Mathematical development of stress-strain law for rock block contacts

The fracture behavior of rock block contacts has been studied for many years. Unfortunately, up to now, there is not a rigorous formulation or a solid theoretical foundation to support it. A mathematical development to represent the failure mechanism which occurs in the contacts between rock blocks is presented to evaluate the performance of breaking mechanism of such blocks relating it to the morphology of the contact and mechanical parameters of the material. The examined framework includes the evaluation of the surface roughness of first order in the failure mechanism of the granular particles of large size and the development of a theoretical model describing the morphology of the contact between rock blocks.