The Discontinuous deformation analysis (DDA) has been widely used to model the motions of blocky masses. A linear polynomial function often used in the DDA can ease the complex contact determination between the blocks. However, this linear displacement function generates constant stress field within a block, which can not effectively model the stress variation within a block or across the block interface. In this paper, a stress recovery procedure is proposed for those DDA blocks which are glutted together as continuous objects. Such a procedure can improve the stress accuracy along the block interfaces and can be used for more accurate contact determination in the future. Two numerical examples are presented to study the stress accuracy of the proposed method, and the results verify that the proposed stress recovery method provides better accuracy than the direct DDA and the averaging method.
The basic framework of the discontinuous deformation analysis (DDA) was proposed and implemented by Dr. Shi in 1988 (Shi, 1988). Due to its special feature in modeling the discontinuous rock mass, many studies on the DDA have been carried out over the last decade, and its applications haven been extended to many rock engineering areas (MacLaughlin et al., 2003). A linear polynomial function is often used in the standard DDAas it can ease the complex contact determination between the blocks. However, this linear displacement function generates constant stress field within a block, which can not effectively model the stress variation within a block or across the block interface (Hatzor et al., 2003).Various developments have been proposed to improve the displacement/stress accuracy, such as the introduction of finite element mesh within the blocks, the coupling of DDA with FEM, or using a higher order DDA. In general, those improvements need either substantial more computing time or extra compatibility along the FEM/DDA interface. Many natural materials (like rock mass) contains weak layers (such as joints), one method in fracture propagation simulation is to consider each mesh line as a potential crack, and evaluate inter-element forces/stresses along the mesh line, and determine the crack opening or sliding based on appropriate strength criteria.As DDA's blocks are all independent with each other, the nodes on the interface of the blocks are originally assigned double nodes.There is no need to insert zero-thickness interface elements with double nodes along each line of the block system as commonly used in the FEM. Therefore, the DDA is ideal to use the block boundary as a potential crack. These interfaces are assigned a relative elastic stiffness which may be interpreted as the penalty coefficient necessary to evaluate stress traction transmitted across their surface. Thus, an accurate stress evaluation for these interblocks will become essential in the crack propagation analysis. As this inter-block stress is not as accurate as the stress field inside the block, it is preferable to use some post-processing techniques to recover the stress along the inter-block boundary.
