This paper presents a coupled finite and discrete-element model (FEM and DEM) to simulate internal erosion. The model is based on ICY, an interface between COMSOL, an FEM engine, and YADE, a DEM code. With this model, smaller DEM subdomains are generated to simulate particle displacements at the grain scale. Particles in these small subdomains are subjected to buoyancy, gravity, drag and contact forces for short time steps (0.1 s). The DEM subdomains provide the macroscale (continuum) model with a particle flux distribution. Through a mass conservation equation, the flux distribution allows changes in porosity, hydraulic conductivity and hydraulic gradient to be evaluated for the same time steps at a larger, continuum scale. The updated hydraulic gradients from the continuum model provide the DEM subdomains with updated hydrodynamic forces based on a coarse-grid method. The number of particles in the DEM subdomains is also updated based on the new porosity distribution. The hierarchical multiscale model (HMM) was validated with the simulation of suffusion. Results for the proposed HMM algorithm are consistent with results based on a DEM model incorporating the full sample and simulation duration. The proposed HMM algorithm could enable the modelling of internal erosion for soil volumes that are too large to be modelled with a single DEM subdomain.

中文翻译：

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具有离散和有限元的内部侵蚀的分层多尺度数值模拟

本文提出了一个耦合有限元和离散元模型（FEM和DEM）来模拟内部腐蚀。该模型基于ICY（COMSOL是FEM引擎，而YADE是DEM代码之间的接口）。使用此模型，可以生成较小的DEM子域，以模拟颗粒级的粒子位移。这些小的子域中的粒子在短时间内（0.1 s）受到浮力，重力，阻力和接触力的作用。DEM子域为宏观（连续）模型提供了粒子通量分布。通过质量守恒方程，通量分布允许以较大的连续尺度在相同的时间步长评估孔隙率，水力传导率和水力梯度的变化。连续模型的更新水力梯度基于粗网格方法为DEM子域提供了更新的水动力。DEM子域中的粒子数量也会根据新的孔隙率分布进行更新。分层多尺度模型（HMM）已通过模拟弥散验证。提出的HMM算法的结果与基于DEM模型的结果一致，该模型结合了完整的样本和仿真持续时间。所提出的HMM算法可以实现对土壤体积的内部侵蚀建模，而这些土壤体积太大而无法使用单个DEM子域进行建模。提出的HMM算法的结果与基于DEM模型的结果一致，该模型结合了完整的样本和仿真持续时间。所提出的HMM算法可以实现对土壤体积的内部侵蚀建模，而这些土壤体积太大而无法使用单个DEM子域进行建模。提出的HMM算法的结果与基于DEM模型的结果一致，该模型结合了完整的样本和仿真持续时间。所提出的HMM算法可以实现对土壤体积的内部侵蚀建模，而这些土壤体积太大而无法使用单个DEM子域进行建模。