A depth-integrated viscoplastic model for dilatant saturated cohesive-frictional fluidized mixtures: Application to fast catastrophic landslides

Fast catastrophic landslides, flowslides, avalanches, lahars and debris flows involve fluidized mixtures of soil and water. To improve safety of human settlements endangered by them it is necessary to predict their occurrence, triggering conditions, path, velocity and depth, and runout distance. Predictions are based on models (mathematical, rheological and numerical). In this paper (i) we introduce a hierarchical set of mathematical models describing solid-pore fluid coupling, (ii) we introduce the concept of dynamical critical state line (DCSL), depending on shear strain velocity, which generalizes the critical state line (CSL) used in Geomechanics to describe residual conditions at failure, (iii) we propose a dilatancy term depending on the distance to the DCSL, (iv) we introduce a viscoplastic law for dilatant cohesive-frictional fluids based on a deviatoric and a volumetric part, and (v) we describe the depth-integrated version of the proposed rheological model, providing all necessary items to be implemented in a numerical model.