Rocking response of rigid blocks under near-source ground motions

In this paper the transient racking response of a rigid block subjected to trigonometric pulses and near-source ground motions is investigated in detail. First, the rocking response to a half-sine pulse motion is revisited. It is shown that the solution presented by Housner for the minimum acceleration amplitude of a half-sine pulse that is needed to overturn a rigid block is incorrect. In reality, under a half-sine pulse, a block overturns during its free vibration regime and not at the instant that the pulse expires, as was assumed by Housner. Within the limits of the linear approximation, the correct conditions for a block to overturn are established and the correct expression that yields the minimum acceleration required to overturn a block is derived. Subsequently, physically realizable cycloidal pulses are introduced and their resemblance to recorded near-source ground motions is illustrated. The study uncovers the coherent component of same near-source acceleration records, and the overturning potential of these motions is examined. It is found that the toppling of smaller blocks is more sensitive to the peak ground acceleration, whereas the toppling of larger blocks depends mostly on the incremental ground velocity. The kinematic characteristics of recorded near-source ground motions are examined in detail, and it is found that the high-frequency fluctuations that occasionally override the long-duration pulse will overturn a smaller block, whereas a larger block will overturn due to the long-duration pulse. A simple, yet dependable, method to determine the level of a recorded ground motion that is needed to overturn a given block is developed and illustrated through examples. The method examines the acceleration amplitude, and the duration and the type of distinct local pulses that are identifiable within the record, including the pulse that contains the peak ground acceleration. According to the type of each pulse identified, the method estimates the minimum acceleration amplitude needed to overturn a given block, and this value is compared with the recorded acceleration amplitude of each pulse identified,within the record. In this light, the rocking response of rigid blocks subjected to strong near-source ground motions is shown to be quite ordered and predictable.