In rock slopes, block toppling failure is a prevalent instability. In this instability, rock mass consists of a series of dominant parallel discontinuities that are dipping steeply into the slope face, and a series of cross-joints are located normal to the dominant discontinuities. Blocks may slide or rotate due to their weight along the natural cross-joints at their base, and the tensile strength does not significantly affect the stability of the rock slope. The rounding edge of rock columns is a special feature of spheroidal weathering. Firstly, a literature review of block toppling instability is presented. Next, applying the Sarma approach, a new theoretical analysis is proposed for the rock columns with rounded edges. One of the advantages of the proposed approach is that by determining the sign of a parameter called KC, the stability status can be specified. The suggested solution is compared with a pre-existing analytical method through examples and case study. Comparisons indicate that the proposed approach has a satisfactory agreement. It can be concluded that with weathering and rounding of the block edges, the safety factor decreases non-linearly. Therefore, this solution can be used to evaluate the blocky toppling failure regarding the erosion phenomenon.

Block-flexure is the most common mode of toppling failure in natural and excavated rock slopes. In such failure, some rock blocks break due to tensile stresses and some overturn under their own weights and then all of them topple together. In this paper, first, a brief review of previous studies on toppling failures is presented. Then, the physical and mechanical properties of experimental modeling materials are summarized. Next, the physical modeling results of rock slopes with the potential of block-flexural toppling failures are explained and a new analytical solution is proposed for the stability analysis of such slopes. The results of this method are compared with the outcomes of the experiments. The comparative studies show that the proposed analytical approach is appropriate for the stability analysis of rock slopes against block-flexure toppling failure. Finally, a real case study is used for the practical verification of the suggested method.

One of the most conventional toppling instabilities is the block-flexural toppling failure that occurs in civil and mining engineering projects. In this kind of failure, some rock columns are broken due to tensile bending stresses, and the others are overturned due to their weights, and finally, all of the blocks topple together. A specific feature of spheroidal weathering is the rounding of the rock column edges. In the mode of flexural toppling failure, rounding of edges happens only at the upper corners of the block but in the block toppling failure mode, due to the presence of cross-joints at the base of the block, rounding of edges also occurs at the base of the block. In this work, a theoretical model is offered to block-flexural toppling failure regarding the erosion phenomenon. The suggested methodology is evaluated through a typical example and a case study. The results of this research work illustrate that in the stable slopes with rectangular prismatic blocks, where the safety factor value is close to one, the slope is subjected to failure due to erosion. Also the results obtained show that the recommended approach is conservative in analyzing the block-flexural toppling failure, and this approach can be applied to evaluate this failure.

Toppling failure is one of the most common modes of failure of rock slopes in layered rock strata.Flexural toppling is one of the well-known modes of the failure. This type of failure occurs due to bending stress. In this article, a brief yet comprehensive review of toppling failure is presented. Firstly, the conditions and general mechanism of the failure are described. Then, experimental, theoretical and numerical modeling of the failure is summarized. Next, several case histories are analyzed and the results with the existing theoretical models were compared and presented. Finally, some practical recommendations as how to use these models are made.