The rocking response of rigid free standing bodies subjected to seismic excitation has been studied by many researchers interested in different slender elements such as ancient stone columns, tombstones, rigid building structures. The extension of this model to rock mechanics has been proposed by a few authors. The rocking response of rectangular free standing bodies subjected to horizontal accelerations of natural recorded motions showed that the pseudo-static approach, based on Peak Ground Acceleration (PGA), permits only the determination of the uplift conditions and the beginning of rocking. It does not permit to evaluate the overturning of the blocks. The combined effect of vertical and horizontal seismic motions is negligible and, in some cases, beneficial. This paper presents a new mechanical model, called "one-sided rocking", that takes into account the presence of a rear rigid wall, that is a typical scenario for the rock blocks completely detached from the cliff but close to it. The dynamic response of a great number of rectangular rigid blocks, subjected to 62 recorded earthquake motions on rock soil (from US, Europe and Asia), has been analysed considering only the horizontal acceleration. The results show that the presence of the wall is detrimental for the rocking stability. However, there is still a safety reserve more significant for large blocks and rich frequency content time histories. This reserve could be taken into account in simplified (pseudo-static) analyses through reductive coefficient of PGA.
During an earthquake, different slender elements such as ancient stone columns, tombstones, furniture, reservoirs, electrical equipment may slide, rock or slide-rock and overturn. Rocking motion of a rigid block on a rigid plane subjected to dynamic actions, presented in this work, has been focused on toppling.
Starting from the pioneering work of [1] a number of contribution may be found in literature. The first studies approached the problem by analyzing the dynamic behaviour of the slender elements defining the equations and the parameters affecting the motion by means of deterministic approaches, based on the integration of motion ([2], [3], [4], [5], and [6]) or probabilistic approaches, based on fragility curves ([7], [8], [9]). Other Authors proposed numerical and approximate closed form solutions limited to rectangular and sinusoidal pulses of half-cycle duration ([10], [11], [12], [6], [13]) and also analytical formulations based on natural recorded motions ([3], [5], [14], [15], [16], [17], [18], [19]). Just a few Authors extended this model to rock mechanics ([20], [21]).