The work input to saturated porous media undergoing internal erosion

The mechanism of internal erosion in porous media involves the microstructural evolutions induced by washing out of fine particles under different loading and seepage flow actions. Consequently, the effective stress on the solid skeleton is governed by the transition in velocity and stress of fine particles due to their detachment from the skeleton and then transport through pore channels, in addition to pore pressure. This study is to develop a formulation of work input to account for the interactions and mass exchanges between solid and fluid phases. Coupled mechanical-hydraulic erosion processes can be properly reflected through mass, momentum and energy balances based on Biot's mixture theory of a three-phase model. This leads to three separate stress-like variables, effective stress, erosion force and hydraulic gradient, in conjugation with three strain-like variables, strain, mass loss and seepage velocity, respectively. The effective stress tensor, different from the classical form by Terzaghi due to the effect of erosion, and coupled hydro-mechanical-erosion criteria are naturally derived from the proposed work input. They consider grain scale mechanisms describing the transition of erodible particles from the solid skeleton to the fluidized state. Systematic formulations and discussions are presented to highlight the promising features of our approach.