基于数值流形法的重力坝多裂纹扩展研究

传统数值流形法（NMM）在处理非连续变形问题时，仅限于几何构型不发生破坏的情况。针对这一不足，通过在裂纹尖端附近的物理片上增加用于模拟应力奇异性的增强位移函数，进一步发展了可用于几何构型破坏的扩展的高阶NMM。然后，将其应用到重力坝由连续到非连续的破坏过程分析中。首先，针对一含单裂纹的重力坝模型进行了敏感性分析，结果表明，在不同的扩展长度或网格密度下，其扩展路径基本相同且与文献结果保持一致。进而在此模型基础上又开展了多裂纹扩展分析，结果仅一条主导裂纹发生扩展，与文献结果基本一致。最后，针对印度的Koyna重力坝，通过设置不同的漫顶高度研究了其裂纹扩展路径的变化。结果表明，随着漫顶高度的增大，裂纹扩展路径逐渐趋向于水平方向扩展，而且坝体抵抗破坏的能力逐渐减弱。总体表明，NMM在求解实际工程问题时具有很好的数值稳定性和鲁棒性。

Modelling of multiple cracks growth of gravity dam based on numerical manifold method

The traditional numerical manifold method (NMM) is restricted to the cases of no structure damage when dealing with the discontinuous deformation problems. To overcome the limitation, a high-order NMM for modelling structure damage is further developed by adding the enriched displacement functions for modeling the stress singularity to the physical patches around the crack tips. Then it is applied to the simulation of the fracture process of the gravity dam from continuum to discontinuum. Firstly, sensitivity analysis of the gravity dam with a single crack is conducted; it is found that the crack growth paths are nearly the same as the results in the references, under the conditions of different crack growth lengths or mesh densities. Based on this, the analysis of the multiple cracks growth is conducted; the results indicate that only one dominant crack propagates, which again is quite the same as the result in the references. At last, it is used for the crack growth analysis of Koyna gravity dam, in which the changes of crack growth paths are studied by setting different overflow heights. The results show that the crack growth paths tend to propagate in the horizontal direction and the ability of the resistance to failure of the dam is gradually diminishing. In general, NMM has the good numerical stability and robustness in treating the real engineering problems.