Analysis methods for slope stability are routinely applied by geotechnical engineers. Slope designs, however, are usually based on a "safety factor" which does not account for soil variability (soil variability is due to actual in-place conditions and not due to sampling procedures and/or testing methods). As a result, the true safety of a slope is unknown.
A reliability approach, using probability calculations which account for the variability in soil strength, is superior to the factor of safety approach. The method is based on the point estimate method and allows engineers to calculate a probability of failure for the slope. Knowing the probability of failure improves engineering judgement by providing a rational basis for making a safe and economical slope design.
Examples show how soil variability affects slope reliability and how the method is applied. The factor of safety is 1.30 in the first two examples. In the first example, the soil deposits are uniform and the probability of failure is acceptable; In the second example, the soils have more soil strength variation and the probability of failure is higher than recommended.
Geotechnical engineers routinely calculate a factor of safety (FS) to evaluate the stability of earth slopes. The Simplified Bishop method (Wright, et al, 1973) is a popular basis for computer analysis programs. A minimum FS of 1.3 is commonly considered as the design basis for most slopes. Failure is assumed to occur when the FS is less than 1.0.
Because the FS analysis does not have a way to consider the variability of the soil strength, the true safety of a slope is unknown. A reliability approach, where a probability of failure is calculated, is a better method for slope design because it accounts for variability in soil strengths. Other factors, like an inadequate field investigation, missing a critical geologic detail (Christian, et, al., 1994) or progressive slope failures (Chowdhury, R,. N., Sept. 1994) are not included in the method described in this report.
The probability of slope failure method is based on the "Point Estimate Method" (PEM) which was developed by Rosenblueth (1975 and 1981) and described by Harr (1987). In the PEM method, a distribution of the variable must be found or assumed. If a normal distribution is assumed, the problem is simplified. Details of the PEM method and a discussion of other distributions are contained in a thesis by Garrett (1989) and a paper by McGuffy, Iori, Kyfor and Grivas (1981).