Pseudo-dynamic stability of rock slope considering Hoek–Brown strength criterion

Abstract

Rock slopes with planar joints or weak structural planes are vulnerable in nature, especially suffering from the natural hazards, instabilities of slopes are more prone to occur. Therefore, concerning to the influence of earthquakes, this paper performs a new procedure to evaluate slope stability in a geomaterial governed by Hoek–Brown strength criterion. A rotational failure mechanism determined by 21 dependent angle variables is introduced to respect the Hoek–Brown strength criterion. The earthquake load is characterized by a modified pseudo-dynamic method that does not violate the zero boundary condition and considers the damping properties of geomaterials. A slice approach is adopted to calculate the earthquake-induced inertial force work rate. The stability number of rock slope is considered to measure the safety. The stability number is formulated as a classical optimization problem controlled by 21 dependent angle variables and a time variable which need to be optimized by the genetic algorithm toolbox. Comparisons with the literature are made to prove rationality and accuracy of the proposed procedure. Parametric study is carried out to reveal the influence of dynamic properties. For engineering application, stability charts are provided for a quick assessment of slope safety.

Appendix

$$C_{{\text{S}}} = \cos \left( {y_{{{\text{s}}1}} } \right)\cosh \left( {y_{{{\text{s2}}}} } \right)$$

(28)

$$S_{{\text{S}}} = - \sin \left( {y_{{{\text{s}}1}} } \right)\sinh \left( {y_{{{\text{s2}}}} } \right)$$

(29)

$$C_{{{\text{SZ}}}} = \cos \left[ {\frac{{y_{{{\text{s1}}}} \left( {H - z} \right)}}{H}} \right]\cosh \left[ {\frac{{y_{{{\text{s2}}}} \left( {H - z} \right)}}{H}} \right]$$

(30)

$$S_{{{\text{SZ}}}} = - \sin \left[ {\frac{{y_{{{\text{s}}1}} \left( {H - z} \right)}}{H}} \right]\sinh \left[ {\frac{{y_{{{\text{s}}2}} \left( {H - z} \right)}}{H}} \right]$$

(31)

$$y_{{{\text{S1}}}} = \frac{2\pi H}{{\lambda_{{\text{s}}} }}\left[ {\frac{{\sqrt {1 + 4\xi^{2} } + 1}}{{2\left( {1 + 4\xi^{2} } \right)}}} \right]^{1/2}$$

(32)

$$y_{{{\text{S2}}}} = - \frac{2\pi H}{{\lambda_{{\text{s}}} }}\left[ {\frac{{\sqrt {1 + 4\xi^{2} } - 1}}{{2\left( {1 + 4\xi^{2} } \right)}}} \right]^{1/2}$$

(33)

$$\frac{H}{{r_{0} }} = e^{{\sum\nolimits_{k = 1}^{n} {\eta_{k} \tan \delta_{k} } }} \sin \theta_{n} - \sin \theta_{0}$$

(34)

$$\theta_{c} = \arctan \frac{{r_{n} \sin \theta_{n} - H}}{{r_{n} \cos \theta_{n} + H\cot \beta }}$$

(35)