Robust Calibration of Shaft and Base Resistance Factors for Piles Based on Multiobjective Optimization

Resistance factors are used to account for the uncertainties associated with pile resistance in load and resistance factor design (LRFD). Current design codes and most previous studies recommend a single resistance factor applied to the total pile resistance (shaft and base resistances). However, the uncertainties associated with shaft and base resistances are significantly different. Moreover, resistance factors are generally calibrated based on the statistics of resistance bias factors derived using all data collected from different sites, whereas the variability of the statistics between various sites (i.e., cross-site variability) has been ignored in the traditional calibration approaches, which may result in the designs based on the calibrated resistance factors violating safety requirements. In this paper, a robust calibration approach is proposed to calibrate shaft and base resistance factors, explicitly considering the cross-site variability in the statistics of resistance bias factors in the calibration process. To achieve that, the feasible robustness concept is adopted to describe the probability that the design remains able to achieve the target reliability index when the statistics of resistance bias factor exhibit cross-site variability. The calibration process is implemented through a multiobjective optimization, which leads to a Pareto front that describes the trade-off relationship between shaft and base resistance factors and feasible robustness. The optimal shaft and base resistance factors are determined using the minimum distance approach. The proposed approach is demonstrated and applied to calibrate shaft and base resistance factors for three design methods, the Vesic, Meyerhof, and Nordlund methods. Results show that resistance factors are significantly affected by design methods and the ratio of shaft and base resistances.