The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials

• A novel partition of unity based model is developed to simulate crack growth in porous materials.
• Fluid pressure in the crack is taken as an additional variable.
• High pressure gradients near cracks are resolved accurately.
• Hydraulic fracturing can be simulated by directly prescribing fluid flow in the crack.

In this paper, we present an enhanced local pressure model for modelling fluid pressure driven fractures in porous saturated materials. Using the partition-of-unity property of finite element shape functions, we describe the displacement and pressure fields across the fracture as a strong discontinuity. We enhance the pressure in the fracture by including an additional degree of freedom. The pressure gradient due to fluid leakage near the fracture surface is reconstructed based on Terzaghi’s consolidation solution. With this numerical formulation we ensure that all fluid flow goes exclusively in the fracture and it is not necessary to use a dense mesh near the fracture to capture the pressure gradient. Fluid flow in the rock formation is described by Darcy’s law. The fracture process is governed by a cohesive traction–separation law. The performance of the numerical model for fluid driven fractures is shown in three numerical examples.