Centrifuge validation of a numerical model for dynamic soil liquefaction

Soil Dynamics and Earthquake Engineering 12 (1993) 73-90

Centrifuge validation of a numerical model for dynamic soil liquefaction

Radu Popescu & Jean H. Prevost* Department of Civil Engineering and Operations Research, Princeton University, Princeton, New Jersey 08544, USA

(Received 25 November 1992; accepted 30 November 1992)

The validation of a numerical model based on multiyield plasticity theory is presented. The validation is performed by using a series of centrifuge model soil tests performed by two centrifuge laboratories within the context of the VELACS (verification of liquefaction analysis by centrifuge studies) project sponsored by NSF. The constitutive soil parameters are evaluated based on the results of conventional laboratory soil tests performed by the Earth Technology Corporation, and by empirical correlation formulae available in the literature. The parameter identification procedure is explained in detail, and a unique set of constitutive parameters is used throughout the numerical simulations. Three centrifuge soil experiments performed at Princeton University and Cambridge University are selected for the numerical analysis and validation of the proposed procedures.

1 INTRODUCTION

The VELACS (verification of liquefaction analysis by centrifuge studies) project is a coordinated NSF- sponsored geotechnical centrifuge study of earthquake- like loading on a variety of soil models, aimed at studying the mechanisms of soil liquefaction-induced failure and at acquiring data for the verification of various analysis procedures for liquefaction problems. Nine centrifuge models have been proposed and are to be performed at a number of universities in the US and the UK. One of the objectives of the project is 'to use various numerical procedures for the analysis of the behaviour of the centrifuge model tests in order to verify the accuracy of currently available analytical procedures'. This is the objective of the 'Class A predictions' phase, which includes a-priori predictions in which the relevant experiments are not performed until the computations have been made and the results submitted.

Princeton University submitted 'Class A predictions' for all the nine centrifuge models of the VELACS project. The computer code DYNAFLOW.v931 was used for the numerical simulations. It is a finite element

*To whom correspondence should be addressed.

Soil Dynamics and Earthquake Engineering 0267-7261/93/$06.00 © 1993 Elsevier Science Publishers Ltd.

73

program for nonlinear seismic site response analysis. Dry and saturated deposits can be analysed. The solid and fluid coupled field equations 2 and constitutive equations 3 are general and applicable to multidimen- sional situations. The multiyield constitutive soil model was selected to simulate the nonlinear behaviour of the soil materials. It is a kinematic hardening model based on a relatively simple plasticity theory 3 and is applicable to both cohesive and cohesionless soils. A non- associative plastic flow rule is used for the dilatational component of the plastic deformation. The model has been tailored (1) to retain the extreme versatility and accuracy of the simple multisurface ,]2 theory 4 in describing observed shear nonlinear hysteretic behaviour and shear stress-induced anisotropic effects, and (2) to reflect the strong dependency of the shear dilatancy on the effective stress ratio in both cohesionless and cohesive soils. Nested conical yield surfaces are used for that purpose.

All the required constitutive model parameters can be derived from the results of conventional laboratory (e.g. 'triaxial', 'simple shear') and in-situ (e.g. 'wave velocity', 'standard penetration') soil tests.

The validation of the numerical model and of the method of setting up the constitutive model parameters is carried out by using a series of centrifuge model soil tests performed by two centrifuge laboratories within the context of the VELACS project. The constitutive soil parameters are evaluated based on the results of

74 R. Popescu, J.H. Prevost

conventional laboratory soil tests performed by the Earth Technology Corporation, 5 and by empirical correlation formulae available in the literature. The parameter identification procedure is explained in detail, and a unique set of constitutive parameters is used throughout the numerical simulations. Three centrifuge soil experiments performed at Princeton University 6 and Cambridge University 7 are selected for numerical analysis.

2 CONSTITUTIVE MODEL PARAMETER EVALUATION

The required constitutive soil parameters for the multiyield plasticity model are summarized in Table 1 and are as follows: 8

(a) State parameters (mass density, porosity and permeability)

(b) Low-strain elastic parameters (shear and bulk moduli, reference mean normal stress and power exponent)

(c) Dilation parameters (dilation angle and dilation parameter)

(d) Yield and failure parameters (friction angle at failure, cohesion and maximum deviatoric strain)

The procedure used to derive the constitutive model parameters is detailed hereafter for both the sand and silt materials used in the centrifuge model tests.

2.1 State parameters

The mass density (Ps) for both the sand and silt materials is provided in Ref. 5 from the results of routine soil identification tests. The sand porosity (n w) is computed from the relative density and minimum/ maximum void ratios. For the Bonnie silt, a void ratio e = 0"8 is adopted, and is an average value for the samples used for laboratory tests

Table 1. Muitiyield plasticity model constitutive parameters

Constitutive parameter Symbol

Mass density - - solid Ps Porosity n w Low-strain shear and bulk moduli Go, B0 Reference mean effective normal stress P0 Power exponent n Friction angle at failure ~b Cohesion c

max Maximum deviatoric strain edev Dilation angle Dilation parameter (cyclic) Xpp Permeability k

K (m/s x I 0 -s)

* Constant head permeability test

4.7

4-

-,,,, 2- I

I I

J ' J 40 50 60

Fig 1. Nevada sand permeability values 5 at various relative densities.

Permeability values (kin) are obtained as follows:

(a) for the sand material, constant-head permeability test results 5 provide the permeability values at relative densities D r : 4 0 % , D r = 6 0 % and D r : 90%. The permeability at D r : 70% is estimated by interpolation, as shown in Fig. 1;

(b) for the silt material, the permeability is estimated from the results of triaxial permeability tests; 5 only the test results obtained for low confining pressures are considered.

The centrifuge model permeability at the corresponding prototype scale is computed as kp -- N × km, where N × g is average centrifugal acceleration across the model during the test. However, it is well known that there is a conflict between the time scales in a centrifuge for dynamic generation and diffusion of pore water pressure. 9 The conflict, according to Tan and Scott, l° is due to the complicated nature of the fluid behaviour and the non-linearity of the drag coefficient. Numerical simulations performed by the authors, of various centrifuge experiments which used water as the pore fluid, also indicated the necessity of using a lower permeability during dynamic excitation (mainly pore pressure build-up and little, if any, diffusion) than after the shaking (diffusion only). Typically, during dynamic excitation, k d y n ami c excitation ~ k d i f f u s i o n / 4 '

k Kprototype

KmodelX N

Kfn°del X N 4

time p

end of shakin~ time i

nput acceleration

.,,hA AAAAA ,I "v vvvvvvw

Fig. 2. Assumed variation for prototype permeability.

Centrifuge validation of a numerical model for dynamic soil liquefaction 75

9 -

o Nevada Sand - D = 60% - t e s t results

O Nevada Sa~l - D, = a,0% -tcst resdts

0 Bonnie Silt - test results . o - -'n

" I ........ N e v a d a Sand - D , = 60%

" "~ " 0 B o n n i e S i l t

0 0~ i ~I~ Effective mean stress ratio (p / Pc)

Fig. 3. Evaluation of low-strain shear modulus and power exponent from the laboratory test results reported in Ref. 5.

Consequent ly , the following numerical s imulat ions have been performed using a variable permeabil i ty, as shown in Fig. 2.

2.2 Elastic parameters

~dev = 0• 1% are used and computed as

q . 3el - - ~ v o l

G0'I% = 2ede v , q ~--- 0-1 -- 0"3; edev -- T

(1)

The low-strain shear modulus (G) is evaluated from the results of isotropically consol idated dra ined compression tests. Values corresponding to a deviatoric strain

(q, e I and evol are provided). The dependence of the modul i u p o n the effective mean norma l stress is taken into account by referring all modul i to a reference mean

a o

o

.~ o _

;,=

b .

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.=~ o _ p

o Earth Technology Corporation o Rensselaer Politechn/c In~tute O Johns Hopkim University • Univ• of Colorado at Boulder • Adopted values

r l ~ 0

D D

0

IP' 0

I I I I 20 40 60 80

Relative density - D (%)

reck 0953) . - ' " Meyerhot (1956) . - " Schmertmarm (1978) - for uniform fine sand NAVFAC (1982) - for poorly graded sand

o Nev-aa Sand - ,,dopted value; ~ . . ~ ...-

o o ~ , .

o ° ~ ' D

I I I I 20 40 60 SO

Relative density - D r (%)

Fig 4. Friction angle for Nevada sand• (a) Evaluation from isotropically consolidated undrained compression test results presented in Ref. 5. (b) Comparison with available correlation formulae from Refs 11-14.


normal stress P0, as

G= Go(P) n (2)

The reference mean normal stress is selected as P0 = 100kPa for sand and P0 = 4 0 k P a for silt. The initial moduli (Go) and power exponents (n) are evaluated from the laboratory test results 5 using a least-square method, as illustrated in Fig. 3.

The low strain bulk moduli (B0) are evaluated as

B0 - 2G0(1 + v) (3) 3(1 - 2v)

with Poisson's ratios of//sand = 0"3 and Vsilt = 0.4.

2.3 Yield and failure parameters

2.3.1 Nevada sand The friction angle at failure in compression (~bc) for the sand is evaluated from the results of isotropically consolidated undrained compression tests 5 (the friction angles computed from drained test results were very scattered and deemed unacceptable). The friction angle is computed as

t~triax, compr" = arcsin [ 36--~ ] ; rl = Pq at failure (4)

and the results are reported in Fig. 4(a). The values adopted for analysis have been reduced by about 1% (Fig. 4(b)) to account for the influence of imperfect test boundary conditions.

Since the results of the extension tests 5 are quite scattered, the value of the friction angle in extension (~bE) is assumed equal to the one in compression. The values adopted for the friction angle are compared with values obtained from various correlation formulae in Fig. 4(b). 11-14

Only qualitative information about the values of the maximum deviatoric strain (e~e~) could be derived from the laboratory test results. 5 Consequently, this parameter was estimated from previous experience.

2.3.2 Bonnie silt The strength parameters for the silt - - friction angle at failure (~b) and cohesion (c) - - are evaluated from the results of isotropically consolidated drained tests, 5 for a

m a x = 8%. The resulting maximum deviatoric strain eaev values are presented in Fig. 5. An average value is adopted for the cohesion.

2.4 Parameters related to dilation

2.4.1 Nevada sand The dilation angle (~) for sand was evaluated based on the sand particle characteristics, using the formula reported in Ref. 15. The value ~ = 30 ° resulted for the Nevada sand, which has

High sphericity and subrounded shape Effective grain size 0.2mm > dl0 > 0.06mm Uniformity coefficient (Cu < 2.0) Type of mineral - - quartz

At low and moderate relative density, the dilation angle is considered insensitive to the relative density, as suggested by the study reported in Ref. 16. However, at high relative density, a dilation angle ~ = 33 ° is assumedJ 5

The dilation parameter (Xpp) is derived from a liquefaction strength analysis, based on the results of undrained cyclic laboratory tests 5 (triaxial and simple shear). For that analysis, only the experiments with no static bias are selected. The number of cycles to liquefaction, Art, is evaluated from each test by considering the occurrence of initial liquefaction (zero effective mean stress). To obtain a unique liquefaction strength curve from both triaxial and simple shear laboratory test results, the relation

ffT~vhv simple : a ½ q (5) shear 0"3 triaxial

is used to relate the stress ratio in different experiments. The value of a is evaluated on the basis of the criterion proposed by Castro, 17 which relates the effect of the cyclic loading to the octahedral dynamic shear stress/the

il , 0 I00 200 300

Normal stress (KPa)

Fig. 5. Strength parameter (c and ~,) evaluation for Bonnie silt from the results of isotropically consolidated drained tests).


A o

.o

.IJ

k4 4-J cq

SAND - D r = 60%

O ~ [] Simple Shear test

O Triaxial test O~ [] - Element test - Simple Shear

Element test - Triaxial

,_0.t~ 0 ~

) o I

I i i i i i i i i I I i i i

2 3 4 5 6 7 89 ~ 2 3 4 5 i0 ° i0 ~

Number of cycles to liquefaction (N I)

i i i i [

6 789 102

~o D >

o

co

SAND - D r = 40%

o

I"I Simple Shear test O Triaxial test

• ~ Element test - Simple Shear o

oe~ ~ ~ ~ Triaxial

"2. o [ ]

Q

o i i i i i i i i I i i i

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Number of cycles to liquefaction (N I)

Fig 6. Liquefaction strength analysis for Nevada sand - -

static effective octahedral normal stress ratio. The initial condition for the triaxial test ai = a3 leads to a = 2 /v~ . The resulting liquefaction strength derived from the test results is shown in Fig. 6 as a plot of the number of (2) cycles to liquefaction versus stress ratio.

Element tests were performed for different stress ratio values, using several assumed values for the dilation parameter. The final dilation parameter values were (3) determined by fitting the computed liquefaction strength curves with the experimental results. Element test computation results for X~ "=~% = 0.15 and Xp~ '=6°% = (4) 0.13 are shown in Fig. 6

No laboratory cyclic test results were provided at the relative density Dr = 70%. Therefore, the dilation parameter for Nevada sand at relative density Dr = 70% is evaluated as follows:

(1) By correlating the cyclic stress ratio causing liquefaction at D r = 60% (Fig. 6(a)) with the normalised standard penetration resistance (N1) for clean sands, shown in Fig. 7(a) (from Ref. 18). From

I i i i i [

5 6 7 8 9 102

laboratory 5 and numerical test results.

the plot shown in Fig. 7(a) the normalised standard penetration resistance at 60% relative density is estimated as Ni Dr=6°% = 13-4blows/ft. From the relationship 'relative density versus NSl, T versus stress' (Ref. 19), shown in Fig. 7Co), one finds that at the 70% relative density Nl D'=7°% = 19.0 blows/ft. Referring back to Fig. 7(a), one finds that a stress ratio rh/av = 0"19, corresponds to N l = 15 cycles to liquefaction for the sand at D r = 70% relative density. Finally, the element test analysis provides the dilation parameter value X~=7° '°= 0-085 to match the estimated values, as shown in Fig. 7(c).

2.4.2 Bonnie silt The dilation angle for silt is evaluated by observing that typically a difference ~- ~ ~-, 4-5 ° between friction angle at failure and dilation angle was recorded in the undrained monotonic laboratory tests: The corresponding dilation parameter was evaluated by match-


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; ; ; ; ; ; ; I ~5 ; ; ; ; ~ ; ; ; 1 / o 100 101 2

N u m b e r o f c y c l e s to l i q u e f a c t i o n (N])

Fig. 7. Dilation parameter evaluation for Nevada sand at 70% relative density. (a) Correlat ion between field liquefaction behaviour of sand under level ground conditions and modified penetration resistance (Ref. 18). (b) Relative density-Nsr, r -s t ress relationship

(Ref. 19). (c) Liquefaction strength analysis (Reproduced with permission from ASCE).

T a b l e 2. M a t e r i a l p a r a m e t e r s f o r N e v a d a s a n d a n d B o n n i e s i l t

Property Nevada Sand Bonnie silt

Mass density - - solid (kg/m 3) Porosity Low-strain shear modulus (MPa) Low-strain bulk modulus (MPa) Reference mean effective normal stress (kPa) Power exponent Fluid bulk modulus (MPa) Friction angle at failure (compression and extension)

Cohesion (kPa) Maximum deviatoric strain compression/extension (%) Dilation angle Dilation parameter Permeability (m/s)

D r = 40% D r = 60% Dr = 70%

2670"0 2670"0 2670"0 2670"0 0"424 0"398 0"384 0"44

25"0 30"0 35"0 7'5 54'2 65"0 75"8 35'0

1 0 0 ' 0 100"0 100"0 40"0 0'7 0"7 0'7 1 "0

2000"0 2000"0 2000"0 2000"0 33 ° 35 ° 37 ° comp. 28 °

ext. 21 ° 0"0 0"0 0"0 5'3

8"0/7"0 6-0/5"0 4"0/4'0 8"0/8"0 30 ° 30 ° 33 ° 20 ° 0' 15 0" 13 0"085 0"04

6-6 x 10 -5 5-6 x 10 -5 4-7 × 10 -5 1-0 x 10 -8


ing the measured build up of excess pore pressure in the middle of the silt layer, as observed in several comparison tests performed for the VELACS project.

The resulting constitutive parameter values are listed in Table 2.

3 NUMERICAL SIMULATION OF CENTRIFUGE SOIL TESTS

3.1 Analysis method

The saturated soil is modelled as a two-phase porous material. Four-node bilinear finite elements with four degrees of freedom (dof)/node (two for the solid phase and two for the pore fluid) are used. The structural objects - - retaining wall, structure - - are modelled as elastic, one-phase media.

The numerical analyses are performed with the following options:

Several numerical analyses were performed. In the following, three centrifuge experiments performed at Princeton University and Cambridge University are selected for numerical analysis and validation of the proposed procedures. A centrifuge is used to simulate gravity-induced stresses in soil deposits at a reduced geometrical scale through centrifugal loading. Concep- tually, the technique consist of increasing the confining environment in the model soil, so that the confining stress is identical in both model and prototype at homologous points. The technique allows soil liquefaction tests to be performed at a conveniently reduced scale and provides data applicable to full-scale problems. For consistency, all centrifuge test measurements and results presented hereafter are reported in terms of their corresponding prototype geometry.

hyperbolic type analysis compressible fluid small deformation assumption

The solution is performed in two steps. First, gravity loads are applied and the soil allowed to fully consolidate. The consolidation phase is calculated dynamically, by setting the algorithmic Newmark parameters in the integration scheme to 3, = 1.5 and

= 1.0. 2° After consolidation is completed, the nodal displacements, velocities and accelerations are zeroed, the time is reset to zero and the input acceleration is applied at the boundaries. The Newmark parameters in the integration scheme are chosen as 7 = 0.65 and

= (3' + 1/2)2/4 = 0.33, and the time step is selected as A t = 0 . 0 1 s . This choice for 3' introduces a slight

TRANSDUCER LOCATIONS

Test 100g I h Test 100a II

Test 75 g I ,~ Test 75 g II

r l Horizontal and ver'~cal accelerometers

Pore pressure l~msclucers paralbl with the shaking direction

O Pore pressure transducem normal to the shaking direction

e. FINITE ELEMENT MESH

21.50

Fig. 8. Comparison test (Princeton University) - - centrifuge experiment 6 and numerical simulation set-up.


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~ F . , , , ~/V V V r ,~vv . - -,, . . . . . . .

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c. Recorded - Test 100g II - ACC C

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e. Recorded - Test 75g II - A C C B

I I I I I 0 2 4 6 8 10 12

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I I I 14 16 18

Fig. 9. Comparison test - - computed and recorded 6 horizontal accelerations.

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e. Re c o r de d - Tes t 7 5 g II - A C C D

.,/f . AAAAA . . . .

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time (~c)

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Fig. 10. C o m p a r i s o n test - - c o m p u t e d a n d recorded 6 hor izonta l accelerations.

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numerical damping ('y = 0-5 corresponds to no numerical damping) and the selected value for /3 maximizes high frequency numerical dissipation. No additional viscous physical damping is introduced.

3.2 C o m p a r i s o n test - - Pr ince ton Univers i ty

As part of the VELACS project, two types of comparison tests were performed by the collaborating universities, in order to investigate the influence of the centrifuge set-up on the measured behaviour. The model geometry is shown in Figs 8(a)-(d) and consists of a layered soil deposit with a sand layer overlaid by a silt layer. The numerical analysis presented in the following refers to one of these centrifuge model tests - - with saturated Nevada sand at D r = 60% relative density and Silica silt - - performed at Princeton University. 6 Four tests were performed, two of them at 100 g and two at 75 g centrifugal acceleration (Figs 8(a)-(d)), with the same corresponding prototype geometry and input acceleration.

The finite element mesh (Fig. 8(e)) has 132 porous

'ometer

essure leer

medium elements and 156 nodes. The boundary conditions are prescribed as follows:

no vertical motion at the base for both solid and fluid phases prescribed acceleration to the solid phase horizontal dof at the base and lateral nodes impervious lateral boundaries.

Since no information concerning the Silica silt is available, the material parameter values derived for the Bonnie silt are used. The earthquake-like motion, shown in Fig. 9(a), recorded during the Test 100 g 116 is selected as input acceleration for the numerical analysis.

Computed horizontal accelerations time histores at the surface and in the middle of the silt layer are presented, along with the recorded values in Figs 9 and 10, respectively. Good simulation is achieved for the location in the middle of the silt layer. Although the maximum computed horizontal acceleration at the top of the silt layer is lower than the recorded value, the same tendency of decreasing amplitude after 1.5-2 s of shaking is exhibited by both measured and computed results.

Computed excess pore pressure time histories in the sand layer are compared with recorded values in Fig. 11. The locations with at least two available transducer recordings are selected. To account for differences in elevation between transducers and finite element centroids, the ratio excess pore pressure/initial effective vertical stress is shown in Fig. 11. A very good agreement can be observed between computed and recorded values.

3 .3 Structure m o d e l - - Pr ince ton Univers i ty

11.00 .~ _~ 7.00 ~ ~ 10.00

b. FINITE EnL71#EN; ~ n~e #154 l

z o n e ~ ~ _ . ~ z o n e ~ ~ zon?#1 ~_

Fig. 12. Structure model (Princeton University) -- centrifuge experiment 6 and numerical simulation set-up.

The geometry of the model (Fig. 12) was selected to correspond to the Niigata apartment which collapsed due to the 1964 Niigata earthquake-induced soil liquefaction. The structure rests on a layer of Nevada sand initially deposited at a relative density Dr = 60%. Two tests were performed at 100g centrifuge acceleration. 6 The finite element mesh has 154 nodes and 119

elements (Fig. 12(b)). The two-dimensional plane strain assumption is justified by the fact that the structure extends over the whole width of the centrifuge box. The boundary conditions for the centrifuge model are prescribed as follows:

- - no vertical motion at the base for both solid and fluid phases;

- - prescribed acceleration to the solid phase horizontal dof at the base and lateral nodes;

- - impervious boundaries (box); - - impervious surfaces at the sand-structure inter-

face;


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t e,i

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time (see) 18

Fig. 13. Stucture model - - computed and recorded 6 horizontal accelerations.


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- - perfect friction at the base of the structure; - - no friction at the sides of the structure.

The material properties for Nevada sand at 60°/0 relative density are taken according to Table 2. Due to the heavy weight of the model structure (bearing pressure 200kPa), the underlaying material (zone 2 in Fig. 12(b)) is in a denser state than the sand in the free field (zone 1 in Fig. 12(b)), and a relative density Dr = 70% is considered for zone 2 (material parameter values listed in Table 2). The model permeability value was evaluated from the recorded excess pore pressure time histories during the diffusion phase in the centrifuge test (see Fig. 14). A value km= 2"8 x 10-Sm/s resulted for the sand used for these centrifuge experiments. This value is consistent with the Creager correlation formula, 21 but is lower than predicted by the laboratory constant-head permeability tests. 5

The structure is modelled as elastic, with the following material parameters: mass density, Ps = 1520kg/m3; Young modulus, E = 1000MPa; and Poisson's coefficient, v = 0.3.

The top of structure computed horizontal and vertical accelerations are compared with the recorded values in Fig. 13 (Only test No. 2 provided meaningful acceleration records). 6 The same amplitude values and tenden- cies for both computed and recorded time histories can be seen.

The computed excess pore pressures are in good agreement with the recorded values (Fig. 14). In the last part of the shaking period, the numerical model simulates a larger dilation for the locations in zone 2 (below the structure). However, the computed values are still within the range of the recorded ones.

The finite element mesh (Fig. 16) consists of 104 porous media elements (saturated sand) and 28 structural one-phase elements (quay wall and duxseal). The boundary conditions are prescribed as follows:

- - no vertical motion at the base for both solid and fluid phases;

- - prescribed acceleration to the solid-phase horizontal dof at the base and lateral nodes;

- - impervious surfaces at the sand-wall and sand- duxseal interfaces;

- - perfect friction at the base of the wall; - - no friction at the vertical sand-wall and sand-

duxseal interfaces.

The material properties for Nevada sand are taken as for 60% relative density, according to Table 2. Elastic behaviour is assumed for the quay wall and duxseal (Table 3). The duxseal material properties are evaluated from Ref. 22 and by analysing the results of one- dimensional compression tests reported in Ref. 23.

The deformed mesh at the end of the numerical simulation period (t = 20s) is plotted in Fig. 17(b). Figure 17(a) (after Ref. 7) shows the profile of the centrifuge model after the test. Very good simulation of the quay wall displacement is achieved. The computed sand settlements are somewhat lower than the recorded ones, but the deformation pattern is essentially the same.

The computed and recorded excess pore pressure time histories are shown in Fig. 18 and the corespondence between transducers and computed result providing elements is shown in Fig. 16. Overall good simulation is achieved, except at one location (transducer PPT5), where the numerical model overestimates the pore pressure values.

3 . 4 Q u a y w a l l m o d e l - - C a m b r i d g e U n i v e r s i t y

Four preliminary tests for the VELACS project were carried out at Cambridge University. 7 They consist of a quay wall, made of a solid aluminium block, backfilled by dry or water-saturated Nevada sand. A body of duxsea122 was used to create an absorbing boundary at each end wall of the model container. The centrifuge test selected for backanalysis, test XZ8, has water-saturated sand backfill at a 58% relative density. The corresponding prototype geometry and the instrument locations are shown in Figs 15(a) and (b).

The model was tested at 80 g centrifugal acceleration. The input motion - - horizontal acceleration with peak 0"23 g - - lasted for about 8 s and is shown in Fig. 15(c).

T a b l e 3

Material Quay wall (aluminium) Duxseal

Mass density (kg/m 3) 2770 1650 Young modulus (MPa) 68300 0.8 Poisson's ratio 0.21 0.46

4 CONCLUSIONS

1. A systematic parameter identification procedure for setting up the constitutive parameters for a multiyield plasticity model, on the basis of conventional laboratory soil test results, is presented. A unique set of material parameters is provided and used throughout the numerical simulations of various centrifuge model experiments.

2. The overall good agreement between the numerical simulation results and the centrifuge experiment recorded values provides a partial validation of the proposed numerical model to analyse dynamic soil and soil-structure interaction, including soil liquefaction effects.

ACKNOWLEDGEMENT

The work reported in this study was supported by the National Science Foundation under grant No. BCS91-


20028 (Program Manager: Dr C. Astill). This support is most gratefully acknowledged.

REFERENCES

1. Prevost, J.H. DYNAFLOW: A nonlinear transient finite element analysis program, Dept. Civil Engineering Op. Res., Princeton University, 1981; last update 1992.

2. Biot, M.A. Mechanics of deformation and acoustic propagation in porous media, J. Appl. Phys., 1962, 33(4), 1482-98.

3. Prevost, J.H. A simple plasticity theory for frictional cohensionless soils, J. Soil Dynam. Earthq. Eng., 1985, 4(1), 9-17.

4. Prevost, J.H. Mathematical modeling of monotonic and cyclic undrained clay behaviour, Int. J. Num. Meth. Geom., 1977, 1(2), 195-216.

5. Arulmoli, K., Muraleetharan, K.K. & Hossain, M.M. VELACS - - Verification of Liquefaction Analyses by Centrifuge Studies - - Laboratory testing program; Soil data report, The Earth Technology Corporation, Irvine, California, 1992.

6. Krstelj, I. Development of an earthquake motion simulator and its application in dynamic centrifuge testing, MS thesis, Princeton University, Princeton, New Jersey, 1992.

7. Zeng, X. Data of dynamic centrifuge tests on quay wall models, Report for the VELACS project, Dept. of Engineering, Cambridge University, UK, 1992.

8. Prevost, J.H. DYNAID - - A computer program for nonlinear seismic site response analysis, Report No. NCEER-89-0025, Dept. of Civil Engineering and Op. Res., Princeton University, Princeton, New Jersey, 1989.

9. Muraleetharan, K.K. & Arulanandan, K. Dynamic behaviour of earth dams containing stratified soils, Proc. Int. Conf. Centrifuge 91, Boulder, Colorado, 1991, pp. 401-8.

10. Tan, T.S. & Scott, R.F. Centrifuge scaling considerations for fluid-particulate systems, Geotechnique, 1985, 35(4), 461-70.

11. Meyerhof, G.C. Penetration tests and bearing capacity of cohesionless soils, J. Soil Mech. Found. Div., ASCE, 1956, 82(SM1).

12. Peck, R.B,, Hanson, W.E. & Thornburn, T.H. Foun- dation Engineering, John Wiley and Sons, New York, 1953.

13. Schmertmann, J.H. Guidelines for cone penetration test performance and design, Rep. FHWA-TS-78-209, US Dept. Trans., Washington, DC, 1978.

14. NAVFAC, Soil Mechanics (DM 7.1), Naval Fac. Eng. Command, Alexandria, 1982.

15. Koerner, R.M. Effect of particle characteristics on soil strength, J. Soil Mech. Found. Div., ASCE, 1970, 96(SM4), 1221-1234.

16. BoRon, M.D. The strength and dilatancy of sands, Geotechnique, 1986, 36(1), pp. 65-78.

17. Castro, G.. Liquefaction and cyclic mobility of saturated sands, J. Geotech. Eng. Div., ASCE, 1975, 101(GT6), 551- 69.

18. Seed, H.B., Idriss, I.M. & Arango, I. "Evaluation of liquefaction potential using field performance data, J. Geotech. Eng., ASCE, 1983, 109(3), 458-82.

19. Holtz, W.G. & Gibbs, H.J. Discussion of 'SPT and relative density in coarse sand', J. Geotech. Eng. Div., ASCE, 1970, 101(GT3), 439-41.

20. Lacy, S.J. & Prevost, J.H. Nonlinear seismic response analysis of earth dams, J. Soil Dynam. Earthq. Eng., 1987, 6(1), 48-63.

21. Creager, W.P., Justin, J.D. & Hinds, J. Engineering for Dams, John Wiley and Sons, New York, 1945.

22. Coe, C.J. On the feasibility of performing dynamic soil tests in a centrifuge, PhD dissertation, Princeton Uni- versity, Princeton, New Jersey, 1985.

23. Campbell, D.J., Cheney, J.A. & Kutter, B.L. Boun- dary effects in dynamic centrifuge model tests, Proc. Int. Conf. Centrifuge 91, Boulder, Colorado, 1991, pp. 441-8.

Centrifuge validation of a numerical model for dynamic soil liquefaction

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