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Site response at Treasure Island

D. Roy", S. Sharma&

"Department of Civil Engineering, University of

British Columbia, Vancouver, Canada

^Department of Civil Engineering, University of

Moscow, 7D <93& , (75V1

ABSTRACT

The reliability of site response analysis procedures is assessed in terms of strengthsand weaknesses of the available models. The site response analysis was performedfor Treasure Island, in San Fracisco Bay, using the procedures incorporated incomputer programs CHARSOIL (Streeter, et al. [1]), MASH (Martin and Seed [2])and SHAKE (Schnabel, et al. [3]). The base motion for this site was estimated fromthe nearby rock-site at Yerba Buena Island as recorded during the 1989 Loma Prietaearthquake. The computed peak horizontal accelerations compared well with therecorded data but the peak spectral accelerations were underestimated. The porewater pressure computation predicted liquefaction for the event.

INTRODUCTION

During an earthquake, ground motions generated at the surface of soil deposits areconsiderably different from the motions that may occur on outcropping bedrock. Thisdifference is attributed to the impedance contrast between the softer, upper soil layersand the relatively harder, underlying base rock layer. If ground motions are to beestimated at soft-soil sites, a site response analysis is performed to investigate thepropagation of seismic waves from the base-rock level to the surface of the soilprofile. For such analyses, the soil profile is either idealized as an assemblage oflumped masses, springs and dash-pots, or it is viewed as a combination of layers ofviscoelastic media. Typically, the response is calculated using a one-dimensionalanalysis that assumes that the incoming seismic energy can be reasonably modeled byvertically propagating shear waves.

As the earthquake loading can be viewed as a uni-dimensional propagation ofsimple shear disturbance through the profile, the soil model need to reliably simulatethe shear stress-strain characteristics of soil. In a cyclic loading scenario, the shearstress-shear strain characteristic in virgin loading is usually simulated by closed formmathematical functions. The Davidenkov, and Ramberg-Osgood can be cited asexamples of shear stress-shear strain model which have been implemented incomputational procedures. The unload-reload behavior of soils are simulated byempirical schemes proposed by Masing. This scheme, commonly known as theMas ing rule, obtains the unload reload curve from a given virgin loading curve by

Transactions on the Built Environment vol 3, © 1993 WIT Press, www.witpress.com, ISSN 1743-3509

62 Soil Dynamics and Earthquake Engineering

scaling the virgin loading curve by a factor 2. It has been demonstrated that althoughthe simulation of the actual soil behavior in simple shear under virgin loading by themethods mentioned above is quite accurate, the simulation of soil unload-reloadbehavior is often unsatisfactory (Roy and Sharma [4]; Ishihara [5]).

CALIBRATION OF COMPUTATIONAL PROCEDURES

For the assessment of their overall performance, a calibration of the analytical toolsis necessary. In such an exercise the input excitation and the consequent site responseshould be known for a given site so that the computed site response can be comparedwith the actual recorded motion. In this paper, calibration of a three computerprograms is undertaken for the Treasure Island site near San Francisco for the LomaPrieta event of 1989. The base motion for this soft soil site can be estimated from themotion recorded at the nearby rocksite of Yerba Buena Island situated in the SanFrancisco Bay. Variability due to dissimilar propagation paths to the rock and softsoil sites is eliminated in this case due to the fact that both these sites are situatedalmost in the same azimuth and distance (62 ± 0.75 miles) with reference to the eventepicenter (Darragh and Shakal [6]).

Figure 1 Treasure Island and Yerba Buena Island (after Housner [8])

Treasure Island is a man made Island (Figure 1) constructed on a shoal northof the rocky outcrop which forms Yerba Buena Island. The soil profiles at these sitesare shown in Figure 2 (Gibbs, et al. [7]). The top 36 feet at Yerba Buena Islandprimarily consist of deeply to moderately weathered sandstone (minimum shear wavevelocity of 850 feet per second) and so a competent stratum was assumed at a depthof 36 feet. The stratum below this depth is characterized by a shear wave velocity of


Soil Dynamics and Earthquake Engineering 63

TREASURE ISLAND

45

Gravelly Sand (V,- 823 fps)WTd 13ft depthLoose Sand (V,- 442 fps)Loose Silty Sand (V,- 560 fps)

Hotocene Bay Mud (V, - 670 fps)

Dense Fine/Silty Sand(V,-1035 fps)

Pleistocene Bay Mud(V,-870 fps)

Fine Gravelly Sand and Stiff OC Clay(V,-1248 fps)

-Shale and Sandstone(V,-2135 fps)

Figure 2 Soil profile at Treasure Island

YERBA BUENA ISLAND

Gravelly Sand (V,-1250 fps)

Deeply Weathered Sandstone(V,-850 fps)

2613ft depth

Moderately Weathered Sandstone(V,-1250 fps)

_ Moderately WeatheredSandstone (V,- 2240 fps)

NOTE

Depths are in feetfps: feet per second

2240 feet per second while the shear wave velocity in the overlying layer ofmoderately weathered sandstone is 1250 feet per second.

DESCRIPTION OF THE EVENT

The Loma Prieta earthquake of October 17, 1989 has been ascribed to a lateral anda vertical movement of the San Andreas fault (Housner, et al. [8]). The earthquakehad a surface wave magnitude, M,, of 7.1 and a focal depth of 11.5 miles. Thecorrected peak horizontal accelerations in the east-west direction (Figure 3) were0.067g at Yerba Buena and 0.159g at Treasure Island during the Loma Prietamainshock (California Div. of Mines and Geol. Report No. OSMS 89-08). Figure4 illustrates a comparison of the corresponding spectral accelerations for a dampingratio of five percent. The shape of these response spectra are similar but the peakcorresponding to a period of about 0.3 second is not discernible in the responsespectra of Yerba Buena record. Given the fact that all other conditions were similarat Yerba Buena and the Treasure Island sites for the Loma Prieta event, theamplification of ground motion at Treasure Island can be attributed to the deep softsoil deposit at this location. A widespread occurrence of ground failure due toliquefaction was observed at Treasure Island whereas no such ground failure wasreported at Yerba Buena.

The peak horizontal accelerations in the N-S direction at Treasure Island andYerba Buena were O.lOOg and 0.029g, respectively. The recorded peak verticalaccelerations were 0.028g at Yerba Buena Island and a smaller value of 0.016g atTreasure Island. Given the fact that the magnitudes of these accelerations were



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10 15Tim* — seconds

Figure 3 Ground Motion Time Histories (Housner [8])

0.80 -|

Yerba Buena - SurfaceTreasure Island — Surface

0.000.00 t.OO 2.00 3.00

Period, sec4.00 5.00

Figure 4 Response Spectra (5 % damping ratio) for the corrected E-Waccelerograms recorded at Treasure Island and Yerba Buena Island.

substantially lower than the corresponding ones in the east-west direction, the east-west accelerograms were used in the site response analysis, liquefaction potentialevaluation exercise, and for comparison of the computed results with the actualrecorded motion.



METHODOLOGY

The base-rock motions at Yerba Buena and Treasure Island can be expected to be verysimilar. Thus if the base-rock motion at Yerba Buena can be ascertained, it wouldform an ideal input for the Treasure Island profile. The base motion at Yerba BuenaIsland can be found from a deconvolution of the motions recorded at the surface tothe assumed competent layer below 36 feet depth. Due to the proximity of the twosites, the deconvoluted base motion obtained may then be applied without attenuationto the base of the soil profile of the Treasure Island site for solving the site responseproblem.

INPUT SOIL PROPERTIES

For cohesive strata such as the holocene and pleistocene bay muds in the soil profileof Treasure Island, the undrained shear strength under direct shear condition, s% &.,is a required input parameter. This parameter can be inferred from the in-situ vaneshear data available for the nearby Marina district (Mitchell et al. [9]). Alternatively,for the normally consolidated holocene bay mud a c-p ratio of 0.25 can be used (Laddet al. [10]). For overconsolidated clays the range of values for G /s suggestedby Weiler [11] were used for determining s^. Table 1 summarizes the values of thisparameter obtained from alternate means. Since the predicted undrained shearstrength for the pleistocene bay mud was much higher than the range of valuesgenerally assumed acceptable, a value of 3000 psf was assumed for this type of soil.Other input soil properties have been summarized in Table 2 and Table 3.

Table 1 Undrained Shear Strength for Plastic Bay Muds

Soil Type

Holocenebay mud

Pleistocenebay mud

Depth,feet

44.3

69.4

94.4

136.0to

247.4

STJ tor van**pcf"»

764

1034.8

1105.0

Noinforma-

tion

IP, %

40

range:22 to58

A

0.85

Su,pcf:co!2*co!4

649.0

879.5

939.3

Su<w,pcf"

738.0

1048.6

1359.2

Sud^PCf

5210.45

Note:1. Using values obtained from HSA 17 and B-5A (boreholes).2. Using c-p ratio of 0.253. Using G /s value of 520 suggested for OCR equals 2 (Weiler, [11]).


Soil Dynamics and Earthquake Engineering

Table 2 Soil Properties at Yerba Buena Island

Soil Type BetweenDepths in ft.

Gravelly Sand: 0 to 3

Deeply WeatheredSandstone: 3 to 10

ModeratelyWeatheredSandstone

10 to36

Below36

Class"

SW

D,, %

90

Gmax

0.5

^ mm

0.23

Y, pcf

/dry =120

Kdry =115

K.« =125

K.t =130

v,, fps

1254

849

1254

2239

DECONVOLUTION USING SHAKE

This computer program incorporates an equivalent linear solution technique and solvesthe shear wave propagation problem in the frequency domain. This program is oneof the earliest of the site response analysis procedures and due to its simplicity fromthe point of view of the user, it is one of the most popular tools. The soil propertiesused in this analysis are given in Table 4.

The peak ground acceleration of the motion recorded at the rock site of theYerba Buena Island for the Loma Prieta event was 0.061g (channel 1: 90 degree,CSMIP accelerogram). Upon deconvolution, this gave a motion which had a peakacceleration of 0.0599g at the base of the Yerba Buena recording site at 36 feet depth.This motion was subsequently applied as base motion for Treasure Island to obtainestimates of site response using several computer programs detailed below.

SITE RESPONSE COMPUTATION USING SHAKE

SHAKE was used again to solve for the site response at Treasure Island. The peakhorizontal acceleration computed in this analysis was 0.122g (as opposed to actual of0.159g) at 11.98 seconds (actual: 13.60 seconds). Given that this analysis was carriedout in terms of total stresses, the underestimation of peak horizontal acceleration canbe considered significant. The response spectra for the computed and the correctedactual ground motions can be found in Figure 5. This comparison reveals a goodsimilarity between these results and the actual ground motion. However, at periodsless than 0.8 seconds, SHAKE underestimated response by margins as high as 50percent.

The main difficulty with this program lies in the fact that it can onlyaccommodate three types of variation of shear modulus and damping ratio with shearstrain. This creates an unrealistic constraint. In other words, SHAKE requires thedegradation and damping characteristics for all clays sands and rocks to be modelledin the same way. Another well recognized problem with this program is that it can



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Soil Dynamics and Earthquake Engineering

Table 4 Input Data for Deconvolution problem

Shear modulus degradation of gravelly soil (soil type 2): Seedet. al. 1986Y,K.

% .000192.0

.000387.2

.00173.4

.00366.4

.0149.5

0.0333.4

.119.1

Damping of gravelly soil: Seed et. al. 1986Y, % .003 .01 .03 .1 .3 1.0f, % 2.0 5.9 10.5 14.5 18.0 21.0

Shear modulus degradation of rock averagey, % .0001 .0003 .001 .003 .01 .03K, 2000. 2000. 1975. 1905. 1800. 1620.

.38.5

10.025.0

1.04.2

.11450.

1.01100.

Damping in rock averageY, % .0001 .001 .01 .1f, % .4 .8 1.5 3.0

Yerba Buena Island: Number of layers

1.04.6

LayerNo.

Soiltype<"

No. of Thickness Unit wt Shear wave Shear Modsublayers ft. kef velocity factor

fps

3.07.03.07.07.09.0

0.1200.1150.1250.1250.1250.1250.130

1254.0823.01254.01254.01254.01254.02239.0

1.0000.8491.2541.2541.2541.254

Note: Soil type 2 is gravelly sand and soil type 3 is sandstone.

0.80

0.60

Actual ground motionSHAKE

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.<0.00

Figure 5 Comparison of actual and SHAKE spectral accelerations



perform the analysis only in terms of total stresses. Further, the assumption that theeffective strain can be approximated a fixed fraction of the maximum strain amplitudemay not accurately simulate the actual earthquake conditions.

RESPONSE COMPUTATION USING CHARSOIL

CHARSOIL is one of the earliest programs that incorporated a nonlinear soil modelfor response analysis [1]. This method transforms the partial differential equation ofvertical shear wave propagation into an ordinary differential equation using themethod of characteristics, which are then solved numerically. The Ramberg-Osgoodmodel together with Masing rule is utilized to model the nonlinear soil stress-strainbehavior. As CHARSOIL requires a velocity time history as the input motion ofexcitation, the base motion obtained from the solution of the deconvolution problemin the preceding section could not be directly applied at the base of the TreasureIsland site. Instead, the velocity time history recorded at Yerba Buena Island wasscaled by the ratio of the deconvoluted peak horizontal acceleration and the peakground surface acceleration at Yerba Buena. This motion was then applied at the baseof the Treasure Island site.

For obtaining the Ramberg-Osgood parameters r and a, a least square fittingprocedure (Roy [12]) was used for each soil stratum. These parameters were thenweighted using the layer depths to obtain a single set of input values, r and a, asrequired in this program. This stipulation of a single set of Ramberg-Osgoodparameters cannot be expected to give a good simulation of degradation of shearmoduli with shear strain for the entire profile. A parameter, E,, was introduced tolimit the error arising out of the adopted numerical integration scheme [13].Interestingly, the computed maximum horizontal ground acceleration as well as thetime of these maxima were found to be quite sensitive to the choice of number of soillayers. Depending on the choice of the number of soil layers, the estimate of peakhorizontal acceleration varied from 0.13g (for 14 layers) to 0.21g (for 18 layers).Due to the existence of an apparent numerical stability in the estimated peakhorizontal acceleration where 15 - 17 layers (Table 5) were used, an peak value of0.1719g was selected for comparison. These results compare well with the recordedvalue of 0.159g and the estimated time of the maximum amplitude agreed well withthe actual data (13.60 seconds).

Table 5 CHARSOIL response variation for different number of soil layers

MaximumAcceleration, g

Time of maximumAcceleration, sec.

Number of soil layers used in computation

18

0.2063

8.285

17

0.1796

4.155

16

0.1719

7.662

15

0.1643

8.272

14

0.1293

4.165



Figure 6 shows the response spectra for the actual and computed groundmotions. The overall fluctuations of amplitude as a function of frequency arecaptured but the amplitudes are overestimated by as much as 50 percent for periodsup to 1 second. In the period range of 1 and 1.5 seconds, the agreement is generallyvery good.

0.80

0.60

'•§ O'+o

o20.20

0.000.00 0.50 1.00

Period, sec.5.00

Figure 6 Comparison of actual and CHARSOlL spectral accelerations

TOTAL STRESS SITE RESPONSE ANALYSIS USING MASH

The deconvoluted motion obtained earlier was applied at the base of the profile of theTreasure Island site and the site response problem was solved using the computerprogram MASH in terms of total stresses. The model parameters were once againobtained from using the least square technique mentioned earlier. The inputparameter, FACT, was evaluated from the knowledge of the shear wave velocity(Table 1). The response spectra of the computed motion matches the corrected actualmotion (Figure 7) reasonably. However, the response of a simple oscillator for the

0.80Actual ground motionMASH - Total Stress

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.000.00

Figure 7 Comparison of actual and MASH spectral accelerations



motion computed by MASH is lower than actual for periods in the range 0.25 to 0.7seconds whereas it is markedly higher for periods between 1.2 and 1.8 seconds. Thecomputed peak horizontal acceleration and the time of this maximum, 0.174g and11.96 seconds, compare well with actual (0.159g and 13.60 seconds).

Although the results of this program compare well with recorded motion, thesoil stress-strain model as implemented in this program has drawn criticism(Henderson et al. [14]). In

illustrateportion of the ,J Soil UocW of UASH

— Backbone Curve

order to illustrate theproblem, a portion of thestress-strain history ofelement 2 of the soil columnused in the analysis wasexamined as shown in Figure8. In this figure, theunloading curves AB and CDhave different shear moduliat B. This leads to anunrealistic simulation ofmaterial behavior as CD failsto approach the extension ofAB smoothly. Further,contrary to the generalunderstanding (Ishibashi andZhang [15]), MASH assumesthe shear modulus to beindependent of the meaneffective confining pressurefor clays.

0.20 -

0.10

0.00

5-0.10-

-OJO-

-OJO-0.15 -0.05 0.05 0.15

Shear Strain, percent0.25

Figure 8 Stress-strain loop for element 2computed by MASH (A =1.03, B = 0.45,7o = 0.00045, G_ = 637 ksf)

EFFECTIVE STRESS ANALYSIS USING MASH AND APOLLO

Shear stress time histories obtained from total stress site response analysis usingMASH were utilized to calculate the numbers of equivalent significant cycles forindividual soil layers in the profile. These were then used as input for the computerprogram APOLLO (Martin and Seed [16]) to compute the pore water pressureresponse and the water table rise time history. The computer program MASH wasthen employed again for an effective stress site response analysis using the resultsobtained from APOLLO.

Evaluation of Liquefaction Potential Using APOLLO

This program computes the pore water pressure generated by the dynamic loading andpossible dissipation. It was used to investigate whether the widespread report ofliquefaction at Treasure Island could be predicted reliably. Incidentally, the modelupon which this program is based can probably be stated to be the most popular ofthe presently available models of generation and dissipation of pore water pressureunder dynamic loading.



Pore Pressure Rotio

As the undrained cyclic strength for the layers in the profile and the effectivenormalizing pressure to which they are subjected may vary by a wide margin, findinga representative number of equivalent stress cycles for the time history of shaking isvery difficult. To avoid this, the number of equivalent stress cycles for the entireduration of motion was taken to be equal to 11 at r of 0.657 . This value of thenumber of equivalent cycles corresponds to the mean value suggested by Seed [17].As stated earlier, the number of equivalent significant cycles for the layers werecalculated using the shear stress time histories obtained from the total stress analysisperformed by MASH.

For cohesionlesssoils, the cyclic soil strengthwas taken as recommendedin the user's manual ofAPOLLO. The cyclicstrengths for the cohesivesoils were estimateda c c o r d i n g to therecommendation that theliquefaction resistance forsoils with plasticity index of40 is about 50 percent higherthan that of a nonplastic soil(Ishihara [18]). The valuesof nv are as recommended inthe user's manual. Theresults of this analysisindicate liquefaction betweendepths 25 and 45 feet(Figure 9) during the event.There is no evidence ofsecondary liquefaction atshallower depths arisingfrom the upward dissipationof pore water pressure fromdeeper strata after thecessation of event.

50-

100-

150-

Io200-

250-

300

Maxima: 0 to 40 secondsooa Maxima: 40 to GOO seconds

Maxima: 600 to 1800 seconds

Figure 9 Pore pressure ratioscomputed using APOLLO.

The results of this analysis matches the observation of widespread occurrenceof liquefaction in Treasure Island. However, the user faces a number of problems inusing APOLLO. This program idealizes an irregular time history of shaking as aseries of time histories, each characterized by a duration defined by constant rate ofcycling, EQKP, and number of equivalent cycles, NCYCL. It is very difficult toformulate the necessary input for this purpose reliably. In addition, qalthough thestrata may consist of soils with a wide range of properties, but the generation of porewater pressure is assumed to occur at the same time-rate for all layers. This puts anunrealistic limitation on the accuracy of the APOLLO methodology. Some of theseproblems have also been addressed by Chugh and von Thun [19].



Computation of Effective Stress Site Response Using MASH

The earlier input data file for MASH for the total stress site response analysis wasmodified slightly to activate the routines which read and account for reduction ofeffective stress due to generation of pore water pressure under dynamic loading andthe subsequent rise of water table. Also, the data file needs to be appended by theeffective stress information, which essentially provides the program with input suchas the water table rise time history and the effective stress time history, as reportedby an APOLLO analysis. This data can be obtained directly from the correspondingpore water pressure response analysis using APOLLO. The calculated pore waterpressure for soil layers towards the bottom of the profile was negligible and so onlythe effective stress (reduction) time histories for the upper 13 layers were used for theMASH-APOLLO analysis.

In order to simulate the damping associated with the flow of pore water withrespect to the soil solids, a small average damping ratio of 1 percent was used for theprofile. This analysis gave a peak horizontal acceleration of 0.141 g at 11.98 seconds.There was a substantial reduction of the peak horizontal acceleration from thatobtained in the total stress analysis. Given the absorption of energy in generation anddissipation of pore water pressure and the flow of pore water, this was expected. Acomparison of the computed response spectra with the actual (Figure 10) reveals anunderestimation of response between periods 0.5 and 1.0 second and anoverestimation between periods 1.25 second and 1.8 second. For this site there wasonly a minor difference between the response spectra calculated for the effective stressand the total stress analysis using MASH.

-0.40

0.20

Actual ground motionMASH - Effective Stress

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00

Figure 10 Comparison of actual spectral accelerations with those computed by aneffective stress analysis using MASH

CONCLUSIONS

A comparison of the computed ground motion at Treasure Island, Table 5, revealsthat the computer programs CHARSOIL, MASH and SHAKE, failed to capture thepeaks of the actual spectral response corresponding to periods of about 0.35 and 0.8seconds accurately. The corresponding underestimation was about 50 to 70 percent.However, the predicted peak horizontal acceleration for the procedures were within



a reasonable range of accuracy. The pore water pressure response was computedusing APOLLO. It predicted a pore pressure ratio of 100 percent in the loose sandlayers of the Treasure Island soil profile.

Table 6 Comparison of Results of Site Response Analyses

Acceleration, g

Time ofmaximum, sec

ACTUAL

0.1610

13.60

SHAKE

0.1217

11.98

CHARSOIL

0.1719

7.662

MASH

Total

0.1740

11.96

Effective

0.1410

11.98

As has already been mentioned, it is extremely important to model the stress-strain behavior of the stratum accurately in order to arrive at a reliable prediction.Although the three parameter models commonly employed tend to give a good fit tothe virgin stress-strain data, the present techniques of simulating the hystereticbehavior do not imitate experimental data reliably. This may be an important sourceof inaccuracy in the analyses. Since the analyses utilized soil test data reported forsimilar soils from nearby locations, the possibility of mismatch between the predictedand observed ground motion at Treasure Island due to an use of inappropriate test datacan be ignored. Inaccuracy due to numerical approximations can however besignificant. In addition, as pointed out earlier, sometimes the soil models are notimplemented in a consistent manner. The soil model of MASH can be cited as anexample of such an implementation.

It has been pointed out that spectral amplification of ground motion dependson the magnitude of the event (Darragh and Shakal [6]). This makes it necessary tocheck the accuracy of the computational techniques for events with a wide range ofmagnitudes. Evaluations of the procedures are also necessary for various sites withdissimilar soil profiles. Thus, calibration of the computational procedures cannot betreated as complete at this juncture. More recorded data of generation and dissipationof pore water pressure under dynamic loading are also necessary if the models of porewater pressure generation are to be validated for use in liquefaction potential.Unfortunately, very few such records are available at present.

ACKNOWLEDGEMENTS

This study was supported by the National Science Foundation, award number8808131, and the University of Idaho. This support is gratefully acknowledged.

REFERENCES

1. Streeter, V.L., Wylie, E.B. and Richart Jr., F.E. 'CHARSOIL, CharacteristicsMethod Applied to Soils', University of Michigan, Ann Arbor, Michigan 48104,March, 1974.



2 Martin, P.P. and Seed, H.B. 'MASH - A Computer Program for the NonlinearAnalysis of Vertically Propagating Shear Waves in Horizontally LayeredDeposits', Report No. EERC 78/23, University of California, Berkeley,

October, 1978.

3. Schnabel, P.B., Lysmer, J. and Seed, H.B. 'SHAKE: A Computer Program forEarthquake Response Analysis of Horizontally Layered Sites', Report No.UCB/EERC-72/12, December, 1972.

4 Roy, D. and Sharma, S. 'Non-linear Soil Models in Site Response Analysis',Proceedings, 28th Engineering Geology and Geotechnical EngineeringSymposium, Boise, Idaho, 1992, pp. 311-322.

5. Ishihara, K. 'Evaluation of Soil Properties for Use in Earthquake ResponseAnalysis', Numerical Models in Geomechanics, Ed. Dungar, R., Pande, G.N.and Studer, J.A., A.A. Balkema, 1982, pp. 237-259.

6. Darragh, R.B. and Shakal, A.F. 'The Site Response of Two Rock and SoilStation Pairs to Strong and Weak Ground Motion', Bulletin of the SeismologicalSociety of America, Vol. 81, No. 5, October, 1991, pp. 1885-1899.

7. Gibbs, J.F., Fumal, T.E., Boore, D.M. and Joyner, W.B. 'Seismic Velocitiesand Geologic Logs from Borehole Measurements at Seven Strong MotionStations that Recorded the Loma Prieta Earthquake', U.S. Geological SurveyOpen-file Report 92- 287, 1992.

8. Housner, G.W. (Ed), Competing Against Time: Report to Gov. GeorgeDeukmejian from the Governor's Board of Inquiry on the 1989 Loma PrietaEarthquake, May, 1990.

9. Mitchell, J.K., Masood, T., Kayen, R.E. and Seed, R.B. 'Soil Conditions andEarthquake Hazard Mitigation in the Marina District of San Francisco', ReportNo. UCB/EERC-90/08, May, 1990.

10. Ladd, C.C., Foott, R., Ishihara, K., Schlosser, F. and Poulos, H.G. (1977)'Stress Deformation and Strength Characteristics', Proceedings, 9th ICSMFE,Tokyo, Vol. 11, pp. 421-494.

11. Weiler, W. 'Small Strain Shear Modulus of Clay', Earthquake Engineering andSoil Dynamics II - Recent Advance in Ground Motion Evaluation, Ed. vonThun, J.L., Geotechnical Special Publication No. 20, ASCE, 1988, pp. 331-345.

12. Roy, D. 'Site Response and Liquefaction Analysis During Earthquakes', M.S.Thesis, University of Idaho, July, 1992.

13. Wylie, E.B. and Streeter, V.L. 'One Dimensional Soil Transients byCharacteristics', Proceedings, Second International Conferance on NumericalModels in Geomechanics, Blacksburg, VA, Ed. Desai, C.S., June 1976.

14. Henderson, P., Heiderbrecht, A.C., Naumoski, N. and Pappin, J.W. 'SiteResponse Study -Methodology, Calibration and Verification of Computerprograms', McMaster University, Hamilton, Ontario, Canada, EERGReport 89-01, 1990.


76 Soil Dynamics and Earthquake Engineenng

15. Ishibashi I. and Zang, X. 'Unified Dynamic Shear Moduli and Damping Ratiosof Sand and Clay', submitted for publication.

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17. Seed, H.B. 'Soil Liquefaction and Cyclic Mobility Evaluation for Level GroundsDuring Earthquakes', Journal of the Geotechnical Engineering Division, ASCE,Vol. 105, No. GT2, February, 1979, pp. 201-255.

18. Ishihara, K. 'Stability of Natural Deposits During Earthquakes', Proceedingsof the llth International Conferance on Soil Mechanics and FoundationEngineering, San Francisco, 1985, Vol. 1, pp. 321-376.

19. Chugh, A.K. and von Thun, J.L. 'Pore Pressure Analysis for Earthquakes',Canadian Geotechnical Journal, Vol. 22, November, 1985, pp. 466-476.


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