改进的数值流形法在水力劈裂中的应用

Application of enriched numerical manifold method to hydraulic fracture

数值流形法在非连续变形分析领域具有独特优势。结合裂纹尖端场函数的基本概念,分析了水力劈裂破坏问题,模拟了水力劈裂破坏过程,避免了扩展有限元中的阶跃函数和水平集概念。为了避免裂纹尖端在单元内部不同位置而产生误差,对裂纹尖端附近一定范围内的每一个物理覆盖附加奇异覆盖函数。选取一个算例比较分析了内水压力对应力强度因子的影响,当考虑裂纹面内压时,定量分析比较了各因素对应力强度因子的影响大小,并应用于分支裂纹水力劈裂破坏。计算结果表明,改进后的计算结果与解析解相吻合。未考虑裂纹面内压,误差往往较大。考虑裂纹面内压后,随着裂纹长度的增加,误差逐渐减小;随着网格密度的增加,误差也逐渐减小。分支裂纹的渐进破坏结果表明该改进方法的可行性,具有较大的实际应用价值。

The numerical manifold method（NMM） has numerous advantages for discontinuous deformation analysis. In this study, by combining NMM with the basic concept of crack tip function, we conduct hydraulic fracture simulation and analyse the failure process without the concepts of Heaviside function and level set. To avoid the error caused by different positions of the crack tip in an element, singular cover functions are added for every physical cover near the crack tip within a certain range. One example is selected to show the influence of inner water pressure on the stress intensity factor（SIF）. When the force on the crack is considered, the influence of each factor on the SIF is quantitatively analysed, and then hydraulic fracture of branch crack is simulated. The results show that the improved results are in good agreement with the analytical solutions. It is found that the error is often large when the force on the crack is ignored. However, when the force on crack is considered, the error gradually decreases with increasing either crack length or mesh density. The progressive failure of the branch crack shows that the method is feasible and is of great practical value.