Rocking response of rigid blocks to earthquakes

TLDR

The study examines how rigid blocks rock under earthquake ground motion. The authors developed a numerical method and program to solve the nonlinear equations of motion for rigid blocks rocking on a rigid base under horizontal and vertical ground motion. The results show that block response is highly sensitive to size, slenderness, and ground‑motion details, with no simple monotonic trend, but probabilistic analysis reveals that the likelihood of exceeding response levels or overturning rises with ground‑motion intensity and slenderness and falls with block size, suggesting that shaking intensity can be inferred from observed effects on similar monuments.

Abstract

Abstract This investigation deals with the rocking response of rigid blocks subjected to earthquake ground motion. A numerical procedure and computer program are developed to solve the non‐linear equations of motion governing the rocking motion of rigid blocks on a rigid base subjected to horizontal and vertical ground motion. The response results presented show that the response of the block is very sensitive to small changes in its size and slenderness ratio and to 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 increasing size or decreasing slenderness ratio. 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 modelled as a random process. The probability of a block exceeding any response level, as well as the probability that a block overturns, increases with increase in ground motion intensity, increase in slenderness ratio of the block and decrease in its size. It is concluded that probabilistic estimates of the intensity of ground shaking may be obtained from its observed effects on monuments, minarets, tombstones and other similar objects provided suitable data in sufficient quantity is available, and the estimates are based on probabilistic analyses of the rocking response of rigid blocks, considering their non‐linear dynamic behaviour.