The impact of fractures on the Biot and Skempton coefficients of fractured rocks

The Hydro-Mechanical (HM) behavior of fluid-saturated porous materials is crucial in determining the response of the subsurface to natural processes, such as glaciation, and to engineering applications, such as construction/excavation, reservoir impoundments, geo-energy extraction, and deep geological disposal of used nuclear fuel. Two fundamental coefficients, i.e., the Biot coefficient and the Skempton coefficient, define the contribution of the fluid in subsurface media to maintain the mechanical equilibrium against perturbations in stress and pore fluid pressure. Despite the central importance of these two coefficients, which may broadly range between 0 and 1, their estimation is often oversimplified in most scientific and engineering studies that treat large-scale saturated problems by assuming a uniform geological material, with the coefficients estimated experimentally at the laboratory sample-scale or analytically through expressions valid for isotropic homogeneous materials.

In this work, we analyze the impact of fractures on the HM behavior of fractured rocks by looking at the equivalent Biot coefficient and Skempton coefficient. We adopt a recently defined framework in which the equivalent coefficients are estimated from the properties of both the porous intact rock and the discrete fracture network (DFN), including fracture size, orientation and mechanical properties. We extend this theory to incorporate more realistic assumptions on fractures, such as size-dependent and stress-dependent fracture properties. This setting allows us to explore the range of variability of the two equivalent coefficients with respect to the stochastic distribution of fracture size and orientation in the rock, and with respect to depth and stress faulting regime. We show that the coefficients are larger if 1) the network is placed in shallow rocks (i.e., low stress regime), 2) the network is populated by a few large fractures rather than by many small fractures, and 3) the fractures are oriented parallel to the in-situ maximum principal stress and normal to the applied stress.