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.
An orthogonal set of principal axes is defined for earthquake ground motions along which the component variances have maximum, minimum and intermediate values and the covariances equal zero. Corresponding axes are defined which yield maximum values for the covariances. The orthogonal transformations involved are identical in form to those used in the transformation of stress. Examination of real accelerograms reveals that the major principal axis points in the general direction of the epicentre and the minor principal axis is nearly vertical. It is concluded that artificially generated components of ground motion need not be correlated statistically provided they are directed along a set of principal axes.
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