A robust contact detection algorithm based on the Contact Theory in the three-dimensional discontinuous deformation analysis

Abstract The two-dimensional discontinuous deformation analysis (DDA), as a discrete numerical method, has been successfully used to simulate many rock mechanics and rock engineering problems. However, for the development of the three-dimensional DDA (3D-DDA), the contact detection between polyhedral blocks has long been one of the key difficulties awaited to be solved. A universal Contact Theory was proposed by Shi in 2015, in which the complicated contact relationship of two any-shaped blocks is represented by a simple relationship between a reference point and an entrance block, along with a concept of the contact cover. In the present study, a robust contact detection algorithm in the 3D-DDA for convex polyhedral blocks based on the Contact Theory is proposed. In this algorithm, all the six basic contact types of polyhedral blocks are functionally treated as two contact types, namely, the vertex-to-face contact and the non-parallel edge-to-edge contact; meanwhile, the vertex-to-vertex and vertex-to-edge contacts are specially handled to guarantee the effectiveness and efficiency of the algorithm. Two special contact cases with the parallel edge-to-edge contact and the vertex-to-vertex contact, respectively, and two multi-block cases, in which various contact types and the transition between them are involved, are simulated to verify the effectiveness and robustness of the proposed contact detection algorithm. Moreover, failure simulations of sliding and toppling slopes with massive rock blocks are conducted and in the sliding case the effect of a retaining wall is also simulated. Results indicate that, the proposed algorithm can handle the contact detections of convex polyhedral blocks effectively under critical and complex conditions, which builds a good precondition for the successful development and practical application of the 3D-DDA method.