Seismic stability analysis of a rock block using the block theory and Newmark method

Seismic stability analysis of a rock block is an important issue in the field of rock mechanics and rock engineering. To solve this problem, the block theory and the Newmark method are combined, and a general method for seismic response of a rock block is introduced. First, the formation method of a three-dimensional rock block, which includes establishing a topological relationship among the block-polygon face-edge-vertex and dividing a complex block into convex subblocks, is presented, and the simplex integration method is employed to calculate the volume of a rock block and the areas of the polygonal faces. Second, the assumptions and algorithms of the general method for seismic response of a rock block are detailed. The dynamic analysis is carried out in time step. In each time step, the key technologies including analysis of the seismic force and motion mode, trial of the incremental displacement, check for the block entrance, and update of the motion parameters are performed in order. Last, two verification examples and three application examples including a wedge, a rock block of slope, and a combined rock block are used to analyze the correctness and practicality of the general method. The results show that, for a given ground motion record, the Newmark program can effectively simulate the dynamic response process of the motion mode, velocity, and safety factor of the rock block, and the permanent displacement under the earthquake action is obtained, which provides a quantitative parameter to evaluate the dynamic stability of a rock block.