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

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

Numerical modelling of hydraulic fracturing

In this paper we present a numerical model for hydraulic fracturing purposes. The rock formation is modelled as a poroelastic material based on Biot’s Theory. A fracture is represented in a discrete manner using the eXtended Finite Element Method (X-FEM). The fluid flow is governed by a local mass balance. This means that there is an equilibrium between the opening of the fracture, the tangential fluid flow, and the fluid leakage. The mass balance in the fracture is solved with a separate equation by including an additional degree of freedom for the pressure in the fracture. The fracture can grow in arbitrary directions by using an average stress criterion. We show a result of hydraulic fracture propagation for a 2D circular borehole. The fracture direction is consistent with the expected direction

Fluid flow in fractured and fracturing porous media: A unified view

Fluid flow in fractures that pre-exist or propagate in a porous medium can have a major influence on the deformation and flow characteristics. With the aim of carrying out large-scale calculations at reasonable computing costs, a sub-grid scale model has been developed. While this model was originally embedded in extended finite element methods, thereby exploiting some special properties of the enrichment functions, we will herein show that, using proper micro-macro relations, in particular for the mass balance, sub-grid scale models can be coupled to a range of discretisation methods at the macroscopic scale, from standard interface elements to isogeometric finite element analysis

Finite element analysis of knee squat with an osteochondral defect

In this work a 3D musculoskeletal model of the knee joint, that can simulate a squat movement, has been developed. Such a model would be useful to understand the biomechanics of the knee. The model consisted of all the the bones with their articular surfaces, all relevant ligaments, the patella tendon and the quadriceps muscle. The squat movement is only regulated through velocity elongation of the quadriceps only. A squat movement between knee angles of 9° and 47° could be performed before element distortion occurred. The model outcome was compared with other numerical results, obtained from the literature. An osteochondral defect of 1 square mm in the femoral cartilage was mimicked and replaced with cartilage having stiffer, softer and normal properties. The softer defect reached 5.5% more in compression than the normal defect. In the stiffer defect 4% less compression occurred compared to the normal defect

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

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