Revisiting the thermodynamics of hardening plasticity for unsaturated soils

Abstract

International audienceA 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

Review of fundamental principles in modelling unsaturated soil behaviour

“…Interested readers may refer to, e.g. Houlsby [44], Hutter et al [47], Gray and Schrefler [41], Sheng et al [114], Li [63], Samat et al [100], Coussy et al [16] and Zhao et al [157].…”

A fully coupled damage-plasticity model for unsaturated geomaterials accounting for the ductile–brittle transition in drying clayey soils

“…This approach can be extended to a broad range of unsaturated clay-bearing geomaterials, in which damage also represents the loss of bonding due to water menisci. Note for instance that in some thermodynamic frameworks (Coussy et al, 2010), air-water interfaces are part of the apparent solid skeleton.…”

A microstructurally based effective stress for unsaturated soils. E. E. ALONSO, J.-M. PEREIRA, J. VAUNAT and S. OLIVELLA (2010). Géotechnique 60, No. 12, 913–925, http://dx.doi.org/10.1680/geot.8.P.002

“…The authors did not intend to focus the paper on thermodynamics of unsaturated soils. Interested readers are referred to the work of Coussy et al (2010), which discusses the thermodynamics of elastoplasticity for unsaturated soils. This work is highly complementary to the proposition made in the paper mentioned.…”

“…Following the work of Coussy et al (2010) it can be shown that in conceptual unsaturated soil media described by a solid skeleton of particles in contact through interfaces having their own energy, a gas phase and a liquid phase, the work input to the solid skeleton (in a triaxial case: p, average stress; q: deviatoric stress) may be written, for an incompressible solid phase…”

“…This work is highly complementary to the proposition made in the paper mentioned. In brief, Coussy et al (2010) base their work on an energetic approach at the macroscopic scale and establish that the widely used Bishop's stress, the ÷ factor being equal to the degree of saturation, amounts to making strong assumptions on the deformation in both elastic and plastic regimes. This assumption can be called pore iso-deformation and consists in assuming that all pores deform identically, irrespective of their saturation state (and thus irrespective of the pressure to which they are subjected).…”