An essential part of three dimensional Discontinuous Deformation Analysis, 3D-DDA, is a rigorous contact theory governing the interaction of the blocks. In this theory the type of contact is important because it determines the mechanical response of the blocks in contact. The Main Plane (MP) method for contact detection is capable to compute all contact patterns during DDA computational process. In this method, in addition to its similarity to the existing methods in converting all contact types into a simple “vertex to face” contact pattern to enhance computation efficiency, each contact type can also be treated according to its individual behavior. The “face to face” contact pattern is one of the most common modes of contact between two neighbouring blocks in 3D state. Computation of the contact area between two blocks that are in “face to face” contact is useful and is necessary to compute the contribution of the joint cohesion to the shear resistance along contacting block surfaces. The prevailing model of joint shear resistance seems to be purely frictional, so the effect of joint cohesion may not be significant; however, the capability of considering joint cohesion in 3D DDA should still be a useful extension, especially for slope stability analysis. In this paper the importance of common area and the ability of MP method to do so were highlighted first. Then, using the “Simplex Integration” technique, a straightforward procedure was introduced for continuously computing and updating this overlapped area while blocks slide on each other. This method was then verified by solving a simple problem of sliding of two blocks in contact, which is, however, similar in computation process to more complicated sliding problems. In this paper the energy function of cohesive force and its contribution to the total potential energy in 3D-DDA was also derived which could be used in future works in DDA together with the developed method of computing the contact area.


The Discontinuous Deformation Analysis (DDA), a member of the discrete element models family, was developed by Shi to simulate large scale sliding along discontinuities, opening of discontinuities, large rotation and complete detachment of blocks in rock engineering problems. Since discontinuous rock mass behavior is highly directional in nature and is controlled mainly by the orientations of the discontinuities in the rock mass, three-dimensional (3D) solution for DDA has drawn the attention of many researchers in recent years [1]. An essential part of 3D-DDA is a rigorous contact theory which governs the interaction of the blocks [2 and 3]. It must provide algorithms to judge contact locations and the appropriate state of each contact (open, sliding or locked) during the entire computation process [1]. There are many types of contact between 3D blocks, including “vertex to vertex”, “vertex to edge”, “edge to face”, “face to face”, “vertex to face” and “edge to edge”; however all of these contact patterns are converted to one or more “point to face” contacts in 3D-DDA computations in all available methods [2-4].

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