基于连续介质力学的块体单元离散弹簧法研究

STUDY OF BLOCK-DISCRETE-SPRING METHOD BASED ON CONTINUUM MECHANICS

提出一种基于连续介质力学的块体单元离散弹簧法,并将其应用于地质体渐进破坏过程的数值模拟研究。该方法以连续介质力学的基本理论为基础,以八节点正六面体单元为离散对象,根据有限元的形函数理论及正六面体单元刚度矩阵的具体表达式,将正六面体单元离散成为12根棱弹簧,并推导各弹簧的弹簧力计算公式,给出各弹簧的弹簧力分量的物理意义、对应的弹簧刚度及相关联的位移。在弹性部分的计算结果与传统的有限元计算结果一致的基础上,在弹簧中引入Mohr-Coulomb准则及拉伸破坏准则,进行弹簧破坏的判断。如果块体内的弹簧全部断裂,便将其视为散体。在判断破坏时采用双重判断模式,块体单元的判断主要用于选取弹簧潜在的破坏面,离散弹簧的判断用于计算弹簧上的真实弹簧力。最后,通过相关算例验证引入破坏准则后所得计算结果的合理性。块体单元离散弹簧法的实质是通过12根离散弹簧将单元转化为结构,因此可以通过分析各弹簧的断裂情况研究块体的内部破坏特征,更可以通过各弹簧的先后断裂过程来研究地质体的渐进破坏过程。

A block-discrete-spring method based on continuum mechanics is presented and this method would be applied to simulate the progressive failure of geological body. The theoretical basis of this approach is continuum mechanics and the discrete object is regular hexahedron with 8 nodes. According to shape function theory of FEM and element stiffness matrix of regular hexahedron, 12 edge springs are obtained, and the formula, spring stiffness, related displacement and physical meaning of each spring are presented. The elastic result achieved with this method is the same as that of traditional FEM, and on this basis, Mohr-Coulomb criterion and tensile criterion are introduced to calculate the failure of spring. If all springs in the block are broken, the block is treated as particles. Double judgement model is adopted to estimate the failure of block. The purpose of block failure judgement is to choose the potential failure plane for springs, while spring failure judgement is used to calculate the real spring force. Finally, the rationality of the failure result calculated by block-discrete-spring method is approved by some cases. The essence of block-discrete-spring method is to transfer the element of the traditional FEM to structure according to the 12 springs, by which, the inner failure character of block and the progressive failure process of geological body could be studied by analyzing the failure of springs.