Analysis of removability and stability of rock blocks by considering the rock bridge effect

In traditional block theory, the removability and stability of rock blocks are analyzed independently; that is, the stability of a removable block is analyzed in detail, and nonremovable blocks are regarded as stable. However, in practical situations, nonremovable blocks may pose more danger than removable blocks. This paper presents a unified method for analyzing the removability and stability of rock blocks. In this method, the cracking of rock bridges is considered and nonremovable blocks are not assumed to be stable. First, possible cracking rock bridges are identified by extending finite-sized fractures and comparing the boundary surfaces of the resulting blocks with those of the original blocks. Then, the sliding direction associated with each possible moving block is determined by solving an optimization problem. The normal force acting on each sliding surface is determined, and the resisting force on each rock bridge is calculated and integrated into the total resisting force when calculating the safety factor of a possible moving block. Procedures to determine all possible moving blocks are introduced, and the possible moving block with the minimum safety factor is regarded as the actual moving block. The corresponding minimum safety factor is defined as the actual safety factor of the block. The proposed method is verified by considering a few examples. The results show that nonremovable blocks may be unstable if the cracking of rock bridges is considered.