三维可变形圆化多面体离散单元法

Discrete element method based on three dimensional deformable spheropolyhedra

为真实模拟岩体的变形特性与运动形态,将圆化多面体离散元法与有限单元法结合,提出一种三维可变形圆化多面体离散单元法。该方法既能真实表征块体的不规则特征,又降低了接触判断的难度,同时能准确反映块体的变形特性。在求解切向接触力时,将接触判断对象从接触对简化为单元整体,显著提高了计算效率。为分析块体变形特性,在块体离散单元内部划分有限元网格,将最外层有限元网格作为最小接触单元。采用直接平均法,将接触力转化为等效节点力,并采用非线性有限单元法实现对单元变形特性的精确模拟,克服了圆化多面体无法反映单元变形的缺陷。通过5个算例论证了新方法在捕捉单元变形、运动形态以及其力学特征等方面的准确性和高效性。

In order to simulate the deformation characteristic and motion forms of rock mass,a three-dimensional deformable spheropolyhedral discrete element method is presented,by combining the spheropolyhedral discrete element method(DEM)and the finite element method(FEM).This method effectively captures the irregular characteristics of the block,simplifies contact detection,and provides accurate representations of block deformation.The contact detection object is simplified from individual contact pair to the entire element during tangential contact force calculation,which significantly improves the computational efficiency.In order to analyze the deformation characteristics of the block,the finite element mesh is divided inside the discrete element of the block,with the outermost mesh defined as the minimum contact element.Contact forces are translated to equivalent nodal contact forces using the direct average method.Nonlinear finite element methods accurately simulate element deformation,overcoming the rigid body assumption of spheropolyhedra.Five numerical examples are simulated to verify the accuracy of the proposed method in capturing the deformation,motion morphology and mechanical characteristics of the element.