A five-phase approach, SPH framework and applications for predictions of seepage-induced internal erosion and failure in unsaturated/saturated porous media

Seepage-induced internal erosion and failure in unsaturated/saturated porous media is challenging for computational simulations as they involve the behaviour, interactions (solid, air, water) and transformation (fluidization and deposition of fines grains) of different phases. Tackling this challenging problem requires correct mathematical descriptions of phase interactions and transformation together with a robust computational framework, both of which are addressed in this paper. The new mathematical model and coupled governing equations based on the continuum mixture theory enable the use of a single set of SPH particles for the descriptions of behaviour, interactions and phase transformation of all five phases of the porous media (soil skeleton, erodible fines particles, fluidised particles, water, and air), including the effect of both saturation and erosion on the shear strength of porous media. A fully explicit and stabilised SPH framework that allows accurate SPH approximations of spatial gradients is proposed for the numerical solutions of coupled governing equations. The proposed computational framework performs well in benchmark tests against available analytical and numerical solutions and achieved reasonable agreements with experiments. Numerical results obtained from the predictions of seepage-induced erosion and failure demonstrate that the proposed computational framework is efficient for addressing challenging problems involving coupled flow-deformation, seepage-induced internal erosions, and large deformation failures of unsaturated/saturated porous media.