Numerical modeling of the coupled hydro-mechanical internal erosion process

The phenomenon of internal erosion occurs when fine particles are pulled off by seepage forces and transported throughout the matrix of soil particles. The loss of fine particles due to seepage flow affects the mechanical behavior of the soil. Conversely the change of porosity influences the permeability of the soil and therefore the hydraulic behavior as well. It may lead to important damages in geo-engineering works such as earth dams, dikes and tunnels. Under such circumstances, the numerical modeling of the coupled hydro-mechanical internal erosion process by a continuous approach is addressed in this present work. Firstly, a four-phase continuum model of internal erosion was reviewed: in a fluid-saturated granular media, two constituents have been introduced for the fluid suspension to describe its hydraulic behavior, which are water (f) and fluidized particles (a); The soil skeleton itself consists of a mixture of coarse grains (sn) and fine particles (sa), and only the fine particles are erodible. The flow rate in a porous medium was governed by Darcy’s law, whilst Carman-Kozeny equation was adopted to consider the influence of porosity on the physical permeability. This boundary value problem (BVP) was then closed by a formulation for the volume exchange termed by nˆ . Then, the coupling between the hydraulic and mechanical behaviors of soil was addressed. The coupling can conceptually be divided into two parts. In the first part, the erosion results in a porosity redistribution, which leads to the permeability inhomogeneity. As a consequence, the pore pressure and effective stress will be redistributed. In the second part, the loss of fine particles due to seepage flow affects the mechanical behavior of the soil. Therefore, a critical-state-based model was adopted in order to consider the influence of the change of void ratio and fines content on the yield surface. The derived mathematical model, consisting of stress equilibrium equation, mixture flow equation and mass balance equation, is solved numerically by a discretization procedure using the Galerkin finite element method in space and finite differences in time. It was then applied to a 2D computational example. An erosion process takes place leading to a decrease of fines of soil skeleton near the crack. The alteration of porosity and fines was observed. Comparisons of simulations based on different condition of erosion were made, which indicate: (1) for the condition without erosion, the settlement is only caused by the redistribution of pore pressure at the step of boundary change; (2) for the condition coupled with erosion, the settlement is first caused by the redistribution of effective stress at the step of boundary change, and it will keep developing because of the change of mechanical behavior of the soil, which is controlled by the evolution of porosity and fines content