Effect of rear walls on the rocking response of rock blocks under seismic excitations

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.