A logical framework is developed for load and resistance factor design (LRFD) of slopes based on reliability analysis. 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 report. 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 unity. Gaussian random field theory is used to generate random realizations of a 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 mean of the soil parameters is adjusted and this process repeated until the calculated probability of failure reaches to the target probability of failure. Optimal resistance and load factors are obtained by dividing the resisting and driving moments corresponding to the most probable ultimate limit state by the nominal values of resisting and driving moments.

The main goal of this study was to provide specific values of resistance and load factors to implement in limit states and load resistance design of slopes in the context of transportation infrastructure. This report discusses the concepts of load and resistance factors, target probability of failure and the ultimate limit state equation in the context of slope stability analysis. It then presents a detailed algorithm for resistance factor calculation by using reliability analysis. Six cases of real slopes designed and constructed by INDOT are examined by using undrained shear strengths in order to illustrate the LRFD procedure and validate the recommended resistance and load factors.

Report Number



slopes, slope stability, slope stability analysis, load and resistance factor design, LRFD

SPR Number


Performing Organization

Joint Transportation Research Program

Publisher Place

West Lafayette, Indiana

Date of this Version