Improved contact approaches for irregular polygonal or polyhedral blocks and their applications

Abstract

Correct mathematical description and mechanical solution towards contact of polygonal or polyhedral blocks are fundamental issues in discontinuous deformation analysis of fractured rock masses. Encountering irregular polygonal or polyhedral shapes (such as blocks with small edges or tiny faces), traditional contact detection and solution approaches may predict incorrect or inaccurate results due to the inappropriate choice of contact parameters or algorithmic robustness problems. Aimed to solve the above disadvantages of conventional contact detection and solution approaches in treating irregular polygonal or polyhedral block shapes, we developed several improved approaches, including (1) the new cover-based contact detection approach to establish inequality constraints for irregular polygons, and (2) the improved potential-based penalty function approaches to compute contact forces for irregular blocks. These improved approaches were proposed based on the contact theory proposed by Shi and the penalty function approach proposed by Munjiza. Several new algorithms, such as the contact trace tracking algorithm, block overlap examination algorithm, intersection block construction algorithm, contact force integration algorithm, were developed. The correctness of proposed approaches was first verified by several benchmarking tests. Several specially designed cases showed that these improved approaches can correctly treat the contact scenarios involving irregular blocks while previous approaches may fail or produce inaccurate results. The proposed approaches were further applied to several application cases which involves a large number of blocks. The proposed approaches and several embedded algorithms enriched the algorithm database for discontinuum-based computational methods.