Discrete Element Modelling of Kinematics of Void Collapse

土壤是一种由固体颗粒和空隙组成的复杂材料。当土壤被一维压缩时(即在活塞中)，土壤的永久变形使得空洞体积的减少与施加的宏观应力(力除以活塞的面积)有关。在空洞体积和应力之间有各种提出的关系，其中一些有理论上的证明，但还没有实验证明这种关系应该是什么(例如，空洞体积应该是应力的幂函数、应力的对数函数还是其他函数)。离散元方法实现了这一点，因为土壤颗粒可以建模为球、一团块的球或一组粘结的球，然后这些球可能会破裂。颗粒间的接触力与颗粒的相对位移有关。这些力通过牛顿第二定律被用来计算加速度，这些加速度被两次积分得到位移，从而得到新的接触力。通过一次只允许一个粒子破裂(例如，使所有其他粒子都不可粉碎，具有高结合强度)，就有可能研究当单个粒子破裂时，空隙空间的减少，并将其与该粒子的大小、碎片的大小、存在的其他粒子的大小和应力水平联系起来。这将使工程师知道空洞体积和应力之间的正确关系是什么，以及为什么。

Soil is a complex material comprising solid particles and voids. When a soil is compressed one-dimensionally (i.e. in a piston), the permanent deformation of the soil is such that the reduction in volume of voids is related to the macroscopic stress applied (force divided by the area of the piston). There are various proposed relationships between the void volume and stress, some with theoretical justification, but as yet there has been no experimental proof of what the relationship should be (e.g. whether void volume should be a power function of stress, a logarithmic function of stress, or some other function). The discrete element method makes this possible, as a soil particle can be modelled as a ball, a clumped group of balls, or a group of bonded balls which can then fracture. The contact forces between the particles are related to their relative displacements. These forces are used via Newton's 2nd law to calculate accelerations, which are integrated twice to give displacements and hence new contact forces. By allowing only a single particle to fracture at a time (by making all others uncrushable, with high bond strengths for example), it will be possible to investigate the reduction in void space which occurs when a single particle breaks, and relate it to the size of that particle, the sizes of the fragments, the sizes of other particles present, and stress level. This will enable engineers to know what the correct relationship between void volume and stress is, and why.