Estimation of Elastic Compliance Matrix of Rock Mass Containing Penny-Shaped Fractures

Abstract

In geotechnical engineering, fracture fillings or rough fracture surfaces often resist deformation and enhance the equivalent elastic moduli of fractured rock masses. In this study, the normal stiffness and shear stiffness of penny-shaped fractures were incorporated into the open-fracture model to account for the normal and shear resistance of fracture fillings. Based on the derived displacements of a penny-shaped fracture incorporating fracture stiffness, the compliance matrices of two special fracture distributions, the parallel distribution and random distribution, were obtained. The analytical results show that three-dimensional (3D) models predicted larger elastic moduli than the corresponding two-dimensional (2D) models, and models considering fracture stiffness predicted larger elastic moduli than the open-fracture models. Elastic moduli were underestimated by 30–40% in a 2D open-fracture model compared with the result of the corresponding 3D model. The difference in elastic moduli between 2D and 3D models was found to decrease when the fracture stiffness was considered. In the present study, the difference was less than 15%.