Work and energy equations and the principle of generalized effective stress for unsaturated soils

Abstract

SUMMARYThe effective stress principle has been efficiently applied to saturated soils in the soil mechanics and geotechnical engineering practice; however, its applicability to unsaturated soils is still under debate. The appropriate selection of stress state variables is essential for the construction of constitutive models for unsaturated soils. Owing to the complexity of unsaturated soils, it is difficult to determine the deformation and strength behaviors of unsaturated soils uniquely with the previous single-effectivestress variable theory and two-effective-stress-variable theory in all the situations. In this paper, based on the porous media theory, the specific expression of work is proposed, and the effective stress of unsaturated soils conjugated with the displacement of the soil skeleton is further derived. In the derived work and energy balance equations, the energy dissipation in unsaturated soils is taken into account. According to the derived work and energy balance equations, all of the three generalized stresses and the conjugated strains have effects on the deformation of unsaturated soils. For considering these effects, a principle of generalized effective stress to describe the behaviors of unsaturated soils is proposed. The proposed principle of generalized effective stress may reduce to the previous effective stress theory of single-stress variable or the two-stress variables under certain conditions. This principle provides a helpful reference for the development of constitutive models for unsaturated soils.

The input work expression and the thermodynamics-based modelling framework for unsaturated expansive soils with double porosity

“…At the microscopic level, the aggregates are constituted of clay platelets and adsorbed water. Based on the porous media theory, the stress tensors of phases combine additively to form the total stress [25,[27][28][29]  …”

“…The constitutive variables consist of stresses, strains, thermodynamics variables, etc. Based on the thermodynamics theory, the stress and strain variables can be chosen from the expression of input work of unsaturated soils [25,27,28]. At the macroscopic level, the unsaturated expansive soil is composed of aggregates, capillary water, gas and adsorbed water phases.…”

“…Houlsby [27], Zhao et al [28] and Borja and Koliji [25] have developed the expression of the work input of unsaturated soils and unsaturated porous continua with double porosity, respectively, which are different from eq. (12) .…”

Constitutive modeling for unsaturated soils considering gas hardening effect

“…The macroscopic continuum medium theory has already been used in unsaturated soils and has been developing rapidly in recent years [2][3][4]. Zhao et al [5][6][7] has done some research in this area and proposed a model framework for unsaturated soils [7]. Based on that framework [7], some simplifications are made to develop an isotropic elasto-plastic model that could consider the gas effect in the present study.…”

Volume change behavior of unsaturated soils under non-isothermal conditions

“…It appears able to unify the theoretical basis of unsaturated soil mechanics [12][13][14][15][16][17]. Recently, multi-phase porous media theory was used by our research team as the basis for some useful insights into unsaturated soil mechanics including the principle of generalized effective stress and constitutive relations for unsaturated soils [18][19][20], continuum porous medium soil mechanics and its application in constitutive relationships of unsaturated soils [21], and the nonlinear multi-field coupled model for multi-constituent three-phase soils [22]. This paper is based on the above research and is centered on assessment of the theory framework proposed by Cai et al [22].…”