Crack initiation and propagation are the two key issues of concern in the geotechnical engineering. In this study, the numerical manifold method (NMM) is applied to simulate crack propagation and the topology update of the NMM for multiple crack propagation is studied. The crack-tip asymptotic interpolation function is incorporated into the NMM to increase the accuracy of the crack-tip stress field. In addition, the Mohr-Coulomb criterion with tensile cut off is adopted to be the crack propagation criterion to judge the direction of crack initiation and propagation. Then a crack tip searching method is developed to automatically update the position of the crack tips. The inapplicability of the original loop search method in the NMM is also illustrated and a novel loop search method based on manifold elements is developed for physical loop updating. Moreover, methods for the manifold element updating and physical cover updating are provided. Based on the above study, the developed numerical method is capable to simulate multiple crack propagation. At last, typical rock rupture problems are numerically simulated to manifest the effectiveness of the developed numerical method.

中文翻译：

---

多裂纹扩展数值流形法的拓扑更新

裂纹萌生和扩展是岩土工程中关注的两个关键问题。本研究采用数值流形法（NMM）模拟裂纹扩展，研究了多裂纹扩展的NMM拓扑更新。NMM中加入了裂尖渐近插值函数，提高了裂尖应力场的精度。此外，采用具有拉伸截止的Mohr-Coulomb准则作为裂纹扩展准则来判断裂纹的萌生和扩展方向。然后开发了一种裂纹尖端搜索方法来自动更新裂纹尖端的位置。还说明了原始循环搜索方法在 NMM 中的不适用性，并开发了一种基于流形元素的新循环搜索方法，用于物理循环更新。此外，还提供了用于歧管元素更新和物理覆盖更新的方法。基于上述研究，所开发的数值方法能够模拟多裂纹扩展。最后，对典型的岩石破裂问题进行了数值模拟，证明了所开发数值方法的有效性。