Authors
1
Assistant Professor, Department of Civil Engineering, University of Tehran, Tehran, Iran,
2
Ph.D. Student, Department of Civil Engineering, University of Tehran, Tehran, Iran
Abstract
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. With the above presumptions and employing the equations of limit of equilibrium, we can find the forces and moments acting on the section involving the crack are found as follows:
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