Computing the damage and fracture energy in a coal mass based on joint density

Coal joints and cleats are geological discontinuities that are the most important factors that affect the mechanical responses of a coal mass under stress. The joint and coal mass interaction and the mode of failure dominate the mechanical behaviour of jointed coal masses, and therefore the stability of coal excavations. The shear or mixed shear/tensile failure changes to tensile failure by increasing the confining pressure, discontinuity length and angle. This paper extends a thermodynamic approach to constitutive modelling of the coal mass by developing local and non-local damage models based on the joint and cleat density and the dip angle. A consistent and rigorous statistical framework is constructed, which incorporates both local and non-local features into the constitutive modelling. This is an important consideration in developing damage constitutive models based on the trajectory of the failure surfaces in a coal mass.An equation is derived to calculate the fracture energy which is a function of the joint density either in a single direction or crossed conditions.