Reliability index for serviceability limit state of building foundations

Extensive research has been conducted on reliability-based design (RBD) for the ultimate limit state (ULS). Several RBD codes have been developed and implemented around the world that calibrate the ULS design for a target ULS reliability index (β_uls). However, the serviceability limit-state (SLS) design still is considered using conventional deterministic approaches with an unknown SLS reliability index (β_sls). This paper presents a relationship between β_sls and the β_uls that is specified already in the RBD codes. This relationship is linear, and a key variable in it is the ratio (R) of the SLS capacity (Q_sls) to the ULS capacity (Q_uls). Both closed-form approximations and Monte Carlo simulations are used to characterize R probabilistically. For illustration, the relationship then is used to estimate β_sls for augered cast-in-place piles designed in accordance with the RBD methodologies in the National Building Code of Canada. The results are highly dependent on the statistics of the limiting tolerable foundation settlement (y_lt). For larger y_lt values, the calculated β_sls > β_uls, which means that ULS designs automatically satisfy SLS criteria. For smaller y_lt values, SLS criteria begin to control the design. The importance of sound y_lt criteria is stressed.