Study On Method Of Multi-body FEM And Its Application In Discontinuous Deformation Analysis

Rock mass of underground chambers and side slope are likely to be cut into blocks by unfavorable geologic structure such as fault. Currently, one of the most efficiency methods is the method of DDA which was proposed by Prof. Shi Genhua. In this paper, the theory of DDA is systematically studied and two disadvantages were found: First, each block is assumed to have constant strain;Second, dummy spring is used two settle contact problems, which lead to the possible insertion between blocks. Studies are done based on these two problems, the main contents can be shown as follows:(1) Combine the theory of FEM with multi-body system dynamics. Using FEM to calculate the deformation of each body and applying contact forces on the interface, in this way, contact forces between blocks, deformation of each block and whole motion of the block are considered as variables governed by displacement compatibility on interface and global system balance equations. Finally, a complete set of multi-body FEM is formatted to do discontinuous deformation analysis.(2)Based on a series of assumptions, the criterion of contact problem is presented. Combined the theory of force method, the formula of Multi-body FEM is derived from both displacement compatibility on the interface and the equation of FEM inner the block. Corresponding treating scheme is presented to deal with large deformation. Programming the multi-body FEM with FORTRAN, and then two typical examples are analyzed. Finally, the effect of the magnitude of friction coefficients on the state of contact surface is also studied.(3)Using the method of Multi-body FEM in the deformation analysis of underground cavern with cranny and slope with known slip plane. Compared with the schemes adopted by most presently in deformation analysis of underground cavern, the results given by multi-body method make better agreement with the real case.