Stability and sensitivity analysis of slopes based on uncertainty of joint orientations

The orientations of joints which obey the Fisher distribution are simulated according to the Monte Carlo method. The safety factor of each simulated orientation is calculated and the distribution rules of safety factor and the reliability of slopes are obtained by statistical fitting. In order to consider the sensitivity of safety factor to dip direction and dip of joints simultaneously, an idea that the sensitivity of safety factor to the orientation is represented by that to spherical distance of normal vector is proposed. It is also suggested to characterize the sensitivity to arbitrary orientation by means of the sensitivity of average and the maximum value. Drawing safety factor and sensitivity contour map on stereonet makes it possible to visualize the analysis results. The analysis of a specific problem shows that the recommended analytical methods are helpful to gain a complete and intuitive view of the effect of joint uncertainty on safety factor. The potential safety concerns due to the discrete measured data of orientations may be eliminated and the deficiency that the sensitivity analysis is formerly processed by dealing with dip and dip direction respectively can be solved.