基于单元破裂的岩石裂纹扩展模拟方法

传统离散元方法在处理破裂问题时, 采用界面上的准则进行判断, 裂纹只能沿着单元边界扩展. 当物理问题存在宏观或微观裂隙时, 在界面上应用准则具有其合理性; 而裂纹沿着单元边界扩展, 使得裂纹路径受网格影响较大, 扩展方向受到限制. 针对上述情况, 可以基于单元破裂的方式, 构建连续- 非连续单元法, 并应用于岩石裂纹扩展问题的模拟. 该方法在连续计算时, 将单元离散为具有物理意义的弹簧系统, 在局部坐标系下由弹簧特征长度、面积求解单元变形和应力, 通过更新局部坐标系和弹簧特征量, 可进一步计算块体大位移、大转动, 连续问题计算结果与有限元一致, 同时提高了计算效率. 在此基础上, 引入最大拉应力与莫尔-库伦的复合准则, 判断单元破裂状态和破裂方向, 并采用局部块体切割的方式, 在单元内形成初始裂纹. 裂纹两侧相应增加新的计算节点, 同时引入内聚力模型描述裂纹两侧的法向、切向作用与张开度及滑移变形之间的关系. 按此方式, 裂纹尖端处的扩展路径可穿过单元内部和单元边界, 在扩展方向的选取上更为准确. 最后, 通过三点弯曲梁、单切口平板拉伸、双切口试样等典型数值试验, 模拟裂纹在拉伸、压剪等各种应力状态下的扩展问题, 并对岩石单轴压缩试验的破坏过程进行模拟, 分析裂纹形成与应力-应变曲线各阶段之间的对应关系. 结果表明: 连续-非连续单元法通过单元内部破裂的方式, 可以显示模拟裂纹萌生、扩展、贯通直至形成宏观裂缝的过程.

SIMULATION OF CRACK PROPAGATION OF ROCK BASED ON SPLITTING ELEMENTS

In conventional discrete element methods, fracture is judged by criterion of interface and cracks can only propagate along the boundary of elements. However, criterion of interface can only be used rationally on the condition that macro or micro fractures exist in physical problems. The path and direction of crack will be limited severely by the initial mesh when crack propagates along the boundary. Given these two limitations, a continuous-discontinuous element method is proposed and applied to simulate the progressing cracking problem of rocks. Specifically, criterion is applied on element and intra-element fracture will form. In continuous calculation, element is denoted by a discrete spring system which has specific physical meaning and its deformation and stress are calculated by the characteristic length and area of springs in local coordinate system. The continuous calculation results demonstrate a satisfactory agreement with the traditional finite element method. By updating spring information and local coordinate system, large displacement and rotation of elements can be calculated directly. In addition, Mohr-Coulomb criterion is implemented into the new model to specify the failure state and fracture direction, and intact element will be divided into two elements by means of cutting block. In this way, fracture may be inserted along the boundary of elements or within intact element. A cohesive zone model is employed to simulate the fracture and the elements on two sides of the crack are set to two different nodes at the same time, causing the displacement to be discontinuous. Finally, from numerical results of several intense examples with crack propagation, this method can satisfactorily simulate the progressing cracking problems under tensile, compressive and shear conditions, and its rationality is approved. The continuous-discontinuous element method has been shown to be insensitive to quality of mesh and thus has the potential to simulate crack initiation and propagation.