Formulation of strain-dependent hydraulic conductivity for a fractured rock mass

Abstract

By characterizing rock masses as anisotropic continua with one or multiple sets of critically oriented fractures, a methodology is developed in this paper to address the change in hydraulic conductivity resulted from engineering disturbance, material nonlinearity and anisotropy. An equivalent elastic–perfectly plastic constitutive model with non-associated flow rule and mobilized dilatancy is developed to describe the global nonlinear response of the rockmass under complex loading conditions. By separating the deformation of fractures from that of the equivalent medium, a strain-dependent hydraulic conductivity tensor is formulated. This not only considers the normal compressive deformation of the fractures, but also and more importantly, integrates the effect of material nonlinearity and post-peak shear dilatancy. Using this methodology, a closed-form solution is derived to describe the hydraulic behavior of a single fracture during combined normal and shear loading processes. The closed-form solution is validated by an existing coupled shear-flow test under wide ranges of normal and shear loads. Numerical simulations are performed to investigate the changes in hydraulic conductivities of a cubic block of fractured rock mass under triaxial compression and shear loading, as well as a circular underground excavation in a biaxial stress field at the Stripa mine, Sweden. The simulation results agree well with the in-situ experimental observations and an existing elastic strain-dependent analytical solution, respectively. The evaluation results clearly demonstrate that the proposed model is capable of predicting the changes in hydraulic properties of fractured rock masses under loading or excavation.