Rocking of Rigid Block under Random Wave Excitations

This investigation deals with the rocking response of rigid blocks subjected to barrow band random excitations. The numerical procedure and computer program are developed to solve the nonlinear equations of motion governing the rocking motion of rigid blocks on rigid base subjected to horizontal excitations. The analytical results presented show that the response of the block is very sensitive to small changes in its slenderness ratio, the energy dissipation, the friction condition - between block and base, and the details of ground motion. Systematic trends are not apparent : The stability of a block subjected to a particular ground motion does not necessarily increase monotonically with decreasing slenderness ratio or excitation intensity, occurrence of sliding motion, increasing bandwidth of random wave. Overturning of a block by a ground motion of particular intensity does not imply that the block will necessarily overturn under the action of more intense ground motion. In contrast, systematic trends are observed when the problem is studied from a probabilistic point of view with the ground motion modeled as a random process. The probability of a block exceeding any response level, as well as the probability that a block overturns, increases with increases with increase in ground motion intensity and slenderness ratio of the block, and occurrence of violent sliding motion.