On the rocking instability of a three-rigid block system under ground excitation

The nonlinear equations of motion governing the overturning (rocking) instability of a freely standing three-rigid block assembly under ground horizontal excitation are analytically derived. Under certain conditions regarding the slenderness of each rigid block, the aforementioned nonlinear equations of motion can be linearized and then, after integration, lead to closed-form solutions. Assuming that the friction between consecutive blocks as well as the lower block and the ground is sufficiently large to prevent sliding, attention is focused on determining the minimum amplitude of ground excitation, which leads to overturning (rocking) instability with or without impact either between blocks or between the lower block and the ground. To this end, all possible configuration patterns that may lead to rocking instability (with or without impact) through an escaped motion are properly discussed.