Stability analysis of fractured rock masses based on an extended key block theory considering the forces between blocks and block rotation

Key block theory is a widely used method in rock engineering for analyzing the stability of fractured rock masses. However, the traditional theory does not consider the forces between blocks and block rotation very well, its results may differ from real conditions. Therefore, we proposed an extended key block theory by considering the forces between blocks and block rotation. The forces between blocks were calculated by a displacement constraint method of the rigid body based on 3DEC platform. In the analysis of block rotation, block rotatability was analyzed by a geometric condition and mechanical condition. Net moments and rotational safety factors of movable blocks were calculated to judge whether the block rotates. Considering block rotation along an edge and block translation, block failure modes can be divided into free falling, single-plane sliding, double-plane sliding, edge rotation, and sliding rotation. We created a 3DEC-KBM program that incorporates the extended method into the 3DEC platform. This method not only obtains more accurate forces between blocks but also has more efficiency compared with the direct application of 3DEC. The correctness of this method was verified by the 3DEC results of a single-block slope model, and it was adopted to analyze the stability of a fractured rock slope and fractured rock masses surrounding an underground cavern. The research results showed the following: (1) The forces between blocks often decrease block stability, but also improve the stability of some blocks; (2) The forces between blocks is easier to make the blocks rotation comparing with the case only considering the gravity effect, because of the changing position and direction of the resultant force acting on a block; (3) Compared with the traditional key block theory, the extended method has higher accuracy and it is necessary to consider the blocks’ rotation when taking the forces between blocks into account.