Abstract
High-pressure hydraulic fractures are often reported in real engineering applications, which occur due to the existence of discontinuities such as cracks, faults, or shear bands. In this paper, a hybrid finite volume and extended finite element method (FVM-XFEM) is developed for simulating hydro-fracture propagation in quasi-brittle materials, in which the coupling between fluids and deformation is considered. Flow within the fracture is modelled using lubrication theory for a one-dimensional laminar flow that obeys the cubic law. The solid deformation is governed by the linear momentum balance equation under quasi-static conditions. The cohesive crack model is used to analyze the non-linear fracture process zone ahead of the crack tip. The discretization of the pressure field is implemented by employing the FVM, while the discretization of the displacement field is accomplished through the use of the XFEM. The final governing equations of a fully coupled hydro-mechanical problem is solved using the Picard iteration method. Finally, the validity of the proposed method is demonstrated through three examples. Moreover, the fluid pressure distribution along the fracture, the fracture mouth width, and the pattern of the fracture are investigated. It is shown that the numerical results correlated well with the theoretical solutions and experimental results.
Highlights
Fluid-driven fracture is a common yet complex multi-field physics problem
A hybrid approach called finite volume method (FVM)-XFEM was proposed for hydraulic fractures in quasi-brittle materials
The fully coupled formulation was established based on the linear momentum balance equation and the one-dimensional laminar flow model, which accounted for the coupling effect between the fluid pressure and the fracture opening width
Summary
Fluid-driven fracture is a common yet complex multi-field physics problem. When high-pressure fluids such as water enter into an existing crack, the fracture propagation criterion is met ahead of the fracture tip, which leads to fluid-driven fracture initiation and propagation [1]. Ultra-high concrete dams of 200–300 m or even more have been built all over the world, those dams have a potential risk of hydraulic fracturing due to the structure damage cracks on dam surfaces. Cracks are completely filled with the high-pressure water. Another important application of HF is related to enhance the well production from underground reservoirs [3,4]. It is necessary to complete research and understand the influence of hydraulic fracturing
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