Internal erosion can trigger severe engineering disasters, such as the failure of embankment dams and uneven settlement of buildings and sinkholes. This paper comprehensively reviewed the mechanisms of soil internal erosion studied by numerical simulation, which can facilitate uncovering the internal erosion mechanism by tracing the movement of particles. The initiation and development of internal erosion are jointly influenced by the geometric, mechanical, and hydraulic conditions, which determine the pore channels and force chains in soil. The geometric conditions are fundamental to erosion resistance, whereas the mechanical conditions can significantly change the soil erosion resistance, and the hydraulic conditions determine whether erosion occurs. The erosion process can be divided into particle detachment, transport, and clogging. The first is primarily affected by force chains, whereas the latter two are mostly affected by the pore channels. The stability of the soil is mainly determined by force chains and pore channels, whereas the hydraulic conditions act as external disturbances. The erosion process is accompanied by contact failure, force chain bending, kinetic energy burst of particles, and other processes due to multi-factor coupling.

In this study, an analytical model is proposed to calculate earth pressure considering the displacement of a rigid wall, and this model is developed based on the hyperbolic soil stress-strain relationship. By introducing the soil–failure ratio, the classic limit earth pressure theories can be incorporated into this analytical model. Using the axis-translation method, the earth pressure at rest is the initial state without wall movement. As the wall moves away from the soil mass, the earth pressure decreases and reaches the limit active earth pressure if the wall displacement reaches a threshold value. Similarly, the earth pressure increases to the limit passive earth pressure as the wall moves against the soil mass. This analytical model is verified when compared with experimental and numerical results and can predict the nonlinear earth pressure distribution under various modes of wall movement. This proposed analytical model provides an effective approach to predict the variation of earth pressure, with various wall displacements ranging from the limit active state to the limit passive state.