Estimation of confidence in the calculated resistance factor for simple limit states with limited data for load and resistance model bias

Estimation of the resistance factor in load and resistance factor design (LRFD) calibration for simple soil-structure limit states is most often based on model bias data of limited size. Frequently, the bias data are only available or required for the resistance term. In this paper, the confidence in the estimate of the mean of the resistance factor is computed for the case of one resistance factor and one load factor where limited model bias data are available for both load and resistance terms. The bootstrap method is used to compute synthetic load and resistance bias data sets from which confidence intervals on the point (mean) estimate of the resistance factor and load factor are computed. A closed-form solution is used to calculate the resistance factor for a single prescribed load factor and target reliability index, bias data, and nominal load and resistance variables that are lognormally distributed. However, the approach is general using Monte Carlo simulation. The method is demonstrated using the case of the internal stability pullout limit state for steel strip mechanically stabilized earth (MSE) walls. The example demonstrates the quantitative influence on pullout design using upper and lower 95% confidence interval limits for load and resistance factors.