Contact detection by the Contact Theory in 2D-DDA for arbitrary polygonal blocks

The Contact Theory proposed by Shi in 2015 is expected to solve the contact detection problem of discrete blocks in a perfect and universal manner. In the present paper, a contact detection algorithm for arbitrary polygonal blocks based on the Contact Theory is proposed and coupled into the two-dimensional DDA (2D-DDA). Four different methods to determine the contact entrance lines are presented, and among which the contact vector method is used in the proposed contact detection algorithm because of its advantage in treatment of small overlapping of blocks along the edges and its simplicity in implementation. The vertex-to-vertex contact and vertex-to-edge contact are separately handled to effectively select the final actually needed entrance lines for the contact treatment. The proposed algorithm is examined by some representative and complex simulation examples, and the results are theoretically verified or compared with that by the original 2D-DDA with the direct contact detection algorithm based on the angle method. It is shown that the proposed algorithm can handle the contact detection of convex and concave blocks in diverse scenarios effectively. This work proves the feasibility and robustness of the Contact Theory, and provides 2D-DDA an optional effective approach for the contact detection.