Mechanical properties and energy conversion of 3D close-packed lattice model for brittle rocks

Numerical simulations using the 3D discrete element method can yield mechanical and dynamic behaviors similar to rocks and grains. In the model, rock is represented by bonded elements, which are arranged on a tetrahedral lattice. The conversion formulas between inter-element parameters and rock mechanical properties were derived. By using the formulas, inter-element parameters can be determined according to mechanical properties of model, including Young's modulus, Poisson's ratio, tensile strength (Tu), compressive strength (Cu) and coefficient of internal friction. The energy conversion rules of the model are proposed. Based on the methods, a Matlab code “MatDEM” was developed. Numerical models of quartzite were used to validate the formulas. The tested mechanical properties of a single unit correspond reasonably well with the values of quartzite. Tested Tu and Cu with multiple elements are lower than the values predicted by the formulas. In the simulation of rock failure processes, mechanical energy conversed between different forms and heat is generated, but the mechanical energy plus heat always remains constant. Variations of breaking heat and frictional heat provide clues of the fracturing and slipping behaviors of the Tu and Cu tests. The model may be applied to a wide range of geological structures that involve breakage at multiple scales, heat generation and dynamic processes.