A formalism to compute permeability changes in anisotropic fractured rocks due to arbitrary deformations

The Liu-Elsworth (1997) formalism that predicts permeability in deformed fractured rock has been highly useful and successful in numerous engineering situations involving mining, coal-bed methane and shale gas extraction. The formalism assumes the rock's fractures are aligned with three orthogonal axes and that the rock is subjected to strains along these three directions only. Here we relax these assumptions: our proposed formula yields the permeability tensor for an anisotropic arbitrarily-fractured rock subjected to arbitrary deformations. Unlike the original Liu-Elsworth approach, our formula may therefore be used confidently in situations involving any stress and strain states, including those that are non-diagonal, and with rocks with any distribution of fracture orientations, including those that are non-orthogonal. This is advantageous in numerical simulation and in mining situations that frequently involve such situations. Our formula adds no discernible computational load to numerical simulations. Our proposal agrees with lab and in-situ direct and indirect tests of permeability.