Acta Geotechnica

, Volume 7, Issue 2, pp 69–113 | Cite as

Large post-liquefaction deformation of sand, part I: physical mechanism, constitutive description and numerical algorithm

Research Paper

Abstract

This paper presents a theoretical framework for predicting the post-liquefaction deformation of saturated sand under undrained cyclic loading with emphasis on the mechanical laws, physical mechanism, constitutive model and numerical algorithm as well as practical applicability. The revealing mechanism behind the complex behavior in the post-liquefaction regime can be appreciated by decomposing the volumetric strain into three components with distinctive physical background. The interplay among these three components governs the post-liquefaction shear deformation and characterizes three physical states alternating in the liquefaction process. This assumption sheds some light on the intricate transition from small pre-liquefaction deformation to large post-liquefaction deformation and provides a rational explanation to the triggering of unstable flow slide and the post-liquefaction reconsolidation. Based on this assumption, a constitutive model is developed within the framework of bounding surface plasticity. This model is capable of reproducing small to large deformation in the pre- to post-liquefaction regime. The model performance is confirmed by simulating laboratory tests. The constitutive model is implemented in a finite element code together with a robust numerical algorithm to circumvent numerical instability in the vicinity of vanishing effective stress. This numerical model is validated by fully coupled numerical analyses of two well-instrumented dynamic centrifuge model tests. Finally, numerical simulation of liquefaction-related site response is performed for the Daikai subway station damaged during the 1995 Hyogoken-Nambu earthquake in Japan.

Keywords

Centrifuge tests Constitutive model Earthquake Liquefaction Large deformation Numerical analysis Site response 

List of symbols

e, Dr

Void ratio and relative density

pa

Atmospheric pressure

τ

Simple shear stress

pe, ru

Excess pore water pressure and excess pore water pressure ratio

\({\sigma_{\text{c}}^{\prime } } \hbox{,} \)\({\sigma_{\text{m}}^{\prime } } \)

Initial effective consolidation stress and mean effective stress

p, q

Mean effective stress and deviatoric stress invariant

η, ηm

Shear stress ratio (η = q/p) and its maximum value in loading history

γ

Total shear strain

γd

Solid-like shear strain that occurs in non-zero effective confining stress state

γo

Fluid-like shear strain that occurs in zero effective confining stress state

γmax

Preceding maximum cyclic shear strain

\( \dot{\gamma }_{\text{eff}} \)

Effective shear strain rate

γmono

Monotonic shear strain length

γd,r

Reference shear strain length

γr

Residual shear strain

εv

Total volumetric strain

\( \varepsilon_{\text{v,recon}} \)

Reconsolidation volumetric strain

εvc

Volumetric strain component due to the change in p

εvc,o

Threshold volumetric strain to delimit whether the effective confining stress reaches zero, determined as εvc value at zero effective confining stress state

pmin

Threshold pressure for numerical calculation to delimit whether the effective confining stress reaches zero

εvd

Volumetric strain due to dilatancy

εvd,ir

Irreversible dilatancy component

\( \varepsilon_{\text{vd,re}} \)

Reversible dilatancy component

\( {\varvec{\upsigma} } \)ij), s(sij)

Effective stress tensor and its deviatoric part

\( {\varvec{\upvarepsilon }}\)ij), e(eij)

Strain tensor and its deviatoric part

r(rij)

Deviatoric shear stress ratio tensor

I(ij)

Identity tensor of rank 2 (Kronecker delta)

n

Loading direction in stress ratio space

m

Flowing direction of plastic deviatoric strain increment

α

Projection center

\( \hat{f}(\hat{\varvec{\upsigma} }) \hbox{,} \, \bar{f}(\bar{\varvec{\upsigma} }) \)

Failure surface and maximum prestress memory surface serving as bounding surfaces

L

Plastic loading intensity

G, K, H

Elastic shear modulus, elastic bulk modulus and plastic modulus

D, Dir, Dre

Total, irreversible and reversible dilatancy rates

Dre,gen, Dre,rel

Reversible dilatancy rates in dilative and contractive phases

Mf,c, Mf,o

Failure stress ratios in triaxial compression stress state and torsional shear stress state

Go, n, h, κ

Modulus parameters

Md,c, dre,1, dre,2

Reversible dilatancy parameters

\( d_{\text{ir}} ,\alpha ,\gamma_{\text{d,r}} \)

Irreversible dilatancy parameters

θσ

Lode angle

\( \rho ,\bar{\rho } \)

Mapping distances in stress ratio space

Notes

Acknowledgments

The present study is financially supported by the National Natural Science Foundation of China (No. 51038007, No. 51079074, and No. 50979046). The authors wish to express their sincere appreciation to Professor W. Wu for his valuable comments during preparation of this paper.

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© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Institute of Geotechnical Engineering, School of Civil Engineering/State Key Laboratory of Hydroscience and EngineeringTsinghua UniversityBeijingChina
  2. 2.Ertan Hydropower Development Company LimitedChengduChina

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