of sand does not necessarily control the deformation of an overlying impermeable layer.
4. DATA ANIMATION Liquefaction is a boundary value problem. The stresses and strains imposed on an element are the product of the input motion, and the response of soil layers around the element. Furthermore, in permeable soils, the hydraulic gradient that Figure 4. 859
Figure 5. Snapshot from test U50 at time t = 5.702 s.
accompanies liquefaction will lead to re-distribution of pore water from one layer to other layers. Stress-displacement loops (Fig. 3) attempt to look at isolated behavior in certain soil elements. To help understand the global behavior, animations of the data can be extremely useful. Results from experiments can be compared in space and time. One goal of animation ought to be to reduce the level of abstract thinking required to visualize the mechanisms at work. It is not possible to convey animations in conventional paper publications, but a few frames of such an animation of data from model U50 are shown in Figures 5 and 6. Figure 5 shows one frame (time = 5.702 seconds) after one large cycle of loading, before liquefaction. Acceleration waves, pore pressure waves, and displacement profiles are included in the animation. The data are from the north and south vertical arrays of accelerometers and pore pressure transducers. Data points show transducer locations. Pore pressures are normalized by the initial vertical effective stress. Tick marks on the sides of the figures represent meters in prototype scale. Dynamic (high frequency) displacements presented in the animations are obtained by double integration in time of the accelerometer data. Because integration of acceleration data is subject to drift, it cannot provide accurate information about the permanent (low frequency) displacements. The low frequency horizontal displacement of the clay layer on the south side of the model was directly measured by an LVDT. This LVDT data was combined with acceleration data using a signal processing technique described by Kutter and Balakrishnan (1 998) to calculate the displacement of the clay at the south array.
The low frequency displacement of the sand layer could not be measured continuously by LVDT’s. But, the final lateral displacement profile of the sand was determined from measurements of deformed vertical colored sand columns (Fig. 4). To include permanent and low frequency deformations at various depths in the sand, the low frequency component of displacement was assumed to be a scaled version of the displacement of the clay (from LVDT). The scale factor was chosen to force the ultimate displacement to match the final deformed shape of the sand columns. This is useful for visualization purposes, but it must be regarded as an assumption, not an observation. Also shown in Figure 5 is the time history of base motion applied by the shaker. The base acceleration is plotted with time increasing along the vertical axis. The scale for acceleration is indicated at the bottom of the figure. A horizontal line shows the point in the time history corresponding to the snapshot. At t = 5.702 s (Fig. 5 ) little permanent displacement has occurred. The pore pressure ratios on the south side are approximately 50%. On the north side, the pore pressure happens to be negative near the top of the sand. The negative pore pressures, associated with the dilation that is expected to occur in sand at large shear strains, is consistent with the negative pore pressure spikes seen in Figure 2. It should be noted that the south side of the model had a much larger slope toward the river channel than the north side. In addition, an abutment was placed upon the north flood plain; so, differences in behavior of the north and south sides are expected. At t= 5.702 s the acceleration distribution is very similar at the north and south vertical arrays; the wavelength of the acceleration wave appears to be about 15 m at this particular time. Figure 6 shows several snapshots from the same animation (t = 3.001, 11.54, 11.78, 11.99, 12.5, 17.257 s). Refer to Figure 5 for the legend for this Figure 6. The first frame shows a condition before shaking. The next three (1 1.54, 11.78, and 1 1.99 s) are a sequence after initial liquefaction showing an acceleration wave travelling up the north vertical array. At 11.54 s, the third accelerometer (from the top on the north array) reached a peak acceleration. At 11.78 s, the peak acceleration pulse reached the second accelerometer. The top (clay) acceleration reached a peak at 11.99 s. The wavelength cannot be directly deduced from the snapshots because only one transducer recorded the pulse at a given time; but, this must mean the wavelength is less than the transducer spacing (1.35 m). The shear wave 860
velocity in the soil might be estimated from time delay between peak acceleration at successive accelerometers. The spacing of the 2”d and 3‘d accelerometers is 1.35 m (prototype), providing:
v =
1.35~1 = 5.6m I s (1 1.78-1 1.54)s
The mechanics of non-linear wave propagation in liquefying soil is poorly understood. It appears that
while the effective stress is zero, the wave velocity is nearly zero and no accelerations are transmitted. Deformations may, however, accumulate due to momentum prior to liquefaction. When the liquefied soil reaches a threshold strain, it begins to dilate. When it dilates, it de-liquefies and “grabs”, transmitting the acceleration upward. This in turn propagates strains to the soil above. From the snapshots s h o w in Figure 6, it can be Seen that acceleration spikes are accompanied by pore 861
pressure ratios less than one in the soil beneath the acceleration spike. It seems that an acceleration shock front is associated with the onset of dilatancy. Shock waves are expected in materials that stiffen with increasing strain. A soil that de-liquefies due to dilatancy is certainly a strain-hardening material, so the occurrence of shear shock waves in liquefying/de-liquefying soils would be expected. Very small accelerations were observed in the north vertical array at the times of the snapshots shown if Figure 6. This is consistent with the generally large pore pressure ratios at the south flood plain. At time 17.257 s, the strong shaking is completed, and high pore pressures remain throughout the upper 9 m of sand (Dr = 50% sand) The lower, Dr = 80% sand has smaller pore pressure ratios. The near final deformed shape of the soil layers is seen at t = 17.257 s, and this is seen to be consistent with the data presented in Figure 4. 5. CONCLUSIONS Large-scale experiments with a large amount of instrumentation, layered sloping soil deposits and highly non-linear liquefaction mechanisms are presented. It goes without saying that the is complex. In order to enable readers to comprehend the relationships of the data, it is important to search for new and better ways of presenting the information. We have attempted to present data from animations of acceleration, pore pressure and displacement profiles. Relationships between dilatancy and acceleration waves were discussed in some detail, and it is apparent that a shear shock wave is being observed in the model test. The possibility of a shock wave may be anticipated for a material that stiffens with strain. The measured shock wave velocity was very slow (about 6 d s ) , but this velocity may increase with the magnitude of the stress wave. There is a need to be able to publish movies of the full animations, which of course, is not possible in conventional paper publications. Researchers can pause, rewind or fast-forward movies or they may be viewed in “prototype time” to provide improved comprehension of temporal relationships. Interested readers may access movies of centrifuge test data by accessing the UC Davis Center for Geotechnical Modeling web site (http://cgm.engr.ucdavis.edu). Also, it is apparent that denser arrays of instruments and greater sampling rates would be desirable to provide more resolution of features such as the observed shock wave.
6. ACKNOWLEDGEMENTS The Pacific Earthquake Engineering Research Center (PEER) and the California Department of Transportation supported this research. Construction of the centrifuge and shaker facilities were made possible by support from the National Science Foundation, the Obayashi Corporation, the University of California, and Caltrans. Tom Kohnke, Dennis O’Brien, Dan Wilson, Ross Boulanger, and I. M. Idriss, all contributed to various stages of this research project. 7. REFERENCES Balakrishnan, A., Kutter, B.L., and Idriss, I.M. 1998. Centrifuge testing of remediation of liquefaction at bridge sites. Transp. Res. Rec. 1633, TRB, National Research Council, Washington, D.C., 26-37. Kutter, B.L. and Balahishnan, A. 1998. Dynamic model test data from electronics to knowledge. Proc. Int. Conf Centrifuge ’98,Vol. 11, in press. Kutter, B.L., Idriss, I.M., Kohnke, T., Lakeland, J., Li, X.S., Sluis, W., Zeng, X., Tauscher, R., Goto, Y., and Kubodera, I. 1994. Design of a large earthquake simulator at UC Davis. Proc, Int. Conf Centrifuge 94, Roterdam:Balkema, 169175. Wilson, D.W., Boulanger, R.W., Kutter, B.L., and Abghari, A. 1997. Aspects of dynamic centrifuge testing of soil-pile-superstructure interaction. Observation and Modeling in Numerical Analysis and Model Tests in Dynamic Soil-Structure Interaction Problems, Special Pub., ASCE, (64), New York, 47-63. Zeghal, M., Elgamal, A.W., Tang, H.T., and Stepp, J. C. 1995. Lotung downhole array. 11: Evaluation of soil nonlinear properties. J. Geotech. Engrg., ASCE, 121(4), 363-378.
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Earthquake Geotechnical Engineering, SBco e Pinto (ed.)0 1999 Balkema, Rotterdam, ISBN 90 5809 1 16 3
Dynamic characterisation of soils from laboratory tests Michele Maugeri & Antonio Cavallaro Universityof Catania, Italy
ABSTRACT: This Panel presentation concerns with dynamic characterisationof soils from laboratory tests of undisturbed clays and summarises the research activity undertaken by the writer's at the University of Catania and at the Politecnico of Torino over the last five years. The paper describes and compares the results of laboratory investigations performed on Augusta and Catania clay which were carried out in order to determine the variation of shear modulus and damping ratio during Torsional Shear and Resonant Column tests; the pore pressure build up during the tests are also discussed. Finally the Young's Modulus is evaluated by triaxial monotonic apparatus equipped with local strain gauges.
1 INTRODUCTION
Soil stfiess at small strains is a relevant parameter in solving boundary value problems such as: - seismic response of soil deposits to earthquakes; - dynamic interaction between soil and foundations; - design of special foundations for which the serviceability limit allows only very small displacements. However, it was been pointed out by many researches that the strain level which occurs in many geotechnical problems is quite small even under the static loading condition and even in the case of conventional foundations (Jardine et al. 1986, Burland 1989, Berardi and Lancellotta, 1991, Maugeri et al. 1998). On the other hand, it is known that the hypotheses of homogeneity, elasticity and isotropy are unrealistic for soils. In reality soil behaviour is non linear (non linear elasticity or plasticity) and anisotropic. In particular, many researches (Hardin 1978, Jardine et al. 1984, 1986) have postulated that an elastic or apparently elastic soil response occurs only at small strains (i. e. less than 0.001 %) which are typical strain levels that occurs in many geotechnical design problems involving both static and dynamic loading conditions. Shear modulus (G) and damping ratio (D) of soils are basic input parameters used to compute the equivalent-linear seismic response of soil deposits
and the interaction between soil and structures. A great deal of experimental data are available in literature concerning the dependence of these two important parameters on several factors such as the shear strain level (y) consolidation stresses (&, ag ), void ratio (e), overconsolidation ratio (OCR), etc. However there is limited information about the influence of loading rate or strain rate on G and D. In order to study the influence of strain rate, a comprehensive laboratory investigation has been carried out to obtain the variation of the shear modulus (G) and damping ratio (D) on Augusta and Catania clay. Three different kinds of tests were performed on solid and hollow cylindrical specimens reconsolidated to the in situ geostatic stress: - monotonic loading tests at constant stress rate; - cyclic loading tests at constant strain rate; - Resonant Column tests. Moreover the influence of strain rate on pore pressure build up are also investigated. Finally the Young's Modulus is evaluated by triaxial monotonic apparatus instrumented with local strain gauges.
2 TESTED SOILS The Augusta and Catania sites are located on the east coast of Sicily, which is one of the most seismically active areas of Italy. 863
The Augusta deposits mainly consist of a medium stiff, overconsolidated (OCR = 2.0 to 6.0), marine clay with medium to high PI. The values of the natural moisture content w, prevalently range from between 30 and 35 %. Characteristics values for the Atterberg limits are: w,=60 - 65 % and w,=22 - 26 %, with a plasticity index of PI=30 - 40 %. The deposits shown a very high degree of homogeneity and can be classified as inorganic clay of medium to high plasticity. Detailed information on the Augusta clay deposit is given by Maugeri et al. (1994), Cavallaro and Maugeri (1 996), Cavallaro (1997) and Lo Presti et al. (1998). The Catania deposits mainly consist of a normalconsolidated silty clay with medium PI. The natural moisture content w, range from between 20 and 27 %. The dynamic characteristics of soils in the Catania municipal area is one of the main objective of "Catania Project", that requires a reasonably detailed model of the surface geology and geotechnical characterisation. Detailed information on Catania site is given by Carmbba and Maugeri (1998). Typical range of physical characteristics, index properties and strength parameters of the Augusta and Catania deposits are reported in Table 1. 3 SHEAR MODULUS AND DAMPING RATIO
3.1 Tests procedures The equivalent shear modulus (G,) and damping ratio D were determined in the laboratory by means of a Resonant Column test (RCT) and cyclic loading torsional shear tests (CLTST) performed on undisturbed specimens which were isotropically reconsolidated to the best estimate of the in situ mean effective stress by means of a Resonant ColumdTorsional shear apparatus (Lo Presti et al. 1993). Monotonic loading torsional shear tests (MLTST) were also performed on specimens using the same apparatus, obtaining the measurement of Table 1. Mechanical characteristics of tested soils. e c' [WaI ["I AU 18.7-19.4 29-38 32-46 0.810-1.030 35 17 CT 19.2-20.5 20-27 18-32 0.551-0.695 43 24 where: AU = Augusta; CT = Catania; c' (Cohesion) and 4' (Angle of shear resistance) were calculated from C-U Triaxial Tests for Augusta and from Direct Shear Test for Catania site.
I I
the secant shear modulus G,. For RCTs the damping ratio was determined using two different procedures: following the steady-state method, the damping ratio was obtained during the resonance condition of the sample; following the amplitude decay method it was obtained during the decrement of free vibration.
3.2 Shear modulusfrom laboratory tests For Augusta clay the laboratory test conditions and the obtained small strain shear modulus Go are listed in Table 2. The Go values, reported in Table 2 for Augusta clay, indicate a moderate but measurable influence of strain rate and type of loading even at very small strains where the soil behaviour is supposed to be elastic. In particular, the effect of an increase in the strain rate is that of an increase in the elastic limit which is also called the elastic threshold shear strain (y:) (Vucetic 1994), that is, the strain level below which the stress-strain relationship is linear. Also it is generally recognised that the rate dependence of soil s t a e s s is due to the viscosity of the soil skeleton (Dobry and Vucetic 1987). In order to appreciate the rate effect on Go, it is worthwhile to remember that the equivalent shear strain rate (y = 240. f - y [%/s]) experienced by the specimens at given frequency f during RCT can be three orders of magnitude greater than those adopted during CLTST. The effects of the rate and loading conditions become more and more relevant with an increase of the shear strain level, as can be seen in Figure 1 where the G-y curves obtained from MLTST, CLTST and RCT are compared. It is possible to notice that the lowest decay of G with y is observed in RCT, while the maximum decay occurs during MLTST. Table 2. Test Condition for Augusta Clay Specimens. Tesd o : ~ e IP11MLTSTIG,(1)IG0(2)IG0(3)1Speci CLTST I[MPa]l[MPa]l men No. [kPa]
I
I
I
I
I
I
I I
I
I
155 10.6931301 U 1 4 6 l H 377 0.834 38 U 67 75 H 5 398 0.768 38 U 70 H where: U= Undrained. Go(I) from MLTST, Go(2) from CLTST, G,(3) from RCT. H= Hollow cylindrical specimen (R, = 25 mm R, = 15 mm h=lOO mm). S= Solid cylindrical specimen (R = 25 mm h=lOO mm). 3 4
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3.3 Damping ratio from laboratory tests
Figure 1. G-y curves from MLTST, CLTST and RCT tests for Augusta clay. For Catania clay the Go values are reported in Table 3. As can be inferred fiom data shown in Figure 2 the rate effects on the shear modulus are the same over the entire strain interval investigated where Go(RC)/Go(CLTST)E 1.21. This experimental finding is different than that observed for Augusta clay who have showed an increasing rate effect with an increase of the strain level. This different behaviour can be tentatively explained by considering that in this study solid cylindrical specimens with a shear strain variable fiom zero, at the centre, to a maximum value at the edge have been used, while in previous study mainly hollow cylinder specimens were used. In the case of hollow specimens, the shear strain is quite constant along the radius.
For Augusta clay a comparison between the damping ratio values obtained fiom RCT and those obtained fiom CLTST is shown in Figure 3. It is possible to see that the damping ratio from CLTST, at very small strains, is equal to about 2 %. Greater values of D are obtained fiom RCT for the whole investigated strain interval. After a correction of the experimental data for equipment-generated damping (Dq ) , according to Stokoe et al. (1995), still large differences remain between the CLTST and RCT results. As regard Catania clay a comparison between the results of the CLTST and RCT is shown in Figure 4. The damping ratio values obtained fiom RCT using two different procedures are similar even if for strain level more than 0.2 % higher values of D have been obtained from steady-state method. It is possible to see that the damping ratio fiom CLTST, at very small strains, is equal to about 1 %. Greater values of D are obtained fiom RCT for the whole investigated strain interval.
Table 3. Test Condition for Catania Specimens. Test 1 oiC I e I PI ICLTSTIGo(1)IGo(2)lSpeci No. [kPa] RCT [MPa] [MPa] men 1 172 0.551 26.05 U 91 S 2 I 246 10.582 128.601 U I 45 I 64 I S 3 375 0.653 20.02 U 62 77 S 4 411 0.695 31.40 U 77 93 S where: U= Undrained. Go(1) fiom CLTST, Go(2) froin RCT. S= Solid cylindrical specimen (R = 25 mm h=lOO mm). I
Figure 2. G-y curves from CLTST and RCT tests for Catania clay. 865
Figure 4. Damping ratio from CLTST and RCT tests for Catania clay.
Considering that the influence of N on D has been found to be negligible, in the case of clayey soils for strain levels of less than 0.1 % (Cavallaro 1997, Lo Presti et al. 1996, Lo Presti et al. 1997% Lo Presti et al. 1997b, Lo Presti et al. 1998), it is supposed that RCT provide larger values of D than CLTST because of the rate (fiequency) effect, in agreement with data shown by Shibuya et al. (1995) and Tatsuoka et al. (1995). According to these researchers the nature of soil damping in soils can be linked to the following phenomena: Viscosity of the pore fluid which is relevant at very high fiequencies. - Viscosity of the soil skeleton (creep) which is relevant at very small strain rates. - Non-linearity which governs the so called hysteretic damping controlled by the current shear strain level. This kind of material damping is absent or negligible at very small strains. Soil damping, at very small strains, is mainly due to the viscosity of the soil skeleton or of the pore fluid, depending on the strain rates or frequencies. Moreover, according to Tatsuoka and Kohata (1995) and Tatsuoka et al. (1995) a partial drainage condition can provide very high values of the damping ratio. Shibuya et al. (1995) indicate that, for a given strain level, the damping ratio of cohesive soils increases when the loading frequency is smaller than 0.1 Hz (because of the creep effects), is more or less constant for loading fiequencies between 0.1 and 10 Hz (non linearity is dominant) and increases for frequencies greater than 10 Hz (because of pore fluid viscosity). Figure 5 shows the damping ratio of Vallericca clay (Italy) vs. fiequency, for a strain level of 0.01 % and consolidation pressure between 100 and 800 H a . This data was obtained by d'Onofiio 1996. The considered soil is a stiff, highly overconsolidated,
Pliopleistocene, marine clay with a PI of about 26%. In the same figure the data of Augusta clay, obtained in this research and those of Pisa clay obtained by Lo Presti et al. (1997b) have been reported. The trend of the whole data is in good agreement with the findings of Shibuya et al. (1995).
4 PORE PRESSURE BUILD UP The volumetric threshold shear strain y: (Vucetic 1994, Jamiolkowski et al. 1994) indicates the strain level above which the following phenomena occur: i) the build up of permanent volumetric strains in drained tests; E) the pore pressure build up in undrained tests. The above phenomena, obviously, have to be observed in monotonic or cyclic tests that do not involve a change of the mean total stress. The accumulated pore pressure excess, measured during undrained tests, is plotted in Figure 6 vs. the shear strain. In the same figure the data of Pisa clay obtained by Lo Presti et al. (1996) have been reported. It is possible to observe that: - the values of y r increase with an increase of the strain rate. - the values of the accumulated Au, for a given strain level increase with an increase of the strain rate. - greater values of y: occur during monotonic tests in comparison to cyclic tests, regardless of the strain rate. - the pore pressure build-up, for a given strain level is greater in the case of cyclic tests than for monotonic tests, regardless of the strain rate. A severe shear modulus degradation, which brought the specimen to failure, had been observed in CLTST for y = 0.1%. On the contrary, no failure occurred in RCT even at strains larger than 0.1%.
-
Figure 5. Damping ratio vs. frequency (after Lo Presti et al. 1998).
Figure 6 . Pore pressure build up for Augusta clay.
866
Moreover, the accumulated pore pressure increase, for a given shear strain resulted to be larger in CLTST than in RCT. It is believed that the material degradation and the related pore pressure increase not only depend on y but are also influenced by the rate of loading. In particular, such phenomena become more relevant as the strain rate decreases.
5 YOUNG'S MODULUS For the valuation of Young's modulus at small strain a new triaxial apparatus called DBB Triaxial Cell was designed (Figure 7). The double ball bearing allow a good alignment between loading axes and sample axes. The apparatus, equipped with several sensors, should be able to provide stifEness measurements in the small strain range (i.e. E, = 0.001 - 0.1 %) (Cavallaro 1997, Cavallaro et al. 1998). The specimens were underwent to wet and dry setting procedure (Cavallaro 1997). The Young's modulus results vs. axial strain are reported in Figure 8. For strain level less than of 0.01 % a remarkable influence of setting specimen procedure is shown. It could be done to the swelling of the sample in the wet setting condition.
Figure 8. Young's modulus results vs. axial strain.
6 CONCLUSIONS A dynamic characterisation of two Italian clay has been presented in this paper. On the basis of the data shown it is possible to draw the following conclusions: - the shear modulus and damping ratio obtained by CLTST is considerable less than that obtained by RCT for strain level between 0.001 % - 0.1 %; - the shear modulus and damping ratio are influenced by rate effects; the shear modulus is moderately influenced at small strain and when hollow cylindrical specimens have been used; - the volumetric threshold shear strain y: seemed to be dependent on strain rate, as well as, on loading conditions; - the Young's modulus at small strain, evaluated by the DBB triaxial apparatus, could be used for evaluation of allowable settlement.
ACKNOWLEDGEMENT The Authors would like to thank Prof. Lo Presti and Dr. Pallara of Politecnico of Torino for their contributionto the research activity.
REFERENCES Berardi, R. & Lancellotta, R. 1991. S t a e s s of granular soils from field performance. Geotechnique Vol. 4 1,No. 1 , pag. 149 - 157. Burland, J. B. 1989. Small is beatiful - The stifbess of soil at small strains. Ninth Laurits Bjerrum Memorial Lecture, Canadian Geotechnical Journal, Vol. 26, No.4, pag. 499 516.
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Figure 7. The DBB Triaxial apparatus.
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Cavallaro, A.M.F. & Maugeri, M. 1996. Comportamento tensionale deformativo dell'argilla di Augusta sottoposta a carichi ciclici. Ingegneria Sismica, Vol. XIII, No. 1, pp. 30-40. Cavallaro, A.M.F. 1997. Influenza della velocita di deformazione sul modulo di taglio e sullo smorzamento delle argille. Ph. D. Thesis, University of Catania. Cavallaro, A., Lo Presti, D. C. F., Maugeri, M. & Pallara 0. 1998. Strain rate effect on stiffhess and damping ratio of clays. Italianan Geotechnical Journal, Vol. XXXII, No. 4, pag. 30 - 50. Carrubba, P. & Maugeri, M. 1988. Determinazione delle proprieta dinamiche di un'argilla mediante prove di colonna risonante. Rivista Italiana di Geotecnica, Vol. 22, No. 2, 101- 113. Dobry, R. & Vucetic, M. 1987. Dynamic Properties and Response of Soft Clay deposits. State of the art Report. Proceedings of the Int. Symposium on Geotechnical Engineering of Soft Soils, Mexico city, Vol. 2, pp. 5 1-87. d'Onofrio, A. 1996. Comportamento Meccanico dell'argilla di Vallericca in condizioni lontane dalla rottura. Ph. D.Thesis, University of Naples, Department of GeotechnicalEngineering Hardin, B. 0. 1978. The nature of stress-strain behaviour of soils. Earthquake Engineering and Soil Dynamics, Vol. 1, Pasadena, CA, ASCE, New York, pp. 3-90. Jamiolkowski, M., Lancellotta, R. & Lo Presti, D.C.F. 1994. Remarks on the stiffhess at small strains of six italian clays. Theme lecture session la, Proceedings IS Hokkaido, Volume 2, pp. 817836. Jardine, R. J., Symes M. J. & Burland J. B. 1984. The measurement of soil stiffhess in the triaxial apparatus. Geotechnique, Vol. 34, NO.3, pag. 323-340. Jardine, R. J., Potts, D. M., Fourie, A. & Burland, J. B. 1986. Studies of the influence of non-linear stress-strain characteristics in soil-structure interaction. Geotechnique, Vol. 36, NO.3, pag. 377-396. Lo Presti, D.C.F., Pallara, 0, Lancellotta, R., Armandi, M. & Maniscalco, R. 1993. Monotonic and cyclic loading behaviour of two sands at small strains. Geotechnical Testing Journal, Vol 16, NO 4, pp 409-424. Lo Presti, D.C.F., Jamiolkowski, M., Pallara, 0. & Cavallaro A. 1996. Rate and creep effect on the s t f i e s s of soils. ASCE Convention, Washington, 10-14 Nov. 1996, Geotechnical Special Publication No. 6 1, pp. 166-180.
Lo Presti, D.C.F., Jamiolkowski, M., Pallara, O., Cavallaro, A. & Pedroni, S. 1997a. Shear modulus and damping of soils. Proceeding of the International Symposium on the Pre-failure Deformation Behaviour of Geomaterials, 50th Geotechnique, London, 4 September 1997, Geotechnique Vol. 47, No. 3, pag. 603 - 6 17. Lo Presti, D.C.F., Pallara, 0. & Cavallaro, A.M.F. 1997b. Damping ratio of soils fi-om laboratory and in situ tests. Proceeding of the 14th International Conference on Soil Mechanics and Foundations Engineering, Hamburg, 6 - 12 September 1997, Special Volume TC4, 391 400. Lo Presti, D. C. F., Maugeri, M., Cavallaro, A. & Pallara, 0. 1998. Shear modulus and damping of a stiff clay fi-om in situ and laboratory tests. 1st International Conference on Site Characterization, Atlanta, 19 - 22 April 1998, 1293-1300. Maugeri, M., Castelli, F. & Motta, E. 1994. Pile foundation performance of an earthquake damaged building. Proc. of the Italian-French Symposium on Strengthening and Repair of Structures in Seismic Areas, Nice, France. Maugeri, M., Castelli, F., Massimino, M. R. e Verona, G. 1998. Observed and computed settlements of two shallow foundations on sand. Journal of the Geotechnical and Geonvironmental Engineering, ASCE, Vol. 124, No. 7, July, 1998, pag. 595-605. Shibuya, S., Mitachi, T., Fukuda, F. & Degoshi, T. 1995. Strain rate effect on shear modulus and damping of normally consolidated clay. Geotechnical Testing Journal 18~3,365-375. Stokoe, K.H. 11, Hwang, S.K. Lee, J.N.-K & Andrus, R. 1995. Effects of various parameters on the stiffhess and damping of soils at small to medium strains. Keynote Lecture 2, IS Hokkaido 1994 2, 785-816. Tatsuoka, F. & Kohata, Y. 1995. S t f i e s s of hard soils and soft rocks in engineering applications. Report of the Institute of Industrial Science, The University of Tokyo, March 1995, Vol. 38, NO.5. Tatsuoka, F., Lo Presti, D.C.F. & Kohata, Y. 1995. Deformation characteristics of soils and soft rocks under monotonic and cyclic loads and their relations. 3rd International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamic, State of the Art 1, 2, 85 1-879. Vucetic, M. 1994. Cyclic threshold shear strain in soils. Journal of Geotechnical Engineering, ASCE, Vol. 120, NO. 12, pp. 2208-2228. 868
Earthquake Geotechnical Engineering, S&coe Pinto (ed.) 0 1999Balkema, Rotterdam, ISBN 90 5809 1 163
Soil characterization by shear wave velocity Munenori Hatanaka Takenaka Research and Development Institute, Chiba,Japan
ABSTRACT Based on the results shown in recent studies, the in-situ shear wave velocity has been found as one of the useful indices to characterize the soil properties. Following conclusion can be made from these studies. (1) In-situ shear wave velocity is a useful indicator to evaluate the liquefaction potential for sandy and gravelly soils. (2) %-value of in-situ soils can be evaluated by using the in-situ shear wave velocity. (3) The stress dependency of Gofor in-situ sandy and gravelly soils is larger than that of reconstituted sand samples. In average, the power of the confining stress ( J c ' is about 0.67, and 0.70 for sandy and gravelly soils, respectively. (4)I t is important to take into account of the effect of the &-value on the sample quality evaluation by comparing the initial shear modulus observed both in the field and laboratory. It is also, however, pointed out that many efforts are required for increasing the accuracy in measuring the in-situ shear wave velocity. 1INTRODUCTION
disadvantageof SPT N-value based simplified procedure, shear wave velocity has been studied as a useful index related to the liquefaction potential of in-situ soils (Tokimatsu et a1.(1986, 1988, 1992); Robertson et a1.(1995); Stokoe et a1.(1988); Finn et a1.(1991); Hatanaka et a1.(1997)). This kind of approach to access the liquefaction potential of in-situ soils can be divided into three groups; 1) Directly relating the ground shaking (acceleration at the ground surface) and the field performance during the earthquake (liquefaction or non-liquefaction). 2) Extending a correlation between the initial shear modulus and the liquefaction strength for reconstituted samples to the field performance. 3) Correlating the in-situ shear wave velocity and the liquefaction strength measured in laboratory tests using high-quality undisturbed samples.
The body wave velocity, especially, the shear wave velocity (V,) has been widely used as one of the useful tool to characterize the in-situ soil properties. Compared with other in-situ testing methods, the in-situ shear wave test has an important advantage that it is basically applicablefor any kind of soil. In this paper, recent studies related to the following topics will be reviewed and discussed. 1.Liquefaction potential evaluationby V,. 2. &-value estimation by V,. 3. Initial shear modulus (Go)from V,. 4. Sample quality evaluation by V,.
2 LIQUEFACTION POTENTlALEVALUATIONBY Vs
Group 1)
Evaluation of liquefaction potential for construction sites is one of the major works in foundation designing. At the present time, the simplified procedure for evaluating the liquefaction potential based on the penetration resistance (N-value) of the standard penetration test (SIT) is most often used in practice. As has been pointed out by many researchers (Tanaka, et al.(1989); Suzuki et al.(1993); Tokimatsu et al.(1986)), however, mainly due to the scale effect of the inner diameter of the penetration spoon, the SPT N-value is possible overestimating the in-situ liquefaction strength of gravelly soils because of its large soil particles. Responding to the needs for overcoming this
One method for evaluating the liquefaction potential of sands from shear wave velocity has evolved from the strain approach by Dobry and his colleagues (1982). Bierschwale and Stokoe (1984) and Stokoe et al.(1989) used the strain approach in analytical studies to generated liquefaction assessment charts based on measured Vs and the maximum ground surface acceleration estimated for a stiff site at candidate-site location. Andrus et al (1992) applied these procedures to gravelly soils that liquefied. The assessment chart for 15 cycles of shaking at a level ground site with the liquefiable sand in the upper 12 m is shown in Fig. 1. The lowest values of Vs from each of 869
the four gravelly sites are also shown in Fig. 1. The plotted data from the four gravelly sites lies within the liquefiableregion. Therefore, this procedure correlating predicts liquefaction at all four sites.
Fig.1 Liquefaction assessment chart based on shear wave velocity (Stokoe et al, 1989)withresults from the four liquefaction sites (after Andrus et al, 1992)
Another method relating liquefaction potential and shear wave velocity has been proposed by Robertson (1990). An empirical correlation between in-situ cyclic stress ratio and normalized shear wave velocity, Vsl, has been proposed for evaluatingthe liquefaction potential of sands (Fig.2). The cyclic stress ratio is calculated using the following expression:
z,J CJ v ’ = 0 * 6 5 (/g)( ~ CJ
Grouup 2) Figure 3 shows the procedure belonging to group 2), for evaluating the in-situ liquefaction characteristics of sand and gravel proposed by Tokimatsu et a1 (1986) and Tokimatsu and Uchida (1990). The working principle in this procedure is that the liquefaction strength has a good correlation with elastic shear modulus for a given soil under given confining pressures. The procedure shown on the left corresponds to the shear wave velocity measurement in-situ. Based on the measured shear wave velocity, Vs, the elastic shear modulus in the field, GOF,can readily be determined. The procedure on the right involves laboratory tests on a specimen reconstituted from the sample obtained at the site. Before liquefaction test, the shear modulus at small shear strain, Go, of the specimen is measured, and compared with Gof:. If they are equal, the liquefaction test is run on the same specimen. If they are not equal, that usually means that GOFis larger than Go, cyclic shear stresses are applied to the specimen until the shear modulus reaches the field value; then the liquefactiontest is run. In order to take the effects of void ratio (e) and confining stress ( CJ ,’) on the Go into account, Go is normalized with respect to e and CJ c’ as described by Eq. (3). “n” in Eq. (3) is used as 2/3 for better data fitting.
(1) in which &= maximum ground acceleration, CJ ”= total overburden pressure, CJ ,,’= effective overburden pressure and rd = a stress reduction coefficient. The shear wave velocity is normalized with respect to an effective overburden stress as follows: v’/
CJ v) rd
(3) (4)
In-situ test
v,,=v,,(Pa/CJ v’)o.2j (2) where Pa=reference stress, typically 100 Ha. Cyclic stress ratio and the lowest V,, values for the gravelly sites are plotted in the proposed liquefaction assessment chart by Andrus et al (1992) as shown in Fig. 2. The plotted velocity data lie within the zone of predicted liquefaction which agrees with observed field behavior. This chart (Fig.2) is based on soil, site and earthquake characteristics treated. Reasonable caution should be exercised in applying the chart to other areas.
Fig2 Proposed correlation between V,, and z d/ U ”’ to muse liquefaction for M=7.5, (after Robertson, 1990) and cornpared with Eeld performance of four gravelly cites (after Andrus et al., 1992)
Sampling & lab test
Drestress Evaluation of in-situ
Fig3 Outline of the proposed method (after Tokimatsu et al, 1988)
Fig.4 Relationship between liquefaction resistanceand GKfor various sands with n=213 (after Tokimatsu and Uchida, 1990)
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As shown in Figs.6 and 7, a good correlation between the undrained cyclic shear strength (cyclic stress ratio to cause double amplitude axial strain of 2.0 or 2.5 %, in 5 or 20 cycles) and the normalized shear wave velocity (VSJwas observed for Holocene gravel and gravelly fill (Masado) in the range of shear wave velocity from 100 m/s to 600 m/s. V,, is used for correctingthe effect of the confining stress on V, by using Eq (5).
Figure 4 shows the results for various sands. A good correlation was found between the liquefaction resistance and normalized shear modulus. Figure 5 shows the comparison of field performance with the proposed method. Fairly good agreement can be seen. In this method, it is important to determine the Go, from laboratory test. Go, value highly depends on the confining stress at laboratory. As a result, it is an important work to reasonably estimate the &-value of insitu soils.
V,,=VJ( o v’/98)3M 0“I: kPa (5) The value of 3/8 in EQ (5) is the average value of 0.5 and 0.25 which covered the test results observed in recent studies (e.g. Hatanaka et al., 1999). The data for Pleistocene gravel, however, is indicated in two separate groups. One group of data basically coincides with that of Holocene gravel. The data from another group shows that the liquefaction strength is much higher than that of Holocene gravel for the same shear wave velocity. More studies should be conducted,however, in the future for investigating the cause of differences between these two groups. It is also important, however, to know the Ko-value for converting the liquefaction strength obtained in laboratory (RLab)to that in the field (Rin.sit,J based on EQ (6).
Group 3)
R,,,=0.9{
Hatanaka et al(1997) performed a systematic research relating the undrained cyclic shear strength of highquality undisturbed gravel samples to the shear wave velocity measured in-situ.
3 KO-VALUEESTIMAIION BY VS
Fig5 Comparison of field performance with boundary between liquefiable and non-liquefiable conditionspredicted by the proposed method (after Tokimatsu and Uchida, 1990)
(l+2&)/3}R,
(6)
The coefficient of the earth pressure at rest (&) is an important soil constant to characterize the in-situ stress condition. In recent years, two approaches to access the &-value by using the shear wave velocity measured insitu have been proposed. Hatanaka and Uchida (1996) proposed a simple method (named “Go-equalmethod”) to evaluate the &-value of the in-situ sandy and gravelly soils by equalizing Goboth observed in the field and that measured in laboratory on high quality undisturbed samples recovered by in-situ freezing sampling method. This method is modified by Hatanaka et al(1999) as “Vsequal method”. The Vs measured in the laboratory (Vs3 can be related to the effective confining stress, Oc7,as indicated in E q . 0 V,,=a. o c 7 n (7) where, ”a” and “n” are soil constants. If the 0c 7 can be correctly estimated as that in-situ, the Vs must be same as that observed in the field (V,,) as shown in Eq.(8). VSF=VSL 0c 7 is related to the effective vertical stress value as indicated in Eq.(9).
y7
(8) and &-
(9) By inserting Eqs. (7) and (9) into Eq.(8), &-value can be described as Eq.(lO). 0,7=(1+2&) 0“73
&= {(3/ o v’)*(V,,/a7)”n-1}/2 87 1
(10)
Hatanaka et a1 (1997) improved a simple and reliable method to measure the shear wave velocity in laboratory (shear wave velocity method: SWV-method). Figure 8 shows a schematic cross section of the test apparatus. This method has the following advantages: 1) without bedding error, 2) little personal error, and adjustable to specimen height. In order to examine the validity of Eq. (10) for soils with various stress conditions and stress histories, the effects of the principal stress ratio and the stress history were investigated by Hatanaka et a1 (1999). They reported that the effects of these factors are negligibly small. The physical properties of the high-quality undisturbed gravel samples tested and the KO-value estimated by this method are listed in Table 1. The K,,value obtained by this method is also related to the V, measured in-situ. As shown in Fig.9, although the data is quite limited, there can be seen a good correlation between the Vs measured in the field (V,,) and the coefficient of the earth pressure at rest (&) for gravelly soils, and it can be described by Eq.(ll). Such kind of data on sandy soils is hoped to be accumulated in future. K,,=0.0058VS4.53
(1505Vs,~350)
where, Vs(HH) and Vs(HV) are horizontally and vertically polarized shear wave velocities, respectively. Cs (HH) and Cs (HV)are dimensional material constants, the ratio of which reflects the fabric anisotropy of the soil structure. They have successfully accessed the &-value in ideal laboratory chamber conditions. They also described that their method is difficult to estimate the insitu &-value because it is very difficult to determine the value of Cs (HH)and Cs O N ) and n. Typical test results are shown in Fig.10. A data obtained by this method on sand with rare gravel was also plotted in Fig.9. An agreement between the data and the Eq.(ll) can be seen.
4 INITIAL SHEAR MODULUS (Go)FROM Vs For a long time, stress dependency of Go, which means the value of “n” in Eq. (13) is widely recognized as 0.5 based on the test results of reconstituted samples (Hardin and Richart,(l963)). As described in Section 1, many researchers have tried to correct the effect of the confning stress on the shear wave velocity in the way that the power of the confining stress, 0c7, is adopted to be 0.25 by Robertson, 2/3 by Tokimatsu et al and 3/8 by Hatanaka et al, respectively. In recent years, the stress dependency of G, was again discussed by some researchers (e.g. Nishio and Tamaoki (1988), Suzuki et a1 (1993), Tanaka et al (1994),
(11)
Based on the body wave velociQ, Vioravante et al (1998) have proposed a simple method to estimate the KO-value as to be described in Eq.(12).
Table 1 Physical properties of undisturbed gravel samples tested and values obtained (after Hatanaka et al., 19998)
&,-
0.80
0.19
0.93 0.83
Fig8 Test apparatus for measuring (after Hatanaka et al., 19998)
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Hatanaka et al(1999)) based on the test results for highquality undisturbed samples. Hatanaka et al (1999) have performed a systematic research on the stress dependency of Go for high-quality undisturbed sand and gravel samples obtained by in-situ freezing method. The physical properties of test samples are listed in Table 2 and Table 3 for gravelly and sandy soils, respectively. In order to separate the effect of the void ratio on the Go, Go was normalized by F(e) as indicated in Eq. (14), which is often used as a factor reflecting the effect of the void ratio on Go for sandy soils. As a result, E@ (13) can be rewritten as Eq. (15). By regressing the test data using Q. (15), we can determine the constants “a’ ” and “n’ ” in Eq. (15). (13) (14) (15)
Go=aCJ c”’ F(e)=(2.17-e)’/(l fe) GJF(e)=a’(CJ ,’)”’
Test results are shown in Fig.11 as G/F(e)- CJ c’ relation. As indicated in Fig.11, fairly good liner correlation between GJF(e) and CJ ,’ in log-log scale are obtained for each type of gravelly soil. The constant “n”’ listed in Table 4 are all larger than 0.5. These values basically correspond to the test results obtained by other investigators (Nishio and Tamaoki (1988), Tanaka et al(1994), Suzuki et al(1993)). The average value of “n” is about 0.7. The higher stress dependency of Go for undisturbed gravelly soils were reconfrmed in the present study by Hatanaka et a1 (1999). Because the height of undisturbed sand samples is about 12.5 cm,it is not large to secure enough accuracy in measuring Vs by SWV method. As a result, Go measured by the Non-contact displacement gauge (NDG) method was used for studying the stress dependency of undisturbed sandy soils. The log GJJ?(e)-logCJ ,’ relation obtained for sandy soils is plotted in Fig.12. The values of “n”’ obtained by regressing the test data are listed in Table 5. As shown in Table 5, the constant “n’ ” for Toyoura sand is 0.48. This value is almost corresponding to 0.5 proposed for reconstituted Table 3 Physical properties of undisturbed sand samples and Toyoura sand sand samples by Hardin and Richart (1963). Other insitu sandy soils, however, show larger n-value (between 0.54 and 0.86). This result means that the stress dependency of Gofor in-situ sandy deposits is larger than that for reconstituted sand samples. It is interesting to note that except the SS sample (a volcanic soil), the GJF(e)- 0 ,’ correlation for other sandy soils can be regressed as Eq.(16). GJJ?(e)=2.59(0c7)o.69 (16)
Table 2 Physical properties of undisturbed gravel samples
Table 4 “n”’ value in Eq.(7) for Table 5 “n”’ value in Eq.(7) for undisturbed sand samples and Toyoura sand undistuhed gravel samples
I
Samdename
I
n’
I
5. SAMPLE QUALITY EVALUATION BY Vs As already has been shown by many investigators, the insitu soil properties are si@icantly influenced by the disturbance during the sampling procedure. Especially, it is much more serious for initial shear modulus and 873
evaluate the liquefaction potential for sandy and gravelly soils. (2) &-value of in-situ soils can be evaluated by using the in-situ shear wave velocity. Such a data for sandy soils is hoped to be accumulatedin future study. (3) The stress dependency of Go for in-situ sandy and gravelly soils in larger than that of reconstituted sand samples. In average, the power of the c o n f i i g stress 0,’is about 0.67, and 0.70 for sandy and gravelly soils, respectively. (4) It is important to take into account of the effect of the &-value on the sample quality evaluation by comparing the initial shear modulus observed both in the field and laboratory. It is also, however, pointed out that there are many problems to be solved for increasing the accuracy in measurement of in-situ shear wave velocity.
Fig.13 Summary on modulus ratio, GoL/G,,, versus in-situ shear modulus, Go,-, relationship (after Kokusho,T., 1987)
liquefaction strength of sandy and gravelly soils (e.g. Yoshimi et al. (1984), Hatanaka et al. (1986, 1995)). As a result, it is an important work to know the effect of sample disturbance on these properties for design purposes. Tokimatsu et a1 described that the shear wave velocity (or the initial shear modulus (Go))can be a good index to evaluate the sample quality. Figure 13 shows such a kind of results summarized by Kokusho et a1 (1987). The degree of sample quality has been discussed by the ratio of the initial shear modulus calculated from the insitu shear wave velocity (G0J and that measured on the undisturbed samples in laboratory test (GoJ We must recognize, however, that the initial shear modulus measured in laboratory test highly depends on the effective confining stress( (T ,’) as described in the previous section.
7 REFERENCES 1) Biershwale, J.G. and Stokoe, K.H. (1984): “Analytical evaluation of liquefaction potential of sand subjected to the 1981 Westmoreland Earthquake,” Gcotech, Engrg. Rep. GR-84-15, Civ. Enm. Dcpt, University of Texas, Austin, Tex. 2) Finn, W,D.L. (1991): ” Assessment of liquefaction potential and post-liquefaction behavior of earthstructures: develop-ments 1981-1991, In S. Prakash (ed.),“Proceedings, 2 nd ICRAGEESD II,St. Louis, MI: pp.1833-1850. 3) Hardin, B. 0.and Richart,E E., Jr (1963): “Elasticwave velocities in granular soils, “Journalof the Soil Mechanics and Foundations Division, ASCE, Vo1.89, No.SM1,pp.33-65. 4) Hatanaka,M., Suzuki,Y, Kawasaki,T. and Endo,M. (1988): “Cyclic undrained shear properties of high quality undisturbed Tokyo gravel,” Soils and Foundations, Vol.%, No.4, pp.57-68. 5 ) Hatanaka,M and UchidaJ. (1996): “A simple method for the determination of &-value in sandy soils,” Soils and Foundations, Vo1.36,No.2, pp.93-99. 6) Hatanakq M., Uchida, A. and Suzuki, Y (199‘7): ”Correlation between Undrained cyclic shear strength and shear wave velocity for gravely soils,” Soils and Foundations, Vo1.37, No.4, pp.85-92. 7)Hatanaka, M., Uchida, A. and Taya, U.( 1999): “Ko-value of insitu gravelly soils,” 11th ISSMGE, Asian Regional Conference (to be published). 8) Hatanaka, M., Uchida, A., Taya, U. Hagisawa, T. and Terui, N. (1999): “Some factors affect the initial elastic modulus measured in hiaxial cell,” 2nd ICEGE, Lisboa, Portgal (to be published). 9) Robertson,P.K., Woeller,D.J., Finn,W.D.L(1992): “Seismic Cone Penetration Test for evaluating Liquefaction Potential under Cyclic Loading,” Canadian Geotechnical Journal, Vo1.29, pp.686-695. 10) Robertson,P.K, Sasitharan, J.C., Cunning, J.C. and Sego, D.C. (1995): “Shear-wave velocity to evaluate in-situ state of Ottawa sand,” Journal of Geotechnical Engineering, V01.121 , pp.262-273. 11) R. D. Andrus, KH. Stokoe, 11 , J.A. Bay, and T.L. Youd (1992) :”In situ Vs of gravelly soils which liquefied,” 10 th Earthquake Engineering of World Conference, pp. 12) Stokoe, K H. II., and Nazarian, S.(1985): “Use of rayleigh waves in liquefaction studies,” Proceedings, Measurement and Use of Shear Wave Velocity, ASCE, pp.1-17. 13) Stokoe, K H. II., Roesset, J. M., Bierschwale, J. G. and Aouad, M.(1988):”Liquefaction potential of sands from shear wave
When we are going to compare the Go measured in laboratory with the Gocalculated from in-situ shear wave velocity, we must reasonably estimatethe value of CJ c’ for laboratory test. There are two ways to determine the (T c’ for laboratory test as described in Eqs. (9) and (17). The vertical effective stress, (Tv’, is easily to be evaluated fiom the soil density and the depth of the ground water table. It Is, however, very difficult to evaluate the coefficient of the earth pressure at rest, &. In most cases, for both research and practical purposes, (T c’ is used as (T ”’, in order to exclude the possible effect of overconsolidation on the Go. (7 c 7 = (T v’ means that &= 1.0. As a result, the discussion based on Fig.13 is only valid for the case of &=l.O. 6 CONCLUSIONS Based on the results shown in recent studies, the in-situ shear wave velocity has been found as one of the useful indices to characterize the soil properties. Following conclusioncanbe made from these studies. (1) In-situ shear wave velocity is a useful indicator to
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velocity," Proceedings BWCEE, Vo1.3, pp.213-218 and Abstract Vol.1, pp.474. 14) Suzuki, Y., Goto, S., Hatanaka, M and Tokimatsu, K. (1993): "Correlation between undrained cyclic shear strengths and penetration resistanus for gravelly soils," Soils and Foundations, Vo1.33, No.1, pp.92-101. 15) Tanaka, Y, Kokusho, T., Yoshida, Y and &do, K (1989): "Dynamic strength evaluation of gravelly soils,"Pmceedings of discussion session on influence of local conditions on seismic response, 12th International Conference on Soil Mechanics and FoundationEngineering pp.113-120. 16) Tanaka,Y, Kudo,K., Yoshida,Y, and Kokusho,T. (1992): "Undrained cyclic strength of gravelly soil and its evaluation by penetration resistance and shear modulus," Soils and Foundations, Vo1.32, No.4, pp.128-142. 17) Tokimatsu, K and Uchida, A.(1990): "Correlation between liquefaction resistance and shear wave velocity," Soils and Foundations, Vo1.30, No.2, pp.33-42. 18) Tokimatsu, K., Yamazaki, T. and Yoshimi, Y. (1986): "Soil liquefaction evaluations by elastic shear moduli," Soils and Foundations, Vo1.26, No.1, pp.25-35. 19) Tokimatsu, K and Yoshimi, Y. (1986): "Liquefaction evaluations of gravelly soils based on shear wave velocity,"llth Japan Earthquake Engineering Symposium, pp.661-666.(in Japanese) 20) Tokimatsu, K, Yoshimi,Y. and Uchida, A. (1988): "Evaluations of undrained cyclic shear strength of soils with shear wave velocity," 9WCEE, Vo1.3, pp.207-212.
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Strong motions and site amplification: - Theme lecture - Panelist’s contributions
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Earthquake GeotechnicalEngineering, S&coe Pinto (ed.) 0 1999 Balkema, Rotterdam, ISBN 90 5809 1 163
Strong ground motions and site amplification Atilla M. Ansal Civil Engineering Faculty, Istanbul Technical University, Turkey
ABSTRACT: The major factors that control strong motion characteristics on ground surface are source, path, and site conditions. Acceleration records obtained in near field during recent earthquakes with relatively short distances apart have demonstrated that certain source factors such as fault type, rupture mechanism, rupture directivity, and fault orientation as well as geotechnical site conditions such as soil stratification, depth of ground water table, and properties of soil layers could have significant influence on strong motion characteristics on ground surface. The acceleration records obtained during recent major earthquakes in Turkey will be evaluated based on the source and site conditions to demonstrate the variability and the effects of these factors. An important step in estimating the design ground motion requires a comprehensive assessment of source characteristics as well as geotechnical and geological site conditions taking into consideration variability observed in nature.
1
INTRODUCTION
The basic features of earthquake strong ground motions affecting the man made and natural environment are the amplitude, frequency content and duration of the induced cyclic ground accelerations. The conventional seismic design and structural analysis requires parameters to account for the amplitude and frequency content of strong ground motions generated during earthquakes and for designating design requirements. A more comprehensive approach is to perform dynamic analysis using representative earthquake strong ground motion acceleration records. One alternative is to use synthetically generated accelerograms and the other alternative is to use real acceleration time histories obtained in similar site and source conditions (Bommer et al, 1998). The parameters used in the conventional seismic design and analysis like design spectrum and design acceleration may not characterise the complexity of the earthquake generated strong ground motions. Therefore, one purpose from an engineering perspective is to establish practical procedures to define new parameters or modify the existing ones to account for the effects of important factors that control earthquake ground motions (Hall et al., 1995; Kawashima & Aizawa, 1986; Shome & Cornell, 1998 ). In this respect, a comprehensive dynamic analysis performed using acceleration time histories may be better suited to model the characteristics of earthquake generated strong
ground motions. Since induced earthquake ground accelerations are controlled by earthquake source mechanism, path characteristics between the source and the site, and geotechnical and geological site conditions, the design parameters in conventional approach as well as the acceleration time histories used in the comprehensive approach need to be determined to account for these factors. Due to the variability observed in nature in source, path and site effects, it is generally preferred to adopt a probabilistic approach in defining design parameters or acceleration time histories representing the three basic features of the induced earthquake excitations, its amplitude, frequency content and duration (Marcellini, 1995; McGuire, 1995). The conventional probabilistic approach to estimate the design ground motion parameters accounting for the amplitude, frequency content and duration of a probable earthquake can be considered in three stages. The first stage is the estimation of earthquake source characteristics based on seismological and geological data for all earthquakegenerating sources in the region. The second stage is the estimation of path characteristics based on attenuation relationships. The third stage is the estimation of earthquake characteristics on the ground surface based on geotechnical, geological and topographical site conditions. In evaluating earthquake probabilities, the first component is the tectonic and geologic formations that can produce earthquakes in the region and the
second component is the seismic history. To understand the possible mechanisms that can generate earthquakes, detailed geological and seismological studies are necessary. However, in addition to being more deterministic, such concentrated multi-disciplinary investigations may seldom be available. Even if available, probabilistic evaluation of earthquake hazard may be more meaningful in the light of unknowns regarding to earthquake source characteristics. Earthquake source characteristics could vary significantly, especially in the near field, depending on the fault orientation, stress drop, rupture pattern, directivity effects, fault roughness, and velocity of rupture propagation (Allen, 1995). Due to the fault tectonics and fracture mechanism, each earthquake possesses unique characteristics that are partly reflected in the obtained strong motion records and partly in the observed damage. Damage patterns and distribution in recent earthquakes have indicated that ground motion characteristics such as direction, pulse or fling effects and duration could have significant influence on forces generated and thus could play important role in response of structures (Bolt 1997, Jennings 1997, Naeim 1995). In addition to its magnitude, the source location of the design earthquake also needs to be estimated in accordance with the geological and tectonic formations in the region based on the estimated source zones. The determination of the source zones strongly relies on subjective expert judgements and is affected by many arbitrary factors. The second stage requires the use of a suitable attenuation relationship for assessing the path effects. There are large numbers of attenuation relationships proposed in the literature based on different data sets obtained in different parts of the World (Abrahamson & Silva, 1997; Ambraseys, 1995; Ambraseys et al. 1996; Campbell 1993 & 1997; Campbell & Bozorgnia, 1997; Gregor & Bolt, 1997; Iai et al, 1993; McVerry et al, 1993). Large number of strong motion records compiled during the last decades made it possible to account for the differences in the source mechanisms and site conditions for establishing attenuation relationships with respect to peak accelerations, velocities, displacements and for different response spectra. However, the source and site classifications used in these relationships are different with respect to each other and limited in the classification categories, thus can only represent source and site conditions approximately. Even with these new contemporary attenuation relationships, it is essential to account for the variability to estimate the exceedance probabilities. In addition, several factors such as; azimuth dependence of seismic radiation, limited geophysical and geotechnical information about soil conditions of the recording stations, 880
instability of parameters like peak acceleration may increase the scatter. Other more stable parameters like response spectra are affected by instrumentation limits since the majority of strong motion data were recorded by analog accelerometers. Another option in modelling and assessing strong ground motion or for determining the design earthquake parameters is the use of methods based on the empirical Green’s function (Aguirre et al., 1994; Bernard et al., 1997; Durukal et al., 1998; Dan & Sato, 1999). This approach appears more suitable and justified when selecting scenario earthquakes with predefined or estimated source characteristics. Although it is a deterministic approach, it is also possible to evaluate the obtained results in a probabilistic manner (Berge et al., 1998) or by conducting a parametric study with respect to possible variations in source zones and source parameters. An attempt will be made in this paper to review the literature concerning strong ground motion and site amplification from geotechnical engineering perspective. This review can not claim to be very comprehensive in this vast interdisciplinary field. The main purpose is to demonstrate the variability observed in earthquake source and site conditions and their effects, in the light of the observations and accumulated data during the last three major earthquakes in Turkey, Erzincan 1992, Dinar 1995 and Ceyhan 1998 (GDDA-ERD, 1999). 2
GROUND MOTION CHARACTERISTICS
The observed damage distribution and strong motion acceleration records obtained in recent earthquakes indicate a need for more comprehensive definitions for existing parameters as well as some new parameters to account for the complex characteristics of earthquake induced strong ground motions for engineering analysis and design. The peak accelerations used for representing the amplitude of earthquake excitations in seismic design have poor correlation with observed damage distribution. In addition to amplitude of earthquake strong ground motions, it is also essential to account for the frequency content and duration especially in the field of geotechnical engineering. This issue has been addressed by many researchers and various proposals were made to define other parameters to account for amplitude, frequency content and duration (such as; peak horizontal velocity, sustained maximum acceleration, effective design acceleration, rms acceleration, power spectrum intensity, ratio of peak velocity to peak acceleration, Arias intensity, cumulative absolute velocity, response spectrum intensity, acceleration spectrum intensity, bracketed duration, central frequency, and etc.) as summarised
in detail by Kramer (1997). Although most of these parameters may represent earthquake characteristics more accurately, only few can be used in seismic design and analysis. The acceleration records registered during earthquakes contain significant information about source, path and site effects that is necessary for engineering analysis and design (Takemura et al., 1995). However, the geological differences, the variability in characteristics of different soil and rock layers, the reflection and refraction of earthquake waves from the boundaries of these layers, the effect of these different layers on earthquake waves passing through these layers, as well as the differences in the source mechanisms of each earthquake prevents comprehensive analysis of earthquake characteristics on the ground surface. The problem can be approached in an empirical manner. With the increase in the number of acceleration records obtained at different geological and soil conditions, the local site effects as well as various features of source mechanism can be better evaluated. In addition, large number of acceleration records obtained under different conditions have led to more comprehensive analysis of response of engineering structures during earthquakes. With this perspective, the three major earthquakes that took place in recent years in Turkey, Erzincan 1992, Dinar 1995, and Ceyhan 1998 was studied to evaluate the variability in the source and site conditions. These earthquakes were medium strong to strong earthquakes with different rupture characteristics. The cities or towns affected by these earthquakes were in the near field. Some of the acceleration records obtained in the near field contained relatively high acceleration peaks. The recording stations were situated on different site conditions and some were on soft soil deposits. Therefore it could be rewarding to analyse these strong motion records obtained during medium strong earthquakes on medium stiff to soft soil conditions. The purpose is to demonstrate certain features of strong ground motion records that may be important for engineering design and analysis.
2.1
Erzincan Earthquake
The M,=6.8 earthquake of March 13, 1992 took place in the Erzincan Basin along the North Anatolian Fault (Ansal et al., 1993, Barka & Gulen, 1993; Bayiilke et al. 1993, EERI, 1995). The epicentre was approximately 10 km to east-southeast of Erzincan with focal depth of 9 km (Bemard et al. 1997; Berge et al., 1998). The rupture that caused the Erzincan earthquake was described as pure rightlateral strike slip on a nearly vertical fault plane. The nodal plane of the rupture almost coincides with the northeastern edge of the basin (Eyidogan 1993).
According to the model study conducted by Bemard et al. (1997), the best fault rupture model for the main shock was obtained for the fault direction of N125E for a bilateral rupture, with larger propagation toward southeast with most likely distance of 15 km. It is estimated that the total length of the horizontal rupture was 25 km and the vertical fault width was 9 km (Berge, et al., 1998).
2.2
Dinar Earthquake
The earthquake sequence that affected Dinar was composed of small to medium size foreshocks, main shock, and aftershocks. The foreshocks started on September 26, 1995 and the main shock (ML = 5.9 ERD, M,=6.1 USGS-PDE) took place on October 1, 1995. More than 300 aftershocks were observed with magnitude equal or larger than 3 (Demirta? et a1.,1997; Durukal et al., 1998). The main rupture was located on the northwest of Dinar along NW-SE trending Dinar-Civril fault. The distribution of aftershocks and surface cracks indicates that a rupture length was approximately 1015 km. The fault plane solutions indicate a normal faulting with a strike of N130E and a dip of 41". The vertical offsets were in the order of 25 cm with right lateral offsets of 10 cm. The aftershocks concentrated along the rupture and according to the distribution of slip amounts rupture started from hypocentre and propagated in one direction toward northwest. The hypocentre of the earthquake was located right under Dinar with a focal depth of 24 km. Rupture mechanism determined based on pwave conversion indicate two separated ruptures with rise time of 2.5 sec for each rupture (Eyidogan & Barka, 1996; Durukal et al., 1998).
2.3
Adana-Ceyhan Earthquake
The earthquake took place on June 27, 1998 with estimated epicentre distance of 38 km to Ceyhan strong motion station. There was a relatively dense seismic network in the region operated by Marmara Research Centre of Turlush Science and Technological Research Council. The magnitude of the earthquake was given as ML= 5.9 by Turkish Earthquake Research Department (ERD). The focal depth was reported as 22 km. Most of the fault plane solutions indicate that the earthquake was due to left-lateral strike slip with normal faulting component with a strike of N207E and with a dip of 70" (Aydan et al., 1998). It is estimated that fault rupture propagated toward north. The earthquake was recorded by most of the strong motion instruments operating in south Turkey. Most of the damage was in the town of Ceyhan located on alluvial deposits and around 35 km from the epicentre.
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3
SOURCE CHARACTERISTICS
'The Source mechanism and fault rupture 1s a very complex Phenomenon. It is difficult to make a PriOri estimation of what may happen. However, an engineer who has to design and construct is required to use some parameters to account for the effects of strong ground motions generated during earthquakes. One practical but empirical approach is to modify the conventionally used design parameters to account for the important factors. It was observed that earthquake source characteristics may play more dominant role in the near field (Durukal et al., 1998, Gao et al., 1991; Schneider et al., 1993; Vidale et al., 1991). This issue will be evaluated based on the records obtained in the near field during Erzincan, Dinar and Adana-Ceyhan earthquakes. 3.1
rms accelerations or Arias intensities are calculated for the same duration, the difference becomes more significant with resultant accelerations giving values approximately 35% higher than the values calculated for recorded NS or EW components.
Fault Orientation and Directivity
One source of variability in observed strong motion records is due to the fault orientation and fault type. Another source is the directivity effects caused by the rupture propagation direction (Somerville, 1998). The inertia forces affecting structures during earthquakes are not due to separate accelerations acting in EW and NS directions but rather due to the resultants of these components. Thus, the peak acceleration amplitudes recorded in EW or NS directions are theoretically less than the peak accelerations experienced by the structures. This difference may not be significant in most earthquakes but there may be few exceptions. The other important feature of the resultant accelerations is their direction. The histogram of the directions of the resultants may indicate the dominant direction of the earthquake generated accelerations (Ansal & Marcellini, 1998). The directional effects due to different source characteristics and fault orientation are evaluated with respect to resultant accelerations and with respect to the histograms of resultant acceleration directions based on the strong motion acceleration records from Erzincan, Dinar and Adana-Ceyhan earthquakes. The effect of fault orientation on the dominant direction of the earthquake accelerations can be determined from the histogram calculated for the directions of the resultant accelerations. Assuming 65% of the peak acceleration as an effective acceleration limit, directions of all resultants with larger acceleration amplitudes were calculated with respect to fault orientation as shown in Figure 1 for Erzincan acceleration records obtained at Erzincan strong motion station. In this case, the dominant direction of the resultant accelerations for Erzincan records was exactly normal to the fault. The peak amplitude of the calculated resultant accelerations was only insignificantly larger than the peak acceleration obtained from EW record. However, if 882
The acceleration time histories obtained in Erzincan was near field records. When the same
approach is applied to Refahiye strong motion records obtained during the same event with the epicentre distance of 74 km,the effects of the source characteristics become more visible. It was originally estimated that the Erzincan earthquake consisted of two consecutive ruptures (Eyidogan, 1993). As shown in Figure 2, the arrival of S waves from the second rupture is more visible around 11 seconds in the Refahiye strong motion records. In comparison to Erzincan record that was obtained approximately at a source distance of 13 km, the second spike that may indicate a second rupture is around 4 seconds. The dominant direction of resultant accelerations was also calculated as 90' with respect to fault orientation as shown in Figure 2. This similarity indicates the importance of the source mechanism and fault orientation. Although Refahiye record can not be regarded as a near field record, it was still possible to observe orientation and directivity effects.
acceleration observed with respect to peak recorded acceleration in EW direction. However, as observed for the Erzincan record rms acceleration for the resultant was about 35% higher.
Figure 4. Variation of resultant accelerations with time and histograms of the resultant acceleration directions for Burdur records The same variability is also observed in the strong motion records obtained at Burdur station approximately 48 km away from the epicentre as shown in Figure 4. As also observed for the Refahiye record (Fig.2) the source characteristics were also dominant for the Burdur record.
Figure 3. Variation of resultant accelerations with time and histograms of the resultant acceleration directions for Dinar records In the case of the Dinar earthquake, the variation of resultant acceleration and resultant acceleration directions with respect to fault direction were determined for the main shock as shown in Figure 3. The observed multi directionality of the main shock was very different from Erzincan record. The differences among the dominant directions of the resultant accelerations indicates the variability in the ground motion characteristics arising from the difference in the source characteristics where Erzincan earthquake was due to a strike-slip faulting and Dinar was due to normal faulting. The peak acceleration calculated for the resultant acceleration is insignificantly higher than the peak 883
Figure 5. Variation of resultant accelerations with time and histograms of the resultant acceleration directions for Ceyhan records
In the case of the Adana-Ceyhan earthquake, the resultant acceleration directions with respect to fault direction were determined for the Ceyhan record as shown in Figure 5. It is reported that fault rupture direction was towards Ceyhan. The observed directionality of the main shock was very similar to Erzincan record (Fig. 1). Both earthquakes being caused by strike slip faulting led to similar dominant acceleration directions normal to the fault. However, the peak acceleration calculated from the resultant accelerations were about 18% larger than the recorded peak acceleration in EW direction as well as the rms acceleration value was about 38% higher for the resultant accelerations. A similar difference in peak acceleration values was also observed when NS and EW records were rotated as fault normal and fault parallel. The peak acceleration was in fault normal direction and was about 17% larger (0.32 g) in comparison to peak acceleration (0.27 g) recorded in EW direction. This indicates the possibility that recorded accelerations in EW and NS direction may be lower than what has been experienced by the structures in the region and may be one reason for the scatter observed in attenuation relationships. In the case of Karata? record (Fig.6) that was obtained in the opposite direction of the fault rupture, the dominant acceleration direction was more multi-directional indicating the importance of directivity. In addition the peak amplitude of the recorded and resultant accelerations as well as the rms accelerations were much smaller compared to Ceyhan record although the epicentral distances for both stations were very similar.
Figure 6. Variation of resultant accelerations with time and histograms of the resultant acceleration directions for Karatav records 884
All these observations, indicate that fault orientation, fault type as well as the rupture pattern are very effective on the dominant direction of induced accelerations during earthquakes. Thus in evaluating the structural damage or vulnerability, these aspects need to be taken into account. Recently some proposals were made to take into consideration the effect of these factors in an empirical way by introducing additional coefficients in the determination of design earthquake parameters namely peak ground acceleration and acceleration response spectrum (Somerville et al., 1997). On the other hand as calculated for the Ceyhan strong motion records, the resultant and fault normal peak acceleration can be higher than the recorded peak acceleration in EW and NS direction.
3.2
Frequency Content
The other important ground motion characteristic that needs to be taken into consideration in the engineering analysis and design is the frequency content of the earthquake accelerations. The frequency content of strong motion on the ground surface is much more affected by site conditions. However, source mechanism is also effective especially in the near field zones. From an engineering perspective, the frequency content and site amplification characteristics of strong ground motions can be evaluated based on response spectra. Response spectra are affected by both site conditions and source characteristics in different ratios depending on the relative influence of these two factors. It is also natural that there is going to be some coupling between these factors. This aspect of response spectra has been evaluated by many researchers and some proposals were made to separate source and site effects (Brune, 1970; Atkinson, 1995, Eyidogan & Akinci, 1997). One generally accepted approach is to determine the cutoff and corner frequencies based on Fourier amplitude spectra where corner frequency is more related to source while cutoff frequency is related both site and source characteristics. Another alternative to evaluate the effects of source and site conditions can be to analyse weak and strong motion records obtained at the same station during different earthquakes. As shown in Figure 7, for the records obtained at Erzincan strong motion station, there appears to be peaks in the normalised absolute acceleration spectra for each record independent of its magnitude around 0.2 second period. The first set of these spectra are for the main shock where peak ground acceleration (PGA) was 0.49 g, the second set are for the strongest aftershock with M,=6 and PGA = 0.04 g that took place on March 15, 1992. The epicentre of this event was approximately 40 km away from the Erzincan strong motion station located toward the
southeast of the estimated fault rupture. The third set is for a more recent very small earthquake obtained on Dec. 31, 1994 with magnitude ML= 3.9, PGA = 0.003 g, and epicentral distance around 68
km.
in NS direction with different spectral amplifications clearly indicate two predominant periods. The first set of periods that were approximately 0.07 sec can be considered due to the structural effects where the instrument is located. However, the second set of periods corresponding to 0.15-0.17 sec may reflect the predominant period of the soil layers at the site in the elastic range.
Figure 8. Normalised absolute acceleration spectra for NS component of 25 weak ground motion records obtained at Erzincan
Figure 7 . Normalised absolute acceleration response spectra for records obtained at Erzincan station For weak ground motion that could have only generated elastic excitations, these peaks around (0.2-0.3 sec) correspond to predominant periods of the soil layers in the elastic range. The existence of peaks around the same periods in the case of stronger earthquakes with higher peak accelerations supports this concept. However, other peaks corresponding to longer period levels may be the result of the source characteristics as well as due to the elasto-plastic response of soil layers due to strong ground shaking. The effects of site conditions can also be observed from weak motion records obtained at the second strong motion station in Erzincan. Twentyfive weak motion acceleration records were obtained at this station during the past five years, for events with magnitudes between M~=4.3-3.1,epicentral distances between 105-28km, and peak accelerations between 0.05-0.002g. As shown in Figure 8, the normalised absolute acceleration response spectra of all these 25 records 885
The effect of fault orientation on strong ground shaking can also be observed in Figure 9, where the normalised absolute acceleration spectra are plotted for fault normal and for fault parallel directions. As was shown in Figure 1, the dominant direction of the resultant acceleration was normal to the fault. Thus, it is possible to conclude that ground shaking intensity was much higher in this direction and as observed in Figure 9, predominant period is around 1 second for fault normal direction and amplification is lower as expected in the case of elasto-plastic soil behaviour. One other reason suggested by some researchers is the presence of the long period waves in fault normal direction.
Figure 9. Absolute acceleration response spectra for fault normal and parallel directions for Erzincan earthquake
Similar differences in the normalised absolute acceleration response spectra for fault normal and fault parallel directions can not be observed in the main shock records obtained at Dinar station. Spectral amplification as well as the predominant periods was very similar for both directions indicating no effect of fault orientation in the case of normal faulting (Fig. 10).
Figure 12. Absolute acceleration response spectra for fault normal and parallel directions for Karatas record in Adana-Ceyhan earthquake 3.3
Rupture Characteristics
The particle acceleration trajectories drawn for the time interval corresponding to high acceleration amplitudes can be used to evaluate the effect of fault orientation as well as to observe the fling or pulse effects that may have arisen from the rupture characteristics. In the case of the Erzincan strong ground motion records, one peculiar aspect is the presence of significant east-west pulse or fling, which mounted up to 0.9g (Fig. 13). Even though accelerations during these initial seconds were relatively high, the effective duration of the earthquake was only in the order of 10 seconds as can be observed in Figure 1 that can partly be due to bilateral rupture mechanism.
Figure 10. Absolute acceleration response spectra for fault normal and parallel directions for Dinar earthquake
No significant difference in the normalised absolute acceleration response spectra for fault normal and fault parallel directions was observed in the main shock records obtained at Ceyhan station (Fig.11). Spectral amplification as well as the predominant periods are very similar for both directions indicating no effect of fault orientation.
Figure 11. Absolute acceleration response spectra for fault normal and parallel directions for Ceyhan earthquake In the case of Karata? record as shown in Figure and predominant periods are 12, the very similar as observed for Ceyhan record however, the predominant period is much lower and amplification is higher.
Figure 13. Acceleration trajectory in the horizontal plane for ~~~i~~~~ main shock
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The particle acceleration trajectories of Dinar main shock (Fig.14) when compared to Erzincan record indicate a different pattern that may be partly due to source conditions and fracture mechanism. The main differences between the two records were duration and multi directional nature of Dinar record. However, during the initial 3-4 seconds of Dinar earthquake, it was also possible to observe pulse effects in EW direction as observed in Erzincan.
Figure 14. Acceleration trajectories in the horizontal plane for Dinar main shock In the case of acceleration trajectory for the Ceyhan records as given in Figure 15, the observed trajectory was relatively different in comparison to the trajectories observed for Dinar and Erzincan records. However, it is also possible to observe one pulse approximately normal to the fault direction.
Figure 15. Acceleration trajectories in the horizontal plane for Ceyhan main shock 887
All these trajectories as well as the dominant directions calculated for the three earthquakes indicate the importance and the influence of fault orientation and directivity effects for the structural design and analysis.
4
GEOTECHNICAL SITE CONDITIONS
The earthquake source Characteristics induced by a tectonic source mechanism are on macro level and are not sufficient to explain the variations in structural damage observed within short distances. The geotechnical site conditions that can be very different due to changes in the thickness and properties of soil layers, depth of bedrock and water table may have more significant influence on damage distribution. The effect of coupling between site and source characteristics may also modify earthquake ground motion characteristics. There are large numbers of instrumental field observations obtained during recent earthquakes reflecting the effects of geotechnical site and earthquake source characteristics (Chang et al., 1996; Gazetas et al., 1990; Seekins & Boatwright, 1994; Su et al., 1998) During earthquakes soil layers are subjected to multi-directional cyclic stresses with different amplitudes and frequencies that lead to cyclic deformations and to changes in stress-strain and strength properties of soil layers. Extensive laboratory, model and field studies were conducted concerning response of soils subjected to cyclic stresses. Significant improvements were achieved in the field of insitu tests to obtain more reliable soil properties. Numerous analytical and empirical relationships were developed to model the behaviour of soil deposits subjected to earthquake excitations. A comprehensive approach in estimating local ground motion characteristics is to use one or twodimensional numerical models to characterise local soil and geologic conditions and to perform site response analyses under selected input acceleration time histories. The results obtained in these analyses would be dependent on the characteristics of the input acceleration records. The final stage in the seismic hazard analysis involves the estimation of earthquake characteristics on the ground surface at the selected site to be used for the engineering analysis. The first option is to use contemporary attenuation relationships formulated in terms of site and source classifications. The second option is to use site parameters as suggested by Borcherdt (1994) and Crouse and McGuire (1996). The third option is to adopt the comprehensive approach in estimating the site specific earthquake characteristics based on site response analysis using a more detailed site
The city is located on north part of the Erzincan Basin composed of very thick heterogeneous fluvial and colluvium deposits consisting mostly of medium dense granular soils. An extensive subsoil exploration program comprising of large number of boreholes, static and dynamic penetration tests, seismic wave measurements have been carried out within the city (Ansal, et al., 1994). The soil layers were composed mostly of coarse grained soils with alternating layers of gravelly sandy silts, silty gravelly sands, sandy silty gravels and in limited locations sandy silty clays. Very dense, partly cemented gravel layers were encountered underlying the city, in the north sectors at depths of 5-6 m, and in the south sectors at depths of 15-20 m. The ground water table in the north part of the city is approximately at 30 m and on the south part at 16 m below the ground surface.
were used to assess the effects of site conditions on damage distribution. In the first stage the variation of damage ratios with respect to average thickness of soil layers overlying the dense gravel layer were evaluated as shown in Figure 16. Most likely due to the differences in the soil stratification, the data was very scattered indicating no correlation between layer thickness and damage ratio. One of the factors controlling the earthquake characteristics on the ground surface is soil stratification and properties of soil layers. One alternative to assess the effect of these factors is to define some parameters representing the insitu properties of soil layers (Borcherdt 1994). One such parameter named as equivalent shear wave velocity was defined as the weighted average with respect to the thickness of the soil layers overlying the dense gravel layer in the soil profile (Ansal, et a1.,1994). Based on shear wave velocities measured from down-hole seismic surveys and calculated using the correlation developed in terms of penetration tests, the shear wave velocity. profiles were calculated for all insitu test locations (Iyisan 1996). As shown in Figure 17, even though there was significant scatter in data set, it was possible to observe the decrease in damage ratio as equivalent shear wave velocity increases, indicating a decrease in amplification with increasing soil stiffness. It was possible to obtain a correlation between damage ratios and equivalent shear wave velocities calculated for selected mesh points but the correlation coefficient was relatively low, R=0.37 (Ansal & Lav 1995).
Figure 16. Variation of damage ratio with respect to layer thickness in Erzincan
Figure 17. Variation of damage ratio with respect to equivalent shear wave velocity in Erzincan
To evaluate the damage distribution, Erzincan city was divided into 180 meshes with mesh size of 250m x 250m. The average damage ratios were calculated for each mesh for 3 to 4 storey reinforced frame structures. Based on insitu test results and available damage ratios, the data from 74 meshes
The equivalent shear wave velocity may not be a very suitable parameter for the case of heterogeneous subsoil conditions with alternating layers of different properties. In such cases equivalent shear wave velocity may not be sufficient to differentiate among different types of soil profiles (Bouckovalas 1997). Although equivalent shear wave velocity could be
characterisation. Taking into consideration the possible differences in soil profiles even within relatively short distances and observations in previous earthquakes that site conditions are important (Field & Hough 1997, Hartzell et al. 1997), it may be more reliable to adopt the third alternative for the assessment of site-specific ground motion characteristics. In this section the effects of site conditions on damage distribution as well as on recorded strong ground motion records will be evaluated based on the observations and findings in the case of Erzincan and Dinar earthquakes.
4.1
Site Conditions in Erzincan
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equivalent shear wave velocity and R=0.65 for microtremor measurements) were relatively higher indicating that local soil conditions were more dominant in the damage distribution in Dinar (Ansal et al., 1997). The presence of softer soil layers and high ground water table can be one reason for more significant effect of site conditions.
used for explaining the differences in the damage distribution to a certain extent, it was not possible to accurately model damage distribution only based on equivalent shear wave velocities or layer thickness. This was expected because equivalent shear wave velocity reflects only average properties of insitu soil layers without taking into account the influence of earthquake characteristics. However structural damage may be due to the coupled effects of earthquake source and local site conditions and it would not be sufficient to use parameters only related to site conditions to model structural damage distribution (Ansal & Siyahi 1995).
4.2
Site Conditions in Dinar
Dinar is located partly on the hills and partly in a valley extending below the hills. The surface geology of the hills to the east of the town consists of limestone, mar1 and schist. The flat zone is covered with alluvium deposit containing alternating layers of loose to medium dense silty sands and soft to medium stiff silty fat clays at some locations of organic nature. The damage distribution in Dinar indicates the effects of the differences in the geotechnical conditions. The buildings located on rocky hill slopes suffered relatively minor damage while heavy damage occurred in the valley. The damage survey conducted by the General Directorate of Disaster Affairs revealed large variations in damage ratios within different districts in Dinar. Geotechnical investigations composed of insitu penetration tests, seismic wave velocity measurements were carried out to evaluate the effects of soil conditions. The borings in Dinar have shown soil stratifications consisting of alluvium deposit composed of alternating layers of silty clay and clayey sand. The ground water table is almost at the ground surface. Microtremors measurements were also conducted at different locations within the town to investigate the effects of local site conditions. The amplification ratios are calculated for all the microtremor records taken within each district based on spectral ratios of horizontal to vertical component at each point. In order to minimise the effects of local sources, an averaging procedure was adopted to obtain the representative amplification curve for each district. Although the construction properties of buildings in Dinar were similar, different damage ratios observed in different district indicate that the local soil conditions could be one of the important factors affecting in the damage distribution. Figure 18 shows the damage ratio correlations between amplification ratios determined from microtremors and calculated from equivalent shear wave velocities for the eight districts in Dinar. In comparison to Erzincan, the correlation coefficients (R=0.78 for
Figure 19. Soil profile at Dinar strong motion station
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A detailed geotechnical investigation including in-situ seismic wave velocity tests by Suspension PS Logging technique were conducted to determine the soil stratification and soil properties by the Dinar strong motion station. As shown Figure 19, the soil profile consisted mostly of sandy, silty, clay layers with shear wave velocities ranging between 150-250 &sec in the top 42 m. Very stiff and dense sandy clayey gravel layer with shear wave velocities around 600 d s e c was encountered below this depth.
Figure 20. Normalised absolute acceleration spectra for different earthquake recorded at Dinar strong motion station
It is also possible to demonstrate this source and site effects based on the recorded accelerations at the Dinar strong motion station during different earthquakes. As shown in Fig.20, there are significant differences among the normalised absolute acceleration response spectra for different earthquakes. All of these recorded accelerations were from shallow near field medium strong earthquakes with epicentres ranging from 2 to 19 km and magnitudes ranging between ML=4.1-5.9. The recorded peak accelerations were in the range of 0.069-0.330 g representing medium strong to strong ground motions that may have induced elasto-plastic behaviour of soil layers. As can be observed in Fig.20, the differences in predominant soil periods and amplification ratios are different for each earthquake relatively independent of magnitude, epicentre distance, and peak acceleration values. It is interesting to see the shift in the acceleration spectra towards longer periods and the decrease in the spectral amplifications with the increase in the peak accelerations. In addition, the similar shift is also observed for the records registered in the same day with relatively limited time in between. This indicates that the increase in the pore pressures and degradation of soil stiffness due to the first event can be one reason for the observed behaviour in the second earthquake. It is likely that pore pressure generated during the first ground shaking have not dissipated due to the clayey properties of the soil layers. Consequently during the following earthquake the response of the soil layers are more elasto-plastic with lower spectral amplification and longer predominant periods.
Figure 21. Normalised absolute acceleration spectra at different stations of Dinar strong motion network 890
A strong motion network was established by KOERI (Durukal, et al., 1998) to monitor the aftershocks in Dinar at different site conditions. As can be observed from the observed absolute acceleration spectra the amplification and predominant characteristics are different for each case even under weak ground motions. The spectra given in Figure 21 were calculated from the NS acceleration records obtained during an aftershock with magnitude M L = ~1.. The epicentral distances for the recording stations are between 8.4-5.2 km. The station DSI was located on rock and the station DDH was on weathered rock in the transition zone between the hills and the valley. The other two stations, DJK and DCE were in the town located on medium stiff-soft soil layers of limited thickness and station DKH was located farther in the valley on deeper alluvial deposits. The peak ground accelerations recorded were between 0.088 g (DKH) and 0.016 g (DSI). The recorded peak ground accelerations as well as the spectral accelerations (Fig. 21) were much higher in the stations located in the valley on the soil layers. 4.3
Adana-Ceyhan Earthquake
In the Adana-Ceyhan earthquake, the variation of peak accelerations between Ceyhan and Karatag strong motion stations indicate the importance of the fault rupture directivity as shown in Figure 22. In addition, the strong motion station in Karatag was located on rock formations while Ceyhan station is located on alluvial deposit. The normalised absolute acceleration spectra for Ceyhan (Fig. 1 1) and Karatag (Fig.12) for fault normal and parallel directions indicate a difference in the predominant periods. Predominant period for Karata? record was around 0.1 sec while it is around 0.6 sec for the Ceyhan record indicating the effect of site conditions.
consisting of eight stations to monitor the aftershock activity. The stations were situated on different geological formations with different site conditions that exist in the Adana-Ceyhan valley. Most of the records obtained were from small earthquakes with low peak acceleration amplitudes. All the normalised absolute acceleration spectra obtained at Ceyhan-PTT strong motion station located on relatively deep alluvial deposit are shown in Figure 23. The predominant periods and spectral amplifications are very similar most likely due to the dominant effect of soil layer in the elastic range. The differences due to the earthquake source characteristics are not very visible. This indicates that the effect of source characteristics would be more significant during strong ground shaking with predominant periods longer that the predominant period of the soil layers in the elastic range. However, nonlinear elastoplastic response of soil layers at this range may also be an important factor. This level of ground shaking and the predominant periods of the strong ground motion can be considered as a threshold levels for accounting for the effects of source conditions as well as for the effects of nonlinear elastoplastic behaviour of local soil layers.
Figure 23. Normalised absolute acceleration spectra at different stations obtained from Adana-Ceyhan network
5
Figure 22. Variation of peak accelerations with epicentral distance stations for Adana-Ceyhan earthquake After the earthquake, Earthquake Research Department of General Directorate of Disaster Affairs established a strong motion network 891
CONCLUSIONS
The earthquake strong motion characteristics on the ground surface are affected by the source conditions in the near field. However, the local site conditions especially in the case of softer alluvial deposits, may also be important. Therefore, it is not possible to evaluate the encountered damage distribution if geotechnical site or earthquake characteristics are considered separately. Depending on the earthquake source characteristics such as fault orientation, fault type and rupture mechanism, the induced earthquake
ground motions can have directional properties that could influence the structural damage patterns. The other important issue is related to the response of soil layers under strong ground motions. Soil layers depending on their properties could demonstrate nonlinear elastoplastic response modifying the strong ground motion characteristics. One practical but empirical approach is to modify the definitions of the design parameters used in conventional seismic analysis to account for the observed effects of earthquake source characteristics. However, all of these observations are based on previous earthquakes with very specific source and site conditions. It could be difficult to extrapolate these results to other sites with different geological and tectonic characteristics and deterministic decisions may be necessary to estimate the source parameters (Studer & Koller, 1998). The other possibility as suggested by Bommer et al, (1998) is to utilise actual earthquake acceleration records to estimate the earthquake characteristics on the ground surface talung into consideration site and source conditions. This approach appears more reliable for performing seismic design and analysis. However, it would more comprehensive if the directional properties arising from earthquake source and site conditions could be taken into account in the analysis. Another option is to conduct a much more comprehensive analysis similar to those proposed by Durukal, et al. (1998) and Berge et al., (1998). Even though it may require much more sophisticated tools, the method developed can account for important aspects of earthquake generated strong motion characteristics necessary for engineering analysis and design. The most important but also most subjective aspect of these and all other models is the selection of the input parameters. In order to perform a realistic assessment to estimate the necessary parameters for earthquake resistant structural design, it appears essential to perform an accurate evaluation of input ground motion. Presently deterministic and probabilistic approaches are adopted independently or together. It is preferable to adopt deterministic approach for scenarios or input motion evaluation for special plants, while probabilistic approach is more suitable for seismic design and analysis. In addition, seismicity of the region need to be evaluated and possible range of expected earthquake characteristics should be realistically estimated. The observations and findings strongly indicate that it is essential to conduct a comprehensive source and site response analysis to have a realistic ground motion estimates.
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REFERENCES Abrahamson,N.A. & Silva,W.J. 1997. Empirical Response Spectral Attenuation Relations for Shallow Crustal Earthquakes”. Seismological Research Letters. (68)1:94-127. Aguirre,J., Irikura,K. & Kudo,K. 1994. Estimation of Strong Ground Motion on Hard Rock and Soft Sediment Sites in Ashigara Valley Using the Empirical Green’s Function Method. Bull. Disas. Prev. Res. Inst. Kyoto Uni. 44:45-68 Allen,C.R. 1995. Earthquake Hazard Assessment: Has Our Approach Been Modified in the Light of Earthquake Spectra. Recent Earthquakes. (1 1)3:357-366. Ambraseys,N.N. 1995. The Prediction of Earthquake Peak Ground Acceleration in Europe. Earthquake Engineering and Structural Dynamics. (24):467490. Ambraseys,N.N., Simpson,K.A. & Bommer,J.J. 1996. Prediction of Horizontal Response Spectra in Europe. Earthquake Engineering and Structural Dynamics. (25):37 1-400. Ansa1,A.M. & Marcellini,A. 1998. Variability of Source and Site Factors in Seismic Microzonation, State-of-the-art report. Proc. of 1lrhEuropean Con. on Earthquake Engineering. Balkema. Rotterdam. Ansal,A.M., Iyisan,R. & Ozkan,M. 1997. A Preliminary Microzonation Study for the Town of Dinar. Seismic Behaviour of Ground and Geotechnical Structures. Balkema.Rotterdam. 3-9. Ansa1,A.M. & Siyahi,B.G. 1995. Effects of coupling between source and site characteristics during earthquakes. European Seismic Design Practice. Rotterdam : Balkema. 83-89. Ansa1,A.M. & Lav,A.M. 1995. Geotechnical Factors in 1992 Erzincan Earthquake. 5th Int. Conference on Seismic Zonation. Nice. (1):667-674. Ansal,A.M., Lav,A.M., Iyisan,R. & Erken,A. 1994. Effects of Geotechnical Factors in March 13,1992 Erzincan Earthquake. Performance of Ground and Soil Structure During Earthquakes, 13th Int. Conf. Soil Mechanics and Foundation Engineering, New Delhi. 49-54. Ansal,A.M., $engezer,B., Iyisan,R. & GenCoglu,S. 1993. The Damage Distribution in March 13, 1992 Earthquake and Effects of Geotechnical Factors. Soil Dynamics and Geotechnical Earthquake Engineering. Ed. P.Seco e Pinto, Balkema, Rotterdam. 413-434. Atkinson,M.G. 1995. Attenuation and Source Parameters in the Cascadia Region. BSSA (85)4: 1327-1342 Aydan,O., Ulusoy,R., Kumbasar,H., Sonmez,H & Tuncay,E. 1998. A Site Investigation of AdanaCeyhan Earthquake of June 27,1998. Research Report TDVDR006-30. Turkish Earthquake Foundation, Istanbul Technical University
Barka,A.A. & Giilen, L. 1989. Complex Evolution of the Erzincan Basin. Journal of Structural Geology 11(3):275-283 Bayiilke,N. et al.. 1993. Report of 13 March 1992 Erzincan Earthquake. General Directorate of Disaster Affairs, Earthquake Research Department, Ankara. Berge,C., Herrero,A., Bernard,P., Bour,M. & D0minique.P. 1998. The Spectral Source Model: a Tool for Deterministic and Probabilistic Seismic Spectra. Hazard Assessment. Earthquake ( 14)1:35 -57 Bernard,P., Gariel, J.C & Dorbath,L. 1997. Fault Location and Rupture Kinematics of the Magnitude 6.8 1992 Erzincan Earthquake, Turkey, from Strong Ground Motion and Regional Records. BSSA 87(2):1230-1243. Bolt,B.A. 1997. Discussions of "Enduring Lessons and Opportunities Lost from the San Fernando Earthquake of February 6,1971" by Paul C.Jennings. Earthquake Spectra 12(3):545-547. Bommer,J.J., Scott,S.G. & Sarma,S.K. 1998. Time History Representation of Seismic Hazard" Proc. 11th European C o n . on Earthquake Engineering. B a1kema. Rottterdam. Borcherdt,R.D. 1994. Estimates of Site Dependent Response Spectra for Design (Methodology and Justification). Earthquake Spectra. (10)4:617-654. Bouckovalas,G.D. 1997. Prediction of Soil Effects on Seismic Motions: A Comparative Case Study. Earthquake Spectra 13(3):333-361. Brune,J.N. 1970. Tectonic Stress and the Spectra of Seismic Shear Waves from Earthquakes. Jour. Geophys. Res. (75): 4997-5009 Chang,S.W., Bray.,J.D. & Seed, R.B. 1996. Engineering Implications of Ground Motions from Northridge Earthquake. BSSA. (86)1B:S270-S288 Campbel1,K.W. 1993. Comparison of Contemporary Strong-Motion Attenuation Relationships. Proc. of Int. Workshop on Strong Motion Data. Cal. (2):49-70. Campbel1,K.W. 1997. Empirical Near-Source Attenuation Relationships for Horizontal and Vertical Components of Peak Ground Acceleration, Peak Ground Velocity, and PseudoAbsolute Acceleration Response Spectra. Seismological Research Letters. (68)l: 154-179. Campbel1,K.W. & Bozorgnia,Y.1993. Near-Source Attenuation of Peak Horizontal Acceleration from Worldwide Acceleograms Recorded from 1957 to 1993. Proc. of Int. Workshop on Strong Motion Data. Cal. (2):71-81. Crouse,C.B. & McGuire.,J.W. 1996. Site Response Studies for Purposes of Revising NEHRP Seismic Provisions. Earthquake Spectra. (12)3:407-440. Dan,K & Sato,T. 1999. A semi-empirical method for simulating strong ground motions based on variable-slip rupture models for large earthquakes. BSSA (89)1:36-53
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Demirta2,R. et al. 1997. The Dinar earthquake of October 1,1995, Southwestern Turkey. Earthquake Research Bulletin 2 1(72):5-38, Ankara, Turkey Durukal,E., Erdik,M., Avci,J., Yiiziigiillii,O., Ziilfikar,C., Biro,T. & Mert,A. 1998. Analysis of the Strong Motion Data of the 1995 Dinar, Turkey Earthquake rr Soil Dynamics and Earthquake Engineering 17:557-578. EERI. 1993. Earthquake Spectra Erzincan Turkey Earthquake of March 13, 1992 Reconnaissance Report. Supplement to Vo1.9 Eyido$an,H. 1993. The Erzincan earthquake of March 13, 1992: a discussion on the mechanism and the location of the main shock. Proc. 2nd Nat. Con. on Earthquake Engineering: 10-13. Istanbul. Turkey Eyidogan,H. & Akinci,H. 1997. Investigation of Regional and Site Attenuation Characteristics in Bursa Region Using Acceleration Records of Micro-Earthquakes. Proc. 4th Nat. Con. on Earthquake Engineering: 63-7 1. Ankara. Turkey Eyido$an,H. & Barka,H. 1986. The October 1995 Dinar Earthquake, SW Turkey. Terra Nova (8):479-185 Field,E.H. & Hough,S.E. 1997. The Variability of PSV Response Spectra across a Dense Array Deployed during the Northridge Aftershock Sequence. Earthquake Spectra. 13(2):243-257. GDDA-ERD. 1999. General Directorate of Disaster Affairs, Earthquake Research Department, Data Bank of Strong Motion Records for Turkey, Ankara, Turkey. ftp://angora.deprem.gov.tr Gregor,N.J. & Bolt,B.A. 1997. Peak Strong Motion Attenuation Relationships for Horizontal and Vertical Ground Displacements. Journal of Earthquake Engineering. (1)2:275-292. Gao S., Liu,H., Davis, P.M. & Knopoff,L. 1996. Localized Amplification of Seismic Waves and Correlation with Damage due to the Northridge Earthquake: evidence for focusing in Santa Monica. BSSA. 86(2):S209-S230. Gazetas,G. Dakoulas,P. & Papageorgiou,A. 1990. Local Soil and source-mechanism effects in the 1986 Kalamata (Greece) earthquake. Earthquake Eng. and Structural Dynamics (19):431-453 Hall,J.F., Heaton,T.H., Hal1ingM.W. & Wald,D.J. 1995. Near-source Ground Motion and Its Effects on Flexible Buildings. Earthquake Spectra 11(1):569-605 Hartzell,S., Cranswick,E, Frankel,A., Carver,D. & Meremonte,M. 1997. Variability of Site Response in the Los Angeles Urban Area" BSSA 87(6): 13771400 Iai,S., Matsunaga,Y., Morita,T., Sakurai, H., Kurata,E. & Mukai,K. 1993. Attenuation of Peak Ground Accelerations in Japan. Proc. of Int. Workshop on Strong Motion Data. Cal. (2):3-22.
Iyisan,R. 1996. Correlations Between Shear Wave Velocity an In-situ Penetration Test Results. Technical Journal of Turkish Chamber of Civil Engineers 7(2):1187-1199. Jennings,P.C. 1997. Enduring Lessons and Opportunities Lost from the San Fernando Earthquake of February 6,197 1. Earthquake Spectra. 13(1):25-53. Kawashima,K. & Aizawa,K. 1986. Earthquake Response Spectra taking Account of Number of Response Cycles. Earthquake Engineering and Structural Dynamics (14): 185-197 Kramer,S.L. 1997. Geotechnical Earthquake Engineering. Prentice Hall. New Jersey Marcellini,A. 1995. Probabilistic Hazard Evaluation in Terms of Response Spectra. Proc. of 3rd Turkish National Earthquake Engineering Conference, Istanbul, Turkey. 407-420. McGuire,K.R. 1995. Probabilistic Seismic Hazard Analysis and Design Earthquakes: Closing the LOOP.BSSA. (85)5:1275-1284. McVeny,G.H., Dowrick,D.J., Sritharan,S., Cousins,W.J., & Ponitt,T.E. 1993. Attenuation of Peak Ground Accelerations in New Zealand. Proc. of Int. Workshop on Strong Motion Data. Cal. (2):23-38. Naeim,F. 1995. On Seismic Design Implications of the 1994 Northridge Earthquake Records. Earthquake Spectra 11(1):91-109. Schneider,J.F., Silva,W.J. & Stark,C. 1993. Ground Motion Model for the 1989 M 6.9 Loma Prieta Earthquake Including Effects of Source, Path and Site. Earthquake Spectra. (9)2:25 1-287. Seekins,L.C. & Boatwright,J.1994. Ground Motion Amplification, Geology, and Damage from the 1989 Loma Prieta Earthquake in the City of San Francisco. BSSA, (84)l: 16-30. Somerville,P.G., Smith,N.F., Graves,R.W. & Norman,A. 1997. Modification of Empirical Strong Ground Motion Attenuation Relationships to Include the Amplitude and Duration Effects of Rupture Directivity" Seismological Research Letters (68)l: 199-222. Somerville,P.G. 1998. Amplitude and Duration Effects of Rupture Directivity in Near Fault Ground Motions " Proc. ASCE Spec.Con. Earthquake Engineering and Soil Dynamics. Seattle Studer,J. & Koller,M.G. 1994. Design Earthquake. The importance of engineering judgement" Proc. 10th European Con. on Earthquake Engineering. B alkema. Rotterdam Shome,N. & Cornel1.A. 1998. Earthquake, Records, and Nonlinear Responses. Earthquake Spectra. (14)3:469-500. Su,F., Anderson,J.G., N1,S.D. & Zeng,Y. 1998. Effect of Site Amplification and basin response on strong motion in Las Vegas, Nevada. Earthquake Spectra. (14)2:357376. 894
Takemura,M., Motosaka,M. & Yamanaka,H. 1995. Strong Motion Seismology in Japan" J. Phys.Earth. (43):2 11-257 Vidale,J.E., Bonamassa,O. & Houston,H. 1991. Directional Site Resonances Observed from 1 October 1987 Whittier Narrows, California, Earthquake and the 4 October Aftershock. Earthquake Spectra. (7)l: 107-125.
Earthquake Geotechnical Engineering, Sec0 e Pinto (ed.) 0 1999Balkema, Rotterdam, ISBN 90 5809 1 163
Modeling of liquefaction-induced shear deformation Ahmed Elgmal - University of California, San Diego, La Jolla, Gal$, USA Zhaohui Ymg - Columbia University,A?K, USA Ender Parra -INTEVEP SA, Venezuela Ricardo Dobry - Rensselaer Polytechnic Institute, Troj AX,USA
ABSTRACT: A constitutive model is developed to reproduce salient aspects associated with seismicallyinduced soil liquefaction (medium to dense clean cohesionless soils). Attention is mainly focused on the deviatoric (shear) stress-strain response mechanism. Soil cyclic shear behavior during liquefaction is modeled to display a significant regain in stiffness and strength with the increase in deformation during each cycle of applied load. This behavior appears to play a major role in dictating the magnitude of shear deformations as observed in laboratory tests and manifested in acceleration records from earthquakes and centrifuge experiments (clean sands and non-plastic silts). Constitutive model parameters are selected to represent medium, medium-dense and dense clean cohesionless soils. Using these parameters, the resulting model response is presented under simple-shear cyclic loading situations. Further modeling accuracy may be achieved based on a more thorough understanding of the underlying physical processes. KEYWORDS: Liquefaction, cyclic-mobility, sand, constitutive modeling, earthquake, plasticity
1. INTRODUCTION
During liquefaction, recent records (Holzer al. [9], Zeghal and Elgamal [23], Youd and Holzer [22]) of seismic site response have manifested a possible strong influence of soil dilation during cyclic loading. Such phases of dilation may result in significant regain in shear stiffness and strength at large cyclic shear strain excursions (Figure l), leading to: i) associated instances of pore-pressure reduction, ii) appearance of spikes in lateral acceleration records (as a direct consequence of the increased shear resistance), and most importantly, iii) a strong restraining effect on the magnitude of cyclic and accumulated permanent shear strains. This restraint on shear strain has been referred to as a form of cyclic-mobility in a large number of pioneering liquefaction studies (e.g., Seed and Lee [16], Casagrande [a], Castro [3], Castro and Poulos [4], Seed [17]). For the important situations of biased strain accumulation due to an initial lockedin shear stress, this pattern of behavior may play et
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a dominant role in dictating the extent of shear deformations. Currently, the above mentioned effects are thoroughly documented by a large body of experimental research (employing clean sands and clean non-plastic silts), including centrifuge experiments (e.g., Dobry et al. [5], Taboada Dobry et al. [6]), shake-table tests, and cyclic laboratory sample tests (Arulmoli [l]). A thorough summary has been compiled (Elgamal et al. [S]) of the relevant: i) seismic response case histories, ii) recorded experimental (centrifuge, shake table and laboratory) response, and iii) constitutive models developed to simulate this phenomenon. In the following pages, illustrations of the above-described shear stress-strain mechanisms are presented. Thereafter, the constitutive model is discussed, and the salient model response characteristics are presented.
[?I,
2. CYCLIC LOADING MECHANISM
A thorough review of available relevent literature has been presented recently by Elgamal et
Figure 1 : Wildlife-Refuge NS shear stress-strain and effective-stress histories during the Superstition Hills 1987 Earthquake (evaluated from acceleration histories and computed, after Elgamal et al. 1995).
al. [8]. An illustration of the dilative-tendency mechanism observed in undrained cyclic laboratory tests is shown in Figure 2 (Arulmoli et al. [l]). Similar response (Figure 1) was observed (Zeghal and Elgamal [23]) at the US Imperial County Wildlife Refuge site (1987 Superstition Hills earthquake records). Currently available constitutive models that reproduce important aspects of the above shear mechanism include those by Iai [lO], Iai et al. [ll]and Tateishi et al. [20]. One-dimensional shear stress-strain histories (e.g., Figure 3) calculated from recorded centrifuge experiment acceleration and LVDT records (Dobry et al. [5], Dobry et al. [6], Taboada [18], Elgamal et al. [7], Taboada and Dobry [19]) also display a similar response mechanism. Figures 2 and 3 depict the mechanism of accumulation of cycle-by-cycle deformations. Accuracy in reproducing this mechanism is among the most important goals of the developed constitutive model. 3. CONSTITUTIVE MODEL The model framework follows the procedures developed by Prevost [15], based on the multi-
ple yield surface plasticity concept (Iwan [12], and Mroz [13]). It was modified (Parra [14], Yang [all) from its original form (Prevost [15]) to model the shear stress-strain features discussed above (Figs. 1 - 3). Special attention was given to the deviatoric - volumetric strain interaction under cyclic loading; in particular during loading - unloading - reloading near the yield envelope (Parra [14], Yang [21]).
4. MODEL RESPONSE Figures 4 and 5 illustrates the mechanism of model response. These figures depict a simulation of a biased cyclic shear stress - strain history. A static driving “locked-in” shear stress was simulated by applying load cycles in the range of 0.0 kPa to 60 kPa (Figure 4). Under this loading history, gradual pore pressure buildup and liquefaction occurs (i.e., effective confinement approaches zero, Figure 5). During liquefaction the model reproduces a stable cycle-by-cycle accumulation of shear deformation, along the lines of the experimental response of Figure 2. For engineering applications, three performance scenarios were se-
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Nevada Sand ( D ~ 4%) 0
2
4
6
8
10 Time(sec)
12
14
16
18
Initial deviatoric s u e s s offsett=21.5 k P a
-40
10
0
-lot
1121
A
-1
sec
10
0
10
0 -10
10 0
- 10 Shear strain (%) Figure 3: RPI Model 2 shear stress-strain histories with superposed static stress due to inclination (Taboada 1995, Dobry et al. 1995, Elgamal et al. 1996).
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Figure 4: Simulation of undrained biased cyclic simple shear tests.
Figure 5: Computed stress path during undrained biased cyclic simple shear.
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6. ACKNOWLEDGMENTS
lected t o represent clean medium, medium-dense and dense sand (or silt) situations (relative density in the range of about 40% to 90%). In Figure 4, maximum accumulated cycle-by-cycle shear deformations are about 1.3% (medium), 0.5% (mediumdense) and 0.3% (dense). The medium sand response was calibrated by extensive laboratory tests (Arulmoli et al. [l])and centrifuge experiments (Parra [14], Yang [21]). At this point, the deformation characteristics for the medium-dense and dense situations are qualitative (motivated by the literature review in Elgamal et al. [S]). Further data is needed to refine the estimates of the proposed model, particularly for the medium-dense and dense sand situations.
The research reported herein was supported by the Pacific Earthquake Engineering Research Center (PEER), the United States Geological Survey (grant No. 99HQGR0020) and INTEVEP, SA, Venezuela. This support is gratefully acknowledged. REFERENCES [l]Arulmoli, K., Muraleetharan, K. K., Hossain,
M. M. and Fruth, L. S. (1992). “VELACS: VELACS: Verification of Liquefaction Analysis by Centrifuge Studies, Laboratory Testing Program, Soil Data Report”, The Earth Technology Corporation, Project No. 90-0562, Irvine, California.
Additional Remarks 1. A “damage” parameter can allow the model t o reproduce stiffness and strength degradation (as a function of total accumulated plastic strain) as depicted in Figure 1. 2. Note that loose cohesionless soils will possibly display a dominant contractive response with little dilative tendency and much increased level of accumulated shear deformations. Such deformations can be reproduced by the developed constitutive model (among many others). However, the emphasis placed on the deformation ranges of Figure 4 reflects the interest in: i) estimation of deformations that might be objectionable despite the absence of a flow-failure (performance-based design assessments), and ii) applicability to liquefaction countermeasure effectiveness (e.g., by densification). In this regard, the accurate estimation of very large flow-failure deformations is not a primary goal, since loose soils (that may be vulnerable to flow-failure) are unacceptable from a practical engineering point of view.
[2] Casagrande, A. (1975). “Liquefaction and Cyclic Deformation of Sands - A critical Review”, Proceedings, 5th Pan-American Conference on Soil Mechanics and Foundation Engineering, Buenos Aires, Argentina; also published as Harvard Soil Mechanics Series No. 88, January 1976, Cambridge, Mass.
[3] Castro, G. (1975). “Liquefaction and Cyclic Mobility of Saturated Sands”, Journal of the Geotechnical Engineering Division, ASCE, 101, GT6, 551-569. [4] Castro, G and Poulos, S.J. (1977). “Factors Affecting Liquefaction and Cyclic Mobility”, Journal of the Geotechnical Engineering Division, ASCE, Vol. 103, No. GT6, June, pp. 501-516. [5] Dobry, R., Taboada, V. and Liu, L. (1995). “Centrifuge Modeling of Liquefaction Effects During Earthquakes”, Proc. 1st Intl. Conf. On Earthquake Geotechnical Engineering (ISTokyo), Keynote Lecture, Ishihara, K. Ed., 3, Balkema, Nov. 14-16, Tokyo, Japan, 12911324.
5. SUMMARY AND CONCLUSIONS A new constitutive model is developed to model the cyclic shear behavior of clean cohesionless soils during liquefaction (emphasis on medium to dense sand scenarios). The underlying mechanisms are based on observed soil response during earthquakes, centrifuge experiments and cyclic laboratory tests. A range of response characteristics (pore pressure buildup and accumulated deformations) is proposed as a first step towards a performance-based liquefaction design methodology*
[6] Dobry, R. and Abdoun, T. (1998). “PostTriggering Response of Liquefied Sand in the Ree Field and Near Foundations”, Proc. Geot. Eq. Engrg. and Soil Dynamics 111, V1, Dakoulas, P., Yegian, M. and Holtz., R. D., Eds., Geot. Special Publication No. 75, 899
ASCE, Seattle, Washington, Aug 3-6, keynote lecture, 270-300. [7] Elgamal, A. -W., Zeghal, M., Taboada, V. M. and Dobry, R. (1996). “Analysis of Site Liquefaction and Lateral Spreading using Centrifuge Model Tests”, Soils and Foundations, 36, 2, June, 111-121. [8] Elgamal, A. -W., Dobry, R., Parra, E. and Yang, Z. (1998). “Soil Dilation and Shear Deformations During Liquefaction”, Proc. 4th Intl. Conf. on Case Histories in Geotechnical Engineering, S.Prakash, Ed., St. Louis, MO, March 8-15, 1998. [9] Holzer, T . L., Youd T. L. and Hanks T . C. (1989). “Dynamics Of Liquefaction During the 1987 Superstition Hills, California, Earthquake”, Science, Vol. 244, 56-59. [lO] Iai, S. (1991). “A Strain Space Multiple Mechanism Model for Cyclic Behavior of Sand and its Application”, Earthquake Engineering Research Note No. 43, Port and Harbor Research Institute, Ministry of Transport, Japan. [ll] Iai, S., Morita, T., Kameoka, T., Matsunaga,
Y. and Abiko, K. (1995). “Response of a Dense Sand Deposit During 1993 Kushiro-Oki Earthquake”, Soils and Foundations, 35, 1, March, 115-131. [l2] Iwan, W. D. (1967). “On a class of Models for the Yielding Behavior of Continuous and Composite Systems”, Journal of Applied Mechanics, ASME, Vol. 34, pp. 612 - 617.
[13] Mroz, Z. (1967). “On the Description of Anisotropic Work Hardening”, Journal of the Mechanics and Physics of Solids, Vol. 15, pp. 163 - 175. [14] Parra, E. (1996). “Numerical Modeling of Liquefaction and Lateral Ground Deformation including Cyclic Mobility and Dilative Behavior in Soil Systems”, Ph. D. dissertation, Dept. of Civil Engineering, Rensselaer Polytechnic Institute.
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[15] Prevost, J. H., (1985). “A Simple Plasticity Theory for Frictional Cohesionless Soils”, Soil Dynamics and Earthquake Engineering, Vol. 4, NO. I,pp. 9 - 17. [16] Seed, H. B. and Lee, I(.L. (1966). “Liquefaction of Saturated Sands During Cyclic Loading”, Journal of the Soil Mechanics and Foundations Division, ASCE, 92, SM6, Nov., 105134. [17] Seed, H. B. (1979). “Soil Liquefaction and Cyclic Mobility Evaluation for Level Ground During Earthquakes”, J of the Geotech Engng Div, ASCE, 105, No. GT2, Feb., 201-255. [18] Taboada, V. M. (1995). “Centrifuge Modeling of Earthquake-Induced Lateral Spreading in Sand using a Laminar Box”, Ph. D. Thesis, Rensselaer Polytechnic Institute, .Troy, NY. [19] Taboada, V. M., and Dobry, R. (1998). “Centrifuge Modeling of Earthquake-Induced Lateral Spreading in Sand”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 124, No. 12, 1195-1206. [20] Tateishi, A., Taguchi, Y, Oka, F. and Yashima, A. (1995). “A Cyclic Elasto-Plastic Model For Sand and Its Application Under various Stress Conditions”, Proc. 1st Intl. Conf. On Earthquake Geotech Engng, 1, 399404, Balkema, Rotterdam. [21] Yang, Z. (1999). “Identification and Numerical Modeling of Earthquake Ground Motion and Liquefaction”, Ph. D. dissertation, Dept. of Civil Engineering and Engineering Mechanics, Columbia University, NY, NY (in completion).
[22] Youd, T . L., and Holzer, T . L. (1994). “Piezometer Performance at the Wildlife Liquefaction Site”, J. Geotech. Engrg., ASCE, 120(6), 975-995. [23] Zeghal, M. and Elgamal, A. -W. (1994). “Analysis of Site Liquefaction Using Earthquake Records”, Journal of Geotechnical Engineering, ASCE, 120, No. 6, 996-1017.
Earthquake GeotechnicalEngineering, S&coe Pinto (ed.)0 1999Balkema, Rotterdam, ISBN 90 5809 1 16 3
Site effects: Recent considerations and design provisions K. D. Pitilalus, D.G. Raptakis & K.A.Makra Aristotle Universityof Thessaloniki, Greece
ABSTRACT: This paper discusses some recent developments and results of ground shaking site effects and the few aspects of the definitions and considerations of modern seismic code provisions. (uBC97 and EC8) regarding the evaluation of earthquake motion due to local soils and the surface geology. Instrumental as well as numerical approaches are considered to study the physics of ground motion and 1D-2D amplification phenomena in a specific test site (Euroseistest) of both horizontal and vertical components. Detailed 1D analysis using different soil constitutive models (equivalent linear, nonlinear, elastoplastic-drained and undrained) of a specific typical soil profile is performed and the results are discussed with code specifications. 1 INTRODUCTION Observations from recent strong earthquakes such as that of Mexico (1985), Loma Prieta (1989), Northridge (1994) and Hanshin-Kobe (1995) and from experimental sites like Ashigara Valley, Euroseistest and others, have provided important high quality data regarding the effects of surface geology on ground motion. In all recent congresses and conferences (4" I.C.S.2.-Stanford 1991, 1l* W.C.E.E.-Acapulco 1996, 10" E.C.E.E.-Vienna 1994, 11'" E.C.E.E.Paris 1998 and ESG98, Yokohama, Japan) different aspects of site amplification from experimental and theoretical point of view were extensively discussed. Issues like the nonlinear behavior, effects of irregular geological configurations, near field phenomena, basin edge and 2D effects are better understood and in a certain degree quantified as well. The enhancement of numerical modeling now enables the study of 2D or 3D phenomena making feasible source, path and 3D site effects to be studied as a complete issue in the near future. The motivation of this paper is mainly due to the fact that there is certainly a gap to be filled between research on site effects, which is constantly producing new results and better insights of the physics of ground motion and engineering practice as it is mainly reflected in modern seismic codes (UBC97, EC8). In order to contribute in the discussion on the above statement, we have selected for illustration in the present paper, among the numerous interesting subjects, some recent theoretical and experimental 901
works related to 2D effects. We also discuss the use of empirical methods for site effect estimations and the amplification of the vertical component. Finally, an important part of the work is focused on the discussion and validation of nonlinear 1D models which are still affecting explicitly or implicitly the design response spectra of modern codes. 2 COMPLEX SITE EFFECTS In the last few years many studies have analyzed 2D site effects in the elastic range on ground motions (Aki 1993, Bard 1994, Moczo et al. 1996), showing that differences relative to the 1D response may appear due to the lateral propagation of locally generated surface waves and possible 2D resonance phenomena. Theoretical 3D elastic response studies indicate that differences relative to 2D are only quantitative. In Kobe, it has been demonstrated (Kawase, 1996) that the zone of ground motion amplification is induced by the constructive interference between basin edge diffracted waves and the direct S waves. It is well documented from theoretical and experimental studies that long period surface waves are generated in rather large size structures (Osaka basin, Kanto plaine, Los Angeles basin). From a practical point of view, the consequence is a clear inadequacy of 1D models to describe site effects at long periods. The question is whether these phenomena are likely to occur in smaller size structures (i.e. only a few kilometers wide)? Recent experimental studies using data from
arrays (ESG98 Special Session on Test Sites) demonstrated that the deep geological structure has a significant impact in the ground motion mainly because it affects the incident wave field in terms of incident wave angle, amplitude and frequency content (Uetake & Kudo, 1998). On the other hand, it is well known that modern seismic codes (UBC97, EC8) consider seismic site response as a 1D vertical wave propagation. Nevertheless, seismic response coefficients and spectral shapes for different soil classes are used in order to quantifj site effects. The site classification is based exclusively on the vertical soil profile. Moreover, in UBC97 the uppermost soil layers are taken into account disregarding whether the total thickness of sediments is greater than 30m, and also their dynamic properties of the sediments and bedrock. Three main questions arise: a) Are 2D or 3D phenomena systematically insignificant in engineering practice? b) How representative could an estimation of the site response be if it is derived on the basis of the first 30m only? c) How reliable are the site coefficients of UBC97? The aim of the instrumental and theoretical studies presented herein is to contribute to the discussion on the physics of 2D ground motion phenomena and to try to give some answers to the above questions. As an example of complex structure with irregular geological configuration of sedimentary deposits, we examine the case of Euroseistest instrumented site. This is located on a 5.5 kin wide and 200 m deep sedimentary valley, 30 km eastwards of Thessaloniki in northern Greece. Volvi valley is well investigated in geophysical and geotechnical terms (Pitilakis et al.
Figure 1. NNW-SSE 2D model of the Volvi structure (Pitilakis et al., 1998; Raptakis et al., 1998b). 902
1998, Jongmans et al. 1998 and Raptakis et al. 1998b). The NNW-SSE cross-section of the valley is depicted in Figure 1. In this study the results are based on recordings which come from a seismograph and an accelerograph network. The first included 24 Reftek seismographs and the second 7 free-field and 2 downhole 3-D accelerographs. Both arrays were installed along the cross-section (Fig. 1) and gave a large data set (Raptakis 1995, Raptakis et al. 1998a and Riepl et al. 1998). To examine in detail the relation between observed, 1D (Raptakis et al., 1998b) and 2-D (Chavez-Garcia et al., 1998) site effects in the frequency and time domain, two well recorded events have been selected; the first event (06.25.94, M=3, R=25km) was recorded at the seismograph array and the second one (05.03.95, M=5.8, R=32km) at the accelerograph array. The use of the most commonly applied empirical SSR and HVSR techniques in estimating site effects and the reasons of the amplification of the vertical component are also discussed below. 2.1 Analysis of real data
SSR - Sfvdy in frequency domain The study of site response in frequency domain using spectral ratios of Fourier amplitude (SSR) (Borcherdt, 1970) of entire seisinograms and accelerograms, along the cross-section, show that the lateral discontinuities and the complex geometry of the valley are correlated with the amplification/ deamplification at low resonant frequencies (up to 3Hz). The reference site at the northern edge of the valley is assumed to be free of site effects (Steidl et al., 1996). The dense distribution of the seismographs along the cross-section gave the possibility to correlate the observations in terms of transfer functions (TF) of both radial and transversal components with the underlying soil conditions. Figure 2 illustrated the peaks of fundamental and higher resonant frequencies up to 2.5 Hz commonly and distinctly observed at all TF, for the transversal component. Most of them are amplified by a mean factor of 20 at the center of the valley. However, the amplification is not uniform (Fig. 2). This could be due to the important interactions among waves with low frequency content. The faults play an important role in the amplification pattern at the sites in their vicinity and the center of the valley. Both horizontal components are similar. However, the effect on the transversal component is much more significant than that on the radial one. Additionally, amplification factors of the vertical components are almost comparable with those of the horizontal ones, whereas accelerograms’ TF present similar shape
Figure 3. TF for P, S, and SW time-windows, of the transversal accelerograms of all surface and downhole stations (Raptakis et al., 1998b).
Figure 2. Resonant frequencies and amplification factors of transversal seismograms along the crosssection. 1D amplification factors (bullets) from theoretical TF (Raptakis et al., 1998b). with those of seismograms. The above clearly indicate that the complex geometry of the valley strongly affect the incoming wave-train. Analysis of time-windows The study of individual time-windows (P, S and SW waves) of the accelerograms’ transversal components within the valley, shows large spectral amplitudes of SW-window for frequencies up to 2Hz (Fig. 3). The maximum spectral amplitudes are almost comparable with those of the entire signals at the same frequency band. The S window amplification values within the valley are lower than those of SW window (Fig. 3). As it is well known, TF is only a ratio as a fbnction of frequency and phase information are lost. Therefore, evolutionary spectra of transversal accelerograms at the center of the valley (TSTO) and at the reference site (PRO), filtered with a low pass cut-off 5 Hz filter, are calculated (Fig. 4). The spectrogram at TSTO for frequencies of interest (0.51 Hz), shows all maxima between 16.5-25.0sec, where long period waves dominate. Furthermore, lower maximum appears at the same frequencies in the S time-window (14-16.5 s). The fact that observed maxima in both S and SW time-windows appear at the frequency 0.7 Hz, means that both S and SW time-windows contribute to the spectral amplification of the fkndainental peak. On the other 903
Figure 4. Evolutionary spectra of the transversal accelerograms at TSTO (top) and PRO (bottom) (Raptakis et al., 1998b). hand, the spectrogram at PRO shows that S window presents maxima higher than those of SW window. In combination, these spectra show: a) SW waves
contribute significantly to the resonant peak at 0.7
Observations on time-histories
Hz at the center of the valley and b) the striking difference, between the TSTO and PRO means that SW waves appear at the center of the valley but not at the edges. This is also confirmed with TF for stations at the southern edge of the valley, where SW contribution is lower than that of S waves (Fig. 3). Analysis of downhole data The contribution of SW window with depth has also been observed. Transfer hnctions of S and SW windows at 17 and 72m depth show that the amplification of SW window is constantly 2-3 times larger than those of the S window (Fig. 3). This means that the propagation of locally generated surface waves affect a large volume of soil deposits,
A quick look at the seismograms (Fig. 5), filtered with a low pass cut-off 3.5 Hz filter to include the most energetic phases, is adequate for the distinction of the strong differences in the duration of shaking between the stations at the edges and at the center of the valley. The long duration recorded between the central faults is due to locally generated surface waves which are distributed either in the S or SW time-length. This confirms the fact that S and SW waves appear with the same frequencies (up to 3.5 Hz) along the entire time history. Consequently, it is difficult to distinguish the contribution of these phase types in the frequency domain. The study of accelerograins gave similar results. Vertical coniponent and HVSR technique Recent observations on the vertical ground motion suggest that it is actually amplified and that the coininonly adopted vertical to horizontal response spectra ratio at 2/3 may be significantly exceeded at short periods in the near source distance range (Silva, 1997). In the Euroseistest case, though the earthquakes studied actually come from long distances. Nevertheless, their vertical accelerograms at the center of the valley show amplification of the same order as that of the horizontal ones. This is due to the contribution of Rayleigh waves which appear as a part of surface waves in the vertical component. This explains the significant contribution in the amplification at low frequencies where S-wave resonance occurs. The windowing procedure of the
Figure 5 . Transversal seismograms (bottom) and synthetics (top) with respect to the cross-section (Raptakis et al., 1998b). lying in the center of the valley and not only the shallow soil formations. The contribution of locally generated surface waves remains stable with depth at the center of the valley and affects all three components.
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Figure 6. TF for P, S, and SW windows of all surface and down-hole vertical accelerograms (Raptakis et al., 1998b).
vertical component (Fig. 6), shows for all surface and downhole accelerographs no contribution of P-wave at low frequencies (up to 2.0 Hz), as it is anticipated. Moreover, the S window amplification factor were lower than those of SW at the stations within the valley. Hence in case, Rayleigh waves appear, a part of them would be in the vertical component. In fact, the largest amplification (2-3 times) appeared at the SW window, instead of the S one at the superficial stations within the valley. It is clear that surface waves which are dominant in the SW window contribute significantly to the resonance’s peak. Raptakis et al. (1998a) related directly the mismatch of the amplifications factors between horizontal to vertical ratio method (HVSR) and SSR, with the large amplification of the vertical component. In Figure 7 the mean spectral ratios HVSR and SSR for horizontal and vertical components from a lot of earthquakes are presented. This amplification degrades the usefblness of the vertical component as reference. This fact could justify the disparity between HVSR and SSR.
between 1D and empirical TF, a large disparity of the amplitudes within the valley was observed. Theoretical fbndamental peaks were lower than the empirical ones (Fig. 2). This is natural since the contribution of the locally generated surface waves is not included in 1D site response. The results of the 1D modeling in frequency domain are confirmed by synthetic time-histories obtained from the convolution with a reference record. Convoluted signals were again filtered with a low-pass cut-off 3.5 Hz filter. All of them present the dominant ground motion in a narrow time-window, as the S one of data’s (Fig. 5). The last part of the synthetics, which should correspond to the locally generated surface waves, shows very small amplitude and does not present any variation along the crosssection. This is not surprising since Love waves are generated only within the valley because of lateral propagation (2D effect and not 1D). 2.3 2D theoretical analysis A 2D SH-wave finite difference method (Moczo 1989, Moczo and Bard 1993 and Moczo et al. 1996) was used (Chavez-Garcia et al., 1998), because a) the structure (Fig. 1) is irregular and b) the response of the valley is 2D and not 3D (Riepl et al. 1998). Time domain seismograms (with finite attenuation - damping) from 155 receivers distributed along the free surface are shown in Figure 8. They have been low-pass filtered with corner frequency of 3.5 Hz. The receivers at the center of the valley show clearly the 1D resonance of the sediments, but the largest amplitudes are not related to vertical propagation. The synthetic seismograms are very clearly dominated by locally generated Love waves. The identification of Love waves is confirmed by many
Figure 7. HVSR, SSR for horizontal and vertical components mean spectral ratios from a lot of accelerograms (Raptakis et al., 1998a).
2.2 1D theoretical analysis
The study of the empirical TF and the observations on time-histories showed that the amplification of ground motion was not only due to the resonance of vertically propagated shear waves. 1D theoretical estimates (Kennett 1983) of site response were computed for all instrumented sites. 1D soil profiles were extracted from the 2D model (Fig. 1). The transition from high resonant frequencies with low amplification levels at the edges of the cross-section t o low frequencies (smaller than 1Hz) with high amplification factors showed that the computed site responses were directly related to the depth of the bedrock and Vs velocity contrast. Despite the agreement of resonant frequencies (0.7 and 2 Hz)
Figure 8. Synthetics seismograms from 2D modeling with respect to the cross-section (Chavez-Garcia et al., 1998). 905
other analyses i.e. modal analysis and f-k spectra from downhole and CIES array recordings, respectively. The main result of Chavez-Garcia et al. (1998) is that both S and Love waves appear with the same characteristics. Therefore, surface waves cannot be identified in the frequency domain TF, since they contribute to the main ''resonance peak" of the empirical TF rather than appearing as separate peaks of amplification. Transfer fimctions relative to input ground motion have been calculated based on the seismograms of Figure 8. The center of the valley shows a first peak of amplification at about 0.85 Hz. This peak is not homogeneous across the valley and that it breaks at two points at the center of the valley. This heterogeneity of the TF at the resonant frequency must have resulted from the interaction of surface waves. This is shown in the spectrogram of the synthetic seismogram at the position of TST. Figure 9 shows that the energy that contributes to the "resonant" peak at 0.8 Hz is distributed all along the synthetic, including both ID resonance and surface waves. In other words, the results of 2D model confirms the existence of the surface waves locally generated which have been already observed in the recordings.
Figure 10. Existence condition of the 2D resonance in sedimentary valleys for SH case. The curve was empirically determined by Bard & Bouchon (1985); solid circle show the Volvi valley (after ChavezGarcia & Faccioli, 1998). (1998) have proposed (Fig. 10). In Euroseistest, these parameters are equal to 0.08 and 5.8 assumed as depth, h, 200 in, semi-distance of the valley, a, 2500 in, Vs of bedrock 2600 m / s and a mean value of sediments Vs 450 mds. This point on the hla-Cv diagram in Figure 10 falls in the area where ID and lateral propagation appear and not 2D resonance. As it is evident and Chavez-Garcia & Faccioli (1998) have mentioned, the properties of the materials are not crucial on the basis that the sedimentshedrock velocity contrast controls the shape ratio value for which the main phenomenon shifis from lateral wave propagation to 2D resonance. 2.4 How could 2D phenomena be included in design spectra?
Figure 9. Evolutionary spectrum of synthetic seismogram at the center of the valley (ChavezGarcia et al., 1998).
Does 2 0 resonance exist? We showed above that the main 2D effect is due to the lateral propagation of surface waves because of the complex structure of the valley. At this point it is useh1 to show whether 2D resonance contribute to 2D site effects appeared in Euroseistest experiment. The existence of 2D resonance due to SH waves, in sedimentary valleys, is correlated with the shape ratio (Wa) and the velocity contrast (Cv), as Bard & Bouchon (1985) and Chavez-Garcia & Faccioli
In this section an example is presented for the evaluation of whether the elastic design spectra should be modified in order to take into account site effects of complex nature i.e. 2D caused by irregular geologic structures such as Euroseistest sedimentary deposits. It is well known that ratios of 2D results relative to ID case (aggravation factor) are proposed (Faccioli 1996, Faccioli at al., 1998). To this end, we compute the response spectra of the strong event at the center of the valley and the convoluted signals from ID and 2D TF with PRO (Fig. 11). We observe that response spectra of the recording and 2D convoluted are quite similar for a band of periods ranging from 0.25 to 3 sec. On the contrary, for periods shorter than 0.25 sec the similarity of the 1D spectra and the recording is observed, while for larger periods the disparity is quite large. Moreover, the ratio between 2D and 1D response spectra (Fig. 11) shows that the additional amplification
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of Faccioli et al. (1998) for which the 2D aggravation factor should only be used at periods shorter than the 1D resonance period at the center of the sedimentary deposits, seems to be unconditional in Euroseistest case, where amplification of 1D resonance and lateral propagation appear at the fhndamental frequency. 2.5 Final considerations
Figure 11. Normalized response spectra (top) for the strong event and 1D / 2D convoluted signals at the center of the valley. Aggravation factor (2DAD) in comparison with the ratio of the event relative to ID case (bottom). introduced by 2D effects with respect to 1D response attains a “mean” factor of 6 for periods larger than 0.25 sec. In addition to 2D/1D, the ratio of the accelerogram response spectrum and ID has been calculated. This ratio presents similar shape as that of the aggravation factor (Fig. 11) despite the relative fluctuation for the periods of interest (0.25-3 s). The mean value of this ratio attains a factor of 4. This qualitative result makes clear that a) an aggravation factor may be introduced following a very thorough and extensive theoretical and experimental analysis of many different cases, b) the aggravation factor should be used at periods which correspond to the period content of surface waves locally generated by the lateral propagation at the center of the sedimentary deposits and c) the result 907
Some significant considerations could be clarified by the previous section. An example of a particular structure of 2D sedimentary valleys was examined. However, this example is adequate to confirm though that the discussion started almost 20 years ago regarding the fact in shallow alluvial valleys, such as Euroseistest, locally generated surface waves is an important phenomenon (Bard & Bouchon 1980a,b). In the present study, only linear elasticity has been considered in wave propagation theoretical estimations, empirical determination of transfer hnctions and response spectra obtained because of the weak events which have been used. The specific nature and the non-linear behavior of soil materials are not examined. The previous results may be summarized as follows: -The study of empirical site response in the frequency domain shows that SSR technique is inadequate to give a complete understanding of the physics of site effects because it reveals only a partial image of site response and introduces incertitudines related to the reference site. - Frequency domain analysis of recordings showed that the sediments filling the valley of Euroseistest a) amplify ground motion by factors larger than 10 at low frequencies (up to 3 Hz), b) provoke strong interaction between different wave-types of low frequency content at the center of the valley, because of the irregular geometry of the structure and c) amplify all three components in the same order of amplitudes with emphasis to the vertical component. . Observations on recordings and transfer fknctions of specific time-windows show that surface waves appear at the center of the valley and contribute significantly to the ID resonance, making difficult to distinguish the contribution of different type of waves in “resonance”. . Vertical component is amplified because of the Rayleigh waves locally generated by the lateral propaEation. This amplification influence the reliability of the HVSR amplitudes. 1D inodeling cannot estimate reliably and quantitatively the amplification where complex phenomena are included and cannot represent the effect of locally generated surface waves concerning the duration of shaking within the valley in time domain. This fact may lead to erroneous predictions of design ground motion. ’
- 2D modeling suggest that: a) locally generated surface waves contribute significantly to ground motion, and that they appear at the same frequencies as resonance of vertically propagating waves, b) 2D TF confirm the important interactions between the low frequency different wave-types as they observed on the recordings. All these show that the amplification observed at the center of the valley is due to the 1D resonance and the lateral propagation. The geometry of the Volvi valley does not justify 2D resonance. However, aggravation factor (2D/1D) must be considered in order to modify seismic design spectra since the: -2D/lD attains a factor of 5 and present shape comparable with that of the ratio between recording and lD, -the aggravation factor should be used at periods where surface waves locally generated by the lateral propagation appeared at the center of the valley. Finally, this study illustrates that a complex structure may produce complex site effects inferring 2D phenomena which are governed by the velocity contrast between sediments and bedrock. In this case, the common practice in which the amplification is based on a 1D soil profile of the topmost layers (first 30 m as suggested in Borcherdt 1994) may be not conditional for evaluating safely the additional response induced by 2D response. 3 SITE EFFECTS ESTIMATION: HOW VALID IS THE 30m ASSUMPTION? The new UBC97 code introduced the concept of the uppermost 30m Vs profile as a single parameter to evaluate the design response spectra for different shaking intensity levels (Borcherdt 1994). Certainly, its main advantage is the simplicity and the unambiguous evaluation by conventional geotechnical surveys. But is it accurate enough to estimate site effects using this assumption? The importance of the geometry and the velocity contrast between alluvial deposits and underlying bedrock has already been discussed. In this section, we present two examples where the use of the uppermost 30m to estimate site effect may lead to ambiguous results. The first example comes from Euroseistest downhole array (Figs 12a,b) for the same event presented in previous sections; the second is a strong motion event recorded at Port Island downhole array during the 1995 Kobe earthquake (Figs 12c,d). The elastic response spectra at different depths and their ratios are presented. In Euroseistest, we observe a clear amplification in high frequencies (T 75 m
Figure 4. Attenuation of peak ground acceleration for different soils at the site (data base No. 2). Figure 4 shows the attenuation of peak ground acceleration as a function of epicentral distance, D,, for data base No. 2 and M=6. The following
Seed et al. (1976) studied the influence of soil conditions at the site on the spectral ratio, defined as the ratio of spectral acceleration to maximum ground acceleration, based upon 104 ground motion records, mostly from the western U.S. They distinguished the
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ground types of Table 4. The average resonance period for acceleration increases with the softness and depth of the soil, from ground type 1 (0.18 s) to type 4 (0.83 s). The maximum spectral ratio is smaller for ground type 4 (2.3), followed by types 1, 3 and 2 (2.9). The authors cite similar results from Japanese earthquakes.
Figure 5. Probability of exceeding each resonance period of horizontal acceleration.
Figure 6 . The 50% fractile log absolute acceleration spectra for 2% damping, different ground types and specified values of magnitude and epicentral distance.
Figure 5 shows the probability of exceeding each value of the resonance period of accelerations for the ground types of data base No. 1. The average resonance period increases in a monotonic way with the softness and depth of the soil fiom 0.18 s (hard rock) to 0.74 s (deep, very soR soil). The result nearly coincide with those indicated above. Similar relationships exist between the resonance periods of relative velocity, which are however larger. A seismic hazard study has been undertaken, and the variable whose risk is established is the response. A statistical study of the response for each spectrum has been estimated as a function of magnitude, epicentral distance and ground type using the U.S. National Geophysical Data Base. The results indicated below are for 2% damping. Figure 6 shows the absolute acceleration response spectra corresponding to the 50% fiactile. The resonance period increases with ground softness, specially for low magnitude earthquakes. The resonance period increases clearly with magnitude, this effect being as important as the influence of the geology at the site. The maximum spectral acceleration corresponds to ground type 3 (Table 3) for M I 6.0. The same relationships are obtained with the 95% fractile, although, of course, the spectral ratio is much larger,
Figure 7. The 50% fractile log relative velocity spectra for 2% damping, different ground types and specified values of magnitude and epicentral distance.
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Table 5 . Standard errors of the log relative velocity response about the regression on magnitude and epicentral distance for each ground type.
I Ground I type 1 2 3
4
Table 4. Standard errors of the log absolute acceleration response about the regression on magnitude and epicentral distance for each ground type.
1
Ground type
4
I 1 0:; 1 1 0.02 0.31 0.32 0.32 0.29
I
0.05
0.32 0.30
1
T (s) 0.1 0.33 0.30 0.36 0.34
1
0.2 0.34 0.35 0.38 0.32
I
0.5 0.37 0.43 0.40 0.31
1
1 0.37 0.45 0.41 0.30
2 0.34 0.44 0.43 0.31
5 0.35 0.41 0.45 0.34
10 0.33 0.41 0.40 0.28
The background underlying the soil amplification studies summarized in the Introduction is that it is more exact to estimates the ground motion in the bedrock and then to calculate the soil amplification produced by the overburden, rather than estimating directly the ground motion at the surface of the overburden. Tables 4 and 5 show the standard error about the regression for the estimate of absolute acceleration and relative velocity respectively as a function of magnitude and epicentral distance in the four ground types, and for different periods. The standard error for alluvium and unconsolidated deposits is usually smaller than the standard error for rock, so that the above statement is false. Even more, few records are available to estimate the ground motion in the bedrock at depth.
Figure 8. The 95% fi-actile log relative velocity spectra for 2% damping, different ground types and specified values of magnitude and epicentral distance. The relative velocity of the four ground types of Table 3 follows the trend indicated in Figure 7 for the 50% fiactile. There is no clear relationship between ground softness and resonance period, but this parameter increases clearly with magnitude. The maximum relative velocity corresponds usually to ground type 3 for M 2 6.0. In all cases the order for increasing spectral velocity is: type 1,2 and 4.Some of these relationships might change for the 95% h c t i l e (Fig. 8), but the hard rock’s response is always the lower. The variable whose seismic hazard is determined depends upon the nearness of the structure’s fundamental period to the resonance periods of acceleration, velocity or displacement for the established fiactile. The chosen variable corresponds to the closer periods.
1
T (s) 0.5 0.34 0.41 0.40 0.31
4 CONCLUSIONS
The influence of the ground at the site in the response of structures is twofold: on the one hand loose or soft ground is usually responsible for damage due to liquefaction or ground settlement produced by vibrations, and often buildings founded on rock suffer no damage. On the other hand there is a resonance effect when the predominant periods of the structure and ground motion are similar. Owing to that there is often a direct relationship between the depth of alluvium and the height of the type of structure that suffers the greater damage. For a given magnitude and epicentral distance the ground acceleration, and the spectral relative velocity are usually smaller in rock, and specially in hard rock. On the other hand, the ground acceleration needed for a given intensity (damage) increases with the hardness of the ground. This explains the general good behaviour of rock foundations. The resonance period (for maximum response) of the ground motion increases usually with the softness of the ground, although the relationship is complex and it is not always so. More clear is the increase of the resonance period with the earthquake’s magnitude. Very often the larger peak
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acceleration or response corresponds to not very deep (245 m) stiff soils. It is more exact to estimate directly the ground motion at the surface of the overburden rather than estimating ground motion in the bedrock and then to calculating the soil amplification through the overburden. There is an important increase of the duration of an earthquake with the s o h e s s of the ground. This might be another reason for the small damage in rock foundation. REFERENCES Dickenson, S.E. & H. Kawase 1996. Review of the current state of knowledge on site amplification factor. Proc. Int. Workshop on Site Response, Port & Harbour Res. Inst., Japan, 1:101- 107. Finn, W.D.L. & Z. Lei 1996. Data on dynamics amplification factors under strong shaking. Proc. Int. Workshop on Site Response, Port & Harbour Res. Inst., Japan, 1:5 1-62. Iai, S., T. Morita, T. Kameoka, Y. Matsugana & K. Abiko 1996. Response of a dense sand deposit during 1993 Kushiro-Oki earthquake. Proc. Int. Workshop on Site Response, Port & Harbour Res. Inst., Japan, 2:142-158. Ichii, K. & M. Miyata 1996. Summary on nonlinear site amplification factor. Proc. Int. Workshop on Site Response, Port & Harbour Res. Inst., Japan, 15-21. Idriss, I.M. 1990. Response of soft soil sites during earthquakes. Proc. H. Bolton Seed Memorial Symposium, 2:273-289,Bitech. Justo, J.L. 1974. Cimentacionesy obras de tierra en zonas sismicas. Fundacion Juan March, Madrid, vol. 2. Justo, J.L., A. Jaramillo & R. Garcia 1989. The influence of the ground conditions in the design accelerogram and response of structures. Proc. 12fh Int. Con$ Soil Mech., Rio de Janeiro, 3 :1967-1970. National Geophysical Data Center 1996. Earthquake Strong Motion. Seed, H.B. & I.M. Idriss 1969. Influence of soil conditions on ground motions during earthquakes.J. Soil Mech., ASCE, 95:99-137. Seed, H.B. & I.M. Idriss 1971. Influence of soil conditions on building damage potential during earthquakes. J. Structural Div., ASCE, ST2: 639-663. Seed, H.B., C. Ugas & J. Lysmer 1976. Sitedependent spectra for earthquake-resistant design. Bull. Seism. Soc. Am., 66:1:221-243. Shakal, A.F., R.W. Sherburne & D.L. Parke 1984. Principal features of the strong-motion data fiom the 1984 Morgan Hill earthquake. The
I984 Morgan Hill, California Earthquake:249264. Calif. Department of Conservation Div. of Mines & Geol., Special Pub. 68. Sugito, M., K. Sekigachi, F. Oka & A. Yashima 1996. Analysis of borehole array records fiom the South Hyogo earthquake of Jan. 17, 1995. Proc. Int. Workshop on Site Response, Port & Harbour Res. Inst., Japan, 2 :343-3 5 7. Trifunac, M.D. 1976. Preliminary analysis of the peaks of strong earthquake ground motionDependence of peaks on earthquake magnitude, epicentral distance, and recording site conditions. Bull. Seism. Soc. Am., 66:1:189-219. Trifbnac, M.D. & A.G. Brady 1975. A study on the duration of strong earthquake ground motion. Bull. Seism. Soc. Am., 65:3:581-626. Trifunac, M.D. & V.W. Lee 1978. Dependence of the Fourier amplitude spectra of strong motion acceleration on the depth of sedimentary deposits. Report CE 78-14, Univ. Southern California. Trifunac, M.D. & V.W. Lee 1985a. Preliminary empirical model for scaling pseudo relative velocity spectra of strong earthquake acceleration in terms of magnitude, distance, site intensity and recording site conditions. Report CE 85-04, Univ. Southern California. Trifunac, M.D. & V.W. Lee 1985b. Preliminary empirical model for scaling Fourier amplitude spectra of strong ground acceleration in terms of earthquake magnitude, source to station distance, site intensity and recording site conditions. Report CE 85-04, Univ. Southern California. ‘Westermo, B.D. & M.D. Trifunac 1978. Correlations of the fiequency dependent duration of strong ground motion with the magnitude, epicentral distance, and the depth of sediments at the recording site. Report CE 7812, Univ. Southern California.
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Soil-structure interaction and retaining structures: - Theme lecture - General report - Panelist’s contributions
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EarthquakeGeotechnicalEngineering, Sec0 e Pinto (ed.) 0 1999Balkema, Rotterdam, ISBN 90 5809 1 16 3
Soil-structure interaction studies through shakmg table tests
s.Iai & T. sugano Port and Harbour Research Institute, Japan
ABSTRACT: Recent developments in soil-structure interaction studies through shaking table tests are based on solid understanding of the mechanics of models. One principle in the mechanics of models concerns material behavior of soil and structure, and the other concerns the mechanics of soil-structure systems such as equilibrium and mass balance. The paper points out the importance to differentiate soil-structure interaction in cyclic mobility regime from that in strain softening regime. The two principles of mechanics of models lead to a set of scaling relations. Soil-structure interaction studies on a gravity quay wall and a pile-supported wharf reviewed in this paper indicates that shaking table tests, if carefully performed, have a potential to be a powerful means to study the performance of complicated soil-structure interaction problems.
INTRODUCTION Soil-structure interaction during earthquakes are generally complex. They are affected by mechanical properties of soil and structures as well as initial, boundary, and loading conditions. Simplified idealization of soil-structure systems has been often successful to capture the essential performance of relatively simple soil-structure systems such as a building founded on a firm soil deposit or a signle pile embedded in a firm ground. For more complicated soil-structure systems such as retaining walls and pile supported wharves, simplified idealization often fails to describe essential performance of soil-structure systems. Shaking table tests are, if carefully conducted, one of useful methods for understanding the complicated soilstructure interaction problems. Soil-structure interaction studies through shaking table tests have a long history. Before mid 1980’s when the centrifuge model tests became widely accepted among the geotechnical earthquake engineers and researchers (Schofield 198I), shaking table tests have been the most common model tests for soil-structure interaction studies. The scope of the studies through shaking table tests in those days, however, were generally limited to either qualitative interpretation of soil-structure interactions or quantiative evaluation of relatively simple soil-
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structure systems such as measurement of earth pressures acting on a slowly moving wall. The use of the same soil for the model tests as for the prototype posed a problem for establishing reasonable scaling relations applicable to shaking table tests. Soil-structure interaction studies through centrifuge tests since mid 1980’s triggered a new look at the role of the conventional shaking table tests. In the late 1980’s, comprehensive reviews were offered on scaling relations for shaking table tests (Scott 1989, Iai 1989). Since the Hyogoken-Nambu (Kobe) earthquake of 1995, more and more attentions are directed toward deformation based design approach to evaluate the performance of soil-structure systems during intense shaking. These developments set a new stage for soil-structure interaction studies through shaking table tests. This paper reviews these recent developments in two parts: the first half aims to give a basis for discussion of shaking table tests - mechanics of models, often called scaling relations. The second half will discuss a selection of tests, first on gravity quay walls in liquefiable ground and then on pile supported wharves. The reviews offered from a wider perspective on dynamic model tests were available in Steedman (1995) and Kagawa (1995).
MECHANICS OF MODEL TESTS - SCALING RELATIONS Everyone working on soil-structure interaction studies through shaking table tests has to begin by learning about the mechanics of models. The principles have been understood for more than 40 years (Rocha 1957, Roscoe 1968, Kagawa 1978, Kokusho & Iwatate 1979, Shibata & Ohta 1980). There are two principles. The first principle concerns the material behavior of soil: the material behavior of soil in the model should mimique that in the prototype. This is illustrated in Fig. 1 as an example, in which the stress-strain of soil in the prototype is represented by the stress-strain of soil in the model through the use of scaling factors. Since soil is a pressure/density sensitive material, there are several options to choose from to achieve this principle in the model tests. How to choose these options will be discussed later. A similar principle is required for structures, too: the material behavior of structure in the model should mimique that in the prototype. This is easier to accomplish by choosing appropriate materials and structural dimensions for model structures. The second principle concerns the mechanics of soil-structure systems: the fundamental laws of mechanics such as equilibrium and mass balance of soil skeletodpore water should be satisfied both in the model and the prototype. In particular, the same gravity applies to the model and the prototype in shaking table tests. In its simplest form, these principles are written for dry soil as: L’o + pg = pii (equilibrium) (1) d&= Ldu (strain definition) (2) d o = DdE (constitutive law) ( 3 ) where gf. = (o,, o,,o,,z,,z,,z,,) : stress &’*=
I &22 &33 Y12 Y23 Y31
: strain
uf*=( U , u2U , ) : displacement D : tangent modulus g: acceleration of gravity p: density r-
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Structures are idealized into either a solid, a plane/shell, or a beam. The equations for solid are similar to those presented above and will not be repeated. The equations for a beam are applicable both to piles and sheet piles and are given as:
EI ____ d 4 n T u+ pbn’ii - pbn’g + n T S o= 0 an
(4)
EA d 2 t T U +p,tTii-pPbtTg+t’So=O
(5)
~
dS
where E I flexural rigidity = Young’s modulus x second moment of area EA: longitudinal rigidity = Young’s modulus x cross sectional area n: unit vector normal to the beam t: unit vector tangential to the beam d / dn :differentiation with respect to n d / ds : differentiation with respect to t pb: density of beam (mass per unit length) S: a matrix which transforms the stress into the traction on the beam E stress acting on the beam Bending moment, shear and axial forces are given as
The scaling relations are systematically obtained by introducing the scaling factors for all the variables in Eqs.(l) through (6) and then by demanding that these equations be satisfied both in the model and the prototype. For example, Eq.( 1) demands the following relations: A. / A=A, = A,Au /A,, (7) where A denotes the geometrical scaling factor (prototype/model) and others denote the scaling factors for the variables indicated in the subscripts. The first half of equations in Eq.(7) comes from the balance between the stress gradient L“o and the gravitypg in Eq.(l), and the second half comes from the balance between the gravity pg and the inertia p i . After deriving other relationships from Eqs.(2) through (6), simple algebraic manipulations lead to the scaling factors for various quantities specified in terms of scaling factors for length (A), density (Ap), and strain (AJ.This line of derivations are easily generalized to soil-structure-fluid interaction problems with saturated soils, including liquefiable deposits (Iai, 1989). Major scaling factors obtained are shown in Table 1. Physical background to these scaling factors may be given as follows. Displacement is a product of strain and length and accordingly scaled by AAF Time
Fig. 1 Illustrative example of model and prototype 929
Quantity
Ta e 1 Major scaling factors for shaking table tests Scaling factor (prototype/model) Generalized scaling factors
Scaling factors in practice Type I1 Type I11 Type I ;1 ,203 ;lP=1 2&=1
aP=I
Length Density Time Acceleration Velocity Displacement Stress Strain Stiffness Permeability Pore pressure E1 EA Moment Shear Axial Force
2
1
10.75
20.5
1
1
20.75
20.5
.5
2 20.5
a
A5/A.& A3/As
A4 A3 A3
A3AP A3AP
should be scaled to satisfy the balance between gravity and inertia (i.e. the second half of Eq.(I)), This naturally and accordingly scaled by (22&)0-5. leads to the scaling factor for acceleration and velocity as shown in Table 1. Stress should be scaled to satisfy the balance between stress gradient and gravityhnertia (i.e. the first half of Eq.(l)), and accordingly scaled by AAp Similar background is given to the relevant terms for a beam type structure,
A.
1
2 2
20.5
1 2
20.75
20.5
/t
2
14.5
2
22.5
A3 A4 A3 A3
A4 A3 A3
increase during shaking but the deformation cease to increase as soon as the shaking stops. This type of soil behavior is classified as cyclic mobility type, in which strain continues to increase during shaking but never goes into the state of strain softening as shown in Fig. 2. Soil-structure interaction involving this
SCALING FACTORS IN PRACTICE Various insights and wisdoms have been offered on the use of scaling factors in practice of shaking table tests (Scott 1989, Iai 1989 & 1990, Hettler 1990, Steedman 1990). The central issue concerns with the question of how to mimique the behavior of soil in the prototype. In particular, saturated soil behavior may be classified in two types (Whitman, 1985).; one is limited deformation, the other unlimited flow type deformation. ( 1) Soil-structure
interaction with limited deformation The soil in the prototype is often medium to dense sand deposit and exhibits pore pressure increase close to the initial confining pressures during shaking. The deformation of soil-structure systems continues to
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Fig. 2 Example of cyclic mobility (Ishihara 1985)
type of soil behavior will be called limited deformation type. In this type of soil-structure interaction studies, it is important to take into account the scaling factor for strain in order to capture the essential features of the transient and cyclic response of soil-structure systems. The scaling factor for strain is best determined by (Iai, 1989 & 1990): r
72
where (Ys),,, and (V,), denote shear wave velocities of soil deposits in the model and the prototype, respectively. This is useful when the shear wave velocity of the model is already known by preliminary model tests or other relevant source of information. Once the scaling factor for strain is determined by Eq.(8), other scaling factors are obtained as shown in Type I in Table 1. It is important to note that the density of the soil in the model is not required to be the same as that in the prototype as long as both the model and the prototype sand exhibit cyclic mobility type performance. Thus, it may be possible to use looser soil deposit in the model than in the prototype to make the scaling factor for strain AEcloser to unity. If this were indeed possible, then the Type I scaling factors in Table 1 would be reduced to the type I11 in the same table. This, however, is generally known to be rather difficult to achieve in practice. If the shear wave velocities of soil deposits in the model is not known, then it is often the practice to adopt an assumption that the elastic shear modulus is proportional to the square root of the confining pressure, provided the density of the soil in the model is about the same as that in the prototype. This is equivalent to assume that: Other scaling factors are obtained as shown in the column of Type I1 in Table 1. This is only an approximation of Type I but often convenient to use in practice. The scaling factors for a beam type structure shown in Table 1 are given for pile type structure. For a sheet pile type structure, the dimensions and the cross sections are generally specified per unit breadth, and thus the scaling factors should be accordingly specified per unit breadth. This is done by deviding the scaling factors shown in Table 1 by A;the scaling factor for E1 per unit breadth for type I, for example, is given as A~/A,, etc. Unfortunately a wrong scaling factor was printed for the scaling factor for EI in some of the previous
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publications (Kagawa, 1995; KO, 1995); this should be corrected as the scaling factor for EI shown in Table 1. (2) Soil-structure interaction including strain softening regime If the soil in the prototype soil-structure system exhibits strain softening type behavior, then the deformation becomes too large to allow the introduction of scaling factor for strain. In this case, the density of the model soil deposits should be appropriately determined to mimique the strain softening behavior of the prototype soil (Roscoe 1968, Schofield 1980, Scott 1989). In general, looser deposits should be made in the model than in the prototype to take into account the difference in the confining stress. An example of strain softening behavior reproduced by the looser deposits in smaller confining stress is shown in Fig. 3 (Ghalandarzadeh et a1 1996). In this case, the scaling factors of Type I11 in Table 1 is applied. Both for cyclic mobility or flow type behavior of soil model tests, viscous fluid is often used for substituting pore water in the model to adjust the permeability in accordance with Table 1. Some concerns on this point have been raised in a literature (Poorooshasb 1995 & 1997, Iai 1997). The discussions offered so far, however, are limited to qualitative arguments and need further investigations to validate or negate those concerns in quantiative manner.
Fig. 3 Strain softening type behavior and its representation with looser material in lower confining stress (Verdugo 1992 as reported by Ghalandarzadeh et a1 1996)
In order to review how well these scaling relations work in practice, two soil-structure interaction studies will be discussed. The first set of models are for gravity quay walls, in which structure itself is rigid so that a major attention is directed toward the deformation of soil. The second is for a pilesupported wharf, in which more complicated soil structure interaction phenomenon is involved. GRAVITY QUAY WALL Gravity quay walls constructed on a loose saturated backfill foundation provide an example of soilstructure interaction problem which involves cyclic behavior of sand subjected to anisotropic stress conditions; where the principal stresses of cyclic shear due to earthquake shaking are not coaxial with those of the quasi-static anisotropic streses due to gravity (Iai, 1997b). The Great Hanshin earthquake of 1995 in Japan provided a solid case history data on the performance of this type of soil-structure interaction problems. Many of the caisson walls in Kobe Port were constructed on a loose saturated backfill foundation of decomposed granite, which was used for replacing the soft clayey deposit in Kobe Port to attain the required bearing capacity of foundation. Shaken with a strong earthquake motion having the peak accelerations of 0.54g and 0.45g in the horizontal and vertical directions, these caisson walls were displaced an average of 3 m (maximum displacement = 5m) toward the sea, settled I to 2 m and tilted about 4 degrees toward the sea. Figure 4 shows a typical example of the cross section and the deformation after the earthquake (Inagaki et al., 1996). The geotechnical investigations were performed to evaluate the soil properties, including cyclic triaxial tests of undistrubed samples 60 cm long with a diameter of 30 cm obtained by an in-situ freezing technique. The cyclic triaxial tests showed cylcic mobility type behavior and never exhibited the strain softening type behavior (Ichii et al. 1997). In the shake table tests, the caisson type quay wall was modeled at a scale of 1/17 (A=17) of the prototype (Sugano et a1 1996, Inagaki et a1 1996). The quay wall model including foundation and backfill soils was made in a steel container 3.5 m long by 1.5 m wide and 1.5 m deep on a shaking table, which was set in the middle of a water pool 2 m deep and 15 m by 15 m wide to simulate the effect of sea water. The decomposed granite obtained from a site nearby the quay wall was pluviated into the water to simulate the dumping process of sand replacement and backfill soils at the construction.
The cross section of the model quay wall is shown in Fig. 5. The front end (i.e. left hand side in the figure) of the container above the model seabed level was open to the water pool whereas the back end of the container was sealed with unwoven textile reinforced with steel wire mesh to relieve adverse effects of rigid boundary conditions. Both sides of the container, however, were made of rigid steel plates to constrain the normal component of ground strain between these plates. Three model caisson were placed along the quay wall face line 1.5 m long and the caisson in the middle was used for monitoring accelerations and displacements. The clay layer at the quay wall site was idealized in the model test by densely compacted layer of coarse grained Soma sand as shown in Fig. 5 to simulate the stable behavior of the clay layer during the earthquake. The surface of this layer was sealed with a thin bentonite layer to simulate the impermeable behavior of the caly layer during the earthquake. The scaling factors of Type I1 in Table 1 was adopted for this study as shown in Table 2. Three dimensional shaking was appoied using the subsurface motion recorded at a depth of 32 m by the vertical seismic array at Port Island in Kobe Port, shown in the inset of Fig. 1, successfully recorded by the Development Bureau of Kobe City. The peak accelerations were 544, 461, and 200 cm/s2 in NS, EW and UD directions. The input motions was applied in accordance with the direction of the quay wall, facing west. Table 2 Scaling factors for shaking table tests for a gravity quay wall Quantities Scaling Scaling factors factors for 1/17 model a 17.0 Length Time 10.75 8.4 Acceleration 1 1.o Displacement .5 70.1 Stredpore a 17.0 water pressure Strain a0.5 4.1 A total of nine tests have been performed with various conditions for the model tests. After each text, the model foundation soils and backfill soils were excavated for measuring the deformation, then completely removed from the container and new virgin soils transported from Port Island were pluviated into the water to form a new model foundation and backfill for the next case. Three cases, Case-2, 6 and 7, were performed to repeatedly
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Fig. 4 Location, cross section and residual deformation of a caisson quay wall at Port Island, Kobe Port during Great Hanshin earthquake of 1995
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Fig. 5 Cross section of a model quay wall for shaking table tests
Fig. 6 Residual displacement of model quay wall (scaled in terms of prototype) simulate the performance of the quay wall during the earthquake. To facilitate the comparison to those measured in the field, the test results are presented in terms of the prototype scale. The initial densities are shown in Table 3. The dry densities ranging from 1.6 to 1.9 g/cm3 as shown in this table are very large, probably because the decomposed granite contians fair amount of large particles. The dry densities of the in-situ frozen samples of the decomposed granite range from 1.7 to 2.1 g/cm3, basically consistet with those measured in the model foundation and backfill.
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Table 3 Initial dry densities and void ratios of model foundation and backfill soils for a gravity quay wall Void ratio Case Soil deposits Dry No. density (g/cm3) 1.843 0.440 Case-2 Sand replacement Backfill soil 1.598 0.661 Case-6 Sand replacement 1.580 0.679 Backfill soil 1.913 0.387 Case-7 Sand replacement 1.592 0.667 Backfill soil 1.906 0.392
Residual displacements of the model caisson wall after shaking are shown in Fig. 6 together with those measured in the field as reproduced from Fig. 4. The model test results are basically consistent with those induced in the field during the earthquake. In order to obtain a comprehensive picture of the dynamic performance of the quay wall during the earthquake shaking, time histories of the response of the quay wall obtained by the model tets are shown in Fig. 7. Accelerations of the quay wall continued for about 20 seconds. In particular, the wave form at the ground surface is similar to that recorded at the ground surface at the vertical seismic array site in
Port Island shown in the upper right hand corner in the same figure. Displacements and excess pore water pressure were gradually induced with the shaking for about 10 seconds. The order of magnitude of velocity of the model caisson wall (i.e. 0.2 to 0.3 m/s) was consistent with that of the prototype caisson evaluated based on the response of a container craine (Scott, 1997). In summary, the model test results compare well with those observed, including dynamic response of backfill, movement of the caisson as well as residual deformation of soil-structure system.
Fig. 7 Time histories of model quay wall response (scaled in terms of prototype) and the recorded time history of acceleration at.the ground surface at the vertical seismic array site in Port Island
PILE-SUPPORTED WHARF A pile supported wharf is composed of a deck supported by a substructure consisting of piles and a dike. The presence of the sloping dike causes the supporting piles to have varying unsupported lengths between the deck and the dike. When the geotechnical material suitable for the dike is hard to obtain, as being often the case in Japanese practice, a gravity or sheetpile retaining structure is also
constructed to replace a portion of the dike. During the Great Hanshin earthquake of 1995 in Japan, a pile supported wharf suffered damage at Takahama Wharf in Kobe Port (Iai 1997b). The horizontal residual displacement of the wharf ranged from 1.3 to 1.7m with a typical example of the cross section and deformation of the pile supported wharf as shown in Fig.8. As shown in this figure, the wharf was constructed on a firm foundation deposit consisting of alternating layers of pleistocence clay
935
Fig 8 Cross section of a pile supported wharf at Kobe Port and deformatiodfailure during 1995 Great Hanshin Earthquake, Japan 936
Fig. 9 Cross section of a model pile-supported wharf for shaking table tests and sandy gravel. The SPT N-values ranged from 10 to 25 for the clay and 30 to 50 or higher for the sandy gravel. The firm deposit was overlain by an alluvial sand layer having SPT N-values of about 15, the thickness of which was variable, about two meters on average. Behind the retaining wall made of concrete cellular blocks was a hydraulic backfill of decomposed granite having SPT N-values of about 10. The deck of the wahrf was made of reinforced concrete slabs and beams supported by steel pipe piles having a dimater of 700 mm. The steel piles buckled at the pile heads except for the piles located most landward. A crack was found at the pile cap - concrete beam connection located most landward. The piles, pulled out after the earthquake for investigation at the site shown in Fig. 8(b), also showed buckling below the mudline at the depths shown in Fig. 8(a). As shown in this figure, some of the buckling was located close to the boundary between the layers of alluvial sand and pleistocence gravel. This boundary happend to be located close to the level where the thickness of the piles were reduced through factory weld joints with
937
the exception of the row of piles located most seaward. Displacements of the rubble dike, measured by divers at five locations 5 m apart, were about the same as those of the deck as shown in Fig. 8(c). The backfill behind the retaining structure settled about 1 m. These measruements indicated a somewhat uniform movement of the dike and the retaing wall toward the sea. In the shake table tests, the pile-supported wharf was modeled at a scale of 1/15 (A=15) of the prototype. The steel container and the shaking table used was similar to that for the gravity quay wall. The cross section of the model wharf is shown in Fig. 9. The boundary conditions imposed by the container were also similar to those for the gravity quay wall. Three models of pile-supported decks were placed along the quay wall face line 1.5 m long and the pilesupported deck in the middle was used for monitoring accelerations and displacements. The scaling factors of Type I1 in Table 1 were also adopted for this study as shown in Table 4. Three dimensional shaking was applied using the subsurface motion recorded at a depth of 32 m by the
vertical seismic array at Port Island in Kobe Port mentioned earlier. The input motions was applied in accordance with the direction of the quay wall. Table 4 Scaling factors for shaking table tests for a tile-supported wharf Quantities Scaling Scaling factors factors for 1/15 model 15.0 Length A ~0.75 7.6 Time 1 1.o Acceleration ill .5 58.1 Displacement 15.0 Stresdpore A water pressure Ao.5 3.9 Strain A4.5 El 196000 87 1 EA A2.j A total of three tests have been performed with various conditions for the deck-retaining structure connections. After each text, the model foundation soils and backfill soils were excavated for measuring
the deformation, then completely removed from the container and new virgin soils transported from Port Island were pluviated into the water to form a new model foundation and backfill for the next case. One case is reported here, in which the deck is fixed to the top of the retaining structure. To facilitate the comparison to those measured in the field, the test results are presented in terms of the prototype scale. Time histories of the response of the quay wall obtained by the model test are shown in Fig. 10. Residual bending moments of the model piles after shaking are shown in Fig. 11 together with those of buckling locations observed in the field. Displacement of the deck from the model test was about half of that observed. This inconsistency, however, may be partly explained by the fact that the effect of yielding of piles were not taken into account in the model tests. The buckling locations observed in the prototype piles approximately coincided with the maximum locations of bending moment distribution.
Fig. 10 Time histories of model pile-supported wharf response (scaled in terms of prototype)
938
SUMMARY AND CONCLUSIONS This paper reviewed recent developments in soilstructure interaction studies through shaking table tests. More and more sophisticated use of shaking table tests has lead our attentions back to the fundamental mechanics of models. The mechanics of models consist of two principles. The first concerns the material behavior of soil and structure; the material behavior of soil and structure in the model should mimique that in the prototype. The paper pointed out the importance to recognize the difference in soil-structure interaction problems in cyclic mobility regime and strain softening regime. The second concerns the mechanics of soil-structure systems; the fundamental laws of mechanics such as equilibrium and mass balance should be satisfied both in the model and the prototype. These two principles naturally lead to the scaling factors for various quantitites such as time, displacement, stiffness, etc. specified in terms of scaling factors for length, density and strain. Soil-structure interaction studies on a gravity quay wall and a pile-supported wharf indicated that shaking table tests, if carefully performed, have a potential to be a powerful means to study the performance of complicated soilstructure interaction problems. Fig. 11 Residual bending moments in the piles (scaled in terms of prototype) obtained by shaking table tests At the current stage of the study, the agreement between the model test results and those observed in the field are obviously not perfect and limited to the extent described above. Considering the complexity of the soil-structure systems discussed here, however, the extent of agreement discussed here may be understood as an encouraging sign. In addition to those model tests discussed above, significant studies have been performed through the comparison of 1 g shaking table and centrifuge tests. One study is a series of model tests on composite deposits of dense and loose sand and Type I11 scaling factors were used (Gibson & Scott 1995). The other is a series of model tests on an embankment founded on liquefiable foundation and Type I1 scaling factors were used (Hayashi et a1 1997). In both of these studies, the results of l g model tests agrees well with those of centrifuge tests, suggesting a good applicability of the scaling relations for shaking table tests.
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REFERENCES Ghalandarzadeh, A., T. Orita, I. Towhata & F. Yung, 1998. Shaking table tests on seismic deformation of gravity quay walls, Soils and Foundations, Special issue on Geotechnical Aspects of the January 17 1995 Hyogoken-Nambu earthquake No.2, 115-132 Gibson, A.D. & R.F. Scott, 1995. Comparison of a 1g and centrifuge model dynamic liquefaction test: Preliminary results, Earthquake Geotechnical Engineering, IS-Tokyo '95, Balkema, 773-778. Hayashi, K, Fujii, N., Murakami, T., and Houjyou, K. 1997. Direct comparison of gravity model and centrifuge model for the seismic problem, Journal of Geotechnical Engineering, Japan Society of Civil Engineers, 111-41(582):207-216 (in Japanese) Hettler, A. 1990. Similitude for shaking table tests on soil-structure-fluid model in 1g gravitational field (discussion), Soils and Foundations, 30(2): 150151. Iai, S. 1989. Similitude for shaking table tests on soilstructure-fluid model in 1g gravitational field, Soils and Foundations, 29(1):105-118. Iai, S. 1990. Similitude for shaking table tests on soil-
structure-fluid model in 1g gravitational field (closure), Soils and Foundations, 30(2):153-157. Iai, S. 1997a. One gravity model testing (discussion), Soils and Foundations, 37( 1): 137. Iai, S. 1997b. Seismic analysis and performance of retaining structures, Geotechnical Earthquake Engineering and Soil Dynamics 111, Geotechnical Special Publication No.75, ASCE, 1020-1044. Ichii, K., S. Iai & T. Morita, 1997. Effective stress analyses on the performance of caisson type quay walls during 1995 Hyogoken-nanbu earthquake, Report of Port and Harbour Research Institute, 36(2):41-86 (in Japanese). Inagaki, H., S. Iai, T. Sugano, H. Yamazaki. & T. Inatomi, 1996. Performance of caisson type quay walls during 1995 Great Hanshin Earthquake, Soils and Foundations, Special Issue on Geotechnical Aspects of the January 17 1995 Hyogoken-Nambu Earthquake, 119-136. Ishihara, K.1985. Stabilit of natural deposits during earthquakes, Proc. 1I ICSMFE, San Francisco, 321-376 Kagawa, T. 1978. On the similitude in model vibration tests of earth structures, Proc. of Japan Society of Civil Engineers, 275:69-77 (in Japanese) . Kagawa, T. 1995. Dynamic model testing in Earthquake geotechnical engineering, IS-Tokyo '95, Geotechnical Engineering, Balkema, 1435-1447. KO, H.Y. 1995. Summary of discussions in Session4: Verification by dynamic model tests, Earthquake Geotechnical Engineering, IS-Tokyo '95, Balkema, 1463-1467. Kokusho, T. & T. Iwatate, 1979. Scaled model tests and numerical analyses on nonlinear dynamic response of soft grounds, Proc. of Japan Society of Civil Engineers, 285:57-67 (in Japanese). Rocha, M. 1957. The possibility of solving soil mechanics problems by the use of models, Proc. dth ICSMFE, 183-188. Poorooshasb, H.B. 1995. One gravity model testing, Soils and Foundations, 35(3):55-59. Poorooshasb, H.B. 1997. One gravity model testing (closure), Soils and Foundations, 37( 1): 137-138. Roscoe, K.H. 1968. Soils and model tests, Journal of Strain Analysis, Institution of Mechanical Engineers, 3(1):57-64 Scott, R.F. 1989. Centrifuge and modeling technology: a survey, Revue Francaise de Geotechnique, 48: 15-34 (in French). Scott, R.F. 1997. Crane response in 1995 Hyogoken Nanbu earthquake, Soils and Foundations, 37(2) :8 1- 87 Schofield, A.N. 1980. Cambridge geotechnical 940
centrifuge operations, Geotechnique, 30(3):227268. Schofield, A.N. 1981. Dynamic and earthquake geotechnical centrifuge modelling, Proc. of International Con$ on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, St. Louis, 1081-1 100. Shibata, T. & H. Ohta, 1980. Similitude in soil-model tests, Tsuchi-to-Kiso, JSSMFE, 28(5):9-14 (in Japanese) Steedman, R.S. 1990. Similitude for shaking table tests on soil-structure-fluid model in l g gravitational field (discussion), Soils and Foundations, 30(2):151-153. Steedman, R.S. 1995. Verification by dynamic model tests, Earthquake Geotechnical Engineering, ISTokyo '95, Balkema, 1407-1410. Sugano, T., T. Morita, M. Mito, T. Sasaki, & H. Inagaki, 1996. Case studies of caisson type quay wall damage by 1995 Hyougoken-Nanbu earthquake, Proc. 1lth World Conference on Earthquake Engineering, Acapulco. Verdugo, R. 1992. Characterization of sandy soil behavior under large deformation, Dissertation to Ph.D. degree. The University of Tokyo Whitman, R.V. 1985. On liquefaction, Proc. I I 'I' ICSMFE, San Francisco, Balkema, 1923-1926.
Earthquake GeotechnicalEngineering, S&coe Pinto (ed.) 0 1999 Balkema, Rotterdam, ISBN 90 5809 1 16 3
Soil-structure interaction and retaining structures George Gazetas National Technical University,Athens, Greece
Summary
Thirty three papers have been submitted for this sessioh, covering a range of topics within the field of dynamic response of foundations and retaining structures. The topics can be broadly classified into the following five categories : (a) Seismic behavior of quaywalls, including the analysis and design of countermeasures to resist strong seismic motions and liquefaction “flow” failure. Essentially all papers in this category refer to, or have been motivated by, the extensive quaywall failures (and successes) in Kobe, during the 171- 1995 Great Hanshin Earthquake. [Papers Numbered : 32, 43, 59, 66, 92, 61, 1011. (b) Analysis of piles and pilesupported structures subjected to lateral-spreading type of ground deformation. Again, the papers in this session seem to have been motivated by the numerous incidences of liquefaction-induced large ground deformations and their effect on nearby piles in the 1995 Kobe Earthquake. [Papers Numbered : 55, 86, 90, 132, 1371. (c) Dynamic response of pile foundations, under inertial and kinematic vibratory loading. The papers in this group include studies on the effect of pile response on soil-structure interaction. [Papers 941
Numbered: 10A 28, 53, 57, 83, 98, 1081. (d) Analysis of the dynamic responses of shallow and embedded foundations, in a variety of situations. [Papers Numbered: 4 1, 43, 52, 127, 63, 134, 140, 1411. (e) Dynamic response and design of retaining walls, which retain and are supported by “stable” soil. [Papers Numbered: 3 1, 122A, 231. One interesting remark is that the methods used in the papers for analysis, design, or just interpretation of the observed phenomena include :
a
theoretical analyses (numerical. analytical, and hybrid) large scale shaking table tests centrifuge model tests.
In several of the papers the results of such theoretical andor experimental analyses are contrasted against field observations, to reach reliable conclusions regarding the seismic behavior of complex soil-structure systems. Overall, the papers in this session reflect the considerable progress during the last 4 years in the state of the art of analyzing the behavior of retaining structures and pile foundations under very strong seismic shaking and large ground imposed deformations.
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Earthquake GeotechnicalEngineering,SBco e Pinto (ed.)0 1999Balkema, Rotterdam, ISBN 90 5809 1 16 3
Dynamic soil-structureinteraction of adjacent structures Stavros A. Savidis & Reinhold Hirschauer Geotechnical Institute, Technical University,Berlin, Germany
ABSTRACT: The presented paper describes a numerical procedure to analyze structures of arbitrary geometry on the surface of a layered soil with constant stiffness and damping in each layer. The mixed boundary value problem is solved numerically using influence-functions for the layered soil. The soil-structure interaction is realized by a discrete weighted residual technique formulated in the frequency domain. Examples are given for two structures under seismic excitation and for a system of railway ties exposed to harmonic excitation. 2 METHOD OF SOLUTION
1 INTRODUCTION Considering dynamic soil-structure interaction problems for foundation systems the dynamic subsoil coupling of the foundations is an important factor. A number of methods to solve this mixed boundary value problem in the frequency domain have been introduced during the past decades. Semianalytical methods, Savidis and Richter (1977), Savidis and Sarfeld (1980), Wong and Luco (1986), numerical finite element and boundary element techniques, Roesset and Gonzalez ( I977), Mohammadi and Karabalis (1995), as well as analytical methods, Triantafyllidis and Prange ( I 987) have been used. While numerical techniques allow the treatment of foundation systems of arbitrary geometry, analytical methods are restricted to regular geometries. Regarding the soil, as nonhomogeneous and layered, special influence functions are required to construct the corresponding stiffness matrix of the subsoil. One of the possibilities is, to use half-space influence functions in terms of displacements for dynamic point loads determined by the thin-layer method developed by Waas (1972) and Kausel (1 98 1). Using this method and the substructure technique, Wolf (1985), the interaction effects between structures with foundations of irregular geometry on a layered soil, excited by seismic waves or external loads are studied here.
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2. I Equation of motion The substructure technique is the basis for the calculation of the soil-structure-interaction. Here the soil and the rigidelastic foundations are defined as substructures. To compute the dynamic response of structures resting on a layered soil and subjected to seismic excitation or external loads respectively , the principle of d’Alembert in the form of Lagrange is applied to obtain the equation of motion (eq. 1)
Herein M, DIJ,and C,J,represent the mass, damping and stiffness matrix of the elastic foundations. C, and D,ydescribe the stiffness and damping matrix of the underlying layered soil. The vector U represents the absolute displacement whereas uo is the ground base motion in the case of seismic excitation. Finally p represents the external loads. Seismic Excitation (External loadp = 0 )
Performing the Fourier transformation eq. (1) gives
(- Q ~ M + K )U = K U,, (2) where K = K\.+ K,>,represents the complex stiffness
matrix of the entire system with K,,, = D,,, -I-C,,, being the complex stiffness matrix of the elastic foundation and K,Y= D, + C, the complex stiffness matrix of the soil, considering the boundary conditions at the soil surface. U and U. denote the complex ampli-
tudes in the frequency domain of the respective quantities U and U, in the time domain.
External Loads (No seismic excitation (U, = 0) Having no seismic excitation (U, = 0) and performing the Fourier transformation equation (1) yields
(- Q*M + K)U = P
(3)
P denotes the complex amplitudes of the external
method to compute the influence functions, the finite layers of the above soil profile have to be divided into sublayers in order to linearize the transcendental functions which govern the displacements in the direction of the layering. The thickness of the sublayers have to be small compared to the wavelengths involved. 3 RESULTS AND DISCUSSION
3.1 Seismic excitation
loads in the frequency domain.
2.2 Complex stiffness of soil The contact area underneath the elastic plates is divided into a finite number N of subareas A; with uniformly distributed pressures qi = {e,qy,q z } and weighted displacements U; = {U,, U?,,u z } over each subregion (i = 1, 2, ..., N). Rearranging the vectors q and U and imposing relaxed boundary conc&ions at the contact g e a the influence matrix F yields U = F q with F having the following form:
The first system analyzed here is shown in figure 1 (Savidis et al, 1996). It consists of two structures based on rigid plate foundations resting on a layered soil. Foundation A is a circular plate with a radius of r = 20 m. The superstructures are modelled by lumped masses connected by rigid massless rods. The masses rn and mass moments of inertia 0 are shown in Table 1. Foundation B is circumscribed by a rectangle of 32.6 m x 48 m. The side next to foundation A has a curved edge. The distance between the two structures is 5 m.
The components of the matrix F are derived by integrating the surface influence functions f k l as described below over the area Ai.Assembling the influences over all soil elements leads to a frequency dependent flexibility matrix of the layered soil. Inversion of the flexibility matrix yields the complex soil stiffness matrix K(iQ. The soil stiffness matrix K , v ( i Qwhich ) includes the compatibility of the displacements of the rigid or elastic foundations with the soil displacements is obtained by multiplying the matrix K with a respective transformation matrix T and its transposed T'.
K, =T ' K T
(3)
2.3 InjZuencefunctions The surface influence functions f k l for the case considered here are determined by using the thin layer method by Kausel (1981). The method is a semianalytical technique, in which the layered soil is discretized in vertical direction by polynomials and in horizontal direction described by analytical functions. This formulation leads to algebraic expressions, whose integral transforms can readily be evaluated. The frequency dependent influence functions for layered media due to dynamic unit loads are then computed with high accuracy and reasonable computational effort. By using the thin layer
Figure 1.
Perspective view and ground plan of the system
The soil profile consists of three layers overlying a half-space. The first layer, representing sand, has a thickness of h, = 8 m. The soil properties of the second layer with a thickness of h2 = 6 m can be classified as marl. The third layer (dense sand) has a thickness of h, = 15 m. The soil properties of the underlying halfspace are those of gravel. The values of the soil properties, i.e. density p, shear wave ve944
locity v , ~Poisson's , ratio v and damping ratio Ps are given in Table 2. Mass distribution
Table 1. Node NO.
9 10 ~
Y
Y
wl
11 12 27 28 29
m [Mgl 35000 38000 20000 7000 31000 34000 5000
Table 2.
8
Z
[Mgm21 4.2~ 106 4 . 6 106 ~ 1.2 x 106 0 . 8 106 ~ 6.5 x 106 7 . 0 106 ~ 2 . 5 106 ~
[m] 0.0 10.0 22.0 35.0 0.0 12.0 30.0
Soil properties
[Mg/m3] [m/s ] 2 Mar1 3 Sand 4 Sand
2.0 1.9
220 250 300
0.45 0.02 0.33 0.01 0.33 0.01
6.0 15.0 CO
Both foundations are excited by a seismic base motion. As time input function a recorded accelerogram of the earthquake of Friaul is chosen (figure 2). The system response due to a seismic excitation is computed for two cases. In case 1 only the response of structure A is calculated, whereas in case 2 the complete system, i.e. both structures is analyzed. In ail graphs the results are denoted by dashed lines for case 1 and with solid lines for case 2. Figure 3 shows the normalized horizontal acceleration of node 9 and 12 due to a unit horizontal harmonic ground acceleration. At both graphs amplifications at the frequencies of fi = 1 Hz and f2 = 1.8 Hz can be seen clearly. The amplification at frequencyfi increases from the bottom (node 9) to the top (node 12) of the superstructure. This indicates that the rocking eigenmode around the y-axis is located at this frequency. The amplification at frequency fi can interpreted as a horizontal translation eigenmode combined with a rocking mode. A significant effect of interaction appears only in the frequency range of 1.5 to 2.5 Hz. Figure 4 shows the vertical normalized accelerations on node 1 and 5 for the same unit horizontal ground acceleration. Again the two dominant frequencies fi and f2 can be identified. The interaction effects are stronger on node 1, since this node is located next to the structure B. At node 5 the interac'non e%em are'ies pnfurmnh.
Figure 2. Time history, Fourier and response spectrum of Friaul eathquake
Figure 3. and 12
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Normalized horizontal acceleration for the nodes 9
dominant frequencies of the input function are 10cated in the range of 2 to 3 Hz and the eigenfrequency for the horizontal translation mode is in the same range an amplification occurs in this range. The same effect can be seen in the response spectra for the vertical accelerations in figure 6. In order to illustrate the interaction influence between both structures the response curves for case 2 are divided by the respective curves for case 1 by defining the parameters Y,, and Y, for the horizontal and vertical response. The variation of these parameters with frequency is also shown in figure 5 and 6.
Figure 4.
Normalized vertical acceleration for nodes 1 and 5
Figure 6. Response spectra and interaction influence factor of the vertical acceleration for node 1 and 5
3.2 External Loads
Figure 5. Response spectra and interaction influence factor of the horizontal acceleration for node 9 and 12
In figure 5 the reponse spectra for the horizontal acceleration for Node 9 and 12 are plotted. Since the 946
The second system analyzed here is a system of railway ties on the halfspace as shown in figure 7. The middle tie is exposed to harmonic loading. Hereby the influence of the number of ties (1,3,5) involved in the investigation upon the absolute Vertical displacement of the middle tie is examined. In this case the halfspace is assumed to be a homogeneous one with density p = 2000 kg/m3, shear wave velocity v, = 200 m/s and Poisson’s Ratio v = 0.33.
solute vertical displacement is decreasing monotonously with increasing frequency. Calculating the 3 - tie system, three distinct resonance peaks are obtained. Increasing the number of involved ties the number of resonance peaks increases. The influence of the number of the investigated ties as well as the kind of the soil layering upon the number and the shape of the resonance peaks are shown and discussed in Savidis and Hirschauer (1997) in more detail for the vertical and the rotational modes. Figure 7. Investigated System. Number of investigated ties: 1 , 3 , 5 and 21
4 CONCLUSIONS The dynamic interaction of two adjacent structures supported by rigid foundations exposed to horizontal seismic excitation and of a railway tie system exposed to harmonic excitation are presented. The numerical procedure applied includes the complete dynamic subsoil coupling and can be used to model arbitrary shaped foundation resting on layered soil. The results demonstrate the influence of frequency in the dynamic soil coupling of adjacent structures.
5 REFERENCES
Figure 8. Absolute vertical displacement of the middle ties as a function of the frequency f
The absolute vertical displacements of the middle tie 0 as a function of the frequency f are shown in figure 8. Due to the low mass of the tie there is no peak in the plot for the single tie system and the ab-
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Kausel, E. (1981). An explicit solution for the Green’s functions for dynamic loads in layered media, Research Report R81-13, Publ. No. 699, Dept. of Civil Engineering, M.I.T., Cambridge, Massachusetts Mohammadi, M. & Karabalis, D.L. (1995). Dynamic 3-D soil railway track interaction by BEM-FEM. Earthquake Eng. Struct. Dyn. 24, 1177-1193 Roesset, J.M. & Gonzalez, J.J. (1978). Dynamic interaction between adjacent structures. In Dynamical Methods in Soil and Rock Mechanics (B. Prange, ed.), Vol. I, pp. 127-166. A.A. Balkema, Rotterdam. Savidis, S. A., Faust B. & Sarfeld, W. (1996). Threedimensional Interaction between Structures on Layered Soil under Seismic Excitation, Proc. 11th World Con$ on Earthquake Engineering, Acapulco1996 Savidis, S. A. & Hirschauer, R. (1997). Dynamische Steifigkeiten von Schwellensystemen auf geschichtetem Untergrund. Zwischenbericht, DFGSchwerpunktprogramm Systemdynamik und Langzeitverhalten von Fahrwerk, Gleis und Untergrund Savidis, S. A. & Richter, T. (1977). Interaction of rigid foundations under dynamic loading. Proc. 9th Int. Con. Soil Mech. Found. Engng., Tokyo, Vol. 11,pp. 369-374. Savidis, S. A. & Sarfeld, W. (1980). Verfahren und Anwendung der dreidimensionalen, dynamischen
Wechselwirkung. Vortrage der Baugrundtagung, Mainz, 47-78. Triantafyllidis, T. & Prange, B. (1987). Dynamic subsoil coupling between rigid rectangular foundations. Soil dyn. earthq. eng. 6 , 164-179. Waas, G. (1972). Linear Two-Dimensional Analysis of Soil Dynamics Problems in Semi-Infinite Layered Media. Ph.D. thesis, University of California, Berkeley. Wolf, J.P. (1 985). Dynamic Soil Structure Interaction. Prentice-Hall, Englewood Cliffs: Wong, H.L. & Luco, J.E. (1986). Dynamic interaction between rigid foundations in layered halfspace. Soil dyn. earthq. eng. 5, 149-158
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Earthquake GeotechnicalEngineering, S6co e Pinto (ed.) 0 1999Balkema, Rotterdam, ISBN 90 5809 1 163
Seismic soil-structure interaction of rigid and flexible retaining walls R.S.Steedman GIBB Limited, Reading, UK
ABSTRACT: The nature of residual earth pressure behind a cantilever retaining wall is determined to be a function of the relative mass and stiffness of the soil and wall. Elasto-plastic theory is used to analyse the stress condition on the interface between the soil and wall, and to predict the wall top deflections. Comparisons with data from centrifuge model tests show good agreement, even after three separate episodes of base shaking. Permanent wall movement is concluded to be due to soil yielding in the backfill, generating locked-in lateral stresses on the back of the wall. The method is applicable to the full range of wall stiffnesses from rigid to flexible, and the implications of the analysis for design are discussed.
vital to the prediction of wall displacements during a succession of earthquakes.
1 INTRODUCTION The problem of dynamic earth pressure against walls during earthquakes has been widely considered since the early quasi-static solution of Okabe (1924). However, a lack of well instrumented prototype data has precluded a more fundamental understanding of the interaction problem. Design techniques have therefore usually been justified in relation to the behaviour of small models.
There are two significant components to retaining wall movement, namely sliding and rotation. Each component results in a different distribution of strains within the backfill, sliding, for instance, leading to the development of a slip plane and highly localised strains whereas rotation results in a much more distributed pattern of strain.
Horizontal shaking caused by an earthquake is an event of limited duration that causes fluctuations in the earth pressure on a wall and may result in some permanent ‘residual’ increase in stress. The dynamic pressure distribution and amplitude have been the subject of wide discussion, from the landmark paper by Seed and Whitman (1970), through more recent texts such as Ebeling and Momson (1992). Although few retaining walls above the water table have suffered total collapse during an earthquake, the phenomenon of serviceability failure caused by wall movement is common. In the majority of cases, such outward wall movement will have been caused by a permanent increase in the horizontal stress on the wall after the earthquake. Thus although calculations for the maximum dynamic lateral force are important in considering plastic collapse of soil-wall systems, an understanding of the mechanism of residual stress is 949
Okabe’s (1924) solution for dynamic earth pressure on a retaining wall was based on Coulomb wedge A simplified version, published by theory. Mononobe and Matsuo (1929) has subsequently become known as the Mononobe-Okabe analysis. Bolton and Steedman (1982) showed that dynamic earth pressure coefficients of similar magnitude to Mononobe-Okabe can be obtained for a wall without appeal to the kinematics of sliding wedges, and therefore that Mononobe-Okabe was relevant to the problem of cantilever walls. Prediction of displacements, however, requires that closer attention be paid to the pattern of strains within the backfill. A quasi-static elasto-plastic analysis is presented below which considers in detail the dynamic stress history within the backfill during shaking, Steedman (1984). The model enables calculations of wall top displacement to be made in the time domain.
2 LATERAL ACCELERATION FIELD
and soil, where the stiffness of the soil is governed by a shear modulus G varying with depth.
An initial stress state in a homogeneous soil fill at depth z has vertical and horizontal stresses yz and Kip, where y is the unit weight of the soil. Consider a uniform lateral acceleration field of magnitude khg superimposed on the existing vertical field of magnitude lg, Figure 1. D’Alembert body forces act in a direction opposed to the direction of the lateral acceleration field, of magnitude yzlcos p, where the angle p, is defined by tan p = kh to the vertical. The resulting shear and normal stresses on a horizontal plane will be :
3.1 Elastic soil free field defection, ys In the elastic free field, each elemental soil column may be idealised as a shear beam, with adjacent elements having negligible bending stiffness and therefore unable to transmit extra normal stresses but fully able to respond with complementary shear stresses. The local change in angle on the boundary is therefore given by the shear angle : dy/dz=z/G
=
yztan P I G
(2)
The shear modulus G may be approximated as varying with the square root of the effective confining pressure p’, Hardin and Dmevich (1972), such that G = hldz . Substituting and integrating over the wall height H gives an expression for the wall top deflection in terms of the shear modulus at depth H ( G z = ~ = Gb) and the lateral acceleration field.
3.2 Elastic wall free field defection, yw Applying a uniform lateral force field khg while the soil exerts unchanging normal stresses enables the wall top deflection to be readily calculated. For simplicity, let the cantilever wall have uniform bending stiffness along its length, given by E1 = E, D3/12. The wall top deflection is then : Figure 1 Lateral acceleration field y,
=
3ywH4tanP/2E,D2
(4)
where y, is the unit weight of the all, D the thickness and E, the Young’s Modulus.
3 DEFLECTIONS Consider the effect of such an acceleration field on a retaining wall and the adjacent soil. The resultant deflection must be the result of interaction between wall and soil as each component attempts to reach a ‘fiee field’ profile. Both soil and wall can deform ‘elastically’, and both can also deform plastically. For a conventional cantilever wall to deform plastically would imply the formation of plastic hinges and the onset of wall failure, but prior to this stage, permanent wall movements will still be caused by plastic yielding within the soil once the stress state reaches a yield condition. In this paper, the soil is idealised as obeying a Mohr-Coulomb yield criterion whose strength is characterised by an angle of internal shearing resistance.,,$, Consider first, however, elastic free field deflections of wall
3.3 Interaction correction Both the magnitude and profiles of deflection calculated for soil and wall free-field are different. If a tensile stress increment, equivalent to a destressing of the soil-wall interface is applied between the soil and the wall to marry the deflections at the top, an approximate solution can be found. Let the tensile stress increment (ie. destressing) be proportional to depth in the soil, oe = & yz. The corresponding wall movement is then : ywe= - 0.4 & yH5/ E, D3
950
(5)
In the soil, such a stress decrement allows a 45” triangle of fill to deform in simple shear. The shear stress increment mobilised on 45” lines would be :
which equals half the decrement of lateral stress, and hence :
To find a solution, assume temporarily that the shear modulus varies linearly with depth, agreeing at middepth with the Hardin and Dmevich solution above. So G = h2 z, where h2 = h, d2/H . The soil deflection at the surface is then given by :
3.4 Relative stiffness The relative magnitudes of the deflection corrections ywe and Yse are an indication of the relative stiffness of the wall and the soil during elastic vibrations. A simplified expression may be readily obtained in terms of Gb, where Gb = hi dH
For conventional flexible cantilevers, this relation indicates that the soil may be up to twenty times ‘stiffer’ than the wall. This reinforces the concept of a destressing between soil and wall during that half of the cycle when the D’Alembert forces act outwards from the wall. 3.5 Compatibility Compatibility between the soil and the cantilever is crudely satisfied if the backfill remains in contact with the wall at the top. Hence
The tensile stress increment oewas defined above as being proportional to &. From equation (1 l), the stress increment is also therefore proportional to the lateral acceleration field and to the interaction parameter Ci, describing the relative mass and stiffness of wall and soil. It is worth considering the significance of the interaction parameter in more detail. Clearly it may be positive or negative, depending on the flexibility of a particular wall. For infinitely stiff walls, the parameter tends to a negative limit of about -3.77 . Although there is no theoretical upper limit, for walls of high mass but low stiffness simple calculations for a variety of unpropped cantilever walls indicate that the parameter Ci is usually less than 0.5 . A sheet pile wall, for example, which has a finite mass but low stiffness may yield a value of about 0.3, whereas a reinforced concrete cantilever with a higher stiffness to mass ratio may yield a value of about Ci = 0 . In dynamic soil-structure interaction, then, the interaction parameter Ci provides a quantitative measure of the relative soillwall mass and stiffness. 3.6 Elastic deflections Assuming that Ci remains unchanged with time it is then simple to calculate the corrected wall top deflection.
This equation provides an estimate of deflection within an elastic region. For a rigid wall, for example, y = 0, as would be expected. Once yielding starts to occur on some plane within the backfill, however, permanent plastic deflections set in.
4 ELASTIC STRESS STATE substituting and solving for & gives :
where Ci is an interaction parameter, given by :
Figure 3 shows the initial and subsequent change in state for a soil element following the application of a lateral force field. In this example, the element remains within the elastic region in stress space. Using s, t and (Gh)e to denote the average, shear and elastic horizontal stresses respectively, then it may be shown that :
951
and ((Th)e = s - {t2- (yztan
5 PLASTIC STRESS STATE ’>O.’
(14)
The magnitude of the stress decrement or increment between soil and wall depends on the computed value of the interaction parameter Ci,
Yielding starts to occur on a plane within the backfill once the Mohr circle in Figure 2 touches the $,a, line. At this instant, t = s sin $,a, . During hrther increases in k,,, a new expression is required for s, as the expanding Mohr’s circle is now constrained to remain touching the Coulomb line, as shown in Figure 5 :
Figure 2 Elastic Mohr circle construction In s, t space, therefore, there are a range of elastic stress paths from any initial point depending on the value of Ci. Figures 3 and 4 show a variety of stress paths for positive and negative increments Of kh.
Figure 5 Plastic Mohr circle construction The positive and negative signs refer to the ‘active’ and ‘passive’ Mohr’s circles respectively. Assuming that on unloading a similar mechanism is followed to the initial loading, with unchanged elastic moduli, then horizontal stresses become jacked into the backfill following a period of yielding. The in-situ vertical stress remains unchanged after the event, and therefore the lateral earth pressure coefficient K is increased. The end point in t, s space must lie on a line at 45” down from the start point. Figure 6 shows the effect of elastic loading, plastic yielding and elastic unloading for a flexible wall (Ci = 0.2, K, = 0.4) caused by a full cycle of acceleration, Figure 7.
Figure 3 Stress paths in t,s space for +k,,
Figure 4 Stress paths in t,s space for - kh Figure 6 Cycle of lateral acceleration
952
strikes the yield surface depends on the initial condition and the interaction parameter Ci. Note that for this ‘flexible’ wall, on the negative cycle of kh, the stress path is heading towards a yield condition with a value of K still less than 1, indicating yielding in an ‘active’ condition, although on different planes in the soil to the condition reached during the positive half of the cycle.
Figure 7 Cycle of acceleration, amplitude kl, = 0.5
Using the standard expressions for static loading of a cantilever, an expression for the wall top deflection may easily be reached. To this must be added a deflection due to wall inertia, which also exerts a lateral load on the wall. The total deflection is therefore :
6 PLASTIC DEFORMATIONS Implicit thus far in the analysis as been the assumption that the dynamic pressure distribution can be approximated as triangular. Evidence this has been Presented, and From the Steedman (1985)* construction of Figure 5 , the horizontal stresses plane Of the acting On the may be deduced :
y = 0.4yKwH5 / E wD3 + 3ywH4tan p / 2EwD2 (17) IMPLICATIONS OF THE ANALYSIS Elastic behaviour has been shown to be dependent on an interaction parameter related to stiffness and inertia. The acceleration for a particular soilwall system depends not only on the interaction parameter but also on the initial stress state, as defined by the lateral earth pressure coefficient J&,. As shown in Figures 6 and 8, the rotation of the principal stress directions caused by the increasing shear stresses can lead to yield on ‘active’ planes in the soil, regardless of the direction of the acceleration field, at least for flexible walls in a near active condition. Careful consideration must be given to the use of limit state solutions such as Mononobe-Okabe under conditions where soilstructure interaction is likely. 2.5 2
0.5
Figure 8 Normal stress on the wall during full cycle of loading, showing one period of yielding
0
The effects of the full cycle of loading shown in Figures 6 and 7 on the normal stress acting on the wall can then be plotted, as shown in Figure 8. The shape and location of the yield surface, defined in this example by $ = 45”, is independent of the stiffness of the wall. However, where the stress path
I
I
I
I
I
0.2
0.4
0.6
0.8
1
kh
Figure 9 Yield surfaces as a function of
omax
A system of yield surfaces can be plotted as a function of the peak angle of internal shearing resistance $,a, as shown in Figure 9. General instability is predicted when tan $max = kh ie. for $,a, 953
= 45”, instability occurs for kh = k 1. In Figure 10, the normal stress acting on the wall varies as elastic stress paths lead from an initial condition defined by = 0.3 towards the yield surface. A soil-wall system is defined uniquely by its interaction parameter Ci. Figure 11 shows the effect on Ci, .of a range of values of soil base shear modulus and wall thickness. For this example, H = 15m, y, = 24 kN/m3, y = 20 kN/m3, E, = 28 x 106 kN/m2. (The wall thickness is used here as a measure of stiffness because it also defines the wall inertia, for a given wall unit weight.)
Secondly, high lateral residual stresses may become jacked in following cycles of acceleration on a backfill with initially low KO. Similarly, backfill compacted to high values of K, behind rigid walls, for instance, may lose much of that lateral stress during yielding. Thirdly, it should be emphasised that the principal stress directions are rotating continuously during shaking. In certain circumstances it is possible for principal stresses to rotate through more than 180” although in general this would not be the case.
8 COMPARISON WITH DATA The model was used to analyse the data from dynamic centrifuge model tests of a fixed base aluminium alloy cantilever wall of uniform thickness, retaining dry sand. At 80g in-situ stresses exist in the model identical to those behind a 14m high prototype wall. Successive episodes of base shaking provoked displacements of the wall outwards from the backfill. Data and predictions for the first three earthquakes are presented here. Base acceleration for the three earthquakes is shown in Figure 12.
Figure 10 Horizontal stress as a function of kh
Figure 11 Interaction parameter as function of soil and wall stiffness
Figure 12 Earthquake 1, average peak kh = 0.18 (top), E’quake 2, kh = 0.25 (middle), E’quake 3, kh = 0.27 (bottom), base input acceleration; fundamental frequency 80 Hz (model), 1 Hz (prototype)
1 Wall unit weight I y,
I 2220 kN/m’
y
1368 kN/m” 0.175 m 0.00935 m
Soil unit weight Wall height Wall thickness
There are a number of interesting implications of the analysis. Firstly, the terms ‘active’ and ‘passive’ are of no use in describing the yielding events. A positive acceleration pulse might provoke yielding on ‘active’ or ‘passive’ planes, depending on the relative soil-wall stiffness. In fact, the model predicts that yielding occurs on successive different planes as a further increment in lateral acceleration provokes a further rotation of principal stresses. Yielding may start on planes oriented at more than 45” to the horizontal and proceed through to planes oriented at less than 45” to the horizontal.
H
145000 kN/m
Table 1 Specifications for model test RSS.30 Table 1 gives the key parameters for the model. The wall top deflection, measured and predicted, is shown in Figures 13, 14, 15.
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calculated following the approach above. Permanent displacements and elastic vibrations are both predicted with good accuracy in the time domain, even after three earthquake events. The stress histories in Figures 16, 17 and 18 show the development of high lateral stresses jacked in behind the wall which prevents subsequent permanent deformation unless accelerations exceed past maxima.
Figure 13 Displacement time history, earthquake 1
Figure 14 Displacement time history, earthquake 2
Figure 16 Stress path behind wall, earthquake 1 Figure 15 Displacement time history, earthquake 3 Examining the measured wall displacement records qualitatively there are several points to note. Firstly, although the shaking consisted of ten pulses of roughly similar magnitude, the wall is observed to undergo most of its permanent displacement in the first few cycles, and in a manner not proportional to the amplitude of the cycle. Earthquake 3, although in amplitude almost exactly equal to earthquake 2, caused virtually no permanent outward deflection. There was, however, ‘elastic’ vibration about a mean value of a similar magnitude to the cyclic vibration in earthquake 2. Computing a value for the interaction constant Ci as above for this soil-wall system gives a value of Ci = 0.2, a flexible system. Fully active earth pressures were therefore assumed to have developed in the backfill before the start of shaking. Using the raw base acceleration time history as an input enables the wall top displacements and stress paths to be 955
Figure 17 Stress path behind wall, earthquake 2
6. Locked in lateral (residual) stresses following yielding of a flexible soil-wall system are seen to be explained by following the dynamic stress history of the event. ACKNOWLEDGEMENTS The work described in this paper arose from studies carried out at Cambridge University. The author acknowledges the valuable input of Dr M D Bolton in the completion of this analysis.
REFERENCES
Figure 18 Stress path behind wall, earthquake 3
9 CONCLUSIONS 1. Stress history is seen to be crucial to the prediction of the dynamic behaviour of cantilever walls. 2. Simple elasto-plastic mechanisms prove capable of quite accurate and detailed prediction of timevarying displacements. 3. The relative stiffness of soil and wall may be described using elastic theory and is then of great significance in the prediction of subsequent behaviour. The model addresses the full range of cantilever wall stiffnesses from flexible to rigid.
4. The terms ‘active’ and ‘passive’ are irrelevant to the dynamic cantilever wall problem due to the continuous rotation of principal stress directions during shaking. 5. Whereas the limiting ‘active, dynamic earth pressure on a wall may be approximated by the Mononobe-Okabe solution, -the concept of a limiting ‘passive’ pressure is less clear, as soilstructure interaction is shown to significantly affect the nature of the normal stress on the soilwall interface.
Bolton M D and Steedman R S (1982) Centrifugal testing of microconcrete retaining walls subjected to base shaking, Proc. Conf. Soil Dynamics and Earthquake Engng, Southampton, Balkema, pp 3 11329 Bolton M D and Steedman R S (1 985) Modelling the seismic resistance of retaining structures, Proc. XI Int. Conf. Soil Mech. Fndn. Engng, San Francisco, 4, Balkema, pp 1845-1848. Ebeling R M and Morrison E E (1992) The seismic design of waterfront structures, Tech. Report ITL92-1 1, USAE, Waterways Experiment Station, Vicksburg, MS. Hardin B 0 and Drnevich V P (1 972) Shear modulus and damping in soils: design equations and curves, Proc. ASCE, JSMF Divn., 98, SM7. Mononobe N and Matsuo H (1929) On the determination of earth pressure during earthquakes, Proc. World Engng. Congress, 9, pp 177-185. Okabe S (1924) General theory of earth pressure, J. Japan Civil Engng. Soc. 12 (1). Seed H B and Whitman R V (1970) Design of earth retaining structures for dynamic loads, ASCE Spec. Conf. Lateral stresses in the ground and design of earth retaining structures, Cornell, pp 103-147. Steedman R S (1984) Modelling the behaviour of retaining walls in earthquakes, Cambridge University, PhD Thesis.
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Earthquake Geotechnical Engineering, Sec0 e Pinto (ed.) 0 1999Balkema, Rotterdam, ISBN 90 5809 1 16 3
Performance of pile foundations in laterally spreading soils Kohji Tokimatsu Tokyo Institute of Technology,Japan
ABSTRACT: The field performance of various pile foundations that experienced lateral ground spreading during past earthquakes is summarized. It is shown that: (1) damage concentrated near the top and bottom of the liquefied layer of non-ductile piles, leading to the tilt of their superstructures in many cases; (2) the piles within a building near the waterfront show different failure modes in the direction perpendicular to the waterfront, while those away from the waterfront show similar deformation patterns; ( 3 ) pile foundations enclosed by cement mixing walls, diaphragm walls, and cement column walls did not suffer any vital damage; and (4) the earth pressures acting on rigid foundations from non-liquefied crusts overlying laterally spreading soils may be as large as the passive ones, whereas those acting on deformable foundations appear considerably smaller. A pseudo-static analysis is conducted for well-documented case histories of pile foundations to estimate the scaling factors for p-y springs of laterally spreading soils. The analytical results show that both the coefficient of the horizontal subgrade reaction of piles and the maximum reaction force of laterally-spreading soils are 0.05-0.2 times those of non-liquefied soils. INTRODUCTION Extensive soil liquefaction that occurred in the Hyogoken-Nambu earthquake of January 17 of 1995 damaged various structures in the reclaimed land areas along the coastline of Kobe. Particularly, many of the quay walls in these areas moved up to several meters towards the sea due to liquefaction of their foundation soils andor back-fills. This induced large horizontal ground movements as well as differential ground settlements near the waterfront. As a result, many supported on piles settled andor tilted without little damage to their superstructures (Photo 1). Similar damage patterns were also observed even in the liquefied level ground far away from the waterfront. The field investigation conducted after the quake suggests that the piles of those buildings might have been damaged not only by the inertia force from the superstructure but also by the kinematic force arising from permanent ground movement. This in turns suggests that the effects of liquefactioninduced ground movements on piles should be properly taken into account in foundation design. However, little is known concerning the actual failure and deformation patterns of those piles, and their relation to ground displacements.
The object of this study is to investigate the effects of liquefaction-induced lateral spreading on failure and deformation modes of piles, in an effort for improving aseismic design of pile foundations and their remedial measures against lateral ground spreading. For this purpose, the failure and deformation modes of the piles that experienced liquefaction-induced lateral spreading in the past earthquakes are summarized, with emphasis placed on those observed during the 1995 Kobe earthquake.
Photo 1 Typical damage pattern of building subjected to lateral ground spreading (Building A)
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Photo 2
Borehole camera survey after excavation
A pseudo-static analysis is then conducted for welldocumented case histories of pile foundations from the Kobe earthquake to estimate scaling factors for p-y springs of laterally spreading soils.
Photo 3 Inclinometer
FAILURE AND DEFORMATION MODES OF PILE FOUNDATIONS IN LATERALLY SPREADING GROUND
Detailed Field Investigations after 1995 HyogokenNambu Earthquake Many field investigations were performed on pile foundations that experienced liquefaction-induced ground movements during the Kobe earthquake [e.g., Kansai Branch of Architectural Institute Japan (AIJ), 1996; AIJ et al., 1998; BTL Committee, 19981. In addition to the excavation and examination of pile heads, several methods were specially invented and used in those investigations, which enable one to estimate the failure and deformation modes of piles. Borehole camera observation (Photo 2) identified damage portion and severity for precast hollow piles (Oh-oka et al., 1996) and for cast-in-place concrete piles cored vertically. Inclinometer surveys (Photo 3 ) provided data to estimate deformed shapes with depth of precast hollow piles (Shamoto et al., 1996). Aerial photographic surveys delineated the distributions of permanent ground displacement around the investigated areas. The results of the above investigations indicate that the spatial variations and damage patterns of piles within a building are somewhat different depending on its location.
Damage Patterns near the Waterfront The main findings from the field investigations near
the waterfront are summarized as (Tokimatsu and Asaka, 1998; Tokimatsu, 1998): 1) Damage concentrated near the pile head, or the top andor the bottom of the liquefied layer (Figs. 1(a>-1(4>. 2) Damage was not limited to PC and PHC piles but extended to some S piles (JASPP, 1996) and cast-in-place concrete piles (Tokimatsu et al, 1996). 3) The damage to PC and PHC piles often resulted in a large tilt of the superstructure, whereas the damage to S and CC piles rarely led to similar consequences. 4) A cast-in-place concrete pile foundation that carried only a small load was also damaged and displaced horizontally by as much as 1 m (Kuwabara and Yoneda, 1998). 5) Damage to pile caps and foundation beams often preceded or accompanied the damage to S and CC piles. 6) The piles within a building near the waterfront showed different failure and deformation modes
Fig. 1 'l'ypical damage pattern of building subjected to lateral spreading 958
the top and the bottom of the liquefied layer. Damage to piles near the pile head or the bottom of a thin non-liquefied crust often resulted in tilts of buildings with high aspect ratios. Damage to piles did not necessarily lead to tilts of buildings particularly with thick non-liquefied crusts (Fig. l(c); BTL Committee, 1998). Unlike the foundations near the waterfront, the failure and deformation modes of piles within a building were very similar to each other, as shown in Figs. 2(c) and 2(e). Damage concentrated on PC and PHC piles, but no extensive damage to S and CC piles was reported. PHC piles without any vertical load also suffered extensive damage near the bottom of the liquefied layer (Fig. l(e); Horikoshi and Ohtsu, 1996). An 11-story building that was supported on 40cm diam reinforced concrete piles driven at spaces of 1.1 m survived without any damage and settlement, despite 2 m of horizontal ground displacements nearby (Yoshimi, 1990). In this case, the ground surface on the upstream side of the building heaved by about 1 m (Hamada and O’Rourke, 1992).
Fig. 2 Typical failure and deformation modes of pile foundations due to lateral spreading in the direction perpendicular to the shoreline as shown in Figs. 2(a) and 2(d) (Tokimatsu et al., 1998). In such a case, when facing the span side of the building with the sea on the left, the seaside pile cap rotated clockwise around its longitudinal axis, whereas the land-side pile cap rotated counterclockwise (Oh-oka et al., 1997). 7) While a passive earth thrust was reportedly created on the upstream side of structures with rigid foundations (Berrill et al., 1997), an active state was created with large ground settlement on the same side of structures with deformable foundations (Tokimatsu et al., 1996). 8) Cast-in-place concrete piles surrounded by deep mixing walls as well as steel pipe piles driven in the ground treated by sand compaction piles did not suffer any serious damage (Fig. l(f); BTI, Committee, 1998). Moderate to severe damage to their superstructures was, however, observed in these cases. 9) Cast-in-place concrete piles surrounded by cement column walls or continuous diaphragm walls did not suffer any serious damage (BTL Committee, 1998). The permanent horizontal displacements of bridge piers founded on diaphragm walls were negligibly small, while those of bridge piers founded on piles or caissons were as large as a half of the permanent ground displacements nearby (Yokoyama et al., 1997).
Damage Patterns away ji-om the Waterji-ont Even in the liquefied level ground far away from the waterfront, permanent horizontal ground displacements did occur and damage pile foundations during several past earthquakes. The damage patterns of those cases are summarized below (Tokimatsu and Asaka, 1998; Tokimatsu, 1998): 1) Damage also concentrated near the pile head, or
Lessons Learnt ji-om Field Observations The above findings confirm that, in addition to horizontal forces and overturning moments imposed on pile heads from superstructures, kinematic forces induced by dynamic and permanent ground displacements of liquefied and laterally spreading soils had significant impact on pile damage. In particular, the damage to piles without vertical loads confirms significant effects of ground movements. The difference in failure and deformation modes of piles within a building near the waterfront as shown in Figs. 2(a) and 2(d) probably reflects rapid changes in horizontal ground displacement. In addition, Fig. 2 suggests that the effect of lateral ground movement on foundation damage is more serious in the span direction than in the longitudinal direction. This indicates that to place the longitudinal direction of the building perpendicular to the shoreline is effective for mitigating damage due to lateral ground movement near the waterfront. The difference in damage to piles of different type indicates that to use ductile piles or rigid foundations is also effective for mitigating damage resulting from lateral ground movement. Conversely, however, the inertial forces acting on the superstructures and foundations during shaking would be higher for rigid or treated foundations than for deformable or untreated foundations. Besides, the earth pressure acting on the upstream side the building from laterally spreading soils would
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Fig. 3 Schematic figure showing earth pressures acting on foundations from laterally spreading soils increase with increasing the rigidity of the foundation as shown in Fig. 3 . The effects of these factors should be properly taken into account. PSUEDO-STAIC FOUNDATIONS
ANALYSIS
FOR
PILE
One of the key issues in the design of foundations in laterally spreading soils is to quantifl the forces arising from ground displacement, defined as p-y relations. Thus, such p-y relations are estimated based on well-documented case histories in the Kobe earthquake.
SimpliJied Design Method considering Inertial and Kinematic Forces Acting on Piles Fig. 4 schematically illustrates the soil-pile-structure interaction in laterally spreading soils. Prior to the development of pore water pressure, only the inertia force from the superstructure may dominate (Phase I). With the development of pore pressure during shaking, the cyclic shear strain in the deposit increases, producing large cyclic ground displacements. In this phase, not only the inertial force but also the kinematic forces resulting from the cyclic ground displacements come to play important roles (Phase 11). Towards the end of shaking, residual components of shear strain may accumulate, resulting in permanent horizontal ground displacements. In this phase, the intensity of ground shaking may be negligibly small. As a result, the kinematic forces due to permanent ground displacements may have a dominant effect on pile
Fig. 5 Analytical model of soil-pile-structure system performance (Phase 111), particularly near which quay walls failed or moved seaward. The above discussions and previous studies indicate that piles in laterally spreading soils would experience most severe loading condition in either Phase I, I1 or 111; however, the final failure and deformation modes would be controlled by the loading condition in Phase 111. Thus, only the failure and deformation modes in Phase I11 will be discussed hereafter. Fig. 5 schematically shows an analytical model for the soil-pile-structure interaction in laterally spreading ground in Phase I11 in which a group of piles connected with a foundation beam is subjected to lateral ground spreading. A simplified pseudostatic design method using p-y curves for pile foundations is extended and used. The basic equation may be expressed as: EI(d4y/dz4)=k,B{ f,,(z)-y3 in which E and I are Young’s modulus and moment of inertia of pile, y is horizontal displacement of pile, z is depth, k,, is coefficient of horizontal subgrade reaction, B is pile diameter, and fiS(z)is a permanent ground displacement profile with depth near the pile. To calculate stress and deformation of piles, the characteristics of non-linear p-y springs and the spatial variation of lateral ground displacement must be defined, together with the moment-curvature (M@)relation of the pile that defines the non-linear flexural rigidity of the pile, i.e., EI= MY@.
Fig. 4 Schematic figures showing soil-pile-structure interaction in laterally spreading soil
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Permanent Ground Displacement near Waterpont When lateral spreading occurs near the waterfront, the permanent horizontal ground displacement generally decreases towards inland with a maximum value at the waterfront. The affected distance of such lateral spreading from the waterfront, L, for a level ground with a liquefied layer of a constant thickness, H, may be given by (Tokimatsu and Asaka, 1998; Tokimatsu et al., 1998): Fig 6 Analytical model for p-y spring
-
L/H =(25 1OO)Do/H
(8)
in which Do is the permanent horizontal ground displacement at the waterfront and is defined as: Definition ofp-y Springs The p-y relations of soil under non-liquefied and liquefied states may be modeled as shown in Fig. 6. The coefficient of subgrade reaction of pile and the maximum reaction force of non-liquefied soils may be defined as (AIJ, 1988; JRA, 1997):
in which N is SPT N-value, B is pile diameter, K,>is the coefficient of Rankine’s passive earth pressure, and o is the initial effective vertical stress. The degradation of k,, with increasing displacement may be expressed as:
in which D, is the displacement of the quay wall and D,, is the maximum possible permanent ground surface displacement of the liquefied soil, estimated by the procedure such as proposed by Tokimatsu and Asaka (1998). The horizontal ground displacement at distance x from the waterfront, D(x), is expressed in a normalized form as shown in Fig. 7 and defined as (Shamoto et al., 1998):
va
in which y, has to be equal to Pyo/kh0. The coefficient of subgrade reaction of pile and the maximum reaction pressure for laterally spreading soils are defined as:
in which D,, is the permanent horizontal displacement of the level ground far away from the waterfront and may be assumed to be zero or approximately equal to the maximum possible cyclic ground surface displacement defined by Tokimatsu and Asaka (1 998). The permanent ground displacement profile with depth at distance x of a laterally spreading deposit, fis(z,x),may be approximated as :
in which o is the total vertical stress, and cy , a ’, and /?are scaling factors for laterally spreading soils. The maximum earth pressure acting on the embedded part of the building may be given by:
in which K may be assumed, based on the field observations and Fig. 3, to be the coefficient of passive earth pressure if the ground pushes the foundation or to be the coefficient of active earth pressure if the ground moves away from the foundation.
Fig. 7 Relation of horizontal ground displacement with distance from waterfront
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Forz>z, fiS(z,x)= D(X)COS( 7~ (z- Z, )/2H) = D(x)( 1-(z- z, )/H)
(12) (13)
in which z is depth below the ground surface, and z, is depth of the groundwater table or the top of the liquefied layer. Thus, once knowing Do, the horizontal and vertical distributions of ground displacement may be approximately estimated. BACK-CACLULATED SCALING FACTORS FOR P-Y SPRINGS IN LATERALLY SPREADING SOILS The remaining unknown values in the above analysis are the scaling factors for p-y springs. Thus, those values are estimated for the case histories of Buildings A and B in the 1995 Kobe earthquake (Tokimatsu et al., 1998). Building A was situated 6 meters from the quay wall on a reclaimed land. The building of three stories was supported on hollow prestressed concrete piles 400 mm in diameter and about 20 meters long. A loose fill 8-m thick comprising of gravelly sands liquefied and spread seawards in the 1995 Kobe earthquake. Consequently, the building inclined by 3 degrees towards the sea without any structural damage. Fig. 8 shows the deformation pattern of the pile foundation in the span direction, which looks like that shown in Fig. 2(a).
Building B was located at about 100 m away from both the northern and western waterfronts of a reclaimed island. This building of two stories was supported on steel pipe piles 406 mm in diameter and about 27 meters long. A fill about 15-m thick comprising of gravelly sands liquefied and spread seawards in the 1995 Kobe earthquake. Fig. 9 shows the deformation mode of the pile foundation in the span direction (Sakate et al., 1997), which looks like that shown in Fig. 2(c). Figs. 10 and 11 show the effects of a and p on the deformation modes of both seaside and land-side piles in Buildings A and B (Tokimatsu and Niwano, 1998). It seems that a = 0.05-0.2 and p = 0.05-0.2 are appropriate for accounting for the variation in deformation mode of piles within a building. The a-values of 0.05-0.2 approximately correspond to @'-values of 0.25-1.O, which are consistent with the results of other studies (e.g., JRA, 1997). The appropriateness of the above result is examined for a building that was under construction and experienced lateral spreading in the 1995
Fig. 10 Effects of a and p on deformation modes of piles of Building A
Fig. 11 Effects of a a n d p on deformation modes ofpiles OfBuilding B
Fig. 9 Deformation modes of piles of Building B
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CONCLUSIONS
Fig. 12 Observed and computed vector angles of pile head inclination of pile foundation subjected to lateral spreading (computed values are indicated in circles) Hyogoken-Nambu earthquake (Kuwabara and Yoneda, 1998). Since this building carried only a small vertical load, the major force acting on the foundation was the kinematic force arising from ground movements. The building, 7 by 2 spans and 4 1.8 m long in the east-west direction and 16.1 m wide in the northsouth direction was located on a reclaimed land, with coastlines about 25 m east and 90 m south of the building. It was supported on cast-in-place concrete piles 47-49m long, having diameters of 1.2-1.7 m. The ground to a depth of 15-16 m was reclaimed with weathered granite soils that were supposed to have liquefied. As a result, the foundation was displaced southeastwards by about 1 m and the pile heads within the building were inclined in different directions as shown in Fig. 12. It seems that the deformation modes of the foundation in the span and longitudinal directions look like those shown in Figs. 2(c) and 2(d), respectively . The stress and deformation in the piles are calculated for both the N-S and E-W directions of the building, which yields the vector angles of the pile head inclinations. It is assumed that the horizontal ground surface displacements on both sides of the building are 125 cm and 40 cm in the EW direction and 75 cm and 60 cm in the N-S direction, with a = 0.1 and p = 0.1. The computed results are also shown in the circles in Fig. 13. The computed result shows that, while the seaside and land-side piles inclined towards the opposite directions in the E-W direction, both the seaside and land-side piles inclined similarly toward the sea in the N-S direction. They are reasonably consistent with the field observations, indicating the assumed values of a and p are appropriate.
The field performance of the pile foundations that experienced liquefaction-induced lateral spreading during past earthquakes have been compiled and summarized. A simple p-y analysis was conducted to estimate scaling factors for p-y curves of laterally spreading soils. The field observation together with the analytical results leads to the following conclusions: 1) Damage tends to occur in non-ductile piles and at the interface between liquefied and nonliquefied layers. 2) The piles of a building near the waterfront show different failure modes in the direction perpendicular to the waterfront, while those away from the waterfront show similar deformation patterns. 3) Pile foundations enclosed by cement mixing walls, diaphragm walls, and cement column walls successfully resisted lateral ground spreading. 4) The earth pressures acting on rigid foundations from non-liquefied crust overlying liquefied soils may be as large as the passive ones, whereas those acting on deformable foundations appears considerably smaller. 5 ) The analytical results show that both the coefficient of the horizontal subgrade reaction of piles and the maximum reaction force of laterally-spreading soils are 0.05-0.2 times those of non-liquefied soils. ACKNOWLEDGMENTS The study described herein was made possible through the post-earthquake field investigation and their compilation conducted by the Committee on Building Foundation Technology against Liquefaction and Lateral Spreading (BTL), Japan Association for Building Research Promotion. Professor Fumio Kuwabara, Nippon Institute of Technology, kindly provided the information concerning the case history of damaged cast-inplace concrete piles used in this paper. REFERENCES Architectural Institute of Japan (1988): Recommendations for design of building foundations, 430pp. (in Japanese). Architectural Institute of Japan et al. (1998): Report on the Hanshin-Awaji earthquake disaster, Building Series Volume 4, Wooden Structure and Building Foundations (in Japanese).
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Berrill, J.B. et al. (1997): Lateral-spreading loads on a piled bridge foundation, Seismic Behavior of Ground and Geotechnical Structures, pp. 173183. BTL Committee (1998): Research report on liquefaction and lateral spreading in the Hyogoken-Nambu earthquake (in Japanese). Hamada, M., and O’Rourke, T.D.: Case studies of liquefaction and lifeline performance during past earthquakes, Technical Report NCEER-92-0001, 1992. Horikoshi, K. and Ohtsu, H. (1996): Investigation of PC piles damaged by the Hyogoken-Nanbu earthquake, Proc., 3 1st Japan National Conf. on Geotechnical Engineering, Vol. 1, pp. 1227-1228 (in Japanese). Japanese Association for Steel Pile Piles (1 996): Investigation report on steel pipe pile foundations in the Hyogoken-Nambu earthquake- Part 11, 156pp. Japan Road Association (1997): Specifications for road bridges, Vol. IV (in Japanese). Kansai Branch of Architectural Institute of Japan (1996): Report on case histories of damage to building foundations in Hyogoken-Nambu earthquake, Report presented by Committee on Damage to Building Foundations, 400pp. (in Japanese). Kuwabara, F. and Yoneda, K. (1998): An investigation on the pile foundations damaged by liquefaction at the Hyogoken Nanbu earthquake, Journal of Struct. Constr. Engrg., AIJ, No. 507 (in Japanese). Oh-okay H., Iiba, M., Abe, A., and Tokimatsu, K. ( 1996): Investigation of earthquake-induced damage to pile foundation using televiewer observation and integrity sonic tests, Tsuchi-tokiso, JSG, Vol. 44, No. 3, pp. 28-30 (in Japanese). Oh-oka, H., Katoh, F., and Hirose, T. (1997): An investigation about damage to steel pipe pile foundations due to lateral spreading, Proc., 32nd Japan National Conf. on Geotechnical Engineering, Vol. 1, pp. 929-930 (in Japanese). Satake, K., Oh-oka, H., and Tokimatsu, K. (1997): Investigation of earthquake-induced damage to steel pipe pile foundation, Proc., 32nd Japan National Conf. on Geotechnical Engineering, Vol. 1,pp. 927-928 (in Japanese). Shamoto, Y., Sato, M., Futaki, M., and Shimazu, S. (1 996): A site investigation of post-liquefaction lateral displacement of pile foundation in reclaimed land, Tsuchi-to-Kiso, JSG, Vol. 44, No. 3, pp. 25-27 (in Japanese). Shamoto, Zhang, J.-M. and Tokimatsu: Methods for predicting residual post-liquefaction ground settlement and lateral spreading, Soils and Foundations, Vol. 38, Special Issue, pp. 69-83, 1998.
Tokimatsu, K., Mizuno, H., and Kakurai, M. (1996): Building damage associated with geotechnical problems, Soils and Foundations, Special Issue, pp. 219-234. Tokimatsu, K. (1998): Damage to foundations due to lateral ground spreading, Proc., 10th Earthquake Engineering Symposium, Panel Discussion, pp. 135-140 (in Japanese). Tokimatsu, K., and Asaka, Y.: Effects of Liquefaction-induced ground displacements on Pile Performance in the 1995 Hyogoken-Nambu Earthquake, Soils and Foundations, Special Issue, pp. 163-177, 1998. Tokimatus, K. and Niwano, A. (1998): Evaluation of earth pressures on pile foundations subjected to lateral spreading, Proc., 3rd Symposium on Mitigation of Urban Disasters by Near-Field Earthquakes, pp. 213-214 (in Japanese). Tokimatsu, K., Oh-okayH., Satake, K., Shamoto, Y., and Asaka, Y.: Effects of lateral ground movements on failure patterns of piles in the 1995 Hyogoken-Nambu earthquake ; ASCE, Geotechnical Earthquake Engrag. and Soil Dynamics 3rd Conf., pp. 1175-1186, 1998. Yokoyama, Tamura, and Matsuo (19971: Design methods of bridge foundations against soil liquefaction and liquefaction-induced ground flow, Second Italy-Japan Workshop on Seismic Design and Retrofit of Bridge, pp. 1-23, Rome, Italy. Yoshimi, Y. (1990): Liquefaction of sandy ground, Second Edition, Gihodo, 182pp (in Japanese).
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Earthquake Geotechnical Engineering, S&coe Pinto (ed.)0 1999Balkema, Rotterdam, ISBN 90 5809 1 16 3
Seismic soil-pile-structureinteraction in soft clay Chstina J.Curras, Ross W. Boulanger, Bruce L. Kutter & Daniel W.Wilson Department of Civil and Environmental Engineering, University of California, Davis, Calg, USA
ABSTRACT: A dynamic beam on a nonlinear Winkler foundation (BNWF) model for analyzing seismic soilpile-structure interaction was evaluated against the results of a series of dynamic centrifuge model tests. Three different structures supported by piles, including a 3x3 group, in soft clay overlying dense sand were subjected to nine different earthquake events. Representative examples of recorded and calculated behavior are presented.
1 INTRODUCTION
2 CENTRIFUGE EXPERIMENTS
Methods of analyzing seismic soil-pile-structure interaction have included two- and threedimensional modeling of the pile and soil continuum using finite element or finite difference methods, dynamic beam on a nonlinear Winkler foundation (BNWF) methods (Fig. 1), and simplified two-step methods that uncouple the superstructure and foundation portions of the analysis. Dynamic BNWF methods are considerably less complex than modeling the pile and soil as a continuum, and yet offer several potential advantages over the simplified sub-structuring methods when dealing with soft soil conditions. The reliability of any of these analysis methods under soft-soil conditions has not been fully evaluated because the available case histories and physical model studies are limited in number and detail. This paper describes an evaluation of dynamic BNWF analyses against the results of a series of dynamic centrifuge model tests of pile-supported structures in a profile of very soft clay overlying dense sand. Calculated and recorded responses of three structures, two supported by single piles and one supported by a 3x3 pile group, are compared for nine earthquake events with peak base accelerations ranging from 0.02 to 0.7g. The results provide an evaluation of the analysis procedure’s ability to reliably capture soil-pile-structure interaction effects on different structures over a wide range of shaking intensities and earthquake motions.
Tests were performed using the large servohydraulic shaking table on the 9-m radius centrifuge at UC Davis (Kutter et al. 1994). Models were tested in a Flexible Shear Beam (FSB) container at a centrifugal acceleration of 30 g. All results presented herein are in prototype units unless otherwise stated. The soil profile, structural model, and instrumentation are illustrated in Fig. 2. The lower soil layer was fine, uniformly graded Nevada sand (C,=1.5, Dso=0.15 mm) at a relative density (DJ of about 75-80%. The upper soil layer was 6 m of reconstituted Bay Mud (LL-88, PIz48) placed as a
Figure 1. Schematic of Dynamic BNWF Model.
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slurry (water content = 140%) in four equal layers, with each layer consolidated under an applied vertical stress prior to placement of overlying layers. The two single-pile-supported systems (SPl , SP2) consisted of a superstructure mass attached to an extension of the pile. SPl had a superstructure mass of 49.1 Mg centered 3.81 m above the ground surface, and SP2 had a superstructure mass of 45.1 Mg centered 7.32 m above the ground surface. The pile group (PG33) consisted of nine piles in a 3x3 grouping spaced at 4 diameters on center with a 2.3-m thick cap. PG33 had a superstructure mass of 468 Mg centered 10.7 m above the pile cap. All piles were approximately equivalent to a 0.67-m diameter steel pipe pile with a 19-mm wall thickness. Piles were installed at 1 g (prior to spinning the centrifuge), and remained elastic during all earthquake events. Two centrifuge model configurations were each shaken with several simulated earthquake events. Figure 2. Schematic of Layout and Instrumentation Each event was a scaled version of a record prepared by filtering and integrating strong motion records from Port Island in the Kobe Earthquake or Santa 4 DYNAMIC ANALYSES Cruz in the Loma Prieta Earthquake. Each earthquake event was separated by sufficient time 4.I Nonlinear p - y Element for dissipation of any shaking-induced excess pore pressures. Test details and all time histories are A nonlinear p-y element was developed and available in data reports (e.g., Wilson et al. 1997). implemented into an FE program for this study. The The undrained shear strength (c,) of the Bay nonlinear p-y behavior is conceptualized as Mud layer versus depth was measured using a small consisting of elastic (ye), plastic (yp), and gap (yg) torvane immediately after the centrifuge stopped components in series. Details of the p-y elements are spinning. These strengths were found to be in Boulanger et al. (1999). consistent with a normalized shear strength of C,/CT~~’ The backbone of the p-y curves for the Bay Mud = 0.35 OCRo.* with the overconsolidation ratio was based on Matlock’s (1970) recommendations (OCR) being slightly greater than one due to for soft clay. Gapping behavior was modeled similar earthquake induced consolidation. The static c, was to the procedure of Matlock et al. (1978). The ratio increased by 20% to obtain a c, for seismic loading of maximum drag force (once a gap has formed) to based on our judgment of the various factors the ultimate resistance of the p-y element was taken involved (e.g., loading rate, cyclic degradation). as 0.3 for the analyses presented herein. The backbone of the p-y curves for the lower sand layer was based on American Petroleum 3 FREE-FIELD SITE RESPONSE ANALYSES Institute (API 1993) recommendations for sand, with modifications for the increase in stiffness with depth Free field site response analyses were performed and the effect of the overlying soft clay. using the I-D equivalent linear site response Lateral soil resistance against the pile cap was program SHAKE91 (Schnabel et al. 1972, Idriss and also modeled using p-y elements. Ultimate capacity Sun 1991). Maximum shear modulus (Gmm) and the was estimated using the c, data described earlier and modulus reduction (G/Gma) and damping (p) versus allowing for passive pressure on the front of the pile shear strain (y) relationships were selected using cap, active pressure on the back, and skin friction on typical design assumptions. For the clay, the G/G,, both sides. Lateral stiffness and gapping behavior curve at large strains was modified to limit the peak were selected based on our judgment of several shear stress to the seismic c, value (i.e., possible approaches. ~peak=ypeakG, giving GIG,, = Cu/Gmaype&). The Radiation damping was modeled by a dashpot in mass of the container rings was distributed over the parallel with the elastic (p-ye) component, with the soil profile by increasing the soil unit weights in the dashpot coefficient approximating elastic theory analyses. 966
Figure 3. Recorded Accelerations in Soil for Santa Cruz Base Motion of amax=O.12g.
Figure 4. Calculated Accelerations in Soil for Santa Cruz Base Motion of amax=O. 12g.
below ground with each node connected to a p-y element. The pile group was modeled as a single row of three piles, perpendicular to the direction of shaking, with the appropriate tributary masses, column stiffness, and soil resistances. Each pile node below ground was connected to a horizontal py element as well as a vertical t-z element. The p-y element strengths were modified from those used for the single piles by a p-multiplier to account for group efficiency effects. The nodes at the pile tips also had q-z elements. The pile cap was modeled as a rigid frame connected to p-y elements, and the piles were fixed into its base. Horizontal displacement time histories from the SHAKE91 analyses were input to the free field ends of the p-y elements. The solution technique involved Newton-Raphson iteration with a line search, and 6 p=0.3025. the Newmark method with ~ 0 . and
solutions (Gazetas and Dobry 1984). This dashpot arrangement is termed “series hysteretic/viscous damping” since hysteretic damping from the plastic p-yp component is in series with the viscous damping on the elastic p-ye component. This arrangement is preferred over having the dashpot in parallel with the entire nonlinear p-y element (“parallel hysteretic/viscous damping”) because a parallel arrangement can result in excessive dashpot forces when the p-y element is loaded into the highly nonlinear range (Wang et al. 1998). 4.2 Nonlinear t-z and q-z Elements Nonlinear t-z elements for skin friction on the pile were conceptualized as consisting of elastic and plastic components in series. Nonlinear q-z elements for point resistance were conceptualized as consisting of elastic, plastic, and gap components in series. The q-z element allowed for different capacities in compression and uplift. The capacities and stiffnesses of the t-z and q-z elements were estimated using typical design procedures. Radiation damping was modeled by a dashpot in parallel with the elastic component of these elements, as recommended by Randolph (1991).
5 TYPICAL SET OF RECORDED AND CALCULATED RESPONSES A typical set of centrifuge and analysis results are presented in Figures 3 to 7 for SPl and PG33 for a Santa Cruz motion with a maximum base acceleration of 0.12 g. Recorded and calculated accelerations for four depths in the soil profile are shown in Figs. 3 and 4, and the corresponding acceleration response spectra (ARS) are shown in Fig. 5. These results show amplification of the base motion up through the soil profile. For this event,
4.3 Finite Element Analyses The dynamic BNWF analyses were performed using the FE platform GeoFEAP (Bray et al. 1995) with the added elements described above. The models of the single pile structures had 15 beam elements 967
Figure 5. ARS (5% damping) in Soil for Santa Cruz Base Motion of amax=O.12g. calculated motions in the clay layer overpredict the recorded motions, particularly in the shorter period (higher frequency) range. Recorded and calculated accelerations and ARS are shown for the SPI superstructure in Fig. 6, and for PG33's superstructure and pile cap in Fig. 7. The calculated superstructure responses for both SP 1 and PG33 are in good agreement with recorded responses, while the pile cap motion for PG33 is overpredicted. This overprediction of the pile cap response can be attributed to the site response calculations having overpredicted the site response at short periods (coinciding with a response mode for the pile cap) while being in better agreement with recorded site response at longer periods (coinciding with the range of superstructure "fundamental" periods). Reasonably good agreement was also obtained between calculated and recorded superstructure displacements, pile cap displacements (rocking and lateral), and pile loads (bending moments and axial forces). These centrifuge and analysis results illustrate the type of experimental data obtained, the general features of the soil profile and structural responses, and the analysis method's ability to reasonably reproduce those responses for this one shaking event.
Figure 6. Accelerations and ARS (5% damping) for SP1 Superstructure During Santa Cruz Base Motion of amax=O. 12g.
these comparisons provided an evaluation of the method's ability to reliably capture soil-pilestructure interaction effects over a range of earthquake motions of different intensities and frequency characteristics. For example, the nonlinear response of SP1 is illustrated in Fig. 8, showing the ARS for the superstructure during four of the Kobe shaking events. The equivalent "fundamental" period of this structural model increased from about 1.O second under the smallest shaking level to about 2.0 second under the strongest shaking level. In addition, calculated and recorded peak bending moment distributions showed the depth to maximum moment increasing with increasing loading level as expected. Parameter studies showed that the sensitivity of the calculated structural response to individual parameters varied for each shaking event, illustrating the complexity of the interaction between the free-field motions and the soil-pile-structure system. These results served as a reminder that conservative parameter selection for a static analysis is not always conservative for dynamic analyses. The parameter studies also showed that the primary source of differences between recorded and calculated responses had originated from the site response calculations, which is not surprising given
6 FURTHER COMPARISONS OF RECORDED AND CALCULATED RESPONSES Recorded and calculated responses for the soil profile and structural models SPI, SP2, and PG33 were compared for the nine earthquake events. All analyses used one set of input parameters selected using current engineering procedures. The results of
968
Figure 7. Accelerations and ARS (5% damping) for PG33 Superstructure and Pile Cap During Santa Cruz Base Motion of amax=O. 12g.
results of this study show that the dynamic BNWF analysis method can be an effective design tool for seismic soil-pile-structure interaction problems.
the known limitations in modeling the soft clay and strong shaking conditions of these tests with an equivalent linear soil model. Nonetheless, the overall agreement between recorded and calculated responses was reasonably good for the range of conditions covered by these tests.
ACKNOWLEDGMENTS
A dynamic BNWF analysis method was evaluated
The California Department of Transportation (CALTRANS) supported this research under contract 65V495. C. Curras was supported by a National Science Foundation Graduate Research
against a set of centrifuge model tests involving pilesupported structures in a profile of soft clay (6-m thick) overlying dense sand. A total of nine earthquake shaking events on three model configurations, including five scaled Kobe motions (amax= 0.02 to 0.7 g at the base) and four scaled Santa Cruz motions (amax= 0.04 to 0.6 g at the base) were analyzed. A baseline set of analysis parameters was selected using current engineering procedures. Representative examples of recorded and calculated responses were presented. Reasonable agreement was obtained between the dynamic BNWF analyses and the centrifuge model data over the full range of shaking intensities and earthquake motions covered in this study. The
Figure 8. Superstructure ARS for SP1 During Kobe Base Motions of amax=0.02-0.6g.
7 SUMMARY AND CONCLUSIONS
969
Fellowship. This support does not necessarily represent endorsement by the State or Federal government. Abbas Abghari of CALTRANS provided valuable suggestions and comments throughout this study. REFERENCES American Petroleum Institute 1993. Recommended practice for planning, designing and constructing fixed offshore platforms. API Recommended Practice 2A (RP 2A). Boulanger, R. W., C. J. Curras, B. L. Kutter, D. W. Wilson, & A. Abghari 1999. Seismic soil-pilestructure interaction experiments and analyses. Accepted, ASCE J. of Geotechnical and Geoenvironmental Engineering. Bray, J. D., R. D. Espinoza, K. Soga, & R. Taylor 1995. GeoFEAP - Geotechnical finite element analysis program.” Dept. Civil & Environmental Engineering, Univ. of California, Berkeley, CA. Gazetas, G. & R. Dobry 1984. Simple radiation damping model for piles and footings. Journal of Engineering Mechanics, llO(6): 937-956. Idriss, I. M., & J. Sun 1991. User’s manual for SHAKE91. Center for Geotechnical Modeling, University of California, Davis, CA. Kutter, B. L., I. M. Idriss, T. Kohnke, J. Lakeland, X. S. Li, W. Sluis, X. Zeng, R. Tauscher, Y. Goto, & I. Kubodera 1994. Design of a large earthquake simulator at UC Davis.” Centrifuge 94, Balkema, 169-175. Matlock, H., S. H. C. Foo, & L. M. Bryant 1978. Simulation of lateral pile behavior under earthquake motion. Proc., ASCE Specialty Conference on Earthquake Engineering and Soil Dynamics, Pasadena, CA, 600-619. Matlock, H. 1970. Correlations for design of laterally loaded piles in soft clay. Proceedings, 2nd Annual Ofisshore Technology Conference, Houston, Texas, OTC 1204. Randolph, M. K. 1991. Analysis of the dynamics of pile driving. Chapter in Developments in Soil Mechanics and Foundation Engineering: Vol. 4 - Advanced Geotechnical Analyses, Elsevier, 223-27 1. Schnabel, P. B., J. Lysmer, & H. B. Seed 1972. SHAKE: a computer program for earthquake response analysis of horizontally layered sites. UCBEERC-72/12, Univ. of Calif., Berkeley. Wang, S., B. L. Kutter, J. M. Chacko, D. W. Wilson, R. W. Boulanger, & A. Abghari 1998. Nonlinear seismic soil-pile-structure interaction.
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Earthquake Spectra, EERI, Oakland, CA, 14(2): 377-396. Wilson, D. W., R. W. Boulanger, & B. L. Kutter 1997. Soil-pile-superstructure interaction at soft or liquefiable soil sites - Centrifuge data report for Csp4. Report UCD/CGMDR-97/05, Ctr. for Geotech. Modeling, Univ. of California, Davis.
Underground and buried systems: - Theme lecture - General report - Panelist’s contributions
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Earthquake GeotechnicalEngineering, Sec0 e Pinto (ed.) 0 1999Balkema, Rotterdam, ISBN 90 5809 1 16 3
Responses of large-diameter buried pipes to earthquakes J. I? Bardet Civil Engineering Department, University of Southern California, Los Angeles, Calif:, USA
C.A. Davis Los Angeles Department of Water and Power, Calif:,USA
ABSTRACT: This paper reviews the field observations and analyses on 61 corrugated metal pipes (CMP) shaken by the 1994 Northridge earthquake. These CMPs, which include 29 small diameter (below 107 cm) CMPs and 32 large diameter (above 107 cm) CMPs, are located within a 10 km' area encompassing the Van Norman Complex in the Northern San Fernando Valley of Los Angeles, California. Ground motions were extensively recorded within the study area during the 1994 Northridge earthquake. During the earthquake 28 of the small diameter CMPs performed well while the 32 large diameter CMPs had performances ranging from no damage to complete collapse. The investigation was initially prompted by the collapse of the 2.4-m diameter drain line of the Lower San Fernando Dam (LSFD). A detailed investigation revealed that this particular failure could not be attributed solely to either large ground accelerations, or liquefaction of hydraulic fills. Additional field investigations identified ground strains as the main cause of damage to large-diameter CMPs. Based on the 32 large-diameter CMPs data set, the factors controlling CMPs performance were identified and a simplified pseudo-static method of analysis was proposed for evaluating the response of large diameter flexible underground pipes to earthquakes. Peak ground velocity was found to be a more reliable parameter for analyzing pipe damage than peak ground acceleration. These analysis results are useful for the seismic design and strengthening of flexible buried conduits. gitudinal failures for small-diameter underground pipes have been recorded and studied extensively for transient ground motion (e.g., Ariman et al., 1981; O'Rourke and Hmadi, 1988;) and permanent ground deformations (e.g., O'Rourke and Hamada. 1992; O'Rourke and O'Rourke, 1995; and Tawfik and ORourke, 1985). Ground strains induced by earthquakes have also been studied extensively in seismology (e.g., Bouchon and Aki, 1982; Lee and Trifunac; 1985, 1987; Smith et al., 1982; and Trifunac and Lee, 1996). Surface strains have been indirectly measured from recordings in pipes, tunnels and underground structures (e.g., Nakamura et al., 1981). Differential motions and average strains have been computed from specialized arrays (e.g., Arakawa et al., 1985; Bycroft, 1983; Iwamoto et al., 1988; and Smith et al., 1982). A simplified procedure for analysis of maximum strains in the soil was proposed by Newmark (1967) and Newmark and Rosenblueth (197 l), and applied by several investigators (e.g., Kuesel, 1969; and Tamura, 1976). The impacts of seismic ground strains on engineering structures have mainly been studied for horizontally elongated structures (e.g., pipelines) which
1. INTRODUCTION
Until recently large-diameter underground structures were thought to be relatively safe during earthquakes, with the exceptions of fault crossings and areas with landslide potential near the portals of tunnels (e.g., Burridge et al, 1989). The 1995 Hyogoken-Nanbu (Kobe) earthquake raised serious concerns about the safety of underground facilities when it damaged the Daikai Subway Station (Iida et al., 1996), and revealed the vulnerability of underground structures to near-field earthquakes. A related, but less publicized, example of the failure of a buried structure took place during the 1994 Northridge Earthquake at the Lower San Fernando Dam (LSFD) in the Los Angeles Department of Water and Power's (LADWP) Van Norman Complex, in the northern San Fernando Valley in Southern California. In this event, 76 meters of 2.4-m diameter buried pipe were crushed, and 23 meters deformed (Davis and Bardet, 1998). Youd and Beckman (1996) pointed out that the transverse failure of large-diameter conduits is still not well understood because they have rarely been observed during past earthquakes. In contrast, lon973
are sensitive to differential motions (e.g., Christian, 1970; Iwamoto et al., 1984; Iwamoto et al., 1988; Japan Road Association, 1992, O'Rourke and Castro, 1980; O'Rourke et al., 1984; Sawada et al., 1999; Tsuchida and Kurata, 1976; Yeh, 1974). However, the effects of ground strains have not yet fully been investigated for the transverse response of large-diameters flexible conduits. This paper summarizes the results of field investigations on 61 corrugated metal pipes (CMP) shaken by the 1994 Northridge earthquake. These investigations were prompted by the collapse of the LSFD drain line after the 1994 Northridge Earthquake, and by the scarcity of case histories and methods of analysis on the response of large-diameter flexible conduits to strong near-field earthquakes. Based on these case histories, a simplified strain-based analysis is proposed to identify the parameters controlling the seismic performance of CMPs and is compared with the acceleration-based analysis of Davis
and Bardet (1998). These case studies and the companion analysis are intended to help engineers to improve methods for designing new buried structures and strengthening existing ones.
2. CASE STUDY OF COLLAPSE OF LSFD DRAIN LINE Figures 1 and 2 show a plan and profile of the drain line of the LSFD, which is the large-diameter buried pipe under consideration. 2. I . Drain line characteristics The 116-m long drain line is made of 17 segments, which are numbered 1 to 17 in Fig. 2. Each segment is 7.3 m long, except for the shorter segments 1 and 2. Each segment is made of 2.4-m diameter, unencased, corrugated metal pipe. Segment 1 connects to a 2.6-m diameter reinforced concrete tunnel.
Figure 1. Drain line in Lower San Fernando Dam: (a) General view; (b) Close view showing crack patterns and sand boils observed after 1994 Northridge earthquake.
974
Figure 2. Longitudinal profile of LSFD drain line along section AA' of Fig. 1. The 2.4-m nominal inside diameter, 8 gauge (0.43 cm thick), galvanized, corrugated metal pipe was fabricated according to ASTM A 444 specifications. The base metal had a minimum yield strength of 230 MPa and tensile strength of 3 10 MPa (ASTM A 446). The corrugations had a pitch of 6.8 cm and depth of I .3 cm (ASTM A 760). The pipe segments were joined by butting them together and wrapping a metal strap around them. The joints were secured tightly but were not sealed with rubber gaskets. The drain line, which is inclined 0.312% to the south, maintains a relatively constant flow of water throughout the year, and is the only outlet to empty the storm basin. The drain line was constructed in 1973, after the 1971 San Fernando Earthquake extensively damaged the LSFD (e.g., Seed et al., 1973). The upstream face of this hydraulic fill embankment underwent a massive liquefaction induced slide. Following the 1971 earthquake, the LSFD was removed from service, and reconstructed to serve as a storm water detention basin. Its upstream slope was rebuilt and its outlet lines were modified to release water from the detention basin. 2.2. Soil characteristics The geologic and soil cross-section parallel to the drain line was obtained by logging the northern and eastern slopes (1.5H to 1V) of the excavation, which was dug seven months after the 1994 earthquake to expose the drain line, and by projecting these observations onto a vertical plane. The drain line was constructed through seven different geologic units and fill materials. Pipe segments 1 to 6 were founded on alluvial soil, while the other segments were founded on soft sedimentary rock (mainly sandstone and siltstone) hereafter referred
to as bedrock. Segments 1 to 6 were located in hydraulic fill slide debris, segments 7 to 9 in alluvium, and segments 10 to 17 in bedrock. In 1973, the drain line was placed in the natural ground, which was cut to fit the pipe curvature. The pipe construction was carefully supervised and inspected by LADWP engineers (LADWP, 1975). The 5.5-mwide trench was backfilled with compacted sand bedding and overlain by compacted trench fill material. In 1975, the trench was covered by an additional embankment fill, the thickness of which varies from 1.5-m on segment 16 to 7.3-m on segment 1. The sandbedding, trench and embankment fills were placed under controlled conditions. The trench and embankment fills were laid in 20-cm lifts and rolled to a minimum relative compaction of 92%. Direct shear tests were performed on the compacted embankment fill during reconstruction of the upstream slope (LADWP, 1975). The trench and embankment fills have similar material properties. The groundwater elevations along the pipe vary with the embedding materials, and become higher in the hydraulic fill and alluvium. Based on these field observations, it is concluded that during the 1994 Northridge earthquake pipe segments 1 through 6 were submerged below the groundwater surface and water along the remaining segments was near the crown, saturating most of the sand bedding materials. 2.3. Collapse and deformation of drain line Figure 3 shows a photograph of the drain line after the 1994 Northridge Earthquake: 76 meters collapsed laterally, and 23 meters deformed substantially.
975
Figure 3. View looking south at the collapsed LSFD drain line after the 1994 Northridge earthquake. The excavations that unveiled the pipe were carefully supervised, and the digging operations were performed with extreme caution to avoid any additional damage to the pipe. In other words, the pipe deformation reported below resulted from earthquake damage, not from digging operations. The deformed sections of Fig. 4 were carefully measured over the entire length of the pipe, and were sketched within a 8% accuracy. The accuracy level was estimated by comparing the measured perimeters of the deformed and initial sections, and by assuming that the circumference did not stretch but remain equal to nD,where D is the initial pipe diameter. As shown in Fig. 4, the pipe segments, which have similar characteristics, deformed quite differently. Lateral collapse was the most common failure. The lateral deformations were the largest on segments 7 to 12, and the vertical deformation the largest on segments 1, 2, 11, and 12. The amplitude of lateral deformation ranges from over 60 cm for segment 13 to negligible in segments 16 and 17. Surprisingly, segment 6 did not deform, while adjacent segments completely failed. One end of segment 7 failed and the other end was not even deformed. Segments 11 and 12 deformed in complex ways. The ends of segment 1 collapsed and folded in opposite directions. Segment 12 had a 0.9-m long vertical tear,
one end crushed laterally and folded over, and the other end deformed much less. As shown in Fig. 4, there were vertical tears in segments 2, 5, 7 , and 12, which were less than 1 m long. These tears occurred at the transitions between different deformation patterns. The segments did not systematically deform continuously across their joint connections. They deformed differently at some joints (e.g., 5:6 and 10:1 l), and similarly at other joints, (e.g., 6:7 and 8:9). The largest difference was between segments 1 1 and 12, which folded over in opposite directions. In contrast to the upper parts of segments, which were completely crushed for most segments, the lower parts of all segments did not deform, and left about a 30-cm spacing for water to flow through. 2.4. Ground motion andjeld observations at LSFD As described by Bardet and Davis (1996a), the intensity of the near-field ground motions of the 1994 Northridge earthquake .varied spatially and directionally in the vicinity of the drain line. Figure 1 shows the location of the strong motion instruments closest to the drain line. Station 1 is located at the Rinaldi Receiving Station 500 m south and Station 2 is located at the Los Angeles Dam abutment 900 m north of the drain line. Figures 5a and 5b show the traces of horizontal accelerations at Stations 1 and 2, respectively, in the longitudinal and transverse directions of the pipe axis. Figures 5c and 5d show the traces of the same accelerations, but projected in the vertical plane perpendicular to the drain line. The peak ground acceleration (PGA), which is represented with a square symbol in Figs. 5a and 5b, characterizes the maximum amplitude of horizontal accelerations at Station 1 and 2. The PGA is oriented nearly along the pipe longitudinal axis, and its amplitude is 0.90 g at Station 1 and 0.48 g at Station 2. In comparison, the horizontal PGAs in the transverse direction are 0.49 g and 0.35 g for Stations 1 and 2, respectively. The accelerations transverse to the drain line have a maximum value a equal to 0.91 g at Station 1 and 0.39 g at Station 2, which are represented with a circle symbol in Figs. 5c and 5d. The spatial and directional variation of the near-field ground motion in the Van Norman Complex during the 1994 Northridge earthquake makes it difficult to select a specific value of maximum acceleration for a dynamic analysis of the drain line. However, it can be concluded that the maximum acceleration a applied to the drain line was between 0.39 g and 0.91 g. Figure 1 shows contours of the ground surface deformation, which were observed above the drain line after the 1994 Northridge Earthquake. As de976
Figure 4. Deformed shapes of various segments of drain line (circle represents approximate pre-earthquake shape). scribed in Bardet and Davis (1996b), the reconstructed upstream berm of the LSFD moved laterally in the north east direction, which caused sand boils and ground cracks to form. This motion was caused by the liquefaction of the underlying hydraulic fill slide debris (Bardet and Davis, 1996b). As shown in Fig. 1, there is a sand boil only 24 m east of the pipe, which indicates that the hydraulic fill liquefied at this location. Segments 1 to 6 were therefore located next to a liquefied area, and partially buried under 12 m of compacted fill and liquefied hydraulic fill debris. As shown in Figs. 1 and 2, there was a 30-m long subsidence above pipe segments 7 to 12. The subsidence was the largest above segment 12, where it formed as a sinkhole. The subsidence occurred above a trench that was excavated in bedrock and non liquefiable alluvium (Seed et al., 1973) and mainly resulted from the pipe failure. Therefore, the liquefaction of the hydraulic fill was not the only reason for the collapse of the drain line.
3. STUDY OF OTHER NEARBY CMPS
The collapse of the LSFD drain line prompted the investigation of 60 other CMPs located within a 10 km’ area encompassing the Los Angeles Department of Water and Power’s (LADWP) Van Norman Complex (VNC). The VNC is a critical lifeline facility, which provides water and power to the City of Los Angeles. It is also one of the closest sites to the 1994 ruptured fault surface (Bardet and Davis, 1996a). The CMPs were arbitrarily subdivided into two categories: 29 small diameter (below 107 cm) and 32 large diameter (above 107 cm). They were inspected intermittently from 1994 through 1997, depending on accessibility. All small CMP were circular. Only one small CMP was damaged during the Northridge earthquake, as a result of corrosion. Therefore our observations imply that the current methods of analysis using static loads (e.g. AASHTO, 1992) provides an adequate factor of safety for small CMP to sustain strong seismic 977
sand, silt, or clay mixtures. Bedrock mainly consists of weak sedimentary sandstone and siltstone rocks of various formations. The average shear wave velocities in the upper 30 m were estimated at each pipe location from measurements compiled in Bardet and Davis (1996a, 1996c) and Gibbs et al. (1997). Groundwater levels were noted only with respect to elevation of the pipe invert during the 1994 Northridge earthquake. Groundwater elevations vary with rainfalls, and the exact levels for all pipe locations was not known during the 1994 Northridge earthquake. In this study, it was sufficient to only determine whether the pipes were above or below the water table. 3. I . Transient ground motions during the Northridge Earthquake Nineteen instruments in the VNC recorded the 1994 Northridge earthquake main shock. As described by Bardet and Davis (1996a), the intensity of the nearfield ground motions varied spatially and directionally around the VNC. The VNC is located above the northern end, and right in line with the slip direction of the fau!t that ruptured in the 1994 Northridge earthquake. As a result, it was subjected to strong near-source pulses (Bardet and Davis, 1996a). As pointed out by Somerville and Graves (1993), the intensity of near-field shaking depends on the structure location and orientation with respect to the direction of fault rupture. As shown in Fig. 5, the recorded horizontal ground motion was generally strongest in the N-S direction (direction of slip), and varied largely with azimuth. Similarly. the motions varied with directions i n the vertical plane. This implies that the pipes in the present study were subjected to various intensity of shaking depending on their orientation. The longitudinal, transverse, and vertical axes of the strong motion recordings are denoted x/, x2, and x3, respectively. The xI- and x2-axes are both horizontal, with positive orientation in the northern and western directions, respectively. The positive x3-axis is pointing upward. In this coordinate system, the components of accelerations and velocities are a, and v, ( i = I , 2, 3). Table 1 summarizes the peak ground accelerations and velocities in the x12-planeand along the xs-axis. The ground motions parallel to the longitudinal axes of individual pipes were calculated by rotating accelerations and velocities from the xl-axes to the x '/-axis. The vertical component of ground velocity was practically negligible. The range of peak ground acceleration and velocity was estimated for each pipe from the recordings at the closest stations and those with the most similar soil conditions. Stations 1 to 7 recorded ground motions on a variety of soil conditions. Stations 2, 3, and 7 were located on
Figure 5. Traces of horizontal and transverse ground accelerations recorded at Rinaldi Receiving Station (Station 1) and Los Angeles Dam Abutment (Station 2): (a) Horizontal acceleration at Station 1; (b) Horizontal acceleration at Station 2; (c) Acceleration transverse to drain line at Station 1 ; (d) Acceleration transverse to drain line at Station 2. Orientation of transverse acceleration is 102" Azimuth, and that of longitudinal acceleration is 12" Azimuth. ground motion. Hereafter, only the 32 large- diameter CMPs will be examined. The span distribution for the large-diameter CMPs under study range from 107 cm to 478 cm. The pipes are identified with a number (i.e., Pipe 5). When the pipe characteristics change along their length, additional letters are used to identify pipe segments (e.g. Pipe 5E and 5W). CMPs were divided into five subsets - circular, elliptical, circular arch, pipe arch, and underpass - according to their cross-sectional shape (AASHTO, 1992). The C'MP characteristics were obtained from field inspections and measurements, and supplemented with design and construction drawings when those were available. All of the pipes were made of galvanized steel and except for Pipes 5, 6, and 26, all were fabricated in accordance with ASTM A 444. The drainage slopes were less than 10% on all pipes except for some portions of Pipes 3, 26, and 27, which had 40%, 15%, and 23% slopes, respectively. Corrosion damage was only observable in Pipe 26; therefore, corrosion was not a factor controlling the performance of the large-diameter pipes under study. All pipes were backfilled with soil, except for Pipes 15 and 16, which were encased in concrete. Foundation materials were determined from local geological descriptions from the LADWP and geological maps (Dibblee, 1991). Alluvium consists of 978
Table 1. Peak Ground accelerations and velocities recorded at the Van Norman Complex during the 1994 Northridge earthquake. Shear wave velocity C, Station
Location
1
Rinaldi Receiving Station Los Angeles Dam Abutment Jensen Filtration Plant Generator Building Administratin building Sylmar Converter Station Valve group 7 free-field Valve group 1-6 basement Sylmar Converter Station East FF
2 3 4
5 6 7
Foundation
Peak ground velocity ( c d s )
Peak ground acceleration (9)
AzimuthOi2 a 2 pgai2 Azimuth%2 P P I pgv2 pgv3 (dS) P@I ~ ~ pga3 N-S E-W up (degree) N-S E-W up pgviz (degree)
Alluvium Bedrock
350 650
0 82 0 57 0 8.5 0.48 0.35 0.32
090 0.48
25 90
-162 -86
-94 -51
-42 26
184 86
209 182
Bedrock AIIuvEIII
600 425
0.71 0.82 0.83 -0.43 0.60 -0.39
1.08 0.63
311 109
-84 -108
72 96
-27 35
87 109
164 169
Alluvium Alluvium Bedrock
300 250 500
0.80 -061 0.64 0.60 -0.35 -0.53 0.77 0.47 -0.38
0.91 0.60 0.84
331 0 25
-129 -116 -11 1
80 -90 -67
34 -38 -24
130 128 116
190 207 199
rated due to beam-type bending caused by foundation and embankment defc.rmations. However the concrete surrounding these pipes remained intact. and largely contributed to their good performance. The pipes that could not be accessed or thoroughly inspected were considered to be undamaged based on the absence of (1) reported damage from local highway officials (Youd and Beckman, 1996) and (2) surface deformations above these pipes. However, the lack of reported or surficial evidence is not conclusive evidence for the absence of damage. For example, damage to some Pipes was not discovered for over a year after the 1994 earthquake.
bedrock, Stations 1 and 5 on relatively firm alluvial soils, and Stations 4 and 6 on weak soils which exhibited nonlinear response during the 1994 Northridge earthquake (Cultrera, et al., 1998). Table 1 shows a wide range of peak accelerations and velocities over short distances, even for similar soil conditions. This variation renders difficult the selection of a particular ground motion recordlng for analyzing a pipe. Therefore, all analyses were carried out with the range of ground motions shown in Table 1. 3.2. CMP performance during the northridge earthquake Figure 6 summarizes the seismic performance for the 32 large CMPs under study. Most pipes showed signs of either transient or permanent deflections. The effects of transient motions were mainly noticeable at pipe joints where the ends of loosely connected segments came temporarily into contact or bolted connections had slipped during the earthquake shaking. These transient deformations were clearly identifiable by markings in the pipe coating. In addition to transient deformations, a few pipes sustained permanent deformations. In some cases pipe segments impacted each other with enough force to leave small local deformations while the cross-sectional shapes of others were significantly distorted. Since there were no pre-earthquake measurements made on any CMPs, it was difficult to determine whether small transverse distortions preexisted or resulted from the earthquake. Consequently, small deformations that left the pipe structurally intact are not reported in Fig. 6. As shown in Fig. 6, six CMPs (i.e., 1, 4, 5 , 14, 22, and 26) underwent five forms of damage and significant APformation after the 1994 Northridge e~dhc;:zi*\e. Prior to the 1994 Northridge earthquake, Pipes I , 4, 5, and 14 were in good operating condition, while Pipe 22 had deformed vertically and Pipe 26 was corroded. Pipe 22 had a deflected shape similar to pipes embedded in poorly compacted soils (Moser, 1990). The joints of Pipes 15 and 16 partially sepa-
Figure 6. Distribution of observed performance of CMPs in the viciity of the Van Norma Complex during the 1994 Northridge earthquake.
4. ANALYSIS
Detailed site investigations were performed with the goal of identifying parameters influencing the seismic response of large diameter CMPs. 4.1. Causes of damage Five potential factors of damage to CMPs were not observed on the 32 large diameter CMP data set: (1) 979
fault displacement; (2) pipe foundation failure; (3) standard manufacturing methods; (4) standard construction methods, and; (5) drainage slope. There was no evidence of fault movement or soil foundation failure that could have lead to CMP damage. Manufacturing and construction factors were ruled out as damage causes because all the pipes, except for Pipes 5W, 6W, 22, and 26, were manufactured and constructed to similar standards (e.g. AASHTO, 1992; ASTM A 760 and A 798); this was verified in detail for Pipes 1 to 4 (Davis and Bardet, 1996b). For the range of pipe inclination considered, there was no indication that the pipe drainage slope affected CMP performance. Three other factors were identified as particular sources of damage to Pipes 14, 22, and 26, respectively: (1) permanent ground deformation; (2) settlement of poorly compacted embedding soils (construction method not meeting current standards), and; (3) corrosion. In contrast, causes of damage to Pipes 1, 4,and 5 were not readily apparent from the field investigations. Additional factors controlling CMP performance were identified as follows: (1) ground movement intensity; (2) orientation of pipe relative to ground motion direction; (3) pore pressure buildup within the embedding soils; (4) stiffness reduction of embedding soils; (5) soil-pipe relative stiffness; (6) cross-sectional shape; (7) depth of burial and preearthquake static hoop stress; (8) joint and seam connections; and (9) combination of longitudinal and lateral deformations. The most significant factors were difficult to identify based on the field investigations alone. Some factors may have combined on some pipes, and acted separately with different intensity on others. For example, Davis and Bardet (1998) concluded that axial deformation did not influence the buckling of Pipe 1. On the other hand, field investigations indicate that the damage to Pipes 4 and 5 may have been influenced by the combination of longitudinal and transverse loads. Field measurements alone were unable to show whether the transverse deformations at Pipes 4 and 5 resulted from the direct application of axial forces or from the initiation of a transverse buckling mode. Timoshenko and Woinowsky-Krieger, ( 1970) noted that an analytical solution for axial deformations in CMP is difficult to obtain and generally can not be readily applied in solving practical problems as those described herein. In view of the problem complexity, simplified analyses for transverse buckling of circular flexible pipe were developed to identify the relative importance of different parameters. This report focuses on transverse defor-
mations leaving the effects of longitudinal deformations for further study. 4.2. Static analysis The examination of the CMPs stability under static gravity loading alone is helpful not only for understanding the pre-earthquake conditions but also for formulating the seismic analysis. The static analysis consists of: (1) evaluating the pipe load and calculating the resulting maximum hoop force N, then (2) examining if the pipe can resist that load by comparing N with the critical hoop force Ncr. The factor of safety FS against failure is:
where E, is the applied hoop strain, E,, = N , , / A E , is the critical hoop strain at buckling, A is the cross-sectional area of the pipe shell, and Ep is the pipe Young's modulus. Both E, and E,, are defined with respect to the undeformed area A . The maximum hoop force N is (Moser, 1990): c
where F,, is the vertical resultant force acting on the top of pipe. The vertical and horizontal pipe strains, E" and &h, are determined from: E,
F V Fh and ch = ___ 2AE, 2AEp
=---
(3)
where Fh is the horizontal resultant force acting on the pipe. The maximum hoop force in a flexible buried conduit is difficult to determine due to various factors including trench geometry, compaction effects, variation of soil properties around the pipe, soi I-pipe interaction, effect of sloping ground, and arching effects. Approximate methods such as the limit equilibrium method of Marston (Spangler and Handy, 1982; Moser, 1990) or the elastic closed form solution of Burns and Richard (1964) give a first order approximation of the hoop force in the pipe. These methods can be used to calculate the load applied to the pipe in terms of a dimensionless arching factor p: (4)
where p is the soil density, g the acceleration of gravity, H the depth of fill over the pipe, and D the pipe diameter. As recommended by Moser (1990), p is assumed equal to 1. However, ,8 may be slightly higher or lower than 1 for flexible conduits, depending on the method of analysis and assumptions made. 980
The critical hoop force for buckling is determined from an elastic continuum model for the soil around the pipe (Moore, 1989): /
Ncr
= 0.66( Epl)'
to the limited influence of permanent movement coupled with the lack of permanent ground strain measurements in the vicinity of the CMPs, this analysis was developed in terms of transient ground motions. The transient shear strain y is evaluated as follows:
.-. \ %
[4J 1 - U;
where I is the pipe moment of inertia, E,Tthe soil Young's modulus, andv, the soil Poisson ratio. In this analysis Ep E,, and v, were taken as 200 GPa, 12.4 MPa, and 0.3, respectively, for all the pipes. E, varies slightly from pipe to pipe but was assumed to be the same for all pipes for direct comparison purpose. This is a reasonable assumption in view of the similarities in pipe construction (e.g. AASHTO, 1992; ASTM A 798). For standard sections, the values of A and I were obtained from ASTM A 796. The static factors of safety FS against buckling for all 32 large-diameter pipes FS is greater than 2. FS is very large for some shallow pipes and even exceeds 100 in some cases. These large values are expected because our calculations only account for the fill overburden, and neglect the surcharges and traffic loads which were used in the original design of these pipes. In conclusion, all CMPs were stable under static soil loads. 3.3. Strain-based analysis The proposed analysis consists of determining the changes in applied hoop force N and critical hoop force N,, relative to static conditions, which are generated by seismic ground movement. The change in hoop force results from the seismic shear and compressional strains, whereas the reduction in N,, originate from modulus reduction and porepressure increases in the soil around the pipe during shaking.
v2
Y = r L, s
where v2 is the horizontal particle velocity transverse to the pipe and C,,. is the average shear wave velocity in soil element ABCD. The transient vertical strain &vd is: U.
(7) where C, is the compression wave velocity and v3 the vertical particle velocity. The transient horizontal strain &hd is assumed to be negligible. When there is no slippage at the soil-pipe interface, the strains in the pipe coincide with those in the surrounding soil. Therefore, y and E,d can be superimposed with E, and Eh. Using the Mohr representation of strain (e.g., Bardet, 1997), one can determine the direction for which the shear strain y is zero and the normal strain is maximum (i.e., E = E,J. This case corresponds to the maximum principal strain: E,,
=+(E,
+E,,
+Eh)+
Because the pipes are flexible, v3 > C,, one may assume E, = &h and &,d 0.6 Moisture content > 0.9 times the liquid limit Penetration resistance (N,),,, < 5 or qciN< 1 Mpa
In an area where sensitive soil could develop
criteria are consistent with properties of soils that have lost strength during historic earthquakes.
5 CONE PENETRATION TESTS (CPT) Although not as commonly used as SPT, the cone penetration test (CPT) is becoming a major tool in liquefaction resistance evaluations. The superior capability of the CPT to profile stratigraphic layering makes the CPT particularly advantageous for site reconnaissance investigations. Criteria have been developed for calculating liquefaction resistance (CRR) directly from CPT data (Robertson and Wride, 1997). These criteria may be applied in practice provided adequate samples are retrieved, preferably using SPT procedures, to verify soil types and liquefaction resistances assigned.
FIGURE 2 Curve for calculation of CRR, from CPT Data (after Robertson and Wride, 1997)
The chart potted in Figure 2 is recommended by the NCEER workshop for determining liquefaction resistance for clean sands. That chart shows CSR plotted against corrected and normalized CPT resistance, qc]N,from sites where liquefaction effects were or were not observed after past earthquakes. A CRR curve separates regions of the plot with data indicative of liquefaction from regions with data indicative of nonliquefaction. This chart is valid for magnitude 7.5 earthquakes and clean, sandy materials. Dashed curves, showing approximate shear strain potential, y r , as a function of qclN, are also drawn on the figure to emphasize the fact that cyclic shear strain and ground deformation potential at liquefiable sites decreases as penetration resistance increases. The CUrve Plotted in Figwe 2 may be approximated by the following equations (Robertson and Wide, 1997):
Figure 3. CPT-Based Soil Behavior Type Chart with added data from sediments at Youd and Gilstrap (1 998) sites with low penetration resistances (modified from Robertson, 1990)
1016
where (qclN)csis the equivalent clean-sand cone penetration resistance normalized to one atmosphere of pressure (approximately 100 kPa). For (qc& >160 the soil is too dense to be liquefiable. Procedures for correcting penetration measurements in silty sands to clean-sand values are based on normalized tip resistance, Q, and frictional resistance, F (Robertson and Wride, 1997). Figure 3 is a plot of CPT soil types as a function of Q and F. Boundaries between CPT soil types 2 through 7 were approximated as concentric circles by Jeffries and Davies (1993). They defined the radius of such circles as the soil behavior type index, I,, which can be calculated from the following equation:
I,= [(3.47 - log Q)? + (1.22 + Log F)']'.'
(7)
where
and
F = [f,/(q, - o,,)] x 100%
(9)
qc and f, are measured tip and friction resistances, respectively, and Pa is 100 kPa (approximately atmospheric pressure). The soil-type chart in Figure 3 was developed using an exponent, n, of 1.O, which is the appropriate value for clayey type soils. For clean sands, however, an exponential value of 0.5 is more appropriate, and a value intermediate between 0.5 and 1.0 would be appropriate for silts and silty sands. To correct the normalized penetration resistance, qclN, of silty sands to an equivalent clean sand value, (9,I N)cs, for use in liquefaction resistance calculations, the following relationships are applied: (qclN)cs =
KcqlcN
('O)
where K, is a correction factor for grain characteristics. K, is defined by the following equations (Robertson and Wride, 1997):
Figure 4. Percentages of soil samples that classified as clayey by Chinese criteria with F values in the ranges shown (after Gilstrap and Youd, 1998).
Kc = 1.0
I,
I
1.64
(1 1)
K, = -0.403 1: + 5.581 IC3 - 21.63 IC2+ 33.75 I, - 17.88 With appropriate values for I, and K,, Equation 4.19 is used to calculate (qc,Jcs and that value then substituted into Equation 6 to calculate CRR,,. To adjust CRR to magnitudes smaller or larger than 7.5, CRR,,, is multiplied by an appropriate magnitude scaling factor. Gilstrap and Youd (1998) tested the validity of the Robertson and Wride CPT procedure, as outlined above against liquefaction behavior using 146 CPT soundings at 19 sites investigated. These sites were
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selected based on the occurrence of liquefaction in silty sediments. Based on the occurrence or nonoccurrence of surface effects of liquefaction, liquefaction was predicted with 89 percent accuracy and nonoccurrence of liquefaction was predicted with an accuracy of 86 percent. Given the variability of natural sediments, these percentages indicate that the CPT procedure performs well for silty sediments. Robertson and Wride (1997) suggest that soils with I, greater than 2.6 are generally to clay rich or too plastic to liquefy. To test this limit, we compared calculated I, values with clay contents and liquid limits from soil samples taken from bore holes drilled parallel to CPT soundings at the 19 sites investigated. Comparisons were not made where soils were highly variable or thinly layered. Approximately 6,500 data points were compiled in the data set. For this evaluation, the soil samples were classified as clayey or non-clayey using the Chinese criteria listed in Table 1 or from listed soil classifications of CH, MH, or SC. The percent of samples listed as clayey as a function of I, are plotted on Figure 4. For the 19 sites, more than 93 percent of samples with a calculated I, greater than 2.60 classify as clayey by the Chinese criteria. Twenty-five percent to 50 percent Soils with an I, between 2.36 and 2.60 were classified as clayey. Less than 10 percent of samples characterized by I, less than 2.36 classify as clayey. These results indicate that I, is a generally reliable index for identifying clayey soils. Nevertheless, adequate samples should be taken at each site evaluated to verify soil types and the applicability of the I, criterion. Several sites we investigated contained materials with very low penetration resistance ((N1)60 less than 5 blows per 300 mm or qlcN less than 1 Mpa). By the definition of the CPT classification criteria plotted on Figure 3, all soils with qlcNless than 1 Mpa classify as clayey. Materials with these low penetration values at the sites we investigated, however, encompassed a variety of materials including highly liquefiable, nonplastic silty sands at the Heber Road site (Imperial Valley, California), nonliquefiable soft, plastic San Francisco Bay clays, and highly sensitive Bootlegger Cove soils beneath the Turnagain Heights landslide that failed during the 1964 Alaska earthquake. (The low penetration soils at the Heber Road site are among those that were classified as clayey by the k = 2.60 criterion, when in fact they were non-clayey.) Thus the CPT procedure for evaluating liquefaction resistance of fine grained soils is unreliable for sediments with qlcNless than 1 MPa. Samples are
required from all such low penetration materials to determine soil type, liquefiabilty, and sensitivity.
6 DEFORMATION OF FINE GRAINED SOILS Loose or normally consolidated silts generally have lower post-liquefaction or residual strength than coarser grained soils such as sands and sandy silts. For example several investigators have determined postliquefaction shear strengths in terms of S,/a’,, ratios. From vane shear tests on three tailings dams in Chile, Castro and Tronscoso (1 989) determined S/a’,, ratios (constants) of 0.07 to 0.11. Tests on sands and silty sands by other investigators (Vasquez-Herrera et al., 1990; Baziiar et al., 1992; Ishihara, 1993; Byrne et al., 1993) yield S,la’,, ratios ranging from 0.1 to 0.2. Because of their low residual strengths, saturated loose silts, as found in tailings dams, loess deposits, etc., are prone to catastrophic flow failure during earthquake shaking. The curves and procedure published by Seed and Harder (1990) suggest an increase of residual strength with increasing fines or silt content. This procedure requires addition of one to five blow counts to the calculated (N1)60 to account for the influence of fines, for fines contents ranging from 10 to 75 percent. The blow count is then used with a chart they prepared to estimate residual strength. The added blow counts, however, likely compensate for reduced penetration resistance rather than increased residual strength. Alluvial silts generally are laid down in a moderately dense state and, at shallow depths, are dilative. Because of the tendency to dilate during shear, alluvial silts appear to be more resistant to deformation than cleaner sands. This behavior is demonstrated in laboratory tests on specimens with high silt contents. For example, cyclic triaxial tests by Singh (1 994) show that pore pressures generally build up slowly in silt specimens and do not reach a the condition where strains occur with little shear resistance as typically occurs in sands. Rather, silts tend to develop cyclic strains at lower levels of pore pressure than sands, but with much smaller strains at higher levels of pore pressure. From this behavior, one would expect that strains or deformations in the field would be smaller for silty deposits than for sands which liquefy. Another evidence of the enhanced resistance of silty soils to deformation is embodied in the empirical
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multiple linear regression (MLR) equations of Bartlett and Youd (1995). The equation for gently sloping ground is listed below: LOG DH = - 15.7870 + 1.1782 M - 0.9275 LOG R - 0.0133 R + 0.4293 LOG S + 0.3483 LOG TI5 + 4.5270 LOG (100 - Fl5) - 0.9224 D5015 where DH is predicted lateral displacement, M is earthquake magnitude, R is map distance from the energy source to the site, S is ground slope in percent, TI, is the cumulative thickness, in meters, of liquefiable sediment with an (N,)60 less than 15, F15 is the average fines content in layer T,,, and D50,, is the average mean grain size in layer T,,. Bartlett and Youd derived an equation with similar form for estimating lateral spread displacement toward a free face, such as an incised river channel. The point to be made here is that the coefficient in front of the (100FIS)term is relatively large and negative, indicating that all else being equal, predicted lateral displacement decreases markedly with increasing fines content. Thus lateral spread or ground deformation hazard is usually less at sites underlain by silty sands than at sites underlain by cleaner sands.
7 CONCLUSIONS 1. The SPT and CPT criteria presented in this report predict the occurrence and nonoccurrence of liquefaction with high reliability.
2. The Chinese criteria as listed in Table 1 are reliable for predicting liquefaction of fine grained sediments and are generally conservative. 3. Sensitive soils subject to loss of strength during seismic shaking typically have clay contents and liquid limits that exceed the Chinese criteria as listed in Table I . The criteria in Table 3 may be used as screens for sensitive soils.
4. The post-liquefaction or residual strength of loose silty sediments is commonly less than that of sands. Moderately dense silts at shallow depths are generally dilative, making them more resistant to ground deformation than cleaner sands. REFERENCES Bartlett, S.F. and Youd, T.L., 1995, “Empirical prediction of liquefaction-induced lateral spread,”
Jour. of Geotechnical Engineering, ASCE, Vol. 121, NO. 4, p. 316-329. Baziar, M.H., Dobry, R., and Elgamel, A.W.M., 1992, “Engineering evaluation of permanent ground deformations due to seismically-induced liquefaction,” National Center for Earthquake Engineering Research, Buffalo, New York, Technical Report NCEER-92-0007. Byrne, P.M., Imrie, A.S., and Morgernstern, N.R., 1993, Results and implications of seismic response studies - Duncan Dam,” Proc., 46‘h Annual Canadian Geotechnical Conf., Saskatoon, Saskatchewan, p 27 1-281. Castro, G., and Troncoso, J., 1989, “Effects of 1989 Chilean earthquake on three tailings dams,” Proc., 51h Chilean Conference on Seismology and Earthquake Engineering, Santiago, Chile. Das, B.M. and P u i , V.K., 1999, “Liquefactionof silty soils,” Proc., 2”d Int. Conf. on Earthquake Geotechnical Engineering, Balkema Publishers, in press. Gilstrap, S.D., and Youd, T.L., 1998, “CPT based liquefaction resistance analyses evaluated using case histories,” Department of Civil and Environmental Engineering, Brigham Young University, Technical Report CEG-98-01, 304 p. Ishihara, K., 1993, “Liquefaction and flow failure during earthquakes,” Geotechnique, V. 43, No. 3, p. 351-415. Jefferies, M.G. and Davies, M.P., 1993, “Useof CPTu to estimate equivalent SPT N60,” ASTM Geotechnical Testing Journal, Vol. 17, No.4, p. 458-567. Koester, J., Prerlea, V., and Prakash, S., 1999, “How liquefiable are cohesive soils?” Proc., 2”dInt. Conf. on Earthquake Geotechnical Engineering, Balkema Publishers, in press. Mitchell, J.K., 1993, Fundamentals of Soil Behavior, 2nd Ed., John Wiley and Sons, New York, 437 p. Mitchell, J.K., Houston, W.N., and Yamane, G., 1973, “Sensitivity and geotechnical properties of Bootlegger Cove clay,” The Great Alaska Earthquake of 1964--Engineering,National Academy of Sciences, Washington, D.C., p. 157-178. Robertson, P.K., 1990, “Soil classification using CPT,” Canadian Geotechnical Journal, Vol. 27, NO. 1,p. 151-158. Robertson, P.K. and Wride, C.E., 1997, “Cyclic liquefaction and its evaluation based on the SPT and CPT,” Proc., NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, National Center for Earthquake Engineering, Buffalo, NY, Technical Report NCEER-97-0022, p. 41-88.
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Seed, H.B., and Idriss, I.M., 1971, “Simplified procedure for evaluating soil liquefaction potential,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 97, No. SM9, p. 1249-1273. Seed, H. B. and Idriss, I. M., 1982, Ground Motions and Soil Liquefaction During Earthquakes, Earthquake Engineering Research Institute, Oakland, Calif., 134 p. Seed, H.B., Tokimatsu, K., Harder, L.F. and Chung, R.F., 1985, “Influence of SPT procedures in soil liquefaction resistance evaluations,” Jour. of the Geotechnical Engineering Div., ASCE, Vol. 11 1, NO. 12, p. 1425-1445. Seed, R.B. and Harder, L.F., 1990, “SPT based analysis of cyclic pore pressure generation and undrained residual strength,” Proc., H. Bolton Seed Memorial Symposium, BiTech Publishers, Ltd., Vancouver, B.C., Vol2, p. 351-376. Singh, S., 1994, “Liquefaction characteristics of silts,” Ground Failures Under Seismic Conditions, ASCE Geotechnical Publication No. 44, p. 106- 1 16. Vasquez-Herrera, A., Dobry, R., and Baziar, M.H., 1990, “Re-evaluation of liquefaction triggering and flow sliding in the Lower San Fernando Dam during the 1971 earthquake,” 41h U.S. National Conf. on Earthquake Engineering, p. 783-792. Youd, T.L., 1998, Screening Guide for Rapid Assessment of Liquefaction Hazard at Highway Bridge Sites, Multidisciplinary Center for Earthquake Engineering Research Technical Report MCEER-98-0005, 58 p. Youd, T.L., and Idriss, I.M., eds, 1997, Proceedings of the NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, National Center for Earthquake Engineering Research Technical Report NCEER-97-0022,276 p.
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Earthquake Geotechnical Engineering, S&coe Pinto (ed.)0 1999Balkema, Rotterdam, ISBN 90 5809 1 16 3
Estimation of minimum undrained shear strength for flow liquefaction using the CPT F?K. Robertson University of Alberta, Edmonton,Alb., Canada
ABSTRACT: Sensitive clays, metastable silts and very loose sands can strain soften following earthquake loading resulting in possible instability. This instability is often referred to as flow liquefaction. The minimum undrained shear strength is an important parameter in a stability analysis for soils than can strain soften during undrained shear. However, the estimation of this minimum undrained shear strength is often difficult, especially for sandy soils. Research has shown that the undrained shear strength of soils is usually a function of direction of loading, with compression loading often stronger than simple shear and triaxial extension. For many conditions in practice simple shear often represents the average direction of loading. A method is proposed to estimate the minimum undrained shear strength of soils in simple shear using the CPT.
1 INTRODUCTION Sensitive clays, metastable silts and very loose sands can strain soften following earthquake loading resulting in possible instability. This instability is often referred to as flow liquefaction. Several case histories exist where slopes have failed and flowed due to the strain softening response of the soils. In general, flow liquefaction failures are not common; however, when they occur, they can take place rapidly with little warning and are often catastrophic. Hence, design against flow liquefaction should be carried out cautiously. If a soil is strain softening in undrained shear, flow liquefaction is possible if the soil can be triggered to collapse and if the gravitational shear stresses are larger than the resulting minimum undrained shear strength. The trigger can be either monotonic or cyclic. Whether a slope or soil structure will fail and slide will depend on the relative amount of strain softening soil to strain hardening soil within the structure, the brittleness of the strain softening soil, the geometry of the ground and drainage conditions. The minimum undrained shear strength (Su(min)) is defined as the minimum strength after undrained strain softening occurs and can be an important parameter in any stability analysis for soils that can strain soften during undrained shear. In this study,
the undrained shear strength of interest will be referred to as the minimum strength following strain softening, so as not to confuse the value with the residual strength of some clays associated with particle rearrangement following very large strain. In some clays, the undrained shear strength can drop to very low values due to slippage between clay platelets. In this study, the focus is primarily on sandy and silty soils in which strain softening can occur due to the loose arrangement of particles resulting in a structural collapse of the grain structure and resulting high pore pressures leading to strain softening and low undrained shear strength. This response in sandy soils is referred to as flow liquefaction. The objective of this paper is to describe a new screening technique to estimate the minimum undrained shear strength using the Cone Penetration Test (CPT). The new technique builds upon existing CPT methods for clean sands and extends them to silty sands, silts and some clays.
2 MINIMUM UNDRAINED SHEAR STRENGTH 2.1 Direction of loading Research has shown that the undrained shear strength of most soils is a function of direction of loading (e.g. Bjermm, 1972). In general, the 1021
undrained shear strength in triaxial compression When the undrained strength ratio is less than about (s,,Tc) is larger than that in simple shear (suss) which 0.1 the brittleness is usually high. is larger than that in triaxial extension ( s ~ T E ) ; i.e. S ~ T C > suss > S ~ T E . The appropriate value of the 3 EXISTING METHODS FOR ESTIMATING undrained shear strength for a given project will be a UNDRAINED SHEAR STRENGTH function of the geometry and resulting direction of loading. Case histories indicate that the undrained There are many methods for estimating the shear strength in simple shear loading can often minimum undrained shear strength of soils from inrepresent the average undrained shear strength for situ tests. The existing methods tend to be limited to most projects (Bjerrum, 1972; Yoshimine et al., either clay or sand, but are rarely for both soil types. 1998). Hence, the undrained shear strength in The following is a brief review of the methods simple shear loading is often the key parameter, available. although all projects should be evaluated based on The field vane test is often used to measure both their actual geometry. the peak and minimum undrained shear strength in clay soils. Wroth (1984) showed that the field vane 2.2 Stress normalization undrained shear strength is close to that in simple shear. The CPT has been used to estimate the peak For normally consolidated clays, the undrained and minimum undrained shear strength of clay soils shear strength increases approximately linearly with through empirical correlations. Typically, the peak increasing vertical effective stress and hence, it is undrained shear strength is estimated using: common to define the undrained strength in terms of an undrained strength ratio, For normally consolidated clays, this undrained strength ratio is approximately constant, depending on soil plasticity, direction of loading and soil density. For where: simple shear loading, the undrained strength ratio qt is the total cone penetration resistance for normally consolidated clay is typically between corrected for unequal end area effects = 0.2 and 0.3. ov0 is the total overburden stress For granular soils, Stark and Mesri (1992) Nkt is an empirical cone factor. suggested linking the Standard Penetration Test (SPT) (N1)60 with the minimum undrained strength Typically the cone factor, Nkt, that links the CPT to ratio, Su(min)/Olvo.' Yoshimine et al.. (1998) presented the field vane or simple shear undrained shear a review of laboratory test results on Toyoura sand strength is between 10 and 20, with an average of and showed that, for loose Toyoura sand at a about 15 (Lunne et al., 1997). constant relative density over a low stress range The minimum (residual) undrained shear (oov0 < 300 kPa), the minimum undrained strength strength (Su(min)) in clays is often assumed to be ratio in simple shear loading is approximately equal to the CPT sleeve friction, f,, since the clay is constant. Hence, it appears appropriate to link a almost fully remolded as it passes the friction sleeve. measure of relative density in loose sand with a Hence, clay sensitivity can be estimated from the constant value of undrained strength ratio. CPT using: However, this link may not hold for denser sands and at higher stress levels. Hence, caution should be used when applying this type of relationship s u ( p e W - (4 t - OVO Sensitivity, St = -when granular soils are under a vertical effective SU(ni") f s . Nk, stress greater than about 300 kPa. su/~lvo.
su/~lvo
2.3 Brittleness The possibility of instability in undrained shear is also linked to the brittleness or sensitivity of the soil. Recent laboratory testing on sands has shown a link between the brittleness and the minimum undrained shear strength ratio (Yoshimine et al. 1998). When the minimum undrained strength ratio decreases below about 0.3 the brittleness increases.
The normalized friction ratio Robertson (1990) is defined as: F=[-
fs
(91 - C"0)
I x 100in percent
suggested
by
(3)
Hence, clay sensitivity can be estimated from the CPT using:
1022
100 s, = ___ c hT I'. 1 Y kt
between normalized CPT and minimum undrained shear strength based on other case histories in sands.
(4)
With Nkt typically between 10 to 20, this becomes:
s, =-10 F
4 PROPOSED CPT SCREENING METHOD
5 to F
A new method to estimate the minimum undrained shear strength will be described that builds upon existing methods. If a CPT based method is to be applied over a wide range of soil types, the data must be normalized to correct for effective overburden stress in such a way to fit most soils. In the following sections, first a new method of stress normalization is proposed and then the new CPT-based method of estimating minimum undrained shear strength is described.
In clean sands, the minimum undrained shear strength is often estimated using empirical correlations with penetration resistance from the Standard Penetration Test (SPT). The most commonly used correlations are those proposed by Seed and Harder (1990) and Stark and Mesri (1992). These correlations were based on case histories where instability occurred and the average minimum undrained shear strength was back calculated. A recent re-evaluation of these case histories (Wride et al., 1998) has questioned the validity of the proposed correlations, especially for (NI160 > 10. Yoshimine et al. (1998) suggested correlations between the minimum undrained shear strength values in triaxial compression, simple shear and triaxial extension and the normalized cone penetration resistance, qtl, for clean sands. The normalized cone resistance was defined as:
4.1 Stress normalization of CPT data There has been much discussion in the literature about the correct normalization of CPT penetration resistance. Wroth (1984) suggested a linear normalization for the interpretation of undrained shear strength in clays, as follows: (7)
where: Pal is atmospheric pressure in the same units as qt Pa2 is atmospheric pressure in the same units as the vertical effective stress, dv0 n is a stress exponent, typically equal to 0.5 for clean sands. The correlations were initially based on high quality laboratory results on both reconstituted and undisturbed samples. However, the correlations were evaluated using three case histories of flow liquefaction failures in essentially clean sands where CPT data were available. Yoshimine et al. (1998) found that the case histories agreed well with the laboratory data in simple shear, as shown in Figure 1. The data from Yoshimine et al. (1998) suggests that the critical normalized cone resistance in clean sand above which strain softening in simple shear is unlikely is about 60. The data used to compile Figure 1 were based primarily on subrounded to sub-angular quartz sands for which the vertical effective stress was less than about 300 kPa. Ishihara (1993) proposed a similar relationship
Extensive field experience and theoretical work (Lunne et al., 1997) has shown that this normalization works very well in clay soils to link cone resistance to undrained shear strength ratio, su/ cfv0 (see Equation 1). Baldi et al. (1982), suggested a non-linear normalization to link relative density to CPT penetration resistance using the normalized resistance given in Equation (6) using a stress exponent n = 0.5. In most cases, the cone resistance, qt, is much larger than the total overburden stress, ovo,and hence, (qt - ova) is approximately equal to qt. However, to be consistent, it is recommended to use the following general relationship:
Where n = stress exponent Pal is a reference pressure in the same units as qt and ov0 Pa2 is a reference pressure in the same units as dv0 As stated above, Wroth (1984) showed that a linear normalization (n = 1.0) should be used for clays.
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If I,< 1.64 If I,> 3.30 If 1.64 < L < 3.30
The linear normalization for clays is effective because clays typically have a steep critical state line in void ratio - log mean normal effective stress space (e - log p'), where the slope of the critical state line (h) is often around 0.4. For sands, the critical (steady) state line is typically flatter in e log p' space with a slope (h)often around 0.04 or less. For clean rounded quartz sands, the critical (steady) state line can become almost flat in e-log p' space over the low stress range (i.e. h close to zero). Ishihara (1993) showed that the steady state line for Toyoura sand curves from being essentially flat at low stresses to very steep at very high stresses. Hence, at low stresses, the steady state line is essentially at a constant value of void ratio. At high stresses, grain crushing occurs and the steady state line becomes similar to that of some clays. When the slope of the critical (steady) state line is flat in e - log p' space, the state line becomes a constant value of void ratio (e) and, hence, is analogous to constant relative density. Hence, when the state line becomes very flat, the stress normalization should approach that used for relative density; i.e. n = 0.5. Therefore, a stress exponent of n = 0.5 should be appropriate for dean quartz sands < 200 kPa). In the high in the low stress range stress range where the state line becomes very steep the stress exponent should approach that used for clay, i.e. n = 1.0. Recently, Robertson and Wride (1998) suggested a simple technique to apply a variable normalization, using a soil behavior index (I,) to perform variable stress normalization, where:
Iterate until the change in the stress exponent, An < 0.01. When the in-situ vertical effective stress (o',,) exceeds 300 kPa assume n = 1.0 for all soils. In clean sands, the normalized cone resistance, Q, suggested by Robertson and Wride (1998) is essentially the same as the normalized cone resistance, qtl, used by Yoshimine et al. (1997), since typically qt >> ovain clean sands. A variable normalization, using a stress exponent (n) as a function of L,allows a transition from clean sands at low stresses (n = 0.5) to clays (n = 1.0) using CPT data. The method described by Equation 10 is recommended for stress normalization of CPT results and is used in developing the new CPT-based method of estimating minimum undrained shear strength described in the next section.
4.2 Representative Values
(olv0
= k(3.47 - logQ)* + (logF + 1.22)'J
n = 0.5 n = 1.0 n = (L-1.64) 0.3 + 0.5 (10)
(9)
The CPT soil behaviour type chart by Robertson (1990), uses a normalized cone penetration resistance (Q) based on a simple linear stress exponent of n = 1.0. The procedure using n = 1.0 was recommended by Robertson and Wride (1998) for soil classification in clay type soils when I, > 2.6. However, in sandy soils when L 5 2.6, Robertson and Wride (1998) recommended that data being plotted on the chart be modified by using n = 0.5. The simplified normalization suggested by Robertson and Wride (1998) is easy to apply but produces a somewhat discontinuous variation of the stress exponent, n. To produce a smoother variation of the stress exponent the following modified method is recommended. Assume an initial stress exponent n = 1.0 and calculate Q and F and then L. Then:
When evaluating the potential for either cyclic or flow liquefaction, there is little guidance given on what value of penetration resistance can be taken as representative of the deposit, In the SPT based method for cyclic liquefaction suggested by Seed et al. (1985) and updated by the NCEER Workshop (1997), generally the average SPT (N1)60 value was taken from the case histories to develop the method. Similarly, Seed and Harder (1990) and Stark and Mesri (1992) generally used average values from case histories to develop the relationship between (N1)60 and minimum undrained shear strength. Fear and McRoberts (1995) argued that the minimum value of (N1)bO would be more appropriate. In general, if all values of the measured penetration resistance are used with a relationship that was based on average values, the resulting design will generally be somewhat conservative. A disadvantage of defining a criteria based on minimum values is the, uncertainty that the measured values represent the minimum. In practice, a lower bound relationship is often applied to all measured penetration resistance values. Recently Popescue et al. (1997) suggested that the 20-percentile value would be appropriate as the representative value for liquefaction. The 20percentile value is defined as the value at which 20 percent of the measured values are smaller (i.e. 80 percent are larger). In the authors' opinion, the 20percentile value is likely the more representative value for any given deposit for the evaluation of liquefaction potential.
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4.3 Minimum undrained shear strength: Cohesive soils For insensitive normally consolidated clays, the peak undrained shear strength ratio can be estimated from the CPT using:
As outlined earlier, for insensitive, normally consolidated clays, the peak undrained shear strength ratio in simple shear is between 0.2 to 0.3. Hence, assuming Nkt between 10 and 20, the normalized cone penetration resistance, Q, in normally consolidated insensitive clays is around 2 to 6. Combining an average Su(p&)/dv = 0.25 and an average Nkt of 15 gives Q = 3.75. The normalized friction ratio, F, in insensitive normally consolidated clays is typically between 5 and 10 percent (see Equation 5). As the sensitivity (S,) of the clay increases, the sleeve friction decreases and hence, friction ratio decreases. Using the CPT soil behaviour type chart suggested by Robertson (1990) and the link between minimum undrained shear strength and CPT sleeve friction (Equations 2 and 5), it is possible to plot contours of minimum undrained shear strength ratio in simple shear, Su(min)ss/dvo , on the soil behaviour chart in Zones 2, 3 and 4, as shown in Figure 2. These contours are approximate, but provide a guide to a possible relationship between minimum undrained shear strength ratio in simple shear and CPT data for normally consolidated clays. In overconsolidated clays, the normalized cone resistance and friction ratio tend to increase with increasing OCR, which can offset any tendency for friction ratio to decrease with increasing soil sensitivity. 4.4 Minimum undrained shear strength. Cohesionless soils Using the relationship for clean sands suggested by Yoshimine et al. (1998), it is possible to identify the approximate location of contours of minimum undrained shear strength (Su(min)ss/Glvo ) in simple shear for clean sands (Zone 6) on the CPT soil behaviour chart, as shown in Figure 2. It is clear from Figure 2 that any contours of undrained shear strength ratio should vary from those for the clean sand to those for clay. It is also possible to develop complete contours of minimum undrained shear strength for each direction of loading based on the results from Yoshimine et al. (1998). However, in this study, the
focus is on the value of the minimum undrained shear strength in simple shear. The following describes how to extend the relationship suggested by Yoshimine et al. (1998) for clean sands to silty sands, silts and possibly clays. Robertson and Wride (1998) suggested a method for correcting normalized cone resistance to an equivalent clean sand value, (Q)cs,using a correction factor &, where & is a function of grain characteristics estimated using the soil behavior type index, L.
where if L 5 1.64 if
L > 1.64
& = 1.0
& = -0.403
L4 +
5.581
L3
- 21.63 L2 + 33.75 I, - 17.88
Robertson and Wride (1998) suggested that CPT data that plot in the region defined by 1.64 < I, < 2.36 and F < 0.5% should be assumed to indicate a loose clean sand and hence, & should be set equal to 1.0. The correction factor, &, is approximate since the CPT responds to many factors, such as soil plasticity, fines content, mineralogy, soil sensitivity, age and stress history. However, in general, these same factors influence both the resistance to cyclic loading (Robertson and Wride, 1997) and the undrained shear strength ratio in a similar manner. By combining the relationship between normalized cone resistance and minimum undrained shear strength in simple shear for clean sands, suggested by Yoshimine et al. (1998), with the correction factor, &, it is possible to develop contours of undrained strength ratio on the CPT soil behaviour type chart. The resulting contours are shown in Figure 3. The resulting contours fit the general location of values for sands and clays shown in Figure 2. The resulting contours shown in Figure 3 are approximate and apply primarily to young, normally consolidated, uncemented soils. Sandy soils with angular grains and aged soils would likely have higher strengths. Soils that have a minimum undrained shear strength ratio in simple shear of around 0.30 or higher are generally not brittle. Soils that have a minimum undrained shear strength ratio of around 0.10 or less are often highly brittle (Yoshimine et al. 1998). Hence, the contour of Su(min)/Gtvo = 0.10 represents the approximate boundary between soils that can show significant
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Figure 1.
Minimum undrained shear strength ratio for clean sand as a function of CPT cone resistance (After Yoshimine et al;. 1998)
strain softening in undrained simple shear and soils that are general not strain softening.
5 SUMMARY A proposed screening method has been described to estimate the minimum undrained shear strength of soils from the CPT. The minimum undrained shear strength is defined as the minimum shear strength following undrained strain softening. Research has clearly shown that the undrained shear strength of soils is usually a function of direction of loading, with undrained shear strengths in compression loading often being higher than those in simple shear and triaxial extension. The resulting average minimum undrained shear strength is therefore a function of the slope geometry. Although all projects should be evaluated based on their actual geometry, often the average undrained shear strength is close to that in simple shear loading. The proposed screening technique uses a variable normalization of CPT data based on soil type and in-situ vertical effective stress. The proposed normalization is modified from the method proposed by Robertson and Wride (1997) and makes use of a soil behaviour index (IJ. The proposed screening method builds upon the
technique proposed by Yoshimine et al. (1998) in which normalized cone resistance was linked to the minimum undrained shear strength ratio for clean sands. The relationship proposed by Yoshimine et al. (1998) was based on laboratory test results on rounded sands as well as case histories of flow liquefaction failures in essentially clean sands. Yoshimine et al., (1998) suggested that the undrained shear strength in simple shear is often a reasonable average value for most slope geometries in sands, which was consistent with the observations made by Bjerrum (1972) for slopes and embankments in clays. By combining the results from Yoshimine et al. (1998) and the CPT based approach suggested by Robertson and Wride (1997) contours of minimum undrained shear strength ratio on the CPT soil behaviour chart by Robertson ( 1990) were developed. The resulting contours (shown in Figure 3) are approximate and apply primarily to young, normally consolidated, uncemented soils. Sands that have angular grains may have a minimum undrained strength ratio higher than predicted using the suggested CPT chart. Aged soils (age > 1,000 years) may also be somewhat stronger. For high risk projects, the proposed CPT method provides a useful screening technique to identify potentially critical zones. For low risk projects, the 1026
Figure 2. Approximate contours of minimum unstrained shear strength ratio in simple shear for clays and sands shown on the normalized CPT soil behaviour type chart proposed by Robertson ( 1990).
Figure 3.
Recommended contours for estimating minimum undrained shear strength ratio in simple shear using the CPT.
proposed CPT method will generally provide a conservative estimate of the minimum undrained shear strength ratio in simple shear loading. The proposed relationship conservatively estimates the minimum undrained shear strength ratio in simple shear for a soil structure which contains extensive amounts of loose soils with impeded drainage, such as thick deposits of loose interbedded sands and In soil structures where drainage and silts. consolidation of the liquefied layer can occur during and immediately after the earthquake, higher values of undrained shear strength will likely exist. Such conditions may exist in a thin deposit with free drainage to the ground surface or a deposit interbedded with extensive pervious gravel layers.
6 ACKNOWLEDGEMENTS The author would like to acknowledge the contributions from C. E. Wride. REFERENCES Baldi, G., et al. 1982. Design parameters for sands from CPT. Proceedings 2nd European Symposium on Penetration Testing. Amsterdam. 2,425-432. Bjerrum, L., 1972, Embankments on soft ground. Proceedings of Specialty Conference on Performance of Earth and Earth-supported structures, Lafayette, Indiana, 2: 1-54. fshihara, K., 1993. Liquefaction and flow failure during earthquakes. 33rd Rankine Lecture,
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Geotechnique, 43(3): 349-415. Lunne, T., Robertson, P.K. and Powell, J., 1997. Cone Penetration Testing in Geotechnical Practice. S & F SPON (Routledge) Publishers. Popescu, R., Prevost, J.H., and Deodatis, G., 1997. Effects od spacial variability on soil liquefaction: some design recommendations. Geotechnique, 47(5): 1019-1036 Robertson, P.K., 1990. Soil Classification using the CPT. Canadian Geotechnical Journal. 27( 1),151-158. Robertson, P.K. and Wride, C.E., 1998. Evaluating Cyclic Liquefaction potential using the Cone Penetration Test. Canadian Geotechnical Journal. 35(3), 442-459 Seed H.B. and Harder, L.F., 1990. SPT-based analysis of cyclic pore pressure generation and undrained shear strength. Proceedings of the H. Bolton Seed Memorial Symposium, Vol. 2, pp. 35 1-376. Stark, T.D., and Mesri, G.M., 1992. Undrained shear strength of liquefied sands for stability analysis. Journal of Geotechnical Engineering. ASCE, 118 (1 1): 1727-1747 Yoshimine, M., Robertson, P.K., and Wride, C.E., 1998, Undrained shear strength of clean sands, Accepted for publication in the Canadian Geotechnical Journal. Wroth, C.P., 1984. The interpretation of in-situ tests. 24'h Rankine Lecture, Geotechnique, 34(4), 449489 Wride, C.E., McRoberts, E.C. and Robertson, P.K., 1998. Reconsideration of Case Histories for Estimating Undrained Shear strength in Sandy soils. Accepted for publication in the Canadian Geotechnical Journal.
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Earthquake Geotechnical Engineer~ng,S&co e Pinto (ed.) 0 1999 Balkema, Rotterdam, ISBN 90 5809 1 16 3
Constitutive modeling of cyclic mobility and implications for site response S.L. Kramer & PArduino University of Washington, Seattle, Wash., USA
ABSTRACT: Signlficant advances have been made in understanding the response of liquefiable soils to cyclic loading in recent years. These advances have led to improved techniques for modeling of the mechanics of these soils. Recent constitutive models allow consideration of phase transformation behavior, an aspect of liquefiable soil behavior that has been observed in laboratory and, more recently, field records. However, the practical significance of such phenomena for typical geotechnical earthquake engineering problems has been questioned by a number of practitioners. T h ~ paper s presents a brief review of soil liquefaction and constitutive modehg techniques to investigate the practical significance of phase transformation behavior. Analyses using models that do and do not represent phase transformation behavior indicate that it’s effect is important, from the standpoint of both site response and permanent deformations. The response, however. is sensitive to details of model development and calibration and the reliabihty of a priori predictions has not been estabhhed.
1 INTRODUCTION Liquefaction is one of the most important and most difficult problems in contemporary geotechcal engineering practice. While tremendous advances have been made in understanding and modeling the mechanics of soil liquefaction. the most commonly used procedures for liquefaction hazard evaluation are empirically based. The extent to which empirical procedures reflect many aspects of the known mechanics of liquefiable soil behavior is unknown. As a result, many practitioners question the need for explicit consideration of certain aspects of liquefiable soil behavior. This paper considers one of these aspects the phase transformation behavior associated with cyclic mobility.
2 LIQUEFACTION AND CYCLIC MOBILITY The basic concepts of soil liquefaction are well established and understood by most practicing geotechnical engineers. Undrained cyclic loading in loose saturated so& produces excess porewater pressure that reduces effective stresses and, consequently, the stiffness and strength of the soil. Laboratory tests have shown that the stress-strain and stress path behavior of such soils can he complex, reflecting the complex mechanics of granular media.
Figure I . (a) Stress-strain and (b) stress path behavior of cyclic simple shear specimen from VELACS project (File css6007.dat obtained from http://rccg03.usc.ed~L/velac~.
One clement of the mechanics of liquefiable soil that has reccived increasing attention in recent years is 1029
pressures predicted by such models do not decrease (neglecting dissipation by diffusion) - they remain constant or increase within each loading cycle and from one cycle to the next. In cyclic nonlinear stress-strain models, computed pore pressures are used to degrade, or soften, backbone curves resulting in a soil stiffness that steadily decreases with increasing strain. A pore pressure model based on a modified version of the energy model of Nemat-Nasser and Shokooh (1979) has been implemented into a one-dimensional, nonlinear site response analysis program, WAVE (Home, 1996). The backbone curve is softened in proportion to the square root of effective stress, and pore pressure development is limited to a value that produces a specified residual strength at large strain levels. Because phase transformation behavior is not explicitly modeled, the extremely high pore pressure ratios representative of initial liquefaction are not reproduced.
phase transformation bchavior (Ishhara. 197.5). While phase transformation behavior has becn observed in the laboratory lor many years. clear evidence of its existence in the field has only more recently become avdable (Elgamal et al., 1998). Phase transformation involves the passage from contractive to dilative (and vice versa) states during cyclic loading. At the point of phase transformation, the incremental volumetric strain is zero; laboratory testing indicates that this condition appears to occur at an (approximately) constant stress ratio somewhat lower than that associated with fahre. The transition from contractive to dilative behavior causes the effective stress, and hence the s t f i e s s , of the soil to increase at higher strain levels under undrained conditions, a behavior that can be seen in the final cycles of the cyclic simple shear test shown in Figure 1. Prediction of the response of liquefiable sites is important for evaluation of input motions to structures founded upon them, estimation of post-earthquake settlement, and evaluation of permanent deformations. Such analyses are frequently conducted assuming onedimensional wave propagation. Currently, two approaches to modeling the stress-strain behavior of the soil are commonly employed - cyclic nonlinear stressstrain models and constitutive models.
3 CYCLIC NONLINEAR STRESS-STRAJN MODELS Cyclic nonlinear stress-strain models employ backbone curves and unloading-reloading models to represent nonlinear, inelastic stress-strain behavior. Nonlinear backbone curves may follow some simple functional form (e.g. hyperbolic, Ramberg-Osgood, etc.) or may be more general. Unloading-reloading models typically involve sets of “rules” that may be relatively simple (e.g. Cundall-Pyke) or complex (e.g. extended Masing). Representation of liquefaction behavior with cyclic nonlinear models also requires a pore pressure model. By relating pore pressure development to response, cyclic nonlinear models typically model the softening effect of liquefaction by degrading the backbone curve as pore pressures increase. A number of pore pressure models have been proposed (e.g. Martin et al., 1975; Nemat-Nasser and Shokooh, 1979); Finn and Bhatia, 1981). All relate pore pressure generation to some measure of stressstrain history, and do so in ways that produce steadily increasing pore pressures. As a result, the pore
4 CONSTITUTIVE MODELS A number of constitutive models (Prevost, 1985; Iai, 1991; Parra, 1996) are capable of modehg phase transformation behavior under cyclic loading conditions. Modeling of phase transformation behavior requires particular attention to the flow rule. Under monotonically increasing loading, the flow rule must constrain incremental volumetric strains to being contractive below the phase transformation line and dilative above. At the phase transformation line, the incremental volumetric strain must vanish, i.e. the phase transformation line must correspond to a zero volume change condition. Under undrained conditions, this constraint ensures that the effective stress path is vertical at the phase transformation h e . Under cyclic loading conditions , the incremental volumetric strains also depend on the direction of the stress increment. The flow rule must allow the degree of contraction or dilation to vary with effective confining pressure; above the phase transformation line, dilative response has also been observed to be related to some measure of cumulative plastic deformation. Such models have been used to explain details of observed site response in liquefiable s o h . Elgamal et al. (1996), for example, computed the response of an array at the Port of Kobe in the 1995 Hyogo Ken Nambu earthquake. As illustrated in Figure 3, the model captures the basic phase transformation behavior observed in the interpreted stress paths and stress-strain behavior .
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AWV is a double-deck, reinforced concrete structure that runs along the waterfront of Seattle. Washington. The area surrounding the current alignment of the AWV was originally within the waters of Elliot Bay prior to reclamation by the placement of hydraulic fill in the early part of this century. At the location of the subject profile, compacted fill extends to the groundwater level at a depth of 3 m below which a 6 m thick layer of loose saturated sand ((N&o = 10) extends to the top of the underlying glacial till. Thrs profile was analyzed for two conditions: (1) a level-ground condition in which shear stresses are zero on planes parallel to the (horizontal) ground surface, and (2) sloping ground conditions in which static stresses exist on planes parallel to the (inclined) ground surface. An analysis of the Alaskan Way Viaduct profile using the simplified method indicates that liquefaction at the bottom of the loose, saturated hydraulic fill should take place at peak input motion accelerations of approximately 0.1 lg.
Figure 3. Interpreted (from recordings) and computed stressstrain and stress path behavior at Port Island.
A simple constitutive model for one-dimensional site response analysis has been developed at the University of Washington (Arduino et al., 1999). The model represents the known nonlinear behavior of liqueiiable sands, and the co ntr active/dilative response associated with cyclic mobdity. This constitutive model has also been implemented into the site response program, WAVE.
The response of the Alaskan Way Viaduct profile was computed for three input motions - the 1965 Seattle earthquake motion scaled to peak accelerations of 0.lg (Motion l), 0.2g (Motion 2), and 0.3g (Motion 3). The intermediate of these is shown in Figure 4. It should be noted that the strongest part of the motion is between approximately 5 and 12 sec.
5 EFFECTS OF MODELING ON SITE RESPONSE To investigate the significance of phase transformation behavior on site response, a series of one-dimensional site response analyses were performed using the energy-based model and the new constitutive model in WAVE. The energy-based model predicts nonlinear, inelastic behavior with softening due to monotonically increasing pore pressures; it is not capable of modeling phase transformation behavior and it will not allow effective stresses to drop to zero. The new constitutive model also predicts nonlmear, inelastic behavior but does so with a model that accounts for phase transformation behavior. AU other aspects of the analyses were identical.
Figure 4. 1965 Seattle earthquake input motion (scaled to amax= 0.2g (a) time history of acceleration, and (b) Husid plot.
Energy Model Nemat-Nasser and Shokooh (1979) showed that pore pressure generation could be related to dissipated energy. By m o d w g the Nemat-Nasser and Shokooh equations so that a limiting porewater pressure is
A soil profde taken from the alignment of the Alaskan Way Viaduct (AWV) was analyzed. The
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approached asymptotically (instead of abruptly). the incremental porewater pressure can be expressed as
where crvo is the initial vertical effective stress, ru is the porewater pressure ratio, ru,l is the limiting porewater pressure ratio, e, is the initial void ratio, emin is the minimum void ratio, and a, b, c, and v are empirical constants. The constants were selected to approximate anticipated rates of porewater pressure generation for the saturated hydraulic fill and an estimated mininium residual strength of 4 kPa. The generation of excess pore pressure predicted by the energy model is shown for all three input motions in Figure 5. As would be expected, pore pressures are generated quickly in the loose, saturated sand, particularly with the stronger input motions. The excess pore pressures reach their maximum values after approximately 9 sec or more, so the profde is subjected to relatively strong shalung before effective stress values drop to low levels. As illustrated in Figure 6, nonhear response with backbone curve degradation does take place but, due to the inability of the energy model to reach very low effective stresses, is not pronounced. As a result, the computed spectra (Figure 7) show signficant, though de-amplified with increasing input motion amplitude, motions at the ground surface.
Figure 6. Computed suess-main response to Motion 2 at bottom of liquefiable layer (gm depth) using energy model.
Figure 7. Computed ground surface response spectra using energy model.
accumulate permanent strain in a preferential direction. In the field, t h behavior leads to lateral spreading. The effects of initial shear stress were simulated in WAVE by “tilting” the soil profde to simulate gentle inhite slopes. The computed permanent displacements (obtained by subtracting the computed displacements for the level ground case) are shown in Figure 8. These displacements increase with increasing ground slope; at higher ground slopes, substantial displacements are computed after the strongest part of the input motion (i.e. after about 12-15 sec) when the effective stress is low.
Constitutive Model Figure 5. Time histories of computed porewater pressure at bottom of‘liquefiable layer (9m depth) using energy model.
When subjected to a sustained static shear stress, elements of soil undergoing cyclic mobGty
The constitutive model implemented into WAVE allows representation of nonhear response consistent with a predetermined modulus reduction curve, and was cahbrated to produce behavior consistent with that observed for typical sands in the field. Using the
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Figure 8. Computed displacements for ground surface slopes of l",3 O , and 5 O using energy model. Figure 11. Computed ground surface response spectra using constitutive model.
better comparisons with the energy model, properties consistent with (N1)60= 13 were used for the analyses with the constitutive model.
Figure 9. Time histories of computed porewater pressure at bottom of liquefiable layer (9m depth) using constitutive model.
The generation of excess pore pressure predicted by the constitutive model is shown in Figure 9. The pore pressure response for Motion 1, in which initial liquefaction was not quite reached, was s m d a r to that predicted by the energy model. Initial liquefaction was induced very quickly by the stronger input motions, however, producing phase transformation behavior with dilation-induced stlffening as shown in Figure 10. ~i~~~~ 10 also shows the low stfiess that develops at low strain levels during cyclic mob&ty; these low stiffnesses tend to "isolate" the overlying soil from strong shakmg. Thls effect is mamfested in the ground surface response spectra of Figure 11, in which the computed surface motions for the cases in which initial liquefaction developed were relatively low. The inclusion of initial shear stresses with the constitutive model produced results that appear reasonable up to the point of initial liquefaction, but inconsistent thereafter (Figure 12). Because the occurrence of initial liquefaction produces conditions of near-zero stiffness during the strongest part of the input motion, the resulting displacements are sensitive to the nature of the motions at and after the time of initial liquefaction.
Figure 10. Computed stress-strain response to Motion 2 at bottom of liquefiable layer (9m depth) using constitutive model.
6 CONCLUSIONS
properties associated with = 10 for the loose, saturated sand (at depths of 3-9 m), initial liquefaction was achieved for Motion 1. To achieve consistency with the results of the simplified analysis and to enable
The effects of phase transformation behavior, in whch effective stresses quickly approach zero and then exhbit alternating periods of softening and staening, have a strong influence on site response and on
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Iai, S. (1991). “A strain space multiple mechanism model for cyclic behavior of sand and its application,” Earthquake Engineering Research Note No. 43, Port and Harbour Research Institute, Ministry of Transport, Japan. Ishihara, K. (1985). “Stabhty of natural deposits during earthquakes, ” Proc., I I I h Int. Conf Soil Mech. Found. Eng., 1, 321-376. Martin, G.R., Finn, W.D.L., and Seed, H.B. (1975). “Fundamentals of liquefaction under cyclic loading, ” J. Geot. Eng. Div., lol(GT5), 423-438. Figure 12. Computed displacements for ground surface slopes of l”,3 O , and 5 using constitutive model.
permanent deformations. The development of new constitutive models capable of representing phase transformation behavior is leading to improved understanding of the behavior of liquefiable soils. These models also Illustrate, however, the significant sensitivity of computed response to detalls of soil behavior that may be dfiicult, if not impossible, to characterize in practice. Further research on characterization of liquefiable soil behavior and evaluation of the reliabhty of computed response is warranted.
Nemat-Nasser, S. and Shokooh, A. (1979). ”A urdied approach to denslfication and liquefaction of cohesionless sand in cyclic shearing,” Can. Geot. J., 16(4), 649-678. Parra, E. (1996). “Numerical modeling of liquefaction and lateral ground deformation including cyclic mobllity and dilation response in soil systems, ” Ph.D. Thesis, Department of Civil Engineering, Rensselaer Polytechnic Institute, Troy, New York. Prevost, J.H. (1985). ”A simple plasticity theory for frictional cohesionless soils,” Soil Dyn. Eq. Eng., 4( 1),9- 17.
REFERENCES Arduino, P., Kramer, S.L., Baska, D.A., and Li, P. (1999). “A practical constitutive model for onedimensional analysis of liquefiable soils,” in preparation. Elgamal, A.W., Zeghal, M., and Parra, E. (1996). ”Liquefaction of reclaimed island in Kobe, Japan,” J. Geot. Eng., ASCE, 122( I), 39-49. Elgamal, A.-W., Dobry, R., Parra, E., and Yang, Z. (1998). “Soil dilation and shear deformations during liquefaction,” Proceedings, 4’hZnt. C o n . on Case Hist. In Geot. Eng., St. Louis, Missouri.
Finn, W.D.L. and Bhatia, S. (1981). “Prediction of Int. Con5 on seismic pore-water pressures,” Proc., Soil Mech. and Found. Eng., Rotterdam, The Netherlands, (3), pp. 201-206. Home, J.C. ( 1999). “Effects of liquefaction-induced lateral spreading on pile foundations,” Ph.D. dissertation, University of Washington, Seattle, 37 1 pp.
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Earthquake Geotechnical Engineering,S&coe Pinto (ed.) 0 1999Balkema, Rotterdam, ISBN 90 5809 1 16 3
Soil liquefaction in Peru J. E. Alva-Hurtado CISMID, National Universityof Engineering, Lima, Peru
ABSTRACT: A brief review of soil liquefaction and maximum seismic intensities that occurred in Peru since the XVI th century is presented. Two cases of recent earthquakes that induced soil liquefaction will be described: the May 3 1, 1970 Chimbote event on the peruvian coast and the May 29, 1990 and April 4, 1991 earthquakes in the northern peruvian jungle.
INTRODUCTION The main purpose of this paper is to present the information available on the occurrence of soil liquefaction in Peru, a southamerican country located on the pacific coast, one of the most active seismic regions in the world. Seismic activity in this region is mainly caused by the subduction of the Nazca Plate beneath the South American Plate, but there is also contineqtal fault activity. Several researchers have compiled hstorical information about the most important seismic events that occurred in Peru from the XVI th century to the present time (Silgado, 1978). In tlus presentation two cases of relatively recent earthquakes that induced soil liquefaction will be presented: the May 3 1, 1970 Chimbote event, on the peruvian coast and the May 29, 1990 and April 4, 1991 earthquakes in the Alto Mayo region in the Peruvian Orient.
OBSERVED SEISMIC INTENSITIES AND SOIL LIQUEFACTION A map of maximum seismic intensities observed (MM) in Peru was presented by Alva Hurtado et a1 (1984). The map was based upon thirty isoseismal maps of recent earthquakes and point intensities of historical earthquakes. The map represents the level
of damage irrespective of the cause: ground shalung, liquefaction, landslides triggered by earthquakes or others. This map was prepared as part of a regional project supported by CERESIS. (Regional Center for Seismology in South America). The map indicates high seismic activity on the peruvian coast due to the subduction of the Nazca plate underneath the South American Plate; moderate seismic activity can be noted in the Subandean Zone located in the northeastern jungle, east of the Andes mountain. Intensities up to X were observed on the coast of Peru in large zones whereas in the subandean zone the attenuation is higher with high intensities were noted in specific sites. Figure No1 presents the Distribution of Maximum Seismic Intensities Observed in Peru. A review of historical information of soil liquefaction in Peru was undertaken by Alva Hurtado (1983). Evidence of liquefaction such as developing mud and sand boils, violent expulsion of water from the ground, presence of intense craking and differential subsidence due to seismic events was taken into consideration. A map of Peru showing differences between real and probable liquefaction areas found in the literature was compiled and is presented in Figure No 2. Twenty seven cases of soil liquefaction in Peru were determined. The phenomena occurred on the coast, the hlghlands and the northen jungle. On the
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FIGURE N"1 DlSTFUBUTlON OF MAXIMUM SEISMICINTENSlTlES OBSERVED IN PERU
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FIGURE No2 SOIL LIQUEFACTION AREAS IN PERU
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coast soil liquefaction is more generalized because of hugher seismicity and the existance of more population in this part of Peru. There is a correspondance between higher intensities and soil liquefaction occurrance in Peru. Examples of earthquakes that produced soil liquefaction in the desertic coast and the jungle and their effects will be described in this paper.
SOIL LIQUEFACTION CAUSED BY 1970 EARTHQUAKE One of the best documented cases of soil liquefaction in Peru is the one relevant to the May 3 1, 1970 earthquake in Chimbote. The city is located about 400 kilometers north of Lima, the capital of Peru. On May 3 1, 1970 an earthquake of magnitude Ms=7.8 and focal depth of 45 kilometers occurred 50 km offshore west of Chimbote. A strong motion record of the earthquake was obtained in Lima, with a maximum horizontal acceleration of 0.11 g. No record was obtained at Chimbote. Maximum intensity of IX in the Modified Mercalli Scale was observed. A brief summary of liquefaction effects in Chimbote during the May 31, 1970 earthquake is presented. Ericksen et a1 (1970) and Plafker et a1 (1971) indicated that in Casma, Puerto Casma and near the coast of Chimbote, lateral spreading of the ground caused by liquefaction of deltaic and beach deposits was produced. Cracks that affected structures were observed on the ground. Chimbote’s central zone (Casco Urbano) was evidently an area of soil liquefaction and of differential compaction. In Chimbote, Casma and along the Panamerican Highway ground subsidence due to liquefaction, was noticed on the surface. Cluff (1971) reported ground failure in Chimbote because of saturated and loose beach deposits. Sand volcanoes and water ejection were observed in several areas where the water level was near the surface. Berg and Husid (1973) verified the occurrence of soil liquefaction in the foundation of the Mundo Mejor school in Chimbote. Carrillo (1970) reported settlement of accesses to almost all of the bridges in the Panamerican Highway and subsidence of the Chimbote Port Terminal. He also presented evidence of saturated sand liquefaction at Elias Aguirre street in Chimbote.
Morimoto et a1 (1971) described soil liquefaction in Chimbote and presented a distribution map of ground cracks and sand volcanoes (Figure No 3). In the backswamps and lowlands in alluvial deposit, general liquefaction was developed with cracks due to differential compaction of soil deposits. In alluvial deposits, subsurface liquefaction developed, generating cracks with sand volcanoes and damage to wells. Alva-Hurtado and Parra (1997) presented an assessment of soil liquefaction potential for the city of Chimbote, based on a comprehensive soil exploration program and the evaluation method of TC-4. A good comparison of liquefaction potentid sites with the soil effects produced by the 1970 earthquake was obtained.
GROUND EFFECTS CAUSED BY 1990 AND 1991 EARTHQUAKES On May 29, 1990 and April 4, 1991, two moderate earthquakes occurred in the northeastern region of Peru. Despite their relatively low magnitudes, the severity of the damage was high because of the existing type of construction and soil conditions in the populated areas. The region is located in North Eastern Peru, with hgh precipitation and temperature. Sedimentary rocks fiom the Jurassic to Cretaceous Periods are found in the nearby mountains and Quaternary materials in the Alto Mayo river valley. Quaternary deposits are composed of alluvial, colluvial, fluvial and residual soils. Moyobamba and Rioja are the most important cities in the area. The region is crossed by the Mayo river, whose banks are composed of liquefiable sand deposits. The following earthquake ground effects have been reported: soil liquefaction, instability and soil erosion in the slopes, differential settlements, soil amplification and landslides within the epicentral area. The soil liquefaction effects in Moyobamba city are described. (Alva-Hurtado et al, 1992). The type of faulting in the area corresponds to folds and high angle thrust faults that form imbricated systems. These faults have less dip with depth; producing a thrust and fold belt structure. Several of these faults have visible traces and evidence of recent activity. Valley scarps can be seen to the west of the Alto Mayo, as well as longitudinal valleys and
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FIGURE No4 GROUND EFFECTS IN MOYOBAMBA CITY BY MAY 29,1990 AND APRIL 4,1991 EARTHQUAKES
displaced morphological units, typical of active transcurrent faults. Also, to the north and south of Moyobamba, rectilinear scarps can be seen that could correspond to active normal faults (Martinez and Machare, 1991).
The city of Moyobamba was originally built on a stable plateau constituted by residual soils. The slopes around the city have erosion problems. The lowlands in Moyobamba, such as Tahuishco, Shango and h g u e have soft quaternary soils. The
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geotechnical types of damage are briefly reported, such as: ground cracking, soil liquefaction, soil amplification and landslides. Ground Cracking.- Tension cracks were observed in 1) the crest of the slopes of the Moyobamba plateau, associated with soil liquefaction and lateral spreading, 2) the highways, as tension zones that could developed future landslides and slumps, 3) the soft soils in the Mayo river banks. Soil Liquefaction.- Soil liquefaction occurred in Port of Tahuishco in Moyobamba. Lateral spreading developed in the school of Tahuishco in 1991 with cracks 10 cm wide and 50 cm deep. One classroom floor was destroyed. In 1990 the phenomenom did not reach the school building, but did occur in the school yard; sand volcanoes also appeared in the school yard. During both earthquakes, segments of the highway between Moyobamba and Tahuishco were damaged. In Azunge, located in the lowlands of Moyobamba, ground cracks and lateral spreading developed. Cracks 100 m long and 40 cm wide with depths of 1 m were reported. Most of the houses on the slope collapsed. The sewage pumping station and sewage disposal pipes failed. All tapial houses and some masonry houses on soft ground collapsed. In Shango, tapial houses collapsed. Cracks 80 m long and 20 cm scarps were observed. On Miraflores street, the cracks were 30 m long and 30 cm deep. During the 1990 earthquake soil liquefaction was reported in El Chorro and Molino Valencia in Rioja, also in Segunda Jerusalen-Azunguillo, Negro river and La Conquista. Figure No 4 presents the earthquake ground effects in the city of Moyobamba. The subsoil in the lower parts of the city, such as Tahuishco, Azungue and Shango consists of fine sands and silty sands with low relative densities and high water level. The soil in the slopes is constituted mainly by clayey and silty sands with medium densities and relatively low water table, whereas the ground in the elevated part of the city (plateau) consists of clays and clayey sands of medium to low bearing capacities and deep water table. Seismic intensities in the lower part where two degrees higher than in the elevated part of the city of Moyobamba.
CONCLUSIONS There is hlgh seismic activity on the Peruvian coast due to the subduction of the Nazca plate underneath the South American plate and moderate seismic activity in the subandean zone located east of the Andes mountain. Soil liquefaction has occurred on the coast, highlands and subandean zone in Peru. Most cases were registered on the coast because of higher seismicity and more population. There is a correspondance between hgh intensities areas in Peru and soil liquefaction ocurrence. Two cases were presented one on the coast and the other in the north east of Peru.
REFERENCES Alva-Hurtado J.E. (1983), “Brief History of Soil Liquefaction in Peru”, IV Nacional Conference on Soil Mechanics and Foundation Engineering, Lima, Peru. (Spanish). Alva-Hurtado J.E., Meneses J.F. and Guzman V. (1984). “Distribution of Maximum Seismic Intensities Observed in Peru”, V National Conference on Civil Engineering, Tacna, Peru. (Spanish). Alva-Hurtado J.E., Meneses J.F., Chang L., Lara J.L. and Nishimura T. (1992), “Ground Effects Caused by the Alto Mayo Earthquakes in Peru”, Tenth World Conference in Earthquake Engineering, Madnd, Balkema, pp. 141-145. Alva-Hurtado J.E. and Parra D. (1997), “Liquefaction Potential Map for Chimbote, Peru”, Seismic Behavior of Ground and Geotechnical Structures, Sec0 e Pinto (ed), Balkema, pp 25-31. Berg G.V. and Husid R. (1973), “Structural Behavior in the 1970 - Peru Earthquake”, 5~ World Conference in Earthquake Engineering, Rome, Italy. Carrillo Gil A. (1970), “Some Estimations of Soil Behavior during Ancash Earthquake”, II National Conference on Soil Mechanics and Foundation Engineering, Lima-Peru. (Spanish).
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Cluff L.S. (1971), “Peni Earthquake of May 31, 1970; Engineering Geology Observations”, Bulletin of the Seismological Society of America, Vol61, No 3, pp. 5 11-534. Ericksen G.E., Plafker G. and Fernandez-Concha J. (1970), “Preliminary Report on the Geological Events Associated with the May 31, 1970 Peru Earthquake”, U. S. Geologcal Survey Circular 639. Martinez J.M. and Machare J. (1991). “The Alto Mayo, Peru Earthquake of April 5, 1991”. Technical Report for CERESIS-UNESCO, Lima, Peru. (Spanish). Morimoto R., Koizumi Y., Matsuda T., Hakuno M. and Yamaguchi I. (1971), “Seismic Microzoning of Chimbote Area, Peru”, Overseas Technical Cooperation Agency, Government of Japan, March. Plafker G., Ericksen G.E. and Fernhndez-Concha J. (1971), “Geological Aspects of the May 31, 1970, Peru Earthquake”, Bulletin of the Seismological Society of America, Vol61, No 33, pp. 543-578. Silgado E. (1978), “History of the Most Important Earthquakes that Occurred in Peru ( 15 13-1974)”, Institute of Geology and Mining, Journal No 3, Series C, Lima, Peru. (Spanish).
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Slopes and embankments - Theme lecture - General report - Panelist’s contributions
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Earthquake Geotechnical Engineering, Sec0 e Pinto (ed.) 0 1999Balkema, Rotterdam, ISBN 90 5809 7 16 3
Effect of subsurface liquefaction on stability of embankment resting upon surface 1.Towhata & T. Mizutani University of Tokyo,Japan
ABSTRACT: The present paper is concerned with liquefaction-induced subsidence of embankment. Shakingtable model tests demonstrated that an embedded sheet pile wall is able to mitigate the subsidence. Another series of tests showed that liquefied sand behaves similar to viscous liquid. Finally, an analytical method of prediction of ground deformation was developed which can deal with failure of an embankment during earthquakes and subsoil liquefaction
1 INTRODUCTION Review of damages of structures caused by past earthquakes demonstrates significant differences due to type of composing materials. Those structures made of concrete and steel such as bridges and buildings are able to resist strong motion. The higher strength of the composing materials helps improve the structural resistance so that design seismic force,
which tends to increase in the recent times, is safely resisted. On the other hand, the extent of damage, if it should occur, is so substantial that restoration takes months and even more than one year. In contrast, earth structures such as road embankments and river dikes have limited resistance against earthquakes inainly due to the low material strength of composing soil. Fig.1 illustrates an example of eartliquake-induced damage of river dike during the 1993 Hokkaido-Nansei-Oki earthquake. Although the body of the dike appears to have had sufficient resistance against the seismic inertia force. this damage still occurred because the subsoil liquefaction induced the overall subsidence of this dike. Earth structures cannot survive failure and loss of bearing capacity in its foundation. F i g 2 similarly
Fig.3 Tentatively repaired road embankment after 1993 Noto-Hanto-Oki earthquake. illustrates a failure of a road embankment which was placed on peaty subsoil. This subsoil induced large deformation of the overlying embankment during the 1994 Hokkaido-Nansei-Oki earthquake. The high vulnerability of earth structures to earthquake effects does not necessarily prevent their use in seismically active areas. It is important that restoration of embankment is much easier that steel and concrete structures. For example, a tentative restoration takes only days or weeks. Fig.3 shows a road embankment which was restored within 24 hours after its failure. It has been, therefore, allowed in practice that design of river dikes does not take into account seismic effects. What has been more important is that seismic damage of dike, if any, should be restored quickly within, for example, two weeks before any flooding ceines. One of the lessons learned from the 1995 Kobe earthquake is that seismic design of river dike is necessarily near the river mouth where the protected ground elevation is lower than the level of the high water tide. If the ground surface is thus low, a total failure of a dike directly leads to flooding at the time of high tide which occurs two times a day. The idea of restoration within two weeks does not work properly in this situation. On the other hand, it is not necessary at all to have dikes completely resistant against earthquakes. A limited subsidence of a dike is allowable as long as the reduced height of a dike still lies above the water table of a river. Accordingly, it is desired to 1) determine allowable magnitude of seismic deformation of a dike, 2 ) to develop a practical measure which can reduce the extent of deformation during an expected earthquake. and 3) to predict the magnitude of reduced deformation without itsing unacceptably expensive site investigation and laboratory tests. Ministry of Construction (1 996) conducted an overall study on the subsidence of river dikes caused hy earthquakes
Fig.4 Empirical relationship between earthquakeinduced subsidence and original height of river dikes. in the past one century. Fig.4 shows that the maximum possible subsidence does not exceed 75% of the original height. It appears, therefore, that no counter measure is needed in a dike if the remaining 25% of the original height is still high enough to prevent flooding.
2 REVIEW OF SUBMITTED PAPERS This section is devoted to review of papers which were submitted to this conference and are concerned with seismic behavior of embankment and slope. The first author found after review that interest in prediction of residual deformation of eai-th structures is increasing. This situation is reasonable because the significance of seismic damage of structures are mostly governed by the magnitude of residual
1046
deformation; time history of acceleration and excess pore water pressure are less important. When liquefaction is eliminated, there are three types of predictive measures. The first one is a rigid block analogy resting on a frictional floor (Newmark, 1965). Wartman, J. et al. (1999) examined this analogy by running model tests on clay in which a slip plane developed as assumed by the theory. Troncoso et al. (1999) demonstrated the importance of prediction of minor subsidence of an earth fill dam whose concrete surface lining cannot remain intact after minor subsidence. It is noteworthy, on the other hand, that rigid block approach caimot calculate soil straiiddeforniation which is important in lifeline problems. Furthermore, it is not yet clear what kind of strength should be employed, drained or uiidrained strength, cyclic strength, or anything else. The second type employs the conventional factor of safety combined with quasi-static seismic inertia force. Wahab and Heckel (1999) calculated the yield seismic coefficient at which the factor of safety is unity. They then carried out dynamic analysis on a sliding block to reveal a correlation between the residual displacement and the employed seismic coefficient normalized by the yield coefficient. Nova-Roessig and Sitar (1 999) performed centrifugal model tests in order to develop a similar correlation. This approach is practically useful since it requires only conventionally-available soil data. It is probably possible to improve reliability by assembling many case history records. Be noted that this approach does not take into account the effects of duration time of shaking. When the concerned earthquake is of a short epicentral distance and an intermediate magnitude, the shaking is probably strong but the duration time is short (Chiara, 1999); making the induced damage much smaller than the second type of prediction infers. The third type of prediction uses nonlinear finite element analysis. Wakai and Ugai (1999) as well as Iai et al. (1999) belongs to this category. The same approach is applicable to liquefaction-induced ground deformation as well. Due to such difficulties as need for detailed constitutive model and largedeformation formulation, however, more simplified approach is important. Sasaki et al. (1999) developed a single-degree-of-freedom model of liquefaction-induced subsidence of embankment by examining in detail the behavior of model embankment observed in shaking table tests. Sakenii (1999) compared observation in centrifugal model tests with his numerical prediction. An important role played by centrifugal tests is the assessment of soil-structure interaction which has been out of scope of constitutive models of soil. Madabhushi ( 1 999) studied the validity of Westergaard formula on hydrodynamic action on
dam body. Since experimental work has not been done extensively in this field, more experimental attention is encouraged. In contrast, Koseki et al. (1999) used real earthquake damages of underground walls in order to assess the magnitude of earth pressure during strong earthquake shaking. Last but not least, the target of soil dynamic study is extending to such new material as waste (Sec0 e Pinto et al., 1999; Ratlije & Bray, 1999). Much is not known about dynamic stress-strain and strength characteristics of this material, despite that a possible failure of waste fill causes significant problems in surrounding environment. Hence, more experimental efforts are desired
3 PRINCIPLES IN DEFORMATION-BASED SEISMIC DESIGN OF DIKES AND EMBANKMENTS The magnitude of design earthquake is going to be made stronger due to experiences in 1990's. Since the dynamic strength of soil is limited, as mentioned before, the future seismic design of earth structures such as embankment and dike will resort to a concept of allowable deformation in place of requiring factor of safety greater than unity. The first problem to be solved for development of defonnation-based design is a determination of a suitable allowable seismic deformation. At present, it seems that the magnitude of allowable deformation depends of the following factors; 1) effects on human life, 2) costs of restoration either after complete failure of after allowable deformation, 3) time needed for restoration. and 4) effects on social/economic activities in the coiiceined region caused by pending of function of a structure. Methodology to determine the allowable deformation by using these factors, however, is not clear and, therefore, studies in this direction is strongly expected. Prediction of a residual deformation induced by a design earthquake is a second important issue. This section puts special emphasis on liquefaction problems which appears to generate the most significant distortion of embankments and dikes than other causes of displacement. In addition to the preceding section which showed three kinds of calculations, the present section discusses the importance of site investigation. Design of important and expensive facilities such as ports and thermal power plants allows detailed soil investigation, if necessary. In-situ tests on modulus and strength of soil as well as laboratory tests on undisturbed soil samples help carry out nonlinear finite element analyses so that residual deformation is assessed. In
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Fig.5 Failed shape of the Yodo river dike (photograph by Fudo Construction.)
Fig.7 Comparison between extent of subsidence of Yodo river dike and geotechnical conditions.
4 BRIEF DISCUSSION ON FAILURE OF YODO RIVER DIKE IN 1995
Fk.6 Geological Cross section a h 2 Channel of Yodo River. contrast, construction of road embankment and river dike does not allow detailed soil investigation. Prediction has to be run with limited data obtained by such conventional investigations as SPT and CPT among others. Hence, something other than nonlinear finite element analysis is needed. It is consequently reasonable that the type of suitable analysis varies with the type of facilities to be constructed. Simila points can be made of measures that mitigate the earthquake-induced deformation. When the concerned structure is an important and expensive one, the best measure is the soil improvement which prevents liquefaction. Since ordinary embankments and river dikes, which are tens of kilometers in length, do not allow expensive measures to be taken over the whole length from economical reasons. something less costly is desired. It is then considered acceptable that a less expensive measure allows minor distortion of a structure to occur during strong earthquakes. Therefore. a quick restoration is important especially in river dikes whose function is not affected by limited subsidence (Fig. 1).
Collapse of the Yodo River dike during the 1995 Kobe earthquake was explained by Towhata and Matsuo (1996). Fig.5 shows the shape of this embaidunent after the earthquake. The occurrence of subsoil liquefaction was evidenced by boiled sand which was detected at the foot of the fill. Discussioii on the failure of this dike leads to a proposal of desired mitigation measures. Figure 6 illustrates the geological cross section along the channel of the Yodo River. Located near the sea. the damaged Yodo River dike was underlain by an alluvial said, including an artificial fill near the coast. The thickness of the alluvial material is approximately 10 meters. Since the soils below this sandy layer are clay and pleistocene ones which are unlikely to liquefy, it is reasonable to state that the observed liquefaction (Fig.5) occurred only in the alluvial sandy layer. Figure 7 compares the extent of the subsidence of the dike with such characteristics as local soil conditions and the configuration of the dike. The most significant damage occurred in the area called Torishima, probably because the surface soil in this area was made of recent reclaimed sand. It is not yet known why the areas of artificial fill and deltaic deposits did not suffer damage, despite that such soil conditions often led to liquefaction during past earthquakes. The satisfactory behavior of the river dike in the areas other than Torishima may be attributed. at least partially. to the configuration of the dike. Firstly. the undamaged dikes had a fill. called berm. attached to the river side. The weight of the berm improved the slope stability of the dike.
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Fig.8 Tested model ground. Fig.10 Effects of thickness of liquefiable layer on subsidence of embankment.
Fig.9 Effects of sheet pile walls on subsidence of embankment. Secondly, the undamaged dike had an embedded sheet pile wall that were intended to prevent seepage flow of water into the foundation. Since this wall was longer than 10 meters in the undamaged areas. its bottom probably reached the unliquefiable clayey layer lying below the 10-meter-thick alluvial sandy layer (Fig.6). The fixed boundary condition of a ~vall. therefore, helped the sheet pile wall resist effectively the lateral flow failure of the liquefied sand. Although the Torishima dike had a similar sheet pile wall as well, its length was shorter than 10 meters and was insufficient to reach the unliquefiable layer. 'I'hus. the lateral flo~vof' subsoil and the conscquent subsidence of thc dike in Torishima area \\as substantial. 5 SHAKING TABLE TESTS ON SUBSIDENCE OF EMBANKMENT REINFORCED BY EMBEDDED SHEET PILE WALLS 5.1 iwethod of sliuking tulde test
Figure 8 illustrates the tested model ground. The size of container was 2m in width. 0.4m in depth. and O.6m in height. Both the liquefiable layer and the dense layer were made of Toyoura sand (p,=2.648. e,,,,,=O.974. e,,,,,,=0.605).The relative density of the dense layer was 80%. The liquefiable layer was very
Fig. 11 Effects of intensity of input acceleration on subsidence of embankment. loose with 20% of the relative density, to satisfy the similarity of stress-strain relationship between soil in-situ and in model ground, taking into account that model ground the confining pressure is smaller than in-situ situation. I hc model embanhment bias macfc of gralely crust (D,,)=-35mm). and the steel net of' fine meshes M as placed at the bottom of' the embankment to prc\ ent the g r a ~el sink f r e e l ~~ n t o liquefiable subsoi 1. The sheet pile model \ \ a s made of' an aluminum plate with 2nim of thickness. The bottoin tip of the sheet pile model was fixed to the container. Strain gages were placed on both sides of the sheet pile wall at each 5CIn height, to monitor the bending moment of it. The input excitation was sinusoidal with lOHz of frequency and 20 seconds of duration. The direction of the input acceleration was perpendicular to the sheet pile walls. The behavior of the model ground during testing was observed through the transparent side wall of container. To observe the deformation of the liquefied ground. the grid of colored Toyoura sand was made in the model ground.
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Thickness of liquefiable layer 40cm Input acceleration 250gal without sheet pile wall
1 0
5
$0
15
20
25
50
Time (sec)
Fig.12 Effects of variation of relative density of liquefiable layer on subsidence of embankment..
Fig.15 Ultimate deformation of model ground with fixed walls. thickness of a liquefikd subsoil and the intensity of shaking. Moreover, it was also found that the variation of the relative density from 20% to 0% of liquefiable layer did not affect seriously the subsidence of the embankment (Fig.12).
Fig. 13 Ultimate deformation of model ground without sheet pile wall.
Fig. 14 Ultimate deformation of model ground with sheet pile walls. 5.2 Experimental results (1) Subsidence of the embankment Subsidence measured at the crest of embankment did not suit the study because it included the effects of deformation of the model embankment itself. As an alternative, time histories of subsidence observed at the bottom of the embankment are shown in Figures 9- 12. Accordingly, the deformation of embankment itself was out of scope in this study. Figures 9-11 indicate that the subsidence of the embankment was mitigated by sheet pile walls irrespective of the
(2) Lateral flow in the liquefied subsoil Figures 13-15 illustrate the ultimate deformation of the model ground. In Fig.13, it is clear that lateral flow occurred in the liquefied subsoil. This part of sand under the embankment moved outwards and caused subsidence of the embankment. Moreover, it is noteworthy that the ground surface around the foot of slope of the embankment moved towards the center of container. This means that the embankment pulled the surface soil inward during subsidence. By comparing Figures 13 without sheet pile wall and 14 with sheet pile walls, it can be said that the sheet pile wall reduced the lateral flow of liquefied ground. In case of Fig.14 with sheet pile walls, it was observed that the liquefied soil boiled at the foot of the slope of embankment, probably increasing subsidence. When no wall was installed, the lateral displacement observed in Fig. 15 with 0% of relative density of liquefiable layer was slightly smaller than in Fig.13 with 20% of relative density of liquefiable layer. (3) Excess pore water pressure Figures 16 shows the time histories of excess pore water pressure observed in the liquefiable subsoil at 20cm under the bottom of the embankment. In the earliest phase of shaking, pore pressure generation was greater when no sheet pile was employed (E08); greater than in E14 test with sheet pile walls. This is because the sheet pile wall prevented shear deformation of sand. and. therefore. pore pressure rise was reduced. However, after sufficient time of shaking, the excess pore water pressure accumulated eventualIy to the same extent as in test case without sheet pile wall. Figure 17 also shows the time histories of excess pore water pressure. In test case E18, the sheet pile model was fixed perfectly to the container, and the
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18
E14 (with sheet pile walls)
E14 (with sheet pile walls) Thickness of liquefiable layer 40cm 25
3
35
4
5
0
5
45
10
Fig.16 Effects of sheet pile walls on excess pore water pressure.
20
15
25
30
Time (sec)
Time (sec)
Fig.18 Effects of the rigidity of sheet pile walls on subsidence of the embankment.
I
E18 (with fixed walls)
E08 (without sheet pile wail)
I
"y-E14 (with sheet pile walls) 1 E08 (without sheet pile wall) Thickness of liquefiable layer 40cm Input acceleration 250gal
2
0 5 2
25
3
35
4
45
Time (sec)
Fig.17 Effect of the rigidity of sheet pile walls on excess pore water pressure. lateral displacement in the liquefied subsoil was prevented substantially. The maximum the excess pore water pressure observed at 20cm below the bottom of embankment with fixed walls (El 8), was higher than those observed in case E08 without sheet pile wall and case E14 with deforinable sheet pile walls. And in this case E18, the subsidence of the embankment was smaller than in other two cases E08 (without sheet pile wall) and E l 4 (with sheet pile wall) as shown in Fig.18. Moreover, the increnient of excess pore water pressure in case El 8 with fixed walls just after the onset of input excitation was lower than the pressure without a sheet pile wall. These findings are probably related to the confining effects of limited movement of walls. (4) Acceleration in liquefied layer Figure 19 shows the time histories of acceleration observed at 20cm below the bottom of embankment. At first, there was not difference between the acceleration measured in case E08 without sheet pile wall and in case E14 with sheet pile walls. Acceleration suddenly reduced when it reached around lOOgal of amplitude in case E08. In case E14,
25
3
35
4
Time (sec)
5
Fig. 1 9 Time histories of acceleration in liquefied subsoil. in contrast, acceleration continued to increase to 15Ogal. The sudden decrease of acceleration is attributed to liquefaction and loss of rigidity of sand. The greater accerelation in E14 shows that liquefaction phenomenon was mitigated by the sheet pile walls. After sudden decrease, the records of acceleration became almost similar in case E08 without sheet pile wall and in case E14 wit11 sheet pile walls.
6 RATE-DEPENDENT NATURE OF LIQUEFIED SAND UNDERGOING LARGE DEFORMATION This section is going to present the nature of liquefied sand as observed in laboratory tests. The present topic is important in development of prediction of ground deformation induced by subsoil 1iquefaction. 6.1 Pulling pipe in liquefied sand In the first series of investigation, shaking table tests were conducted in order to study the mechanical behavior of liquefied sand undergoing large 1051
----
40
--
+
Unit crn Direclion 01 shaking
Fig.20 Model container for shaking table tests.
model tests was taken. Fig.20 illustrates a model container in which liquefiable loose sand was deposited and shaken. After liquefaction, an embedded model of pipe was pulled laterally and its displacement was recorded together with the drag force required for the pipe motion. The recorded time histories of drag force and pipe displacement stand respectively for the overall stress and strain in liquefied sand, respectively. Toyoura sand was employed for the model tests. The model test is able to investigate the behavior of liquefied sand undergoing strong shaking effects, and, in this regard, is more suitable to the present study than triaxial and other laboratory devices. Fig21 is indicative of the variation of drag force and the excess pore water pressure. The high void ratio of 1.05 prior to shaking was eniployed because the unrealistically dilatant behavior of sand under low ollerburden pressure in 1 -g model tests was avoided for by this significantly low density of sand. The figure indicates that the drag force was extremsl> small during shaking. Furthermore, the excess pore water pressure maintained the highest value during shaking, showing that the state of liquefaction M as fully attained. After the end of shaking. in contrast. the drag force started to increase with the motion of the pipe, while decreasing suddenly upon reversal of
100
"E
5
50
L
f
o
ffl L c
ffl -50
j n
-100' -0.10
"
"
1
I
'
'
'
-0.05
Shear strain
1
1
0.00 K h (
'
"
1 ' 0.05
"
'
_I
0.10
in decimal )
r-Cyclic undrained Iorsion shear lesl on Toyoura sand
Trnax=60.6 kPa Crc'z294 kPa
Fig21 Variation of drag force and excess pore water pressure around pipe during and after end of strong shaking. deformation as may occur upon flow failure of liquefied subsoil. Since conventional apparatuses such as triaxial and torsion shear devices are not able to generate very large strain. an alternative idea of
lsolropic consolidolion
-0 OL
0 00
0 04
0
Y i n decimal Undrained torsion shear tests of loose Toyoura sand. Shear strain
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Table 1 Apparent viscosity of liqueiied Toyoura sand. Void ratio prior to shaking
Relative density
0.86 0.95 0.98 1.05 I .05 1.10
("/I
Apparent viscosity (kPa sec)
+3 0 6 -2 -20 -20 -30
1.OO-2.16" 0.45 0.69 0.48-0.66 0.07-0.16" 0.10-0.37
*: data during shaking
h
Z
v
a l
Subgrade reaction at 100% liquefac-
-2
10.75
11.00
11.25
T i me (second) 51.91
I
1
I
I
I
I
I
I
I
I
pressure at the top
1.7 .&.
10.75
11.00
11.25
Time (second)
Fig.23 Pulling of pile after end of shaking. the motion. At the same time. the pore pressure record demonstrates decreasing. and the pressure quickly came back to the state of complete liquefaction upon reversal. This finding is related to the effects of dilatancy of sand induced by large deformation. Figure 22 reveals results of undrained torsion shear tests of loose Toyoura sand. It is evident that the stress-strain and the excess-pore-pressure diagrams after the onset of liquefaction are very similar to the drag force vs. displacement and pore pressure change in Fig.21. Since the increase of shear stress and decrease of pore pressure after onset of liquefactim in undrained tests are induced by dilatancy (tendency to expand in volume) of sand, it seems reasonable that the observed changes of drag force and pore pressure are related to dilatancy as well. Accordingly, the constant values of drag force and pore pressure during the shaking suggest that dilatancy effects were substantially reduced. Since
effective stress and shear rigidity did not develop during strong shaking, it seems that liquefied sand is more vulnerable to flow failure and large deformation than in the post-shaking stage. This point has not been taken into account to date by studies on residual or steady-state strength of sand by means of inonotonic undrained loading. Figure 23 manifests the variation of drag force and pore pressure in a test in which an embedded pipe was pulled laterally after liquefaction occurred and shaking was ceased. The drag force increased continuously while the pore pressure decreased. More detailed examination of data indicates that the drag force increased by 4 kPa quickly when the pipe started to move but pore pressure was still high. Thus. the present stud) obtained two kinds of drag force at the state of liquefaction; one during shaking and the other after the end of shaking. Figure 24 sunmarizes the observed drag i'orce during liquefaction and indicates that the force increases with the velocity of the motion of the pipe. This rate dependency is one of the classic topics of fluid mechanics and it is possible to back-calculate the (apparent) viscosity of liquefied sand. Since it is not yet certain whether or not liquefied sand is a viscous material, the calculated viscosity should be called apparent. Table 1 shows the viscosity thus obtained. Be noted that data of very loose sand is included therein. An interesting feature is that the apparent viscosity thus obtained is significantly greater than that of water. At 20 degrees C, pure water without vortex has viscosity of 0.000001 kPa sec. In a turbulent state, in contrast, water has a range of viscosity around 0.01 kPa sec. which is not too far from those values in Table 1. The idealization of liquefied sand as viscous liquid is not a familiar one. It, however, has not only experimental verification as above but support fi-on1 experiences during past earthquakes. Fig4 manifested that the maximum subsidence of river dikes is approximately 75y0 of the height. This fact is understood by the idea i n Fig.25 where liqwiied subsoil is idealized as v\scous liquid with its unil \?:eight equal to 20 kN/rn'. while a dike is niodeled by a block at the surface with its unit weight being typically 15 kN/m3. In the worst situation, as intended in Fig.4, the subsidence is ceased at a state in which the gravity force acting on the dike is balanced by the buoyancy. The gravity force per unit area of cross section is given by 15 X (height of dike) and the buoyancy force is expressed by 20 X (subsidence of dike). At equilibrium, accordingly, maximum possible subsidence = (1 5/20) X (height of dike)
(1)
as suggested by Fig.4. The real subsidence is not always equal to the maximum possible one as discussed above. This is 1053
i n sand is not clearly detined. Undrained torsion shear tests in the present section overcomes this problem, although the magnitude of generated strain is limited and shear tests cannot be conducted when strong shaking is going on. Loose Toyoura sand was isotropicall) consolidated under 100 kPa and was subjected to undrained shear with strain amplitude of 4%. When the effective stress became sufficiently small (less than 2% of the initial stress), a nionotonic undrained shear was started with different rates of strain. Figure 26 reveals that the effective stress was held small during the nionotonic phase of loading until strain (y) exceeded 10%. In the meantime, shear stress (z) increased gradually, similar to linear elasticity. This soil behavior seems equivalent to what was discussed in the previous section. The values of modulus, dzldy, was plotted in Fig.27 against the rate of strain. There seems to be a limited extent of rate dependency in the modulus. It is, however, not so substantial as observed in Fig.24 in which drag force increased linearly with rate of pipe displacement. The cause of different extent of rate dependency between model tests and undrained shear tests is still unknown and seems to be a good topic of study.
Drag force between moving pipe and liquefied Toyoura sand
,' A
A A
,I' ,I'
A
1
OO
Toyoura sand
e=0-86
10
Velocity of pipe ( m d s )
2
Fig.24 Variation of drag force during liquefaction with velocity of pipe.
Y =15 k N / d n
Subsidence
Liquefied sand : Y = ~ Om/m3 Fig.25 Simple inodel of dike resting on liquefied subsoil.
Fig.26 Monotonic undrained shear of liquefied sand.
particularly true when the duration of strong shaking is short and the state of viscous liquid is terminated within a short time. Therefore, it is necessary to assess, for more realistic prediction of subsidence, the duration of strong shaking by analyzing many earthquake motion records. Okada et al. (1999) considered that the state of strong shaking and flow of ground starts at the moment of the maximum acceleration and ends when the amplitude of shaking becomes less than 50 gal. The derived correlation between duration time and earthquake magnitude appears to be useful.
60
-
a
Y
-
. t
-0
40-
30j 0.1
6.2 Torsion shear One of the shortcomings of the model tests in the previous section is that the state of stress and strain
0
Torsional shear tesl
1
10
)O
rate of strain [%/sec]
Fig.27 Effects of rate of strain on undrained modulus of liquefied sand. 1054
7 THEORY FOR PREDICTION OF SUBSIDENCE OF EMBANKMENT Authors have been developing analytical inethods of prediction of large deformation of liquefied subsoil (Towhata et al., 1999). It is going to be applied to subsidence of embanknient in this section. The proposed method requires a limited number of data which is available from standard penetration tests or else and conventional liquefaction investigation. Suppose that the thickness of liquefied layer is known separately by using SPT-N data etc. To reduce the computational load, the lateral displacement, U, in liquefied subsoil is modeled by a sinusoidal function (Fig.28) of which the amplitude F(x) is unknown. Note that “F“stands for the lateral displacement at the surface. The vertical displacement, w, is derived froni “U” by imposing a constant volume condition;
is calculated by solving the Lagrangean equation of motion. Tlie mitigative effects of sheet pile wall are taken into account by considering it as an elastic beam with bending stiffness of EpIp. For details, see Kogai et al. (1998). When its distortion is designated by p(z), the strain energy of a wall is derived by integrating EpIp(d2p/dz’)2/2 from the bottom to the top of a wall. This energy is combined with the potential energy of surrounding soil and facilitates the calculation of displacement. The interaction between a sheet pile wall and soil is accounted for by volume consistency;
which means that volume flux of liquefied sand (left-hand side) is equal to the volume of void opened by lateral deflection of a wall.
8 EXAMPLE ANALYSIS ON SUBSIDENCE OF EMBANKMENT which is valid for undrained deformation. When consolidation settlement is interested in, it can be calculated separately and added to “w” in Eq.2. Integration of Eq.2 gives the vertical displacement as a function of “F” Sasaki et al. (1 992) revealed that a surface dry layer of soil, if any, nioves together with the liquefied subsoil. Hence, both horizontal and vertical displacements in the surface layer and the subsoil are expressed bq F(x). The value of “F“ after large deformation is derived by the principle of’ iiiiniinum potential energy; a search is made of F(x) that minimizes the energy. The time history of F(x)
Change of surface elevation
Tlie section presents two examples of calculation which were conducted by using the theory in the previous section. The first example concerns with a collapse of Shiribeshi-Toshibetsu river dike during the 1993 Hokkaido-Nansei-Oki earthquake. The data required for the analysis consists of configuration of ground, thickness of liquefied layer, unit weight of soil, and the elasticity modulus of dike and surface unliquefied crust. All of them are available from conventional liquefaction site investigation: no need for laboratory tests on undisturbed specimens. When tension occurs, moreover, the elastic modulus is reduced to zero and its precise measurement is not necessary. Figure 29 illustrates the distorted configuration of the dike after 30 seconds of flow (duration of strong motion as assessed by the earthquake magnitude). Calculalion ol liquelac Iton-Induced delormollon R w e r No I
/bysu-loshlDeiru
Landside U
Om
Fig.28 Idealization of displacement,
. ... .~ ..- ._..
....
I
50m
~
1 L-
orayioGiop [30"], and S 2 [1.2] for smaller slope angles. c) Presence of a looser surface layer. In the presence of a looser surface layer more than [5] m thick, the smallest S value given in (a) and (b) should be increased by at least [20%], in accordance with 4.2.2. ( 5 ) Part 1-1 of Eurocode 8. d) Spatial variation of amplification factor. The value of S can be assumed to decrease as a linear function of height above the base of the cliff or ridge, and to become unity at the base. 2.8
Basin Edge Effects
Evidence from recorded strong motion data indicates that ground motions may be large at the edges of fault controlled basins. For example, strong motion recordings in the Santa Monica area from the 1994 Northridge earthquake are characterised by large amplitudes and durations of shaking. In this region, the basin edge geology is controlled by the active strand of the westward striking Santa Monica fault. Despite having similar surface geology, sites to the north of the fault show relatively modest amplitudes, whereas sites to the south of the fault exhibit significantly larger amplitudes, with a clear and immediate increase in amplification occurring at the fault scarp. Graves et al. (1998) used 2D and 3D finite difference ground motion simulations to investigate the significance of the basin-edge structure (Somerville, 1998). Similar effects were noted in the Fraser Delta of British Columbia during the 1966 Duvall earthquake (Finn et al., 1998~). Depths to tertiary bedrock in the Delta range from about 20 m to 700 m. Weak motion amplifications were greatest at the edge of the delta.
3 SOIL EFFECTS UBC (1997) and Eurocode 8 take site conditions into account by defining a limited number of site classes and associating an amplification factor with
each category. categories: 3.1
Eurocode
8 uses three
soil
Subsoil Class A
Rock or other geological formation characterised by a shear wave velocity vs of at least 800 m/s, including at most, 5 m of weaker material at the surface. Stiff deposits of sand, gravel or overconsolidated clay, up to several tens of metres thick, characterised by a gradual increase of the mechanical properties with depth (and by v, values of a least 400 m / s at a depth of 10 m). 3.2
Subsoil Class B
Deep deposits of medium-dense sand, gravel or medium-stiff clays with thickness from several tens to many hundreds of metres, characterised by minimum values of vs increasing from 200 m / s at a depth of 10 m, to 350 m/s at a depth of 50 m. 3.3
Subsoil Class C
Loose cohesionless soil deposits with or without some soft cohesive layers, characterised by vs values below 200 m/s in the uppermost 20 m. Deposits with predominant soft-to-medium stiff cohesive soils, characterised by vs values below 200 m/s in the uppermost 20 m. The modifications to the basic design spectrum in Fig. 1 for the different soil categories is accomplished by shifting the defining periods TB, Tc, and TD and assigning a value of 0.9 to S for Subsoil Class C. The period adjustments are given in Table 1. The spectra for the different sub-soil classes are shown in Fig. 3. Table 1. Values of the Parameters Describing the Elastic Response Spectrum.
I A
Sub-Soil Class B
I C
These spectra are very similar to those proposed by Seed and Idriss (1982). The Eurocode site factors rely primarily on soil description with some limited application of shear wave velocity for identification purposes. UBC (1997) uses more sharply defined soil classes based on either the average shear wave velocity in the top 30 or the
1094
Fig. 3. Site dependent spectra for Eurocode 8 soil categories. average ( N I ) ~or~ the average undrained shear strength for clays. The UBC (1997) soil profile types are given in Table 2. The UBC (1997) has different spectral modification factors for the acceleration and velocity parts of the spectrum, and these factors are dependent on the intensity of shaking. These factors are based on evaluation of data from past earthquakes and extensive analyses. The spectral modification factors in UBC (1997) are equivalent to the amplification factors given in Tables 3 and 4. 3.4
Selection of Ground Motions
Eurocode 8 includes many clauses describing how appropriate ground motions may be selected for time history analysis. Appropriate time histories are essential for evaluating the performance of buildings during an earthquake. When a building enters the damage regime, the motion becomes nonlinear and the theoretical basis for spectral design using mode superposition is no longer appropriate. It is currently fashionable to develop spectrum compatible time histories. This development entails the modification of a time history so that its response spectrum matches within a prescribed tolerance level, the target design spectrum. In such matching it is important to retain the phase characteristics of the selected ground motion time history. Many of the techniques used to develop compatible motions do not retain the phase. Abrahamson (1993) has developed an approach that does preserve the phasing of the original record. The response spectrum alone does not adequately characterise near-fault ground motion. This motion is usually characterised by a long period pulse of strong motion of a fairly brief duration rather than the stochastic process of long duration that characterises more distant ground
motions. Spectrum compatible motions will not have this characteristic unless the basic motion being modified to ensure compatibility has forward directivity effects included. Spectral compatible motions match the entire spectrum within a prescribed tolerance. No real earthquake ground motions will do this. It has been common in the seismic design of critical structures to select representative earthquakes in the nearfield, intermediate-field and far-field with a view to exploring the full range of spectral response in the structure. However, when spectral compatible motions are used all periods are subjected to the full design seismic action. Some designers (Naeim and Lew, 1995) on the basis of nonlinear analysis of structures have expressed the view that these spectrum compatible motions should not be used for damage assessment because they give exaggerated estimates of displacement demand and energy input. Appropriate representative recorded earthquake motions are preferable. In most existing attenuation relationships there is no explicit recognition of directivity effects. These effects tend to contribute to some of the substantial deviations from the median ground motions. If the probabilistic response spectrum is based on median ground motions, then it likely represents average directivity conditions. If the response is based on the mean plus one standard deviation, then it approximates forward directivity conditions and many of the time histories used should have forward directivity characteristics (Somerville, 1998). One of the difficulties with designs based on spectra is determining what are the appropriate scenario earthquakes for selecting appropriate recorded ground motions for nonlinear analyses or for conducting liquefaction analyses. The probabilistic response spectrum represents the aggregated contribution of a range of earthquake magnitudes on different faults and seismic zones at various distances from the site, and also includes the effect of random variability for a given magnitude and distance. Appropriate earthquakes can be determined using a procedure proposed by McGuire (1995) which deaggregates the contributions to the spectrum by magnitude, distance and the parameter E that, for the deaggregated magnitude and distance, defines the number of standard deviations above or below the median ground motion level that is required to match the probabilistic spectrum. 3.5
Orientation of Near-Fault Time Histories
In the near-fault region, the horizontal ground motion in the direction perpendicular to the fault strike is significantly larger than the horizontal component parallel to the fault strike at periods longer than about 0.5 second. Since fault strike is
1095
Table 2. Soil Profile Types.
Soil Profile Type
Soil Profile NamdGeneric Description
SB
Hard rock Rock
SC
Very dense soil and soft rock
SD
Stiff soil
SE' SF
Soft soil profile
SA
Average Soil Properties for top 100 ft (30,480 mm) of Soil Profile Shearwave I Standard Penetration I Undrained Velocity, Vs ft/s Test, N (for NCHfor Shear Strength, ( d S > Cohesionless Soil Layers S, psf (kPa) (blows/ft) > 5,000 (1,500) ----2.500 to 5,000 (760 to 1,500) 1,200 to 2,500 > 50 > 2,000 (100) (360 to 760) 1,000 to 2,000 15 to 50 600 to 1,200 (50 to 100) (180 to 360) < 600 (180) < 15 < 1,000 (50)
'Soil Profile Type SE also includes any soil profile with more than l o f t (3048 mm) of soft clay deJined as a soil with a plasticity index, PI 20, w,,, 2 40 percent and s,, < 500 psf (24 kPa). The Plasticity Index, PA and the moisture content, w,,,,, shall be determined in accordance with approved national standards. Table 3. Fa as a Function of Site Class and Earthquake Spectral Acceleration, S,, at 0.2 Second.
I
I
Spectral Response Acceleration at Short Periods S,10.25 S,=0.5 1 Ss=0.75 Ss=l.OO S,il.25 0.8 0.8 I 0.8 0.8 0.8 A B 1.0 1.0 1.0 1.0 1.0 c 1.2 1.1 1.2 1.0 1.0 D 1.4 1.2 1.1 1.0 1.6 E 1.7 2.5 1.2 0.9 ( >' F ( 1' ( 1' ( 1' ( 1' ( 1' N S : Use straight line interpolation for intermediate values of s,. 'Site-spec@ geotechnical investigation and dynamic site response analyses shall be performed. Site Class
Table 4. F, as a Function of Site Class and Spectral Acceleration, S, at 1 Second Period. Site Class
Spectral Response Acceleration at Short Periods S,
