Confidence intervals for resistance factors in geotechnical LRFD applications

Load and resistance factor design (LRFD) calibration studies in geotechnical engineering typically report resistance factors (ϕ) as fixed deterministic values. However, ϕ is based on a sample of measured and predicted resistances, so in reality the reported; i.e., “nominal” ϕ from a calibration study is an estimate of some underlying “true” ϕ, and as with any other statistic, ϕ is subject to variability arising from both intrinsic randomness and measurement uncertainty. The statistical uncertainty associated with finite sample size can be acknowledged by reporting confidence intervals for the parameter. In this study, confidence intervals for ϕ are calculated using both parametric and nonparametric bootstrap methodologies. These confidence intervals allow for a specific definition of precision for ϕ expressed in terms of the confidence interval coverage and the relative confidence interval width, and these parameters are directly related to sample size. By way of application, a set of charts for coverage and confidence interval width are provided, and the use of these charts is illustrated with selected data from published deep foundation reliability studies. The variability associated with ϕ goes to the very heart of reliability analysis and is significant for at least three reasons: (1) the variability may be linked to the sample size of the calibration study from which ϕ is derived, (2) the magnitude of variability provides a way to judge the quality of ϕ, and (3) by implication, the quality of ϕ affects interpretation of the probability of failure for an LRFD application. Thus, consideration of the confidence interval associated with ϕ provides insight into the probability of failure, which is the proper object of an LRFD resistance factor calibration study.