# Modified Analytical Technique for Block Toppling Failure of Rock Slopes with Counter-Tilted Failure Surface

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## Abstract

A broad mathematical technique for evaluating rock slope stability subjected to toppling of rock columns centered on limit equilibrium is presented. In the current analytical models for evaluating toppling of rock columns for the rock slopes, a single weak plane angle is assumed, running from the top surface of the slope and daylights on the toe of the slope. However, in some physical rock slopes, there exists counter-tilted failure surface within the rock masses of the rock slope and the weak plane may not daylight on the predictable point on the face of the slope following the assumed single weak plane angle. Therefore, applying the current analytical techniques in such conditions may not yield realistic results. A searching technique for estimating angles of counter-tilted failure surface is proposed and incorporated into the existing mathematical technique for evaluating toppling of rock columns centering on limit equilibrium principles. The physical slope with counter-tilted failure surface was comprehensively analyzed using the modified mathematical method and results were validated by numerical simulation using 3DEC 4.1 discrete element method. The influences of relative angles of the counter-tilted failure surfaces on the slope stability have been studied and the results show that, progressive increase of the counter-tilted failure surface angles lead to gradual increase in slope instability. The modified analytical method optimizes and combines the advantages of the traditional analytical techniques and could provide precise analytical method for evaluating stability of rock slopes with counter-tilted planar failure surfaces subjected to toppling of rock columns.

## Keywords

Toppling Counter-tilted weak plane Analytical method Discrete element method Failure mode## Notes

### Acknowledgements

This paper was supported by the National Natural Science Foundation of China, Project No. 51374163.

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