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Extension of the classical linear slip model for fluid‐saturated fractures: Accounting for fluid pressure diffusion effects

We develop extended boundary conditions based on the linear slip model that account for the impact of wave‐induced fluid pressure diffusion between a fracture and its embedding background on the stiffening effect of the fluid saturating the fracture. We include these poroelastic effects into the linear slip model through complex‐valued and frequency‐dependent parameters characterizing the mechanical and hydraulic coupling between the two regions. This new set of effective fracture parameters contains generalized normal and tangential compliances, analogous to those defined in the classical formulation of the linear slip model, and an additional parameter related to the coupling between horizontal and vertical deformation of the fracture. Comparisons of the extended and classical linear slip models with a poroelastic thin layer model show that the extended formulation always performs better when modeling the displacement fields induced by an incident P wave as well as the scattering coefficients. We find that the contribution of the additional effective parameter involved in the proposed boundary conditions is significant at low frequencies with respect to the undrained frequency regime of the fracture and large angles of incidence. These extended boundary conditions can be readily incorporated into viscoelastic modeling algorithms simulating the response of a large‐scale fluid‐saturated fracture or multiple noninteracting fractures of this kind. The proposed model is expected not only to improve the estimation of mechanical characteristics of fractures in corresponding inversion schemes but can also be used for extracting information with regard to other practically important parameters, such as the background permeability.