A plastic strain-based damage model for heterogeneous coal using cohesion and dilation angle

Coal as the fundamental element in underground coal mining is well-known as a heterogeneous geomaterial, and the knowledge of its deformation processes and failure mechanisms is important for the prediction and prevention of dynamic disasters and the design of stable underground structures. In this paper, after analysing the pre-peak strain hardening, the post-peak strain softening, and the associated dilation behaviours of heterogeneous coal under loading, a plastic strain-based damage model that consists of the heterogeneity function, the damage stress-strain function, the cohesion function and the dilation angle function, was developed. In this model, the heterogeneity was characterised by considering the micro-unit strength as referring to the Weibull function. The damage stress-strain function was defined by the Weibull function and the plastic strain based on the continuous damage mechanics theory. The cohesion and the dilation angle were expressed by a modified damage function while the friction angle is constant, which were simultaneously implemented in a geotechnical simulator together with the heterogeneity function and the Mohr-Coulomb yield criterion with an embedded tension cut-off. The numerical results are consistent with the experimental and theoretical results. It can be concluded that a large variety of stress-strain relation curves, characterised by the pre-peak elastic and strain-hardening and the post-peak strain-softening, as well as their dilation behaviour, can be accurately reproduced by a group of fitted parameters.