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.

One of the most important instabilities of rock slopes is TOPPLING FAILURE. Among the types of TOPPLING FAILURE, block-FLEXURAL FAILUREs are a more common instability, which occurs in nature. In this FAILURE, some rock blocks break due to tensile stresses, and some overturn under their weights, and next to all of them topple together. In 2015, the physical and theoretical modeling of this FAILURE has been studied by Amini et al. Due to the complexity of this FAILURE mechanism, no appropriate numerical model has been proposed so far. In this research work, first, a literature review of the TOPPLING FAILURE is summarized. Then using the UDEC software, as a distinct element method (DEM), the experimental models are analyzed numerically, and the Voronoi joint model is applied to simulate the FAILURE. The results of the numerical simulations are compared with the outcomes of the physical models and analytical solutions. This comparison illustrates that the numerical modeling has a good agreement with the corresponding experimental tests and theoretical approaches. Also the results obtained show that although the mechanism of block-FLEXURAL TOPPLING FAILURE is complicated, the numerical code is well-capable of analyzing this FAILURE.

FLEXURAL TOPPLING is a mode of FAILURE that may occur in a wide range of layered rock strata in both natural and excavated rock slopes. As illustrated in Figure 1, a typical FLEXURAL TOPPLING can be occurring in a rock slope when columns of rock are separated by steeply dipping discontinuities and bended forward.

FLEXURAL TOPPLING FAILURE occurs due to tensile stress caused by in-situ rock column moments.Observations and theoretical analyses carried out by researchers show that the total FAILURE plane is perpendicular to the rock mass discontinuity plane. In this paper, to analyze the FLEXURAL TOPPLING FAILURE, each rock column is modeled as a cantilever beam. Then using the laws of the strength of materials, along with the limit of equilibrium, the safety factor is found. Although the result of this analysis is comparable with those of laboratory tests, their use in real slopes shows a safety factor more than what it has to be. This is due to stress concentration around and near the tips of structural defects in the rock mass. Calculation of the amount of stress concentration around structural defects, based on the laws of the strength of materials, is cumbersome and has not been observed in the analysis of FLEXURAL TOPPLING FAILURE. In this paper, for the first time, structural defects of in-situ rock columns, with a potential of FLEXURAL TOPPLING FAILURE, enter the analysis. In nature, structural defects in rock masses appear haphazardly and unevenly in different locations. However, due to brittleness of the rocks, the rock defects generally appear in the form of ended cracks. Keeping this in mind, to analyze rock columns with structural defects, we considered a single ended crack perpendicular to the column length resulting total FAILURE.Hence, in this case, based on the theory of fracture mechanics, each rock column, with respect to the length of the crack, acts like a beam with two infinite ends.  

In layered and blocky rock slopes, TOPPLING FAILURE is a common mode of instability that may occur in mining engineering. If this type of slope FAILURE occurs as a consequence of another type of FAILURE, it is referred to as the secondary TOPPLING FAILURE. “ Slide-headTOPPLING” is a type of secondary TOPPLING FAILUREs, where the upper part of the slope is toppled as a consequence of a semi-circular sliding FAILURE at the toe of the slope. In this research work, the slide-head-TOPPLING FAILURE is examined through a series of numerical modeling. Phase 2, as a software written based on the finite element method, is used in this work. Different types of slide-head-TOPPLING FAILUREs including blocky, blockFLEXURAL, and FLEXURAL are simulated. A good agreement can be observed when the results of the numerical modeling are compared with those for the pre-existing physical modeling and analytical 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.

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.

A common instability in the rock slopes is a TOPPLING FAILURE. If this type of slope FAILURE occurs due to another kind of FAILURE, it is considered as the secondary TOPPLING FAILURE. A type of secondary TOPPLING FAILURE is the slide-head-TOPPLING FAILURE. In this instability, the upper portion of the slope is toppled, and the pressure caused by the overturning of rock blocks leads to a semi-circular sliding in the soil mass at the slope toe. This instability is examined through the theoretical analysis and physical modelling. Firstly, the FAILURE mechanism mentioned above is described. Next, the slide-head-TOPPLING FAILURE is studied through seven numerical simulations. The Phase2 and UDEC softwares, as the finite element and distinct element methods, respectively, are used in this work. Different kinds of slide-head-TOPPLING FAILURE are modelled such as the blocky, block-FLEXURAL, and FLEXURAL TOPPLING FAILUREs. The numerical modelling results are compared with the existing physical tests and theoretical approaches. This comparison illustrates that the safety factor is underestimated due to the plane strain supposition in numerical modelling. However, the side-friction in the physical models has violated this assumption. The results obtained demonstrate that the distinct element method has an acceptable accuracy compared to the finite element method. Thus this numerical code can be used in order to examine the mentioned FAILURE.

Block-flexure TOPPLING FAILURE is a common FAILURE of layered rock masses in rock slopes. In the FAILURE, rock blocks fail due to bending stresses and overturning. In this paper, initially, a brief review of TOPPLING FAILURE in rock slopes is summarized. Then, a theoretical model is suggested for rock slopes with potential of block-flexure TOPPLING FAILURE, and consequently a new analytical approach is presented for analysis of the FAILURE. Next, a computer code is developed for assessment of rock slopes against block-flexure TOPPLING FAILURE on the basis of presented method in the paper. Finally, two case studies are analyzed by the new suggested approach and the theoretical and real results are compared.

On the north-side of Phase 7 gas flare site located in South Pars Gas Complex (SPGC), Assalouyeh, Iran has a discontinuous rock slope that due to tectonic activity has been vertical mode folded. Also, the coastal climate caused to weathering of mass and occurring TOPPLING FAILURE in this slope. This instability causes some problems in accessing the flare site. So, this slope need to stability analysis and stabilization. In order to stability analysis of this discontinuous rock slope, utilized the distinct elements method (DEM). The modelling process of TOPPLING FAILUREs in UDEC is divided to geometrical and mechanical modelling. The result of modelling has good agreement with the TOPPLING FAILUREs definition and process.