Liu Chong, Shen Zhenzhong, Gan Lei, Jin Tian, Zhang Hongwei, Liu Detan
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China.
The College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China.
Materials (Basel). 2018 Oct 9;11(10):1921. doi: 10.3390/ma11101921.
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.
在实际工程应用中经常会出现高压水力裂缝，这是由于诸如裂缝、断层或剪切带等不连续面的存在而产生的。本文提出了一种混合有限体积法和扩展有限元法（FVM-XFEM）来模拟准脆性材料中的水力裂缝扩展，其中考虑了流体与变形之间的耦合。裂缝内的流动采用润滑理论对服从立方定律的一维层流进行建模。固体变形由准静态条件下的线性动量平衡方程控制。内聚裂缝模型用于分析裂纹尖端前方的非线性断裂过程区。压力场的离散化采用有限体积法实现，而位移场的离散化则通过扩展有限元法完成。完全耦合的流固耦合问题的最终控制方程采用皮卡迭代法求解。最后，通过三个例子验证了所提方法的有效性。此外，还研究了沿裂缝的流体压力分布、裂缝口宽度和裂缝形态。结果表明，数值结果与理论解和实验结果具有良好的相关性。
