中文摘要：

数值流形方法（NMM）的最大优势在于可以统一地处理岩土力学中的连续和非连续变形问题。它在求解断裂力学问题时无需强制裂纹与数学网格保持一致，非常适合应用于岩土工程中由连续到非连续的破坏过程模拟。在裂纹扩展过程中，裂纹与数学网格的相对位置将会是任意的，如裂纹尖端可能落在网格内部、网格节点上或网格边上等。因此，对同一条裂纹，通过旋转和移动数学网格构造了它们之间的这种相对位置关系以及一些可能对计算结果产生影响的极端情况，并以应力强度因子作为衡量标准，研究了NMM在处理线弹性断裂力学问题时的网格依赖性。研究表明，NMM即使在处理强奇异性问题时依然有着很好的网格无关性，进一步证实了它在模拟裂纹扩展问题时的鲁棒性。

英文摘要：

One major advantage of the numerical manifold method （NMM） is that it can solve the continuous and discontinuous problems in geomechanics in a unified way. It is not necessary to force the mathematical meshes to match the cracks in the NMM, which is very suitable for the simulation of failure process from continuum to discontinuum in geomechanics. During the crack propagation, the relative position relationships between the cracks and the mathematical meshes will be arbitrary;for example, the crack tip may locate in the interior, on the node or on the edge of the mesh. For the same crack, the mesh independency of NMM in dealing with the linear elastic crack problems is studied by rotating and moving the mathematical meshes to construct the relationships and some extreme cases that may have an influence on the results and taking stress intensity factor as the measurement. The results in this study to the NMM show it has little mesh dependency even in treating strong singularity, implying it will be robust in simulating crack propagation.