Mathematical Model for Piping Erosion Based on Fluid-Solid Interaction and Soils Structure

Piping is the results of soil internal erosion by seepage. In this paper, a mathematic model for the development of piping is formulated based on the principle of mass conservation and the consideration of the solid-fluid interactions. Soil particles are divided into three types, i.e., framework particles, movable particles and moving particles. The moving particles are derived from the movable particles after its statical balancing broken caused by the drag force of the water flow. The transforming of the movable particles to moving ones is considered as the source item of the particle transporting model. A mechanical model for a movable particle is proposed to determine the source item corresponding to the previous studies. As the complex of the model, it is solved by numerical method (The Finite Volume Method in this paper). The finite volume equations for the 2-D model are deduced. With the model and method discussed in the paper, a 2-D example's been solved. The result about the variation of the source item, seepage velocity, permeability coefficient, porosity, and the remaining movable particles density during the piping process are discussed and considered, which are all agreeing with the fact.