Thermodynamic consistent gradient-poroplasticity

Complex degradation processes of partial saturated media like soils during post-peak regime are strongly dependent on humidity, stress state, boundary conditions and material parameters, particularly porosity. To realistically and objectively describe the dramatic change from diffuse to localized failure mode or from ductile to brittle ones, accurate constitutive theories and numerical approaches are required. In this paper, a non-local gradient poroplastic model is proposed for partial saturated media based on thermodynamic concepts. A restricted non-local gradient theory is considered, following (Mroginski, et al. Int. J. Plasticity, 27:620-634) whereby the state variables are the only ones of non-local character. The non-local softening formulation of the proposed constitutive theory incorporates the dependence of the gradient characteristic length on both the governing stress and hydraulic conditions to realistically predict the size of the maximum energy dissipation zone. The material model employed in this work to describe the plastic evolution of porous media is the Modified Cam Clay, which is widely used in saturated and partially saturated soil mechanics. To evaluate the dependence of the transition point between ductile and brittle failure regime in terms of the hydraulic and stress conditions, the localization indicator for discontinuous bifurcation is formulated for both drained and undrained conditions, based on wave propagation criterion