Stability analysis of statically indeterminate blocks in key block theory and application to rock slope in Jinping-I Hydropower Station

Using the movability analysis in block theory, one can easily determine all movable blocks. However, only for a movable block with no more than two structural surfaces, called the statically determinate block, can the factor of safety be determined by the static analysis, which limits more extensive application of key block theory. In order to analyze general movable blocks with multiple structural planes, an optimization model for solving the safety factor of blocks is built in this paper. In the model, the safety factor as well as the normal stress on the slip surface is taken as independent variables; and the objective function is specified as the safety factor alone. The statically admissible conditions include the system of equilibrium equations, non-negativity of both normal stress on the slip surface and thrust inside the block. Since the objective function is linear and the constraint functions are polynomials of no more than degree-2, it is weak in nonlinearity and can be solved by those conventional optimization techniques, and disadvantages of the conventional block theory are overcome. After some typical examples are tested, the stability of the left bank rock slope of Jinping-I Hydropower Station is conducted in detail, and the stability evolution due to excavation is systematically studied by this method.