Modeling hydraulic fracture in saturated porous media through a continuos damage model

The effective use and proper management of nature and its resources still drives research toward the development of increasingly efficient and accurate numerical models suitable for the study and analysis of geomechanical problems or geophysical phenomena. With this in mind, the present work aims to develop a coupled model of deformation with damage and fluid diffusion, in fully saturated porous media, in order to simulate hydraulic fracture propagation in soils and rocks. The mathematical model is based on Biot's theory and on the definition of an effective stress dependent on the elastic properties and the degree of damage of the porous medium; additionally, permeability is assumed to be related to damage so reproducing a coupled fluid-mechanical behaviour. The linear momentum and mass balance of the mixture are hence combined with the constitutive equations obtaining the final coupled partial differential system of equations, subsequently solved via the Galerkin method. The FE approach with inf-sup stable discretization is performed adopting an implicit backward Euler scheme for temporal integration. The final system is solved monolithically via Newton–Raphson. Correctness and effectiveness of the implemented procedure are verified and validated against some available experimental and numerical examples. Particularly, the effects of the injection rate on both the effective stress field and the fluid pressure are examined, evaluating directions and extent of fractures propagation within rocks.