A micro‐macromechanical compression model of crushing in granular materials based on a probabilistic approach and energy aspects

Abstract

This paper presents a micro and macromechanical model to estimate the grading evolution and plastic strain caused by particle crushing in the isotropic compression of granular materials. A joint-probability particle crushing criterion of the maximum contact force and the particle strength is proposed to calculate the incremental particle crushing probability. The dependence of the contact force and particle strength during a multistage loading process is recognized. The distribution of the maximum contact force and the magnitude of the mean contact force are strictly derived from the stress-force relationship and maximizing the statistical entropy. The coordination number of polydisperse particles is derived from the geometric relationship and applies to any grading curve, which enables the consideration of the coupling effects of particle crushing and grading evolution during a multistage loading process. A multipoint load particle crushing criterion involving the particle strength size effect is adapted. To simulate the grading evolution, the fractal distribution assumption and Markov chain model are applied to describe the fragmentation mess after crushing. Finally, following the work equation by Mcdowell and Bolton, the energy consumption of particle crushing and the corresponding plastic strain are correlated with the increase in the particle surface area. The model is verified by published experimental data of silica sand with different initial grading curves and carbonate sand with different grain sizes.