Validation and application of three-dimensional discontinuous deformation analysis with tetrahedron finite element meshed block

Abstract

In the last decade, three dimensional discontinuous deformation analyses (3D DDA) has attracted more and more attention of researchers and geotechnical engineers worldwide. The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation, which would cause block expansion under rigid body rotation and thus limit its capability to model block deformation. In this paper, 3D DDA is coupled with tetrahedron finite elements to tackle these two problems. Tetrahedron is the simplest in the 3D domain and makes it easy to implement automatic discretization, even for complex topology shape. Furthermore, element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly. The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested. Validation is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes, i.e., wedge failure. Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases. Finally, a complex rockslide example demonstrates the robustness and versatility of the coupled method.