Discussing the definition of the second-order work for unsaturated soils

The volumetric compaction due to wetting processes is a phenomenon observed quite often in unsaturated soils. Under certain circumstances, saturation events can result into a sudden and unexpected collapse of the system. These phenomena are usually referred to as wetting-induced collapses, without providing any detailed theoretical justification for this terminology. In order to predict in a general fashion the occurrence of coupled instabilities induced by saturation processes, a generalization of the theoretical approaches usually employed for saturated geomaterials is here provided. More specifically, this paper addresses the problem of hydro-mechanical instability in unsaturated soils from an energy standpoint. For this purpose, an extension of the definition of the second-order work is here suggested for the case of unsaturated porous media. On the basis of some examples of numerical simulations of laboratory tests, coupled hydro-mechanical instabilities are then interpreted in the light of this second-order energy measure. Finally, the implications of the theoretical results here presented are commented from a constitutive modelling perspective. Two possible alternative approaches to formulate incremental coupled constitutive relations are indeed discussed, showing how the onset of hydro-mechanical instabilities can be predicted using an extended form of Hill's stability criterion.