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Slope Equivalent Mohr–Coulomb Strength Parameters for Rock Masses Satisfying the Hoek–Brown Criterion

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Abbreviations

c t :

Intercept of the straight line to τ-axes

D :

Disturbance coefficient varying from 0.0 to 1.0

f1–f3:

Non-dimensional functions

H :

Height of inclined rock slope

k :

Cohesion coefficient

L :

Distance between the sliding surface at the top and the edge

m :

Material constant

m i :

Material constant

n :

Material constant

N L :

Stability factor for linear failure criterion

N n :

Stability factor for nonlinear failure criterion

R 0 :

The initial radius of the log-spiral in Fig. 1

Fig. 1
figure 1

Failure mechanism for a homogeneous slope

Full size image
s :

Material constant

v t :

Velocity at velocity discontinuity

α :

Angle of the slope in Fig. 1

β :

Angle of the slope in Fig. 1

γ :

Unit weight of the rock mass

θ 0 :

Angle related horizontal line to line OB in Fig. 1

θ h :

Angle related horizontal line to line OC in Fig. 1

φ t :

Tangent friction angle

σ 1 :

Maximum principal stress

σ 3 :

Minimum principal stress

σ c :

Uniaxial compressive stress

σ n :

Normal component of the failure surface

τ :

Shear component of the failure surface

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Acknowledgments

The preparation of this paper has received financial supports from the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 200550) and the Foundation for the Hunan Provincial Natural Science Foundation of China (No. 09JJ1008). These financial supports are greatly appreciated.

Author information

Authors and Affiliations

  1. School of Civil and Architectural Engineering, Central South University, 410075, Hunan, China

    **ao-Li Yang

  2. Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

    Jian-Hua Yin

Authors
  1. **ao-Li Yang
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  2. Jian-Hua Yin
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Correspondence to **ao-Li Yang.

Appendix

Appendix

$$ f_{1} = \frac{{\left( {3\tan \varphi_{t} \cos \theta_{h} + \sin \theta_{h} } \right)\exp \left[ {3\left( {\theta_{h} - \theta_{0} } \right)\tan \varphi_{t} } \right] - \left( {3\tan \varphi_{t} \cos \theta_{0} + \sin \theta_{0} } \right)}}{{3\left( {1 + 9\tan^{2} \varphi_{t} } \right)}} $$
(9)
$$ f_{2} = \frac{1}{6}\frac{L}{{r_{0} }}\left( {2\cos \theta_{0} - \frac{L}{{r_{0} }}\cos \alpha } \right)\sin \left( {\theta_{0} + \alpha } \right) $$
(10)
$$\begin{aligned} f_{3} &= {\frac{{\exp \left[ {\left( {\theta_{h} - \theta_{0} } \right)\tan \varphi_{t} } \right]}}{6} \cdot \left[ {\sin \left( {\theta_{h} - \theta_{0} } \right) - \frac{L}{{r_{0} }}\sin \left( {\theta_{h} + \alpha } \right)} \right]} \\ &\quad \times{\left\{ {\cos \theta_{0} - \frac{L}{{r_{0} }}\cos \alpha + \cos \theta_{h} \cdot \exp \left[ {\left( {\theta_{h} - \theta_{0} } \right)\tan \varphi_{t} } \right]} \right\}} \\ \end{aligned} $$
(11)
$$ \frac{L}{{r_{0} }} = \frac{{\sin \left( {\theta_{h} - \theta_{0} } \right)}}{{\sin \left( {\theta_{h} + \alpha } \right)}} - \frac{{\sin \left( {\theta_{h} + \beta } \right)}}{{\sin \left( {\theta_{h} + \alpha } \right)\sin \left( {\beta - \alpha } \right)}} \cdot \left\{ {\exp \left[ {\left( {\theta_{h} - \theta_{0} } \right)\tan \varphi_{t} } \right]\sin \left( {\theta_{h} + \alpha } \right) - \sin \left( {\theta_{0} + \alpha } \right)} \right\} $$
(12)

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Yang, XL., Yin, JH. Slope Equivalent Mohr–Coulomb Strength Parameters for Rock Masses Satisfying the Hoek–Brown Criterion. Rock Mech Rock Eng 43, 505–511 (2010). https://doi.org/10.1007/s00603-009-0044-2

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