Stability analysis of slopes against combined circular–toppling failure

• A theoretical solution was proposed for combined circular–toppling failure.
• Most of parameters were considered that effect on instability of slopes.
• The soil mass considered as a perfectly plastic material and so surface contact of soil and rock can have any inclination.
• Software was developed to ease the use of proposed method.
• Proposed method freely allows for any failure mode combination. In other word all failure modes have been considered.

Circular failure is one of the most probable instabilities on slopes with severely crushed rock or soil slopes. Another type of instability is block–flexural toppling, which is the most common type of toppling failure. In this type of failure, some rock blocks are broken by bending and other topples due to their weight. In some slopes, a soil mass has direct contact with the rock mass with the potential of block–flexural failure. If so, the total slope failure potential is the combination of circular–toppling failure. This instability can be called secondary toppling failure, for which there is no solution available in the literature. Studies on circular and toppling failure are reviewed. Then the interaction between soil mass and rock blocks is studied. Considering the interaction between soil and rock, this study proposes a theoretical model for stability analysis for the combination of circular–toppling failure and the required equations are developed. Solving these equations manually is time-consuming; thus a special computer code is programmed to analyze the combination failure. The code receives slope׳s information from the user and calculates the factor of safety subject to combination failure circumstances. Finally, a real case (instability of a slope in Vana village along Haraz road in northern Iran) is analyzed with this code and results are compared with the observed data.

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