Non-orthogonal elastoplastic constitutive model with the critical state for clay

Jingyu Liang,Dechun Lu,Xin Zhou,Xiuli Du,Wei Wu

doi:10.1016/j.compgeo.2019.103200

Abstract

A non-orthogonal elastoplastic model for clay is proposed by combining the non-orthogonal plastic flow rule with the critical state concept, and the model framework is presented from the perspective of the magnitude and direction of the plastic strain increment. The magnitude is obtained based on the improved elliptical yield function and the plastic volumetric strain dependent hardening parameter. The direction is determined by applying the non-orthogonal plastic flow rule with the Riemann-Liouville fractional derivative to the yield function without the necessity of additional plastic potential function. The presented approach gives rise to a simple model for soil with five parameters. All parameters have clear physical meaning and can be easily identified by triaxial tests. The model performance is shown by analyzing the evolution process of the yield surface, the hardening rule and the plastic flow direction. The capability of the proposed model to capture the mechanical behaviours of clay with different stiffness is also confirmed by predicting test results from the literature.

Highlights

A non-orthogonal elastoplastic model for clay is proposed by combining the non-orthogonal plastic flow rule with the critical state concept and presented from the perspective of the magnitude and direction of the plastic strain increment
If the plastic potential function is chosen to be the same with the yield function, the associated flow rule is adopted [1,2,3,4], in which the plastic flow direction is orthogonal to the yield surface
The associated flow rule has been reported to be unsuitable for describing the mechanical behaviours of geomaterials function is not identical to the yield function, the non-associated flow rule is adopted [8,9,10,11], and the plastic flow direction perpendicular to the plastic potential surface is non-orthogonal to the yield surface

Summary

Introduction

The constitutive model can be used to determine the two basic elements of the strain increment produced by the current stress increment, namely (i) magnitude and (ii) direction. Within the framework of plasticity theory, the magnitude of the plastic strain increment can be determined by the consistency condition together with the yield function and the hardening parameter. The direction of plastic strain increment can be directly determined by the non-orthogonal gradient of the yield function. In order to determine the general tensor form of the plastic strain increment based on the commonly used yield function for soil, a general form of non-orthogonal plastic flow rule [22, 23] is proposed based on the fractional partial derivative and the covariant transformation. During establishing non-orthogonal elastoplastic models for soil [21, 22], the plastic flow direction is expressed by the Caputo fractional derivative. As indicated by Eq (13), mp associated with the volumetric strain dependent hardening parameter affects the calculation of Λ, which will be discussed in the below section

Direction of plastic strain increment

Model predictions

Conclusions