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In this paper, a new approach has been developed for predicting the hydraulic and mechanical relationship of individual fractures subjected to normal stress and compression-shear stress. Considering that the closure process of rough fracture subjected to normal stress can be divided into two phases (linear behavior and nonlinear behavior), a relationship between normal stress and fracture aperture is derived through the minimum potential energy principle. Then, a formulation for calculating fracture permeability during shearing and compression processes is developed. Furthermore, a formulation for determining fracture aperture during the crack growth process is obtained, which is further implanted into the permeability model to predict the hydraulic behavior of fractured rock during fracture propagation. This new model not only considers the normal deformation of the fracture but also, and more importantly, integrates the effect of fracture propagation and shear dilation. Theoretical studies demonstrate that fracture permeability increases nonlinearly during fracture propagation. At last, experimental results and analytic results are compared to demonstrate the usefulness of the proposed models, and satisfactory agreements are obtained.

Hydraulic and Mechanical Relationship of Individual Fracture in Rock under Compression and Shearing: Theoretical Study