A Unified Model for Characterisation and Mechanical Behaviour of Rock Fractures

Roughness and aperture are two important characteristic parameters of rock fractures. It has been demonstrated by many authors that the knowledge of roughness does not directly lead to that of aperture, and aperture is to be handled as a separate geometrical descriptor. For determining normal deformability and flow response of a fracture, the aperture distribution and the mechanical properties of the rock matrix are required. When shearing of joints and fractures is considered, roughness comes into play and affects the evolution of the aperture distribution. The aperture distribution can be evaluated by knowing the correlation between the asperity profiles of the rock walls of a rock fracture. Thus, the distributions of the contact area and void space determine the fracture dilation and hydraulics during shearing. In this study, a mathematical formulation of roughness and aperture of rock fractures is proposed. Both aperture and roughness are interpreted as scale-dependent quantities, and their statistical models are described by fractal theory. The theoretical results are in very good agreement with experimental results and published data. Furthermore, a constitutive model for the hydro-mechanical behaviour of rock fractures is developed based on the new theoretical description of the geometry. The model is based on a fractal-island description of the contact areas and on an approach of micromechanics.