模拟岩石破裂过程的块体单元离散弹簧模型

A block-discrete-spring model to simulate failure process of rock

在变形体离散元的基础上建立块体单元离散弹簧模型,并应用于岩石破裂过程的数值模拟研究。该模型以连续介质力学理论为基础,将块体单元离散为具有明确物理意义的弹簧系统,通过对弹簧系统的能量泛函求变分获得各弹簧的刚度系数,进而可以直接利用弹簧刚度求解单元的变形和应力,提高计算效率。以重力作用下的岩质边坡计算为例,通过与传统的有限元进行对比,验证该模型弹性计算结果的正确性。在该基础上,引入Mohr-Coulomb与最大拉应力的复合破坏准则,判断单元的破坏状态及破裂方向。当单元的内部破坏面确定后,则通过块体切割的方式实现单元破坏,并建立单元边界和单元内部的双重破裂机制,实现块体由连续到非连续的破裂过程,进而显示的模拟裂纹的形成和扩展。最后,以巴西圆盘劈裂、单轴压缩破裂以及三点弯曲梁等典型算例验证该方法,结果表明该方法可以较好地模拟拉伸、压剪等应力状态下裂纹的形成和扩展,从而可模拟岩石介质由连续到非连续的破裂过程。

A block-discrete-spring model based on deformable discrete element method is established; this model would be applied to simulate the rock failure process. In this model, the theoretical basis is continuum mechanics and block element is divided into discrete spring system with specific physical meaning. The stiffness of the spring can be obtained from the energy functional. In this way, element deformation and stress would be calculated by spring stiffness directly and efficiently. In the case of rock mass slope under gravity, the elastic result achieved with this model is the same as that of traditional finite element method. （FEM）. On this basis, Mohr-Coulomb criterion with a tensile cntoffwhich used to judge the failure state and broken direction is proposed and implemented into the block-discrete-spring model. After the internal failure face established, the element will be divided into two elements by means of cutting block; and double judgement including element boundary and element interior is adopted to realize the crack initiation and propagation, which could mitigate the effect of initial mesh. Finally, the rationality of the failure result calculated by block-discrete-spring model is approved by some cases including split test with flattened disk, uniaxial compression and three point bending. The results show that this method can well simulate the crack initiation and propagation under tensile, compressive and shear conditions, by which the rock failure process can be realized from continuum to discontinuum.