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Assessing the Stability of Rock Slopes with Respect to Block-Flexure Toppling Failure Using a Force-Transfer Model and Genetic Algorithm

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Abstract

Block-flexure toppling is the commonest type of failure in anti-dip bedding rock slopes. In this work, a new model called the force-transfer model (FTM) for this kind of failure is proposed, which is based on cantilever beams and limit equilibrium theory. A genetic algorithm (GA) was further employed to predict the safety factor and failure surface of the rock slope. A centrifuge test was also conducted to check the feasibility of using the combined FTM–GA method to model block-flexure toppling failure. The centrifugal results showed that a complex failure surface was produced in a slope undergoing block-flexure toppling. The failure surface is stepped and has a step height approximately equal to the spacing of the cross joints. Comparing these results with the theoretical ones shows that it is eminently feasible to use the FTM–GA method to analyze the stability of slopes liable to undergo block-flexure toppling failure. Moreover, the safety factor (i.e., failure load in the centrifugal test) and failure surface of the slope can be accurately determined using the new method. The newly proposed method can, therefore, be used as a theoretical tool for evaluating and designing anti-dip bedding rock slopes.

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Abbreviations

H :

Height of the slope

\( \beta_{\text{s}} \) :

Angle of the slope

\( \beta_{\text{c}} \) :

Angle of the set of cross joints

\( t_{\text{c}} \) :

Spacing of the cross joints

\( t_{\text{d}} \) :

Spacing of the joints dipping steeply into the slope face

\( i \) :

Number of continuous or discrete rock layers, both numbered from the crest to the toe of the slope

\( P_{{{\text{c}},i}}^{l} \) :

Normal force acting on the left-hand side of the continuous rock layer under consideration

\( Q_{{{\text{c}},i}}^{l} \) :

Shear force acting on the left-hand side of the continuous rock layer under consideration

\( P_{{{\text{c}},i}}^{r} \) :

Normal force acting on the right-hand side of the continuous rock layer under consideration

\( Q_{{{\text{c}},i}}^{r} \) :

Shear force acting on the right-hand side of the continuous rock layer under consideration

\( w_{{{\text{c}},i}} \) :

Weight of the continuous rock layer under consideration

\( h_{{{\text{c}},i}} \) :

Height of the continuous rock layer under consideration

\( c_{\text{d}} \) :

Cohesion of the set of joints dipping steeply into the face

\( \varphi_{\text{d}} \) :

Friction angle of the set of joints dipping steeply into the face

\( l_{i} \) :

Height of left-hand side of the continuous rock layer under consideration

\( r_{i} \) :

Height of right-hand side of the continuous rock layer under consideration

\( \chi \) :

Dimensionless parameter related to the distribution of normal stresses

\( P_{{{\text{d}},i}}^{l} \) :

Normal force on the left-hand side of the discrete rock layer under consideration

\( P_{{{\text{d}},i}}^{r} \) :

Normal force on the right-hand side of the discrete rock layer under consideration

\( w_{{{\text{d}},i}} \) :

Weight of the discrete rock layer under consideration

\( P_{{{\text{c}},i,t}}^{l} \) :

Normal force acting on the left-hand side of the continuous rock layer that enables it to be in the equilibrium state of flexural toppling

\( N_{{{\text{c}},i}} \) :

Normal force acting on the base of the continuous rock layer under consideration

\( S_{{{\text{c}},i}} \) :

Shear force acting on the base of the continuous rock layer under consideration

\( M_{{{\text{c}},i}} \) :

Moment acting on the base of the continuous rock layer under consideration

\( \sigma_{{{\text{c}},i,t}}^{\hbox{max} } \) :

Maximum tensile stress on the base of the continuous rock layer under consideration

\( I \) :

Inertia of the continuous rock layers (given by \( I = t_{\text{d}}^{3} /12 \))

\( F_{\text{s}} \) :

Safety factor of the slope

\( c \) :

Cohesion of the intact rock

\( \varphi \) :

Friction angle of the intact rock

\( \sigma_{\text{t}} \) :

Tensile strength of the intact rock

γ :

Unit weight of the intact rock

\( P_{{{\text{c}},i,{\text{s}}}}^{l} \) :

Normal force acting on the left-hand side of the continuous rock layer that enables it to be in the equilibrium state of shearing

\( h_{i,\hbox{max} } \) :

Maximum height of a rock layer

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Acknowledgements

The research was financially supported by National Natural Science Foundation of China (Grant nos. 11602284 and 11472293), Natural Science Foundation of Hubei province, China (Grant no. 2018CFB450), and the Open Research Fund of the State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences (Grant no. Z018009).

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Authors and Affiliations

  1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei, 430071, China

    Yun Zheng, Congxin Chen, Fei Meng, Haina Zhang & Kaizong Xia

  2. Faculty of Science, Engineering and Technology, Swinburne University of Technology, Hawthorn, VIC, 3122, Australia

    Fei Meng

  3. School of Civil Engineering, Central South University, Changsha, Hunan, 410075, China

    Xiaobin Chen

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  1. Yun Zheng
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  2. Congxin Chen
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Correspondence to Fei Meng or Haina Zhang.

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Zheng, Y., Chen, C., Meng, F. et al. Assessing the Stability of Rock Slopes with Respect to Block-Flexure Toppling Failure Using a Force-Transfer Model and Genetic Algorithm. Rock Mech Rock Eng 53, 3433–3445 (2020). https://doi.org/10.1007/s00603-020-02122-2

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