SCIENCE CHINA Technological Sciences, Volume 63 , Issue 2 : 303-318(2020) https://doi.org/10.1007/s11431-018-9469-9

A new method of developing elastic-plastic-viscous constitutive model for clays

More info
  • ReceivedNov 19, 2018
  • AcceptedFeb 22, 2019
  • PublishedMay 15, 2019


A new method is presented to develop the existing elastic-plastic constitutive model into an elastic-plastic-viscous one for clays. The actual loading process is divided into an instant process and a delayed process denoting the elastic-plastic strain and viscous strain, respectively. The elastic-plastic strain is determined by either an elastic-plastic model for overconsolidated clays or an improved model based on the elastic-plastic model for normally consolidated clays. In order to calculate viscous strain, a reference state line is defined based on the actual loading path. Combining the reference state line, an existing elastic-plastic model can be conveniently developed into an elastic-plastic-viscous model. Furthermore, using the proposed method, the modified cam clay model is extended into an elastic-plastic-viscous model. Comparisons with test results demonstrate that the extended model can capture the main time-dependent behaviours of clays, including creep, stress relaxation and strain rate effects.

Funded by

the National Natural Science Foundation of China(Grant,Nos.,51522802,51778026,51421005,&,51538001)

the National Natural Science Foundation of Beijing(Grant,No.,8161001)


This work was supported by the National Natural Science Foundation of China (Grant Nos. 51522802, 51778026, 51421005 & 51538001) and the Natural Science Foundation of Beijing (Grant No. 8161001).


[1] Liingaard M, Augustesen A, Lade P V. Characterization of models for time-dependent behavior of soils. Int J Geomech, 2004, 4: 157-177 CrossRef Google Scholar

[2] Sivasithamparam N, Karstunen M, Bonnier P. Modelling creep behaviour of anisotropic soft soils. Comput Geotech, 2015, 69: 46-57 CrossRef Google Scholar

[3] Feng W Q, Lalit B, Yin Z Y, et al. Long-term non-linear creep and swelling behavior of Hong Kong marine deposits in oedometer condition. Comput Geotech, 2017, 84: 1-15 CrossRef Google Scholar

[4] Wang Z, Wong R C K. Strain-dependent and stress-dependent creep model for a till subject to triaxial compression. Int J Geomech, 2016, 16: 04015084 CrossRef Google Scholar

[5] Yin Z Y, Zhu Q Y, Zhang D M. Comparison of two creep degradation modeling approaches for soft structured soils. Acta Geotech, 2017, 12: 1395-1413 CrossRef Google Scholar

[6] Zhu J G. Experimental study and elastic visco-plastic modelling of the time dependent behavior of Hong Kong marine deposits. Dissertation of Doctoral Degree. Hong Kong: Hong Kong Polytechnic University, 2000. Google Scholar

[7] Li D W, Fan J H, Wang R H. Research on visco-elastic-plastic creep model of artificially frozen soil under high confining pressures. Cold Regions Sci Tech, 2011, 65: 219-225 CrossRef Google Scholar

[8] Madaschi A, Gajo A. A one-dimensional viscoelastic and viscoplastic constitutive approach to modeling the delayed behavior of clay and organic soils. Acta Geotech, 2017, 12: 827-847 CrossRef Google Scholar

[9] Zhou H W, Wang C P, Han B B, et al. A creep constitutive model for salt rock based on fractional derivatives. Int J Rock Mech Min Sci, 2011, 48: 116-121 CrossRef Google Scholar

[10] Desai C S, Sane S, Jenson J. Constitutive modeling including creep- and rate-dependent behavior and testing of glacial tills for prediction of motion of glaciers. Int J Geomech, 2011, 11: 465-476 CrossRef Google Scholar

[11] Kong Y, Xu M, Song E. An elastic-viscoplastic double-yield-surface model for coarse-grained soils considering particle breakage. Comput Geotech, 2017, 85: 59-70 CrossRef Google Scholar

[12] Yin Z Y, Karstunen M, Chang C S, et al. Modeling time-dependent behavior of soft sensitive clay. J Geotech Geoenviron Eng, 2011, 137: 1103-1113 CrossRef Google Scholar

[13] Wang S, Wu W, Yin Z Y, et al. Modelling the time-dependent behaviour of granular material with hypoplasticity. Int J Numer Anal Methods Geomech, 2018, 42: 1331-1345 CrossRef ADS Google Scholar

[14] Yang C, Carter J P, Sheng D, et al. An isotach elastoplastic constitutive model for natural soft clays. Comput Geotech, 2016, 77: 134-155 CrossRef Google Scholar

[15] Yao Y P, Kong L M, Zhou A N, et al. Time-dependent unified hardening model: Three-dimensional elastoviscoplastic constitutive model for clays. J Eng Mech, 2015, 141: 04014162 CrossRef Google Scholar

[16] Yao Y P, Kong L M, Hu J. An elastic-viscous-plastic model for overconsolidated clays. Sci China Tech Sci, 2013, 56: 441-457 CrossRef Google Scholar

[17] Yin Z Y, Xu Q, Yu C. Elastic-viscoplastic modeling for natural soft clays considering nonlinear creep. Int J Geomech, 2015, 15: A6014001 CrossRef Google Scholar

[18] Tong X, Tuan C Y. Viscoplastic cap model for soils under high strain rate loading. J Geotech Geoenviron Eng, 2007, 133: 206-214 CrossRef Google Scholar

[19] Cassiani G, Brovelli A, Hueckel T. A strain-rate-dependent modified Cam-Clay model for the simulation of soil/rock compaction. Geomech Energy Environ, 2017, 11: 42-51 CrossRef Google Scholar

[20] Adachi T, Oka F, Mimura M. Mathematical structure of an overstress elasto-viscoplastic model for clay. Soils Found, 1987, 27: 31-42 CrossRef Google Scholar

[21] Yin Z Y, Hicher P Y. Identifying parameters controlling soil delayed behaviour from laboratory and in situ pressuremeter testing. Int J Numer Anal Meth Geomech, 2008, 32: 1515-1535 CrossRef ADS Google Scholar

[22] Rowe R K, Hinchberger S D. The significance of rate effects in modelling the Sackville test embankment. Can Geotech J, 1998, 35: 500-516 CrossRef Google Scholar

[23] Perzyna P. Fundamental problems in viscoplasticity. Adv Appl Mech, 1966, 9: 243–377. Google Scholar

[24] Perzyna P. The constitutive equations for rate sensitive plastic materials. Quart Appl Math, 1963, 20: 321-332 CrossRef Google Scholar

[25] Hinchberger S D, Rowe R K. Modelling the rate-sensitive characteristics of the Gloucester foundation soil. Can Geotech J, 1998, 35: 769-789 CrossRef Google Scholar

[26] Islam M N, Gnanendran C T. Elastic-viscoplastic model for clays: Development, validation, and application. J Eng Mech, 2017, 143: 04017121 CrossRef Google Scholar

[27] Kutter B L, Sathialingam N. Elastic-viscoplastic modelling of the rate-dependent behaviour of clays. Géotechnique, 1992, 42: 427-441 CrossRef Google Scholar

[28] Qiao Y, Ferrari A, Laloui L, et al. Nonstationary flow surface theory for modeling the viscoplastic behaviors of soils. Comput Geotech, 2016, 76: 105-119 CrossRef Google Scholar

[29] Katona M G. Evaluation of viscoplastic cap model. J Geotech Eng, 1984, 110: 1106-1125 CrossRef Google Scholar

[30] Sekiguchi H. Theory of undrained creep rupture of normally consolidated clay based on elasto-viscoplasticity. Soils Found, 1984, 24: 129-147 CrossRef Google Scholar

[31] Yin J H, Graham J. Elastic viscoplastic modelling of the time-dependent stress-strain behaviour of soils. Can Geotech J, 1999, 36: 736-745 CrossRef Google Scholar

[32] Yin J H, Zhu J G, Graham J. A new elastic viscoplastic model for time-dependent behaviour of normally and overconsolidated clays: Theory and verification. Can Geotech J, 2002, 39: 157-173 CrossRef Google Scholar

[33] Bjerrum L. Engineering geology of Norwegian normally-consolidated marine clays as related to settlements of building. Géotechnique, 1967, 17: 83–118. Google Scholar

[34] Xiao Y, Liu H L, Liu H, et al. Unified plastic modulus in the bounding surface plasticity model. Sci China Tech Sci, 2016, 59: 932-940 CrossRef Google Scholar

[35] Dafalias Y F. Bounding surface plasticity. I: Mathematical foundation and hypoplasticity. J Eng Mech, 1986, 112: 966-987 CrossRef Google Scholar

[36] Yao Y P, Hou W, Zhou A N. UH model: Three-dimensional unified hardening model for overconsolidated clays. Géotechnique, 2009, 59: 451-469 CrossRef Google Scholar

[37] Bodas Freitas T M, Potts D M, Zdravkovic L. Implications of the definition of the Φ function in elastic-viscoplastic models. Géotechnique, 2012, 62: 643-648 CrossRef Google Scholar

[38] Kelln C, Sharma J, Hughes D, et al. An improved elastic-viscoplastic soil model. Can Geotech J, 2008, 45: 1356-1376 CrossRef Google Scholar

[39] Leoni M, Karstunen M, Vermeer P A. Anisotropic creep model for soft soils. Géotechnique, 2008, 58: 215-226 CrossRef Google Scholar

[40] Yin Z Y, Chang C S, Karstunen M, et al. An anisotropic elastic-viscoplastic model for soft clays. Int J Solids Struct, 2010, 47: 665-677 CrossRef Google Scholar

[41] Wang L Z, Dan H B, Li L L. Modeling strain-rate dependent behavior of KR0-consolidated soft clays. J Eng Mech, 2012, 138: 738-748 CrossRef Google Scholar

[42] Yin Z Y, Zhu Q Y, Yin J H, et al. Stress relaxation coefficient and formulation for soft soils. Géotech Lett, 2014, 4: 45-51 CrossRef Google Scholar

[43] Kongkitkul W, Kawabe S, Tatsuoka F, et al. A simple pneumatic loading system controlling stress and strain rates for one-dimensional compression of clay. Soils Found, 2011, 51: 11-30 CrossRef Google Scholar

[44] Nash D F T, Sills G C, Davison L R. One-dimensional consolidation testing of soft clay from Bothkennar. Géotechnique, 1992, 42: 241-256 CrossRef Google Scholar

[45] Zhang X, Lytton R L. Modified state-surface approach to the study of unsaturated soil behavior. Part III: Modeling of coupled hydromechanical effect. Can Geotech J, 2012, 49: 98-120 CrossRef Google Scholar

[46] Lu D, Ma C, Du X, et al. Development of a new nonlinear unified strength theory for geomaterials based on the characteristic stress concept. Int J Geomech, 2017, 17: 04016058 CrossRef Google Scholar

[47] Ma C, Lu D, Du X, et al. Developing a 3D elastoplastic constitutive model for soils: A new approach based on characteristic stress. Comput Geotech, 2017, 86: 129-140 CrossRef Google Scholar

[48] Voyiadjis G Z, Song C R. Finite strain, anisotropic modified cam clay model with plastic spin. I: Theory. J Eng Mech, 2000, 126: 1012-1019 CrossRef Google Scholar

[49] Yin Z Y, Jin Y F, Shen J S, et al. Optimization techniques for identifying soil parameters in geotechnical engineering: Comparative study and enhancement. Int J Numer Anal Methods Geomech, 2018, 42: 70-94 CrossRef ADS Google Scholar

[50] Jin Y F, Yin Z Y, Zhou W H, et al. A single-objective EPR based model for creep index of soft clays considering L2 regularization. Eng Geol, 2019, 248: 242-255 CrossRef Google Scholar

[51] Yin Z Y, Jin Y F, Shen S L, et al. An efficient optimization method for identifying parameters of soft structured clay by an enhanced genetic algorithm and elastic-viscoplastic model. Acta Geotech, 2017, 12: 849-867 CrossRef Google Scholar

[52] Yin Z Y, Yin J H, Huang H W. Rate-dependent and long-term yield stress and strength of soft Wenzhou marine clay: Experiments and modeling. Mar Georesources Geotech, 2015, 33: 79-91 CrossRef Google Scholar

[53] Lacerda W A. Stress-relaxation and creep effects on soil deformation. Dissertation of Doctoral Degree. Berkeley: University of California, 1976. Google Scholar

[54] Jiang J, Ling H I, Kaliakin V N, et al. Evaluation of an anisotropic elastoplastic-viscoplastic bounding surface model for clays. Acta Geotech, 2017, 12: 335-348 CrossRef Google Scholar

Copyright 2020  CHINA SCIENCE PUBLISHING & MEDIA LTD.  中国科技出版传媒股份有限公司  版权所有

京ICP备14028887号-23       京公网安备11010102003388号