8. Conclusion
We have presented an enhanced local pressure model, within the framework of X-FEM, for fluid pressure driven fracture in porous saturated materials. By exploiting the partition-of-unity property of finite element shape functions the method captures the discontinuous fracture. The fracture process is modelled by means of a cohesive zone description. The local, additional, degree of freedom for the pressure ensures that fluid flow goes exclusively in the fracture. The steep pressure gradient that may occur locally near the fracture surface is reconstructed based on Terzaghi’s analytical solution. We have illustrated this effect with an example where fluid is being injected in an opened fracture. Using a X-FEM model with a continuous pressure approach the pressure gradient cannot be resolved at low time scales. The pressure in the fracture calculated with the ELP model is consistent with the analytical solution. We also have showed that at higher time scales the continuous X-FEM does describe the pressure gradient near the fracture surface. This indicates that the ELP model is better capable to model hydraulic fracturing at early stages while at later stages a switch to the continuous X-FEM should be considered.
