应用单元劈裂法模拟三维内嵌裂纹扩展

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摘要对于岩石内嵌裂纹很难通过物理试验进行研究，在应用有限单元法模拟内嵌裂纹扩展时，三维节理面建模、网格划分以及节理扩展后的网格处理一直是难点问题。为简单、高效地分析含有内嵌型不连续面的节理岩体的破坏模式，利用三维单元劈裂法来解决这一问题。单元劈裂法是利用四面体单元的几何性质来构造的一种特殊的四结点节理单元。当有裂纹穿过四面体单元时，位于裂纹两侧的结点可形成3或4个接触点对，由此推导出劈裂单元的刚度矩阵。采用该方法模拟内嵌裂纹扩展时，可以不用考虑节理岩体的几何完整性，而直接对整个岩体进行网格划分。因而一些单元则被内嵌裂纹相切，对于与裂纹相切的单元采用劈裂单元刚度矩阵，而其余单元则采用常规单元刚度矩阵。由此免去了单独设置三维节理单元的麻烦以及为设置节理单元而不断改变网格划分方案的麻烦。这种优势在裂纹数目较多时尤为突出，非常适合节理岩体计算。通过对内嵌椭圆裂纹扩展模拟并与相关物理试验做对比，得出该方法能够再现三维内嵌裂纹扩展的基本特征，说明该方法是有效的。

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关键词 ：数值模拟, 三维单元劈裂法, 内嵌裂纹, 节理岩体

Abstract：The jointed rock mass contains numerous embedded cracks，their propagation have significant impact on the stability of rock mass. However，it is very hard to study the embedded crack propagation through physical experiment. But when using the numerical method，i.e. finite element method，to numerically investigate this problem，the representation of 3D interface and mesh generation with consideration of setting up joint element has been a tough problem. To provide a simple and efficient method for failure analysis of jointed rock mass，the paper employs the 3D element partition method. The 3D element partition method actually develops a four-node contact element by taking advantage of the geometry character of the tetrahedron element. When a fracture cuts through a tetrahedron element，the nodes at different sides of fracture can construct 3 or 4 contact pairs，based on which the stiffness matrix of partitioned element is derived. When using this method，the cracked body can be directly meshed regardless of geometric integrity of jointed rock mass. Thereafter，many tetrahedron elements are intersected by pre-existing fracture. For those intersected element，the partitioned element stiffness matrix is adopted whereas for the rest，the normal element stiffness matrix is adopted. This makes the simulation of jointed rock mass highly simple and efficient. The comparison between the tested and the simulated results of elliptic crack propagation suggests that the present method can capture the features of 3D embedded crack propagation and is effective.

Key words： numerical simulation 3D element partition method embedded crack jointed rock mass

收稿日期: 2012-04-11

引用本文:

王德咏1，张振南1，葛修润1，2 . 应用单元劈裂法模拟三维内嵌裂纹扩展[J]. 岩石力学与工程学报, 2012, 31(10): 2082-2087.
WANG Deyong1，ZHANG Zhennan1，GE Xiurun1，2. SIMULATION OF THREE-DIMENSIONAL EMBEDDED CRACKS WITH ELEMENT PARTITION METHOD. , 2012, 31(10): 2082-2087.

链接本文:

http://www.rockmech.org/CN/Y2012/V31/I10/2082

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