| This dissertation presents a refined version of Shi's Discontinuous Deformation Analysis (DDA) for simulated testing of two dimensional heterogeneous and discontinuous rock masses, which may involve cohesive and incipient joints as well as blocks containing complex features. This refined DDA can determine a variable stress within each selected block with any shape and detail, analyze the behavior of block-in-matrix materials, and even simulate the fracture propagation of intact blocks.; Heterogeneous and discontinuous rock masses are in nature complex materials having numerous discrete blocks bounded by different discontinuities (generally called "joints"). One discrete block may differ in deformability from another. In some instances, one or more block may contain complex features like holes, interior blocks and cracks, so that a block itself is heterogeneous and discontinuous. Each joint is frictional, and may be cohesive. Potential joints, that become developed at certain stress states, may be included; these are called "incipient joints". All joints do not necessarily have the same friction angle, cohesion and tensile strength.; Because DDA has a complete scheme of block kinematics in dealing with complicated interactions between discrete blocks, it was selected as the prototype numerical method for simulated testing in this thesis. Additional refinements were undertaken to expand the capability of DDA: (1) DDA was modified to handle joints with unequal values of friction, cohesion and tensile strength; (2) the "artificial joint" concept was introduced to accommodate analyses of blocks containing holes, interior blocks and cracks. As artificial joints are added within a block, the continuous domain of the block is refined into sub-blocks and the features of holes, interior blocks and cracks can be modelled. If the artificial joints are assumed to be infinitely strong, a refined stress field within the block can be obtained. If the artificial joints are assigned finite strengths, fracture propagation within the block can be simulated.; The adequacy of refining a block by various regular grids of artificial joints were verified through three examples, in which the DDA results were compared with analytical or separate numerical solutions. Further, DDA results with artificial joints successfully demonstrated the development of stress concentration near a crack tip. To demonstrate the applicability of this refined DDA to heterogeneous and discontinuous rock masses, two block-in-matrix materials were investigated, as well as idealized problems with a rock slope, a dam foundation and a tunnel. |
