一种模拟节理岩体破坏的新方法:单元劈裂法

Novel numerical approach to jointed rock mass simulation: element partition method

在有限单元法中,三结点三角单元在几何上具有独特的优点,即当一条裂纹贯穿单元(单元劈裂)时,总有一结点位于裂纹的一侧,而另外两个结点位于裂纹的另一侧。位于一侧的两个结点与位于另外一侧的一个结点可以潜在地构成两个接触点对,从而可以利用这两个接触点对来推导劈裂单元的刚度矩阵,以再现裂纹面之间的接触和摩擦效应。利用该三角单元的几何特点,提出了单元劈裂法,用于模拟节理或其它裂纹的扩展问题。由于劈裂单元刚度矩阵与原三角单元享有共同的结点,因而在模拟裂纹扩展过程中无需为设置节理单元而改变原网格划分方案,这为节理扩展的数值模拟提供了很大方便,提高了计算效率。在劈裂单元刚度矩阵推导过程中,没有考虑单元劈裂后所形成两个块体自身的弹塑性变形,所以该方法只是一种近似方法。对相应试验进行了数值模拟,结果表明该方法是有效的。

In the finite element method, the tri-node triangular element exhibits a geometrical characteristic, that is, when a fracture runs through it, one node is always located at one side of the fracture and another two nodes located at the other side. The former node can potentially construct two contact pairs with the latter two nodes. Through the two contact pairs is the stiffness matrix of the partitioned element derived to represent the contact and friction effect between interfaces of joint or fracture. Based on the advantage of this geometrical characteristic of triangular element, an element partition method （EPM） is developed to simulate the joint or fracture propagation of jointed rock mass. Due to the fact that the stiffness matrix of the partitioned element shares the common nodes of the corresponding intact triangular element, it doesn＇t need to modify the original mesh configuration for setting up the joint element. The fracture propagates in the manner of successive element partition. To represent the newly generated and pre-existing fractures, it is just to displace the stiffness matrix of original intact triangular element with that of the partitioned element. This makes the simulation of the fracture propagation highly convenient and efficient. However, the present method is only an approximate method for the elastic-plastic deformation of the two bodies generated by the element partition. By simulating an experiment of fracture propagation and coalescence, good agreement is found between the experimental and the simulated results, which suggests that the present method is validated and feasible.