Extensions of the dynamic Newmark method for seismic stability analysis of a rock block

The Newmark sliding block method combined with block theory (referred to as the dynamic Newmark method) can be used to calculate the dynamic safety factor and the permanent displacement, which provides a quantitative tool to evaluate the dynamic stability of a rock block under seismic action. Frequent changes in the position of a rock block under seismic action may lead to the changes in contact areas and modes of contact between sliding faces. These problems that are not considered in the original dynamic Newmark method are solved to extend the dynamic Newmark method. First, the loop analysis method is introduced to obtain the contact polygonal faces of a sliding surface, and the simplex integration method is used to calculate the contact areas. Second, the reference point method is defined to identify the mode of contact between a structural plane and the surrounding rock mass, and the possible mode of motion of the rock block is determined. Based on these extensions of the dynamic Newmark method, an Extended Newmark Method (ENM) program is developed, and a verification example, three comparison cases, and an application are used to validate the correctness and effectiveness of the extended method. The results show that the ENM program can be used to calculate the effects of the change in contact areas and modes of contact on block motion, which better reflects the dynamic response of a rock block under seismic action compared with the original dynamic Newmark method.

Automated summary

The Newmark sliding block method combined with block theory can be used to evaluate the dynamic stability of a rock block; frequent changes in the position of a rock block under seismic action may affect the contact areas and contact modes of sliding faces; extending the dynamic Newmark method can better reflect the dynamic response of a rock block under seismic action.