Equivalent Biot and Skempton coefficients for fractured rocks

Biot coefficient and Skempton coefficient are key descriptors of the coupled hydro-mechanical (HM) behavior of fluid-saturated porous materials. Biot coefficient defines a relationship between an applied load, fluid pressure and the stress that effectively acts on the solid skeleton. Skempton coefficient defines the temporary pore pressure variation caused by the application of a load in undrained conditions. The product of the two coefficients establishes the impact of an applied load on the solid skeleton, and thus the material deformation, under undrained conditions. The two coefficients are generally estimated through analytical expressions valid for isotropic homogeneous materials, or they are experimentally estimated at the laboratory sample-scale.In this work, we define a framework for the evaluation of equivalent Biot coefficient and Skempton coefficient at the scale of a fractured rock mass. We derive theoretical expressions that estimate the two equivalent coefficients from the properties of both the porous intact rock and the discrete fracture network (DFN), including fractures with different orientation, size, and mechanical properties. These formal expressions are validated against results from fully coupled hydro-mechanical simulations on systems with explicit representation of deformable fractures and rock blocks. We show that the coefficients largely vary with the fracture orientation and density, which implies that disregarding the presence of fractures may incur an incorrect evaluation of the HM response. We also discuss the variability of the coefficients under different settings of DFN properties, including realistic scaling conditions of size-dependent and stress-dependent fracture properties.