Critical Hydraulic Gradient of Piping Erosion Under Free Flow and Seepage Flow Coupling Model

This paper proposes a coupling model for evaluating the occurrence of piping erosion under free flow and seepage flow. The model employs the Navier–Stokes equation to describe free water flow in a pore channel and the Brinkman-extended Darcy equation to describe seepage flow in soft soils. The expression of the critical hydraulic gradient of piping erosion was derived based on the force limit equilibrium of a single soil particle within the pore channel. The results of the theoretical calculation of the proposed model are in good agreement with the results obtained by two classical piping tests. However, compared with existing formulas, the proposed formula has better generalization and accuracy. Moreover, the critical hydraulic gradient varies linearly with the soft soil porosity (negative correlation), the soil particle diameter (positive correlation) inside the pore channel, and the stress jump coefficient (positive correlation) at the interface between the pore channel and the soft soils.