Revisiting the thermodynamics of hardening plasticity for unsaturated soils

TL;DR

This paper extends the thermodynamic framework for unsaturated soils, revealing the necessity of three stress variables and unifying existing models as special cases, to better describe soil behaviour under unsaturated conditions.

Contribution

It introduces a comprehensive thermodynamic approach requiring three stress variables for unsaturated soils, unifying existing models as special cases.

Findings

Three stress variables are necessary for accurate soil behaviour modeling.

A simplified model with a Bishop-like effective stress is derived.

Existing models are special cases of the proposed thermodynamic framework.

Abstract

A thermodynamically consistent extension of the constitutive equations of saturated soils to unsaturated conditions is often worked out through the use a unique 'effective' interstitial pressure, accounting equivalently for the pressures of the saturating fluids acting separately on the internal solid walls of the pore network. The natural candidate for this effective interstitial pressure is the space averaged interstitial pressure. In contrast experimental observations have revealed that, at least, a pair of stress state variables was needed for a suitable framework to describe 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 invasion of the soil by the liquid water phase through the retention curve; two effective stresses, which are required to describe the soil deformation at water saturation held constant. However a simple assumption related to the plastic flow rule leads to the final need of only a Bishop-like effective stress to formulate the stress-strain constitutive equation describing the soil deformation, while the retention properties still involve the suction and possibly the deformation. Commonly accepted models for unsaturated soils, that is the Barcelona Basic Model and any approach based on the use of an effective averaged interstitial pressure, appear as special extreme cases of the thermodynamic formulation proposed here.