Reliability Analysis of Load and Resistance Factor Design of Slopes

A logical framework is developed for the LRFD of slopes based on reliability analysis. The LRFD of slopes with resistance factors developed in this manner ensures that a target probability of slope failure is not exceeded. Three different target probabilities of failure (0.0001, 0.001, and 0.01) are considered in this paper. The ultimate limit state for slope stability (formation of a slip surface and considerable movement along this slip surface) is defined using the Bishop simplified method with a factor of safety equal to 1. Gaussian random field theory is used to generate random realizations of the slope with values of strength and unit weight at any given point of the slope that differ from their mean by a random amount. A slope stability analysis is then performed for each slope realization to find the most critical slip surface and the corresponding driving and resisting moments. The probability of slope failure is calculated by counting the number of slope realizations for which the factor of safety did not exceed 1 and dividing that number by the total number of realizations. The means of the soil parameters are adjusted, and this process repeated until the calculated probability of failure is equal to the target probability of failure. Resistance and load factors are obtained by dividing the resisting and driving moments corresponding to the most probable ultimate limit state (the design point) by the nominal values of resisting and driving moments. Although this paper focuses on the presentation of the methodology of resistance factor determination, resistance and load factors are calculated for some slope cases, and preliminary load and resistance factors are suggested for use in applicable codes.