Mathematical capture of failure processes in elastoplastic geomaterials

This paper discusses a strategy to identify failure conditions in geomaterials simulated by elastoplastic constitutive laws. The main objective is to express different forms of failure through the same formalism. For this purpose, we use a set of material instability indices combining the concepts of loss of controllability and critical hardening modulus with a simple, but versatile, elastoplastic model for soils and soft rocks. This choice has allowed us to (i) compute the instability indices in analytical form, (ii) capture the implications of non-normality and prior deposition/lithification history and (iii) inspect a broad range of failure modes (e.g., brittle and ductile failure, static liquefaction and compaction banding). It is shown that, although each mode of failure has its own specific features, they can all be encapsulated in a unified mathematical representation. To obtain these results, the instability moduli must reflect the static/kinematic constraints that generate the failure process at stake. Thus, the instability indices are expressed as functions of both the hardening modulus and additional terms of kinematic origin, with the latter terms reflecting a control-dependence of the plastic response. Such results describe a procedure for achieving a unified definition of failure in elastoplastic geomaterials, which is closely linked to the theory of controllability and encompasses the intuitive notions of 'hardening' and 'softening' as particular cases.