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A two-surface plasticity model for cyclic behavior of saturated clay

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Abstract

This paper presents a two-surface plasticity model for describing some important features of saturated clay under cyclic loading conditions, such as closed hysteresis loops, cyclic shakedown and degradation, and different stress–strain relations for two-way loading. The model, namely ACC-2-C, is based on the elastoplastic model ACC-2 (an adapted Modified Cam Clay model with two yield surfaces) developed by Hong et al. (Acta Geotech 11(4):871–885, 2015). The small-strain nonlinearity concept is adopted to achieve the nonlinear characteristics of clay during unloading–loading stage. The new hardening law related to accumulated deviatoric plastic strain is proposed for the inner surface to describe the cyclic shakedown and degradation. Following the advantages of the ACC-2 model, the constitutive equations are simply formulated based on the consistency condition for the inner yield surface. The model is conveniently implemented in a finite element code using a stress integration scheme similar to the Modified Cam Clay model. The simulation results are highly consistent with experimental data from drained and undrained isotropic cyclic triaxial tests in normally consolidated saturated clay under both one-way and two-way loadings.

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Abbreviations

A d :

Model parameter

C :

Model parameter

D e, D ep :

Elastic and elastoplastic stiffness matrix, respectively

f B, f L :

Bounding surface and loading yield surface, respectively

f Bc, f Be :

Bounding surface for compression and extension, respectively

G :

Shear modulus

G 1, G N :

Secant modulus at cycles 1 and N, respectively

g B, g L :

Plastic potentials associated with bounding surface and loading yield surface, respectively

h :

Hardening modulus

K :

Elastic bulk modulus

k :

Material constant

k f, k g :

Model parameters for yield surface and plastic potential, respectively

M f, M g :

Stress ratio at the apex of the yield surface and critical state slope, respectively

M fc, M fe :

Stress ratio at the apex of the yield surface in compression and extension, respectively

m :

Material constant

p′, p′rev :

Mean effective stress at the current stress point and at the stress reversal point, respectively

\(p_{c}^{{\prime }} ,\bar{p}_{c}^{{\prime }}\) :

Actual loading yield stress and conventional yield stress on the normal consolidation line, respectively

q :

Deviator stress

r :

Positive scalar defining the size of the loading field surface

s 0 :

Model parameters

\(s_{{{\text{c}}0}} ,s_{{{\text{e}}0}}\) :

Initial material constant under the first compression and extension cycle, respectively

v 0 :

Initial specific volume

u :

Pore water pressure

X, X s :

Current stress state for mean effective stress and deviator stress, respectively

\(\varepsilon\) :

Strain

\(\varepsilon_{1} ,\varepsilon_{3}\) :

Axial and lateral strains, respectively

\(\varepsilon_{\text{s}} ,\varepsilon_{\text{s}}^{\text{e}} ,\varepsilon_{\text{s}}^{\text{p}}\) :

Shear strain, elastic shear strain and plastic deviator strain, respectively

\(\varepsilon_{\text{v}} ,\varepsilon_{\text{v}}^{\text{e}} ,\varepsilon_{\text{v}}^{\text{p}}\) :

Volumetric strain, elastic volumetric strain and plastic volumetric strain, respectively

\(\varepsilon_{d}^{p}\) :

Total plastic strain

\(\varepsilon^{1} ,\varepsilon^{N}\) :

Axial strains at cycles 1 and N, respectively

\(\eta ,\eta_{\text{rev}}\) :

Normalized deviator stress at current stress point and at the stress reversal point, respectively

\(\kappa ,\kappa_{0}\) :

Elastic slope and initial unloading slope in v − lnp′ space, respectively

\(\varLambda\) :

Plastic multiplier

\(\lambda\) :

Slope of the normal consolidation compression line

\(\mu\) :

Poisson’s ratio

\(\sigma\) :

Stress

\(\sigma_{1}^{{\prime }} ,\sigma_{3}^{{\prime }}\) :

Axial and lateral effective stresses, respectively

\(\omega\) :

Model parameter

\(\zeta\) :

Degradation index

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Acknowledgements

The present work was carried out with the support of the National Key Research and Development Program of China (2016YFC0800207), National Natural Science Foundation of China (41472244, 51608188), the Provincial Key Research and Development Program of Hunan (0105679005), the Industrial Technology and Development Program of Zhongjian Tunnel Construction Co., Ltd. (17430102000417).

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Authors and Affiliations

  1. MOE Key Laboratory of Building Safety and Energy Efficiency, Changsha, 410082, China

    Ren-Peng Chen

  2. International Joint Research Center for Sustainable Building Environment, Changsha, 410082, China

    Ren-Peng Chen

  3. College of Civil Engineering, Hunan University, Changsha, 410082, China

    Ren-Peng Chen, Shu Zhu & Peng-Yun Hong

  4. Department of Civil Engineering, Zhejiang University, Hangzhou, 310058, China

    Wei Cheng

  5. Laboratoire Navier (UMR 8205), CNRS, ENPC, IFSTTAR, Université Paris-Est, 77455, Marne-la-Vallée, France

    Yu-Jun Cui

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  1. Ren-Peng Chen
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Correspondence to Ren-Peng Chen.

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Chen, RP., Zhu, S., Hong, PY. et al. A two-surface plasticity model for cyclic behavior of saturated clay. Acta Geotech. 14, 279–293 (2019). https://doi.org/10.1007/s11440-019-00776-z

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