Reductive coefficients for pseudo-static analysis of seismic toppling of rock blocks

The numerical investigation of the rocking response of freestanding slender rock blocks showed that the pseudo-static criterion, based on the application of peak ground acceleration in seismic stability analyses, is often too conservative. This approach, largely widespread in design codes, is not able to capture overturning potential but only indicates the uplift condition. This study presents the results of overturning analyses of rectangular rock blocks in plane conditions considering also the presence of a rear wall, that is a typical scenario for the rock blocks completely detached from the cliff but close to it. Validation of this new model has been conducted by comparing literature results for idealized simple cyclic pulses as excitation. A sample of 149 recorded earthquake motions on rock soil (from US, Europe and Asia), characterized by different range of PGA, PGV Arias Intensity, energy flux and frequency content, has been used as input seismic excitation. The numerical analyses, carried out for different distances between the block and the rear wall, showed the detrimental effect of the wall for the toppling potential. At the same time, also in this case, the pseudo-static application of PGA in seismic stability analyses appears conservative. The paper is mainly addressed to the evaluation of a cautious reductive coefficient, to be applied to the PGA, in order to carry out pseudo-static rocking stability analyses. Furthermore, a critical analysis on motion parameters showed that PGV is a good index for the toppling potential of the blocks, as already shown in literature.