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Stability Analysis of Flexural Toppling Failure Using the Sarma’s Method

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Abstract

A conventional instability of rock slopes in layer rock strata is flexural toppling, which occurs due to bending stresses. The stability analysis of flexural toppling failure has been studied vastly. Firstly in this study, a literature review of this failure is introduced, and then the Sarma’s method is defined. Using Sarma’s method, a new analytical solution is offered for the stability analysis of flexural toppling. Physical modelling of this failure is conducted by Amini et al. (Int J Min Geo-Eng 49(2):155–171, 2015). Using UDEC software as distinct element method, the experimental model was analyzed numerically. In numerical modelling, the Voronoi joint model was applied to simulate the failure. Then, the proposed analytical method was evaluated for this physical model. Comparison between the current suggested approach with the results of the pre-existing experimental model, two analytical methods, and numerical modelling, demonstrates that the proposed analytical method has an acceptable agreement. So, this method can be used to analyze the flexural toppling failure.

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Abbreviations

\(\sigma_{t}\) :

Tensile strength of blocks

\(\gamma\) :

Unit weight

\(I\) :

Moment of inertia

\(h\) :

Average blocks length

\(t\) :

Block thickness

\(\psi_{f}\) :

Angle of the slope face

\(\psi_{p}\) :

Joint dip angle

\(\psi_{t}\) :

Dip of total failure surface of toppling failure

\(\psi_{s}\) :

Dip of an upper surface of the slope

\(\psi_{b}\) :

Dip of normal to joints

\(\psi_{i}\) :

Angle between total failure surface and normal to the joint dip angle

\(\theta\) :

Angle between face slope with respect to the x-axis (\(\theta = \pi - \psi_{f}\))

\(\alpha_{i}\) :

Angle of the base of the block with respect to the x-axis

\(\delta_{i}\) :

Inclination of the interface measured from the positive y-axis

\(n\) :

Number of blocks

\(H\) :

Slope height

\(N_{{^{i} }}\) :

Normal force acting at the block base

\(S_{{^{i} }}\) :

Shear force acting at the block base

\(\ell_{i}\) :

Application point of \(N_{i}\) with respect to the lower left-hand corner of blocks

\(d_{i}\) :

Length of the sides of the blocks

\(b_{i}\) :

Horizontal distance of the block base

\(\phi_{b}\) :

Angle of interface friction of the block base

\(c_{b}\) :

Cohesive strength of the block base

\(c_{i}\) :

Cohesive strength of intact rock

\(c_{c}\) :

Cohesive strength on the sides of blocks

\(\phi_{i}\) :

Angle of internal friction of the intact rock

\(\phi_{c}\) :

Angle of interface friction between blocks

\(P\) :

Normal force of inter-block

\(Q\) :

Shear force of inter-block

\(Z\) :

Application point of “P” with respect to the block base

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Acknowledgements

The author expresses his science thanks to Professor Ömer Aydan and Dr Mehdi Amini from Ryukyu University and the University of Tehran, respectively, for his invaluable guidance through this study.

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  1. School of Mining Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Hassan Sarfaraz

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  1. Hassan Sarfaraz
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Correspondence to Hassan Sarfaraz.

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Sarfaraz, H. Stability Analysis of Flexural Toppling Failure Using the Sarma’s Method. Geotech Geol Eng 38, 3667–3682 (2020). https://doi.org/10.1007/s10706-020-01244-2

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