Computing the common area of in-contact blocks in case of blocks sliding is essential for taking the contribution of cohesive force into account in three-dimensional Discontinuous Deformation Analysis (3D-DDA). In this paper, using the theory of segments intersections, a straightforward algorithm was developed to detect common area of two convex blocks which have potential of being in "face to face" contact. The possibility of the "face to face" contact pattern is examined by one of the most efficient procedures of contact detection in 3D-DDA, the "Main Plane" method. After finding all contact points in "face to face" state, the common area of two blocks can be computed using two-dimensional Simplex Integration technique.


The Discontinuous Deformation Analysis, a member of the discrete element models family, was developed by Shi [1]. It can be used to simulate large scale sliding along discontinuities, opening of discontinuities, large rotation and complete detachment of blocks in rock engineering problems. An essential part of DDA in three-dimensional state (3D-DDA) is a rigorous contact theory which governs the interaction of the blocks [2]. In this theory the type of contact is important because it determines the mechanical response of the blocks in contact. 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 [3, 4, 5]. Although such conversion of contact types results in simplicity in computations of contact sub-matrices, it ignores the most important aspect of a "face to face" contact: the effect of cohesive force on sliding block along sliding surface. The "Main Plane" (MP) method for contact detection, developed by Keneti et al [3], is capable to compute all contact patterns during 3DDDA computational process so that each contact type can be treated according to its individual behavior, in addition to its similarity to the existing methods in converting contact types to enhance computation efficiency. In this paper, using the MP method for contact detection [3] together with the theory of segments intersections [6] and two-dimensional Simplex Integration technique [1], a straightforward algorithm is developed to detect common area of two convex blocks which have potential of being in "face to face" contact.

Basic Principles of 3D-DDA

DDA is an implicit method, involving formulation and solving of a system of simultaneous equilibrium equations. Individual blocks are connected and form a blocky system by contacts between blocks and by displacement constraints on each single element. The large deformation in a block and the large relative movements betweenblocks are accumulated over many time steps [1]

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