Steady-state subcritical fracture growth of parallel natural cracks in shale governed by osmotic gradient and fluid diffusion

Natural cracks in sedimentary rocks such as shale are potential weak paths for hydraulic fracturing to create fracture networks.The mechanism of formation of natural cracks in sedimentary rocks in the geologic past is an important problem to be understood.Why are the natural cracks roughly parallel and equidistant, and why is the crack spacing in the order of 10 cm rather than 1 cm or 100 cm?Here it is proposed that fracture mechanics must be coupled with the diffusion of pore fluid and solute ions to answer these questions.Parallel equidistant natural cracks are considered to develop in a subcritical manner driven by shear deformation and governed by the Charles-Evans law.Shear dilatancy in the fracture process zones (FPZ) induces a drop in the concentration of ions that increases the material fracture energy, and a drop in pore pressure that increases the resistance to frictional sliding.Both processes will lead to a decrease of the fracture propagation rate, and such an impact will be counteracted by the recharge of pore fluid and ions from the rock matrix to the fracture.We study the steady-state propagation and periodic cracks and derive an analytical solution of the crack spacing as a function of the properties of the rock, the solvent and solute, together with the imposed far-field deformation.