Equivalent Biot and Skempton Poroelastic Coefficients for a Fractured Rock Mass from a DFN Approach

A quantitative and analytical approach is adopted to estimate two important parameters for coupled hydro-mechanical analysis at the scale of a fractured rock mass, namely the equivalent Biot effective stress coefficient \(\overline{\alpha }\) and Skempton pore pressure coefficient \(\overline{B}\). We derive formal expressions that estimate the two equivalent poroelastic coefficients from the properties of both the porous intact rock and the discrete fracture network, which includes fractures with different orientation, size, and mechanical properties. The coefficients are equivalent in the sense that they allow effectively predicting the volumetric deformation of the fluid-saturated fractured rock under an applied load in drained and undrained conditions. The formal expressions are validated against results from fully coupled hydro-mechanical simulations on systems with explicit representation of deformable fractures and rock blocks. We find that the coefficients are highly anisotropic as they largely vary with fracture orientations with respect to the applied stress tensor. For a given set of fracture and rock properties, \(\overline{B}\) increases with the ratio of normal to average stress undergone by the fractures, while the opposite occurs for \(\overline{\alpha }\). Additionally, both \(\overline{\alpha }\) and \(\overline{B}\) increase with fracture density, which directly impacts the deformation caused by a load in undrained conditions. Because the effective stress variation is proportional to the applied load by \(\left(1-\overline{\alpha } \overline{B}\right),\) a factor that partly compensates for the decrease in equivalent rock stiffness caused by the fractures, a fully saturated fractured rock may deform less than an intact rock in undrained conditions, while the opposite occurs in dry conditions.