Internal erosion is one of the main factors that cause failure of soil slopes. This study presents a new modeling method that considers the change in the soil gradation during internal erosion. The porosity and seepage velocity are calculated using the mass-conservation equations of the solid and fluid parts of saturated soil. The erosion, deposition, and migration of fine particles are described by treating particles of various sizes as independent species. The particle size is thus introduced as an extra dimension to supplement the basic dimension of the geometric model. The equations on the basic dimension and the extra dimension are connected by refinement and integration processes. The simulation results show that, in the process of internal erosion, the distribution of particles of any size can be obtained. This method can be further used to study the effects of internal erosion on the hydraulic and mechanical properties of soil, which is important for preventing as well as responding to engineering accidents and natural disasters resulting from internal erosion.

内部侵蚀是引起土质边坡破坏的主要因素之一。这项研究提出了一种新的建模方法，该方法考虑了内部侵蚀过程中土壤等级的变化。孔隙率和渗流速度是使用饱和土的固体和流体部分的质量守恒方程计算的。细颗粒的腐蚀，沉积和迁移是通过将各种大小的颗粒视为独立物种来描述的。因此引入了粒度作为额外的尺寸，以补充几何模型的基本尺寸。基本维度和额外维度上的等式通过优化和集成过程进行连接。仿真结果表明，在内部腐蚀过程中，可以得到任意大小的颗粒分布。