Safety factors and the probability distribution of soil strength

Abstract

For soils exhibiting both cohesive and frictional components of strength, the natural variabilities of the components are compared for soil in the undisturbed state and as compacted in earth dams. The probability distributions of the components are shown to agree more closely with a theoretical beta distribution than with the commonly assumed normal distribution.The cohesive and frictional components can be regarded as independent variables and the design safety factor interpreted in terms of probabilities. Assuming equal probabilities for each component leads to the use of partial safety factors which are larger for the cohesive part than for the frictional part. For long-term stability problems limiting partial safety factors corresponding to zero probability can be obtained.The undrained strength of clays also agrees with a beta distribution but in this case there are no limiting safety factors, and some non-zero probability must be associated with the design.