Calibrating cross-site variability for reliability-based design of pile foundations

The cross-site variability (i.e., variability from site to site) makes the statistics of the bias factor of a design model vary from site to site. How to characterize the cross-site variability of the model bias factor is important for design of pile foundations based on site-specific load test data. In this study, a probabilistic model that allows for explicit modeling of the cross-site variability is suggested. An equation is derived based on Bayes’ theorem to calibrate the suggested model with load test data from different sites, which is applicable even when the number of load tests at each site is small. A procedure based on hybrid Markov Chain Monte Carlo simulation is employed to solve the Bayesian equation. How to update the statistics of the model bias factor, when applied to a future site, with site-specific load test data is also described. As an illustration, the probabilistic model is applied to the design of bored piles in Shanghai, China. It is found that, given a certain number of site-specific pile load tests, the effect of updating depends on the mean and the COV of the measured model bias factor. With the assistance of regional experience, a small number of load tests can significantly reduce the uncertainty associated with the design model, and further increase in the number of load tests may not change the site-specific statistics of the bias factor and hence the resistance factor substantially.