Modelling plasticity of unsaturated soils in a thermodynamically consistent framework

TL;DR

This paper develops a thermodynamically consistent framework for modeling unsaturated soils, revealing the necessity of three stress variables and unifying existing models like the Barcelona Basic Model as special cases.

Contribution

It introduces a general thermodynamic approach requiring three stress variables for unsaturated soils, unifying existing models within this comprehensive framework.

Findings

Three stress variables are necessary to describe unsaturated soil behavior.

The proposed framework encompasses the Barcelona Basic Model as a special case.

A simple internal deformation assumption leads to a single effective stress formulation.

Abstract

Constitutive equations of unsaturated soils are often derived in a thermodynamically consistent framework through the use a unique 'effective' interstitial pressure. This later is naturally chosen as the space averaged interstitial pressure. However, experimental observations have revealed that two stress state variables were needed to describe the stress-strain-strength behaviour of unsaturated soils. The thermodynamics analysis presented here shows that the most general approach to the behaviour of unsaturated soils actually requires three stress state variables: the suction, which is required to describe the retention properties of the soil and two effective stresses, which are required to describe the soil deformation at water saturation held constant. Actually, it is shown that a simple assumption related to internal deformation leads to the need of a unique effective stress to formulate the stress-strain constitutive equation describing the soil deformation. An elastoplastic framework is then presented and it is finally shown that the Barcelona Basic Model, a commonly accepted model for unsaturated soils, as well as all models deriving from it, appear as special extreme cases of the thermodynamic framework proposed here.