Analytical and experimental studies on toppling behavior of blocks misaligned with the slope face

The stability of potentially toppling rock blocks has been typically addressed for the case of regular block geometries showing symmetry planes and resting on surfaces aligned with the slope face, i.e., the strike of the slope is parallel to the block sides and their basal planes. However, these simple geometries with ideally oriented blocks are not often found in nature. This study aims to bridge this knowledge gap through analytical and experimental approaches, in the form of laboratory physical models, to study toppling cases for non-conventional scenarios. An engineering geology review was first conducted, identifying potential non-standard cases in nature. Then, the current analytical solutions for both the factor of safety and critical toppling angle were modified for these misaligned cases, focusing on single block and standard block toppling, and considering the effect of block-edge rounding. Physical models support the analytical approach. It is concluded that toppling stability is slightly improved when the orientation of the basal plane of the blocks differs with the strike of the slope. In this way, for single blocks, the critical toppling angle increases a few tenths of a degree when the difference between strikes is 10 degrees, about 1 degrees with strike differences about 20 degrees and 2 to 3 degrees for misalignments about 30 degrees. Similar increases are observed for block toppling cases. Accordingly, small differences in strike of basal planes and the slope contribute to slightly increasing the factor of safety of slopes prone to block toppling. This approach improves practical engineering toppling stability analyses.