On the ratio of factors of safety in slope stability analyses

Simple algebra is used to demonstrate that the three-dimensional factor of safety of a slope is always greater than the two-dimensional factor of the same slope. The three-dimensional factor of safety corresponding to a surface which includes the critical two-dimensional line is even greater than the two-dimensional factor since it is generally not even the minimum three-dimensional factor. These conclusions hold for the minimum two and three-dimensional factors of safety. Comparisons between other than three minimum factors may produce incorrect impressions of the ratio of factors of safety. Methods that give ratios which are smaller than unity either compare inappropriate factors, or more probably, contain simplifying assumptions which could neglect important aspects of the problem. Any simplifying assumptions should only be used as modifications of a more rigorous method and not as a means of solving a problem without any basis for evaluating the effects of the simplifications. (TRRL)