| This dissertation develops an analytical model for the study of rotational failure modes in jointed rock, and presents a limited generalization of Goodman and Shi's Block Theory to include the failure modes of edge rotation and corner rotation. The language and concepts of block theory, including the joint pyramid and the space pyramid, are used to characterize the rock mass and excavation space or free surface.; The rotation analysis is a three-stage study of kinematics, mode and stability. The kinematic study tests for rotatability; we find that a rock mass can be characterized in terms of rotatable and nonrotatable joint pyramids, independently of the free surface, and that the corresponding blocks are rotatable or nonrotatable accordingly. The mode analysis of block theory is generalized to establish a relationship between the direction of the active resultant and the failure modes of edge and corner rotation. The stability analysis tests the stability of a block with respect to a given rotational mode and produces a factor of safety for edge rotation. Where both rotational and sliding modes apply we find that the rotational modes tend to dominate under high friction conditions, and that blocks safe against sliding may be unstable with respect to rotation.; The analysis focuses on blocks bounded by three joints and a free surface, extending the work of Wittke on one-joint and two-joint blocks. Although the main results of the thesis cannot easily be generalized to blocks formed of four or more joints, a discussion of the kinematics of four-joint blocks is included in which it is shown that blocks nonremovable according to Shi's theorem may have kinematically feasible displacements other than pure translations. An interpretation of four-joint pyramids in terms of intersections of three-joint pyramids is described.; To demonstrate the applicability of some of the main conclusions, three worked examples, which between them draw on nearly every major result of the dissertation, are included. Some possible directions for future research in block theory are discussed. |
