含裂纹岩体模型应力场的理论及数值计算

Theoretical and numerical calculation of stress field in cracked rock mass model

为探究一种获得含裂纹岩体应力场的新方法,采用理论推导、Matlab编程、有限元模拟相结合的方法,将含有裂纹缺陷的岩体简化为平面应力状态下含有I、II型复合单裂纹的力学模型,利用复变函数解法求得该模型应力场的理论解;基于此理论解,通过Matlab编程求得此岩体模型的应力场并使之可视化;再利用有限元软件Abaqus对相同模型进行模拟运算并得出其应力等值线图.通过对比,发现两者具有高度的相似性,证明了基于理论分析基础上的Matlab编程可视化应力场方法的可行性,可以为工程模拟提供一种新的参考和思路.

To explore a new method of stress field on cracked rock, theoretical derivation, Matlab programmmg and finite element modelling were used together. The cracked rock masses can be simplified to be a mechanical model containing a single crack compound Ⅰ ＆Ⅱ in state of plane stress. The theoretical solutions of stress field were obtained with superposition method of the complex function. On the basis of the solutions, the Matlab numerical calculation method was used to make the stress field to be visualized. Abaqus was also used to simulate the stress field in the model. Compared with the Abaqus solution, it can be proved that the Matlab method to visualize the stress field is feasible, which also can be a new reference and method in the engineering simulation.