Analytical Probabilistic Methods to Analyze the Stability of the Rock Wedge with Multiple Failure Modes

Wedge failures are frequently observed in rock slopes. However, these conventional probability analysis methods for rock wedge stability analysis suffer from a known critic of poor efficiency and accuracy. This paper proposes two analytical probabilistic methods (JDRV method and SAPM) to address these issues. The proposed methods are illustrated through a practical rock wedge example. By the comparison with the Monte Carlo simulation (MCs), it can be concluded that the JDRV method is reliable and accurate for the random variables with normal and lognormal distribution, but SAPM is only reliable and accurate for those with normal distribution. The results of the JDRV method and SAPM also indicate that the failure probability of rock wedge will decrease for the random variables with normal distribution with the reduction of correlation coefficient, while the failure probability will increase for the random variables with lognormal distribution. Moreover, the failure probability of rock wedge with biplane sliding mode can greatly be reduced by improving the strength of the discontinuity plane whose effective normal load or area is larger in the two discontinuity planes.