Isotropic and Cross-Anisotropic Stiffness Parameters for Unsaturated Soils Using Conventional and Bishop's Stress State Variables

Abstract

This paper aims to examine the ability of conventional unsaturated stress state variables (i.e., net stress, $\overline{\sigma }$ and suction, s) and alternative unsaturated stress state variables (i.e., Bishop's stress, σ* and modified suction, s*) in demonstrating isotropic and cross-anisotropic stiffness parameters for unsaturated soils in the formulation of stiffness matrices and compliance matrices. To do this, a Matlab code was generated to give outputs of the formulation of the stiffness matrices. The bulky outputs of the code were simplified. To check whether the conventional or alternative unsaturated stress state variables produce less complex outputs, a comparison between them was performed in the form of the stiffness matrices and compliance matrices under isotropic and cross-anisotropic unsaturated conditions. For isotropic unsaturated soils, the comparison showed that the stiffness and compliance matrices could be demonstrated in a similar level of complexity using both conventional and alternative unsaturated stress state variables. For cross-anisotropic unsaturated soils, alternative unsaturated stress state variables successfully formed a manageable level of complexity in formulating the stiffness matrix and uncoupling between the mechanical response and water retention behavior in the formulation of a compliance matrix. Conversely, conventional unsaturated stress state variables could not demonstrate these two key features of the matrices.