An explicit 3D numerical manifold method with potential-based contact force for rock mass system

Abstract

To address the movement and failure of discrete rock mass system in rock engineering, a 3D contact-potential based numerical manifold method (3DCPNMM) using explicit time integration scheme is presented. In this method, tetrahedral finite element grids are utilized to construct the mathematical cover system, enabling flexible discretization of both continuous and discontinuous rock mass systems. Additionally, two types of contact potential, namely, the volume potential and distance potential are introduced to calculate the contact force between the adjacent manifold elements. Note that the potential based contact force can be directly calculated from the overlapping volume of the manifold elements, thereby eliminating the need to differentiate between complex contact types. Several benchmark problems related to rock mass movement are examined using the proposed 3DCPNMM to verify its correctness. The numerical results obtained align well with the analytical solutions, demonstrating the reliability and accuracy of the proposed method. In addition, the distance potential offers higher accuracy than the volume potential for the proposed 3DCPNMM. Finally, the 3DCPNMM is applied to complex engineering cases involving the movement and failure of complex rock mass, which will be helpful for rock mechanics research and engineering design in the future.