Performance-Based Reliability Design For Deep Foundations Using Monte Carlo Statistical Methods

Currently, deep foundation designs for the service limit state are deterministic in nature. The settlements and lateral deflections of deep foundations are calculated by means of numerical techniques whereby the foundation-soil interactions are characterized by discrete load transfer curves such as t-z or p-y curves. The noted deficiency of the deterministic approach is that the uncertainties arising from various sources, such as soil properties and model errors are not considered. To address this deficiency, a performance-based reliability design methodology is developed using Monte Carlo statistical methods. The performance based design criteria are defined in terms of the specified allowable displacement. The input to the numerical solution techniques, including the soil strength parameters, unit weight of the soil are relevant to the generation of the load transfer curves are treated as random field. The well established random field generator algorithm, local averaging subdivision, is used to generate random samples of input, where the mean values, variances, the probability distribution, and correlation structures are required statistical parameters for these random variables. The objective of the performance based reliability design is to determine the optimized foundation dimensions so that the probability of failure is less than the target probability of failure. The probability of failure by the Monte Carlo approach is simply the ratio of the number of unsatisfactory performance to the sample size. A numerical example for laterally loaded drilled shaft is given to illustrate the application of the methodology. The incorporation of the correlation length is shown to be critical for properly accounting for the site soil spatial variability.