3D stability and reliability of concave open pit slope in rock with Hoek-Brown strength criterion

The concave slope is a common feature in open pit mines. Due to the geometric effects, the concave slope can be designed with a steeper angle, which yields substantial economic benefits. However, two-dimensional (2D) analysis methods are unable to consider the additional stability provided by the three-dimensional (3D) effects. Furthermore, the inevitable uncertainties in the strength parameters of rocks severely compromise the slope stability. Therefore, reliance on the safety factor as a sole design acceptance criterion is inadequate and should be supplemented with failure probability. This paper aims to evaluate the 3D stability and reliability of concave open pit slopes. The slope instability in a geomaterial governed by the Hoek-Brown strength criterion is analyzed using a variationally derived 3D rotational failure mechanism. The stability analysis results are presented in dimensionless stability charts. Not surprisingly, the safety measures for slopes are greatly dependent on the Geological Strength Index and the slope geometric 3D effects. A closed-form solution for concave open pit slopes is proposed through regression analysis. It demonstrates high accuracy and can be employed to derive the limit state surface (LSS), which is adopted to conduct reliability analysis using First- and Second- Order Reliability Method (FORM and SORM). A series comparison is conducted to assess the performance of FORM and SORM. The findings reveal that FORM exhibits lower accuracy, whereas SORM maintains robust performance in comparison to the Monte Carlo simulation. Finally, the relationship between the mean safety factor and failure probability is established to guide the slope design of open pit mines.