Three-dimensional rigid limit equilibrium analysis method for multi-block sliding in arch dam abutment

Multi-block sliding is a common and important failure mode in arch dam abutment. The current stability analysis methods established generally have certain deficiencies: a lot of assumptions must be introduced to make the problem static, or some methods only discuss that the sliding mode of the individual block is double-face sliding along the bottom and lateral slip surface. These methods are not suitable for solving the multi-block sliding problems of arch dam abutment. A new 3D limit equilibrium method with a strict theoretical basis and simple calculation steps is proposed. More specifically, considering that the sliding mode of each block is double-face sliding and single-face sliding, the method involves converting the multi-block stability analysis to a non-linear minimum problem containing several degrees of freedom by creating the equations for static equilibrium along x, y and z directions of each block and the equation for displacement compatibility of two adjacent blocks, thus good convergence can be obtained by combining with the global optimization methods. The method proposed is applied to a 3D wedge problem and the abutment stability of Xiaowan arch dam, so the validity and practicability are verified. The method is actually an extension of 2D Sarma method in 3D multi-block field, and is theoretically supported by the upper bound theorem of plasticity. Meanwhile, it gives the closed solution method for multi-block series sliding problems, and can provide an example for the rationality verification of various 3D slope stability programs.