基于节理产状不确定性的边坡稳定性及敏感度分析

用Monte Carlo法对服从Fisher分布的节理产状进行模拟，计算每个模拟产状的安全系数，并统计拟合安全系数的分布规律及边坡的可靠度。为同时考虑安全系数对节理倾角和倾向的敏感度，提出了以安全系数对节理面法向矢量球面距离的敏感度来反映其对产状敏感度的分析方法，并建议用平均值和最大值两个指标来反映任意产状的敏感度。用赤平投影方法在赤平图上绘制安全系数等值线图和敏感度等值线图，实现了计算结果的可视化展示。算例分析表明：此方法实现了对节理产状不确定性的全面直观分析，消除了产状测量数据离散化可能造成的安全隐患，解决了以往产状敏感度分析中需单独对倾角或倾向分析的不足。

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.