Discrete Element Modelling of Kinematics of Void Collapse

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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.