[american society of civil engineers geotechnical earthquake engineering and soil dynamics congress...

Shake-Table Testing and FLAC Modeling ofLiquefaction-Induced Slope Failure and Damage to Buried Pipelines

Lei Qiao1, Chang Yuan2, Masakatsu Miyajima3 and Endi Zhai4

1Assistant Engineer, Geo-Engineering Investigation Institute of Jiangsu Province, China.2President, Geo-Engineering Investigation Institute of Jiangsu Province, China.3Professor, Dept. of Civil Engineering, Kanazawa University, Japan; [email protected] Engineer, Kleinfelder West, Inc., USA; [email protected]

ABSTRACT: This paper presents Shake-Table testing and FLAC numerical modelingof liquefaction-induced large ground lateral movement and settlement, and pipelinebehavior induced by soil movement. A series of laboratory Shake-Table experimentswere performed using a model slope ground and model pipe buried under the crest ofthe slope in a box 1,800 mm long by 600 mm wide by 800 mm high. A typical 2H:1Vslope was prepared with its crest at the center of the box. The model pipe had anoutside diameter of 25 mm and was buried crossing the full box width and 100 mmbelow the crest. The above model ground was repeated for different amplitudes ofinput sine waves varying from 0.1g to 0.25g. Observed and recorded ground failuresincluded lateral spreading and settlement, sand boiling, time histories of excess porewater pressure buildup, input acceleration and model pipe responded acceleration. Theabove experimental cases were modeled using a nonlinear effective-stress modelingapproach with computer code FLAC coupled with a practical-oriented pore pressuremodel based on cyclic stress method by Seed and co-workers (Seed, 1979). Pore waterpressure buildup and dissipation were modeled using alternative stepping of fluidflow-mechanical interaction. The computed ground failures reasonably agree with theobservations in the Shake-Table test. The FLAC modeling further revealed the soilliquefaction mechanism and induced ground deformation and pipe deflection.

INTRODUCTION

Soil Liquefaction during earthquakes has been a subject of continuing research overthe past four decades. Liquefaction-induced ground deformation has caused severedamage to buried pipeline systems during past earthquakes. These permanent lateraldisplacements ranged from few centimeters to 10 meters or more (Bardet et al., 1999).Examples of documented pipeline damages due to liquefaction-induced grounddeformations in terms of lateral spreading and settlement can be found in thereconnaissance reports of major earthquakes.

Geotechnical Earthquake Engineering and Soil Dynamics IV GSP 181 © 2008 ASCE

Copyright ASCE 2008 Geotechnical Earthquake and Engineering and Soil Dynamics IV Congress 2008 Geotechnical Earthquake Engineering and Soil Dynamics IV

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The goal of this research was to better understand the mechanism of liquefactionunderneath a slope and induced ground deformation and pipe deflection. A series oflaboratory Shake-Table experiments were performed using model slope ground andmodel pipe buried under the crest of a typical 2H:1V slope. The above model groundwas repeated for different amplitudes of input sine waves varying from 0.1g to 0.25g.Observed and recorded ground failures included lateral spreading and settlement, sandboiling, time histories of excess pore water pressure buildup, input acceleration andmodel pipe responded acceleration.

The above experimental case was modeled using a nonlinear effective-stressmodeling approach with computer code FLAC coupled with a practical-oriented porepressure model (Dawson et al., 2001) based on cyclic stress method by Seed and co-workers (Seed, 1979). Pore water pressure buildup and dissipation were modeledusing alternative stepping of fluid flow-mechanical interaction. The computed groundfailures were compared with the observed failures in the Shake-Table test. The excesspore water pressures under the top and toe areas of the slope were also compared andthe extent of liquefaction under the slope area was further discussed.

LABORATORY SHAKING TABLE EXPERIMENTS

Test Materials and Test Setup

The Shake-Table experiments used a model slope ground and a model pipe buriedunder the crest of the slope in a box 1,800 mm long by 600 mm wide by 800 mm high.The model ground consisted of 400 mm thick fully-saturated liquefiable No.5 siliconsand made by water-pouring method, overlaid by free-falling 200 mm thick dry No.5silicon sand in a 2H:1V slope with its crest at the center of the box. Figure 1 presents across section of the model ground, locations of pore water pressure gauges, location ofthe model pipe and accelerometer locations. The model pipe had an outside diameter

1800 mm

900 mm 400 mm

400 mm

200 mm

Saturated #5Silicon Sand,Dr=70%

Dry #5 SiliconSand, Dr=72% 100 mm

Φ25 mm

Figure 1 Shake table experimental equipment for the model slope ground and model pipe

PWP1

PWP2

PWP3

PWP4

Location of pore water pressure gauge1800 mm

900 mm 400 mm

400 mm

200 mm

Saturated #5Silicon Sand,Dr=70%

Dry #5 SiliconSand, Dr=72% 100 mm

Φ25 mm

Figure 1 Shake table experimental equipment for the model slope ground and model pipe

PWP1

PWP2

PWP3

PWP4

Location of pore water pressure gauge

80 mm below water

160 mm below water

280 mm below water



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of 25 mm and was buriedcrossing the full box widthand 100 mm below the crest.The above model groundwas repeated for differentamplitudes of horizontalinput sine waves varyingfrom 100 gal (0.1g) to 250gal (0.25g) with a frequencyof 5 Hz. The shaking timeduring each case was 20seconds. Observed andrecorded ground failuresincluded lateral spreadingand settlement, sand boilingduring liquefaction, timehistories of excess porewater pressure buildup,input acceleration and model pipe responded acceleration.

Laboratory testing based on the samples of similarly prepared saturated and dry No.5 silicon sands indicated a relative density of approximate 70% for the saturated sandand 72% for the dry sand. The No. 5 silicon sands are poorly-graded granularmaterials. The distribution of the grain size is shown in Figure 2. The coefficient ofuniformity Cu=D60/D10=0.62/0.33=1.9, where D60 and D10 are the particle sizescorresponding to 60% and 10% finer passing by weight, respectively. The coefficientof curvature Cc=(D30)

2/(D10 x D60) = 0.492 / (0.33 x 0.62) = 1.2, where C30 is theparticle sizes corresponding to 30% finer passing by weight. The coefficient ofuniformity and coefficient of curvature will be used to estimate permeability in thenumerical modeling.

In order to facilitate the observations of lateral spreading uniform grids were markedon the side walls of the sand box, as can be seen from Figure 3. Each grid size is 10cm by 10 cm. Figure 4 shows a close look for the slope portion.

Due to sidewall friction of the sand box and columns used to fix the instruments inthe sand box, soil lateral movements are anticipated to be non-uniform during testing.Therefore, in addition to the meshes marked on the sidewalls, we installed 5 rows by 5columns of small stakes near the crest and toe of the slope. The stake lines lookingfrom one side-wall to the other is defined as rows, and from one end-wall to the otherdefined as columns. 3 rows were arranged at the crest area and the remaining 2 rowswere on the toe area, as shown in Figures 5 and 6, respectively. Each row of stakeswas spaced 10 cm apart, and each stake in a row was 10 cm apart. Row-1 (seeTable 1) was 10 cm from the crest on top of the embankment (dry sand), Row-3 was10 cm from the crest on the slope. Row-2 was just at the crest line. Row-4 was just atthe toe line. Row-5 was 10 cm away from the toe line and on top of the saturated sand.Column-1 and Column-5 were near the sidewalls. Column-3 was in the middle.Column-2 was between Column-1 and Column 3. Column-4 was between Column-3and Column-5. Model pipe was a 2.5 cm diameter PVC pipe with two ends fixed to

0

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0.0010.0100.1001.00010.000100.000PARTICLE SIZE (M M )

PERCENTFINERBYWEIGHT

Figure 2 Grain size distribution of No. 5 silicon sand

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0.0010.0100.1001.00010.000100.000PARTICLE SIZE (M M )

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Figure 2 Grain size distribution of No. 5 silicon sand



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have a simple-support beam boundary condition. A horizontal accelerometer wasfastened on the pipe at the central location, as shown in Figure 7. Also shown inFigure 7 was the saturated portion of the model ground right before dry sand wasplaced.

Figure 3 Test model before shaking Figure 4 A close look of Figure 3

Figure 5 Stakes at top of the slope(used to measure top deformation)

Figure 6 Stakes at toe of the slope(used to measure toe deformation)

Figure 7 Configuration of Model Pipe Figure 8 A side view of 2000 gal post-shaking ground deformation

Figure 3 Test model before shaking Figure 4 A close look of Figure 3

Figure 5 Stakes at top of the slope(used to measure top deformation)

Figure 6 Stakes at toe of the slope(used to measure toe deformation)

Figure 7 Configuration of Model Pipe Figure 8 A side view of 2000 gal post-shaking ground deformation



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Test Results and Observations

The initial planned input motions were 5 Hz 100 gal sine waves for 20 seconds and 5Hz 150 gal sine waves for 20 seconds. These two shaking levels did not result insignificant ground deformation that can be seen by visual observation. The test setupwas repeated for the following two level input motions:

• 5 Hz 200 gal sine wave for 20 seconds• 5 Hz 250 gal sine wave for 20 seconds

The overall model ground performance after shaking was observed at the end ofeach level of input shaking. Figure 8 shows a side view of 200 gal level post shakingground deformations, which compares with the before-shaking side view as shown inFigure 3. It needs to be noted that the photos shown in Figures 3 and 8 were not taken

from the same angle. In addition to these photographs, each stake horizontal andvertical locations before and post shaking were measured using a flexible ruler hangedon a plate that can move on top ofthe sand box.

The measured post-shakinglateral spreads and settlements forthe 200 gal shaking levels arepresented in Tables 1. Thedefinition of rows and columns areprovided in the previous section.The lateral spreads listed in Table1 are plotted in Figure 9. Asanticipated, each row of stakeswas not displaced uniformly, dueto frictions provided by thesidewalls, obstacles of the steelcolumns used to fasten theinstruments and localized failuresdue to sand boils during liquefaction. The movements of stakes in the central column(Column-3) are believed to be the best representatives of the ground deformations.

Liquefaction phenomena, such as sand boiling, were observed during shaking.

Table 1 Observed Ground Deformations after the 200 gal Shaking

LateralSpread

(cm)

Settlement(cm)

LateralSpread

(cm)

Settlement(cm)

LateralSpread

(cm)

Settlement(cm)

LateralSpread

(cm)

Settlement(cm)

LateralSpread

(cm)

Settlement(cm)

Row-1 0.9 2.0 1.0 2.0 1.8 2.0 1.6 2.0 1.7 2.0

Row-2 1.4 2.0 1.7 2.0 1.7 2.0 2.1 2.0 2.1 2.0

Row-3 4.5 5.0 4.7 5.0 6.0 4.8 4.8 5.0 5.0 5.0

Row-4 4.5 1.0 3.5 1.0 3.8 1.0 4.5 1.0 4.0 1.0

Row-5 3.8 N/A 4.3 N/A 4.5 N/A 4.1 N/A 2.4 N/A

Column-3 Column-4 Column-5Column-1 Column-2

Table 1 Observed Ground Deformations after the 200 gal Shaking

LateralSpread

(cm)

Settlement(cm)

LateralSpread

(cm)

Settlement(cm)

LateralSpread

(cm)

Settlement(cm)

LateralSpread

(cm)

Settlement(cm)

LateralSpread

(cm)

Settlement(cm)

Row-1 0.9 2.0 1.0 2.0 1.8 2.0 1.6 2.0 1.7 2.0

Row-2 1.4 2.0 1.7 2.0 1.7 2.0 2.1 2.0 2.1 2.0

Row-3 4.5 5.0 4.7 5.0 6.0 4.8 4.8 5.0 5.0 5.0

Row-4 4.5 1.0 3.5 1.0 3.8 1.0 4.5 1.0 4.0 1.0

Row-5 3.8 N/A 4.3 N/A 4.5 N/A 4.1 N/A 2.4 N/A

Column-3 Column-4 Column-5Column-1 Column-2

Figure 9 Plot of lateral spreads after 250 gal shaking

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Column Number

Lat

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Spre

ad(c

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Row-1 Row-2 Row-3

Row-4 Row-5

Figure 9 Plot of lateral spreads after 250 gal shaking

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1 2 3 4 5

Column Number

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Row-1 Row-2 Row-3

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Significant amount of water occurred above the toe of the slope right after the shaking.The input motions (upper), recorded excess pore water pressures (middle) andresponded accelerations of model pipe (lower) are presented in Figure 10. Hydrostaticpressures were zeroed out before shaking. The locations of PWP1 through PWP4 wereplotted in Figure 1. Sand boiling at the toe areas was observed. Hence, the excess porepressure during sand boiling after about 2 to 4 seconds of shaking reached theeffective overburden pressure, i.e., the excess pore pressure ratio reached unity,indicating the occurrence of complete liquefaction. Under the slope and embankmentareas, no sand boiling occurred. Some portion of the dry sand close to the originalwater level became wet. This rise of moisture might be due to dissipation of porewater pressure upward and capillary phenomena.

FLAC NUMERICAL MODELING AND ANALYSES

Analysis Approach and Model Makeup for FLAC Analyses

FLAC (Itasca, 2006) was used to model the shaking table configuration andliquefaction-induced ground deformation and pipe’s response. Since FLAC is a two-dimensional program, effect of frictions between the model ground and the sidewallsof the sand box will not be modeled. It is believed that soil deformation along thecentral line of the sand box is a good approximation of a plain-strain deformationproblem. The Mohr-Coulomb soil constitutive relationship was used for the modelground. Model pipe was modeled using structural element interacted with soil by non-

Figure 10 Time histories of input motion (200 gal), recorded excess porewater pressures and accelerations of model pipe

-600-400-200

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Acc

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0 2 4 6 8 10 12 14 16 18 20

E.P

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PWP1

PWP2

PWP3

PWP4

-600-400-200

0200400600

0 2 4 6 8 10 12 14 16 18 20Time (s)

Acc

.(ga

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Figure 10 Time histories of input motion (200 gal), recorded excess porewater pressures and accelerations of model pipe

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0200400600

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Acc

.(ga

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linear springs. The pore pressure generation model is a practice-oriented constitutivemodel (Dawson et al., 2001) for performing nonlinear effective-stress analysis ofliquefaction of sands due to earthquake shaking. Pore pressure is generated in responseto shear stress cycles, following the cyclic-stress approach of H.B. Seed (Seed, 1979).However, unlike the standard cyclic-stress approach, pore pressure is generatedincrementally during shaking. Thus, pore-pressure generation is fully integrated withthe dynamic effective-stress analysis. The model requires input as a cyclic-strengthcurve, a plot of the cyclic stress ratio (CSR) versus the number of cycles which wouldcause liquefaction at that stress ratio. The cyclic strength can be adjusted to accountfor an initial static “driving” shear stress acting on horizontal planes using thecorrection factor Kα as described by Seed and Harder (1990). What is actually inputinto the constitutive model is the slope of the Kα versus static-shear-stress-ratio. Thecyclic strength can be adjusted for initial vertical effective stress greater than 1atmosphere pressure, with the variable Kσ as described by Seed and Harder (1990).Again, what is input into the model is the slope of the Kσ versus effective overburdenstress curve.

This static shear stress is typically called initial static “driving” shear stress or “non-zero” static shear stress. The presence of initial static stresses will influenceliquefaction resistance (Zhai et al., 2004). For the problem to be concerned in thisstudy, “non-zero” static shear stresses exist under the slope area.

In the initial static analysis to compute gravity stresses, the base boundary was fixedboth horizontally and vertically and the side boundaries were only fixed horizontally.In the dynamic analysis, the horizontal input acceleration was applied at the baseboundary. The horizontal restraints of the side boundaries were released and replacedby attaching the two sides to force a rigid side boundary condition at both sides. Thehysteretic damping option in FLAC was selected and damping parameters wereobtained by curve-fitting the modulus reduction curve for sand (Seed and Idriss,1970). Input soil and structural parameters are summarized in Table 2.

CSR3 CSR25 CSRlimit

1Dry #5

Silicon Sand1730 34 1.50E+07 0.3 - - - -

2Saturated #5Silicon Sand

2090 33 2.40E+07 0.3 1.3E-04 0.5 0.15 0.15

Pipe Physical Parameters:Elastic Modulus = 2.9E9 Pa; Poisson's ratio = 0.38; Density = 1,039 (kg/m^3)

ShearModulus

(Pa)

Poisson'sRatio

Cyclic Strength ParametersCoefficientof

Permeability(m/s)

SoilLayer

Soil TypeTotal

Density(kg/m^3)

FrictionAngle(deg)

Table 2 Input Soil and Structural Properties

CSR3 CSR25 CSRlimit

1Dry #5

Silicon Sand1730 34 1.50E+07 0.3 - - - -

2Saturated #5Silicon Sand

2090 33 2.40E+07 0.3 1.3E-04 0.5 0.15 0.15

Pipe Physical Parameters:Elastic Modulus = 2.9E9 Pa; Poisson's ratio = 0.38; Density = 1,039 (kg/m^3)

ShearModulus

(Pa)

Poisson'sRatio

Cyclic Strength ParametersCoefficientof

Permeability(m/s)

SoilLayer

Soil TypeTotal

Density(kg/m^3)

FrictionAngle(deg)

Table 2 Input Soil and Structural Properties



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Analysis Results

Contours of the end-of-shaking excess pore pressure ratios are presented inFigure 11. The excess pore pressure ratio is the ratio between excess pore waterpressure and the effective overburden pressure. If it reaches unity, completeliquefaction would occur. This often results in sand boiling if it occurs at a shallowdepth. It can be observed from Figure 11 that the degree of liquefaction was not

FLAC (Version 5.00)

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Static water pressures at adepths of about 28 cm, 16cm and 8 cm, respectively,from water table.

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Figure 11 Contour of excess pore water pressure ratios andsoil/pipe displacements after 200 gal shaking

Figure 12 Time histories of excess pore water pressures duringthe first 5 seconds of 200 gal shaking

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uniform within the soil profile. While close-to-complete liquefaction occurred at thetoe areas, there was a portion under the crest close to the interface between thesaturated sand and the dry sand to have excess pore pressure ratios close to zero,indicating little liquefaction had occurred. The deformed shape after shaking ispresented also in Figure 11. The steep displacement between the left wall and the toemay be due to limitation of the sand-box wall. In the laboratory shaking table tests,such steep displacement may not be observable because the upward dissipated porewater will erode the sand before it reaches the maximum displacement. Time historiesof pore water pressures at depths of 8 cm, 16 cm and 28 cm from the water table underboth the top (izone number=15 in FLAC mesh) and the toe (izone number=8) weresaved and plotted in Figure 12.

The majority of soil horizontal displacements range from approximately 3 cm to 8cm in the slope area. These values are on the same orders compared with the observedhorizontal displacements during the laboratory shaking table test as presented inTable 1. The upper slope and embankment settled 2 to 3 cm. The down slope and thearea between the toe and the left wall moved upward. The computed amount ofupward movement (heave) ranged from about 4 to 7 cm. The observed toe area heavein the centerline of the sand box was not available. The maximum displacement vectorof 20 cm (containing both horizontal and vertical movements) is larger than theobserved maximum value. It is believed that actual difference between the computedand the observed would be less because extensive sand boiling occurred duringshaking that might erode upward displaced sand.

Both the laboratory testing and the numerical modeling indicated that the area underthe crest and near the interface of the saturated and the dry sands appeared to havelittle buildup of excess pore pressure. The maximum measured value at PWP1 (SeeFigure 1) was close to zero and the maximum calculated value is about 1.0 kPa (equalto about 0.2 excess pore pressure ratio, indicating little liquefaction). The maximummeasured value at PWP2 was about 1.5 kPa, compared reasonably well with thecalculated value of about 1.7 kPa. The maximum measured value at PWP3 was about1 kPa; however, the maximum calculated value was about 2.5 kPa. The maximummeasured value at PWP4 was about 0.6 kPa, compared with the calculated value ofabout 0.8 kPa (the calculated excess pore pressure ratio is about 0.7.) Overall, boththe measured and calculated pore water pressure values showed lower excess porewater pressure ratios at PWP1 location and higher ratios at PWP3 and PWP4, whichagreed with what was observed based on soil boiling during shaking.

As shown in Figure 11, the maximum calculated pipe deflection is about 4.0 cm,caused by permanent ground deformation. Since the numerical model was only a 2-Dplain-strain model, it could not simulate the fixed end conditions used in the shake-table test. Therefore, a direct comparison is not available.

CONCLUDING REMARKS

Laboratory shake-table testing and numerical modeling were performed to reveal themechanism of liquefaction-induced large ground deformation and failures, anddamage to buried pipelines. The computed results reasonably agreed with the shake-table testing results, suggesting that the FLAC nonlinear effective-stress model



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coupled with the cyclic-stress-based pore pressure model can fairly predictliquefaction-induced lateral spreading and damage to buried structures. The observedand computed excess pore water pressures suggested that the extent of liquefactionunder the slope was not uniform and little liquefaction had occurred under the top-of-slope close to the toe elevation while nearly complete liquefaction occurred at the toearea at a shallower depth. It appears that a retrofit using a non-liquefiable key at thetoe area could greatly increase the factor of safety against sliding and lateral spreadingresulted from liquefaction.

It is desired that the same test be repeated in a centrifuge testing facility to simulategreater overburden stress condition and with a laminated sand box to minimize effectsfrom the rigid sand box.

ACKNOWLEDGMENTS

Dr. Hong Sun of Kanazawa University is highly appreciated for her help in setting upthe test plan and equipment during the shake-table tests.

REFERENCES

Bardet, J.P., N. Mace and T. Tobita, (1999). “Liquefaction-induced grounddeformation and failure,” A Report to PEER/PG&E, Task 4A – Phase 1, May.

Dawson, E. M., W. H. Roth, S. Nesarajah, G. Bureau and C. A. Davis, 2001. Apractice oriented pore-pressure generation model, Proceedings of the 2ndInternational FLAC Conference, Lyon, France, 47-54.

Itasca Consulting Group, Inc., (2006). “FLAC – Fast Lagrangian analysis of continua,user’s manual.”

Seed, H.B., (1979). “Soil liquefaction and cyclic mobility evaluation for level groundduring earthquakes.” Journal of the Geotechnical Engineering Division, ASCE,105(GT2), 201-255.

Seed, R.B. and L.F. Harder, (1990). “SPT-based analysis of cyclic pore-pressuregeneration and undrained residual strength.” Proceedings, H.B. Seed MemorialSymposium, UC Berkeley, Vol. 2, 351-376.

Seed, H.B. and I.M. Idriss, (1970). “Soil moduli and damping factors for dynamicresponse analysis.” Report No. EERC 70-10, University of California, Berkeley,December.

Zhai,E., K. Bhushan and M. Miyajima, (2004). “Tiggering of liquefaction under non-zero static driving shear stress.” Proceedings of the 11th International Conferenceon Soil Dynamics & Earthquake Engineering/the 3rd International Conference onEarthquake Geotechnical Engineering, pp. 589-596. January.



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