SCIENCE CHINA Technological Sciences, Volume 63 , Issue 5 : 791-808(2020) https://doi.org/10.1007/s11431-019-9536-y

A 3D elastic-plastic-viscous constitutive model for soils considering the stress path dependency

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  • ReceivedMar 27, 2019
  • AcceptedJun 6, 2019
  • PublishedNov 19, 2019


In order to consider the stress path dependency of soils, this paper decomposes any arbitrary stress path into several infinitesimal stress paths. Then the infinitesimal stress path is further transformed into the superposition of two parts, i.e., a constant stress ratio part and a constant mean stress part, which are sufficiently close to the real stress path. The plastic strain increments under the transformed paths are determined separately, and then the plastic strain under any path is obtained. Based on the instantaneous loading line of normally consolidated soil, a reference state line is proposed to determine the overconsolidation ratio and creep time of soil. The overconsolidation ratio is introduced into the viscous flow rule to obtain the viscous strain increment. The stress-strain-time relationship for triaxial compression condition is extended to 3D stress condition by the transformed stress method. The proposed model adopts only seven material parameters and each of them has a clear physical meaning. Comparisons with test results demonstrate that the model can not only reasonably predict the plastic strain under typical stress paths of excavation, but adequately capture the time-dependent behaviours of soils, including creep, stress relaxation and strain rate effect.

Funded by

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

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


This work was supported by the National Natural Science Foundation of China (Grant Nos. U1839201, 51778026, 51421005 & 51538001).


Appendix: Derivation of characteristic strain rate

At characteristic strain rate, the slope of the isotropic compression line is λ. In this case, the isotropic compression line can be described as follows:


where the void ratio increment de is related to dεv via.


Substituting eq. (A1) into eq. (A2), one can obtain:


According to eqs. (3), (19) and (26), the volumetric strain increment under isotropic compression conditions can be expressed as follows:


Substituting eq. (A3) into eq. (A4) yields:


where ξiso in eq. (A5) can be obtained by eq. (15):


Substituting eq. (A6) into eq. (A5), one can obtain the characteristic strain rate ε˙ch:



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