Statistics for the calculated safety factors of undrained failure slopes

Due to the uncertainty and variability involved in ground conditions and analytical methods, the calculated factor of safety (FS) of a slope may not be exact. To know whether the calculated FS is unbiased and also the magnitude of its variability, this paper re-analyzes 43 real cases of undrained slope failure reported in the literature. The FS is re-calculated using two-dimensional (2-D) limit equilibrium methods (LEM) (i.e., the simplified Bishop's method and the Spencer's method) to minimize the human factor in FS calculation. Since all cases failed, the conditions (such as geometries) right before failures were adopted to simulate the nearly failure condition in the LEM. Based on the statistical results of the calculated FS obtained from hypothesis testing, it can be concluded that (a) the 2-D LEM seems to give unbiased FS estimates; (b) the FS variability for natural slopes is significantly larger than that for man-made slopes; (c) the conversion of the undrained shear strength (s_u) to its field value is the most crucial, and the modeling of s_u spatial variability is also crucial; and (d) the standard deviation of the human error in the logarithm of the calculated FS is about 0.25, and the human error appears to be uncorrelated to the logarithm of the calculated FS. Finally, the relationship between the failure probability of a man-made undrained clay slope and its calculated FS is developed to facilitate reliability analysis and reliability-based design.