Efficient sampling of the irregular probability distributions of geotechnical parameters for reliability analysis

Values of site-specific geotechnical parameters are generally estimated based on the results of in-situ and/or laboratory tests. In most cases, the field test data in geotechnical engineering practice are so limited and sparse that their histograms may only be described using an irregular probability distribution. In addition, the posterior distributions of geotechnical parameters obtained from the Bayesian updating may also be an irregular probability distribution. The irregular probability distributions that exhibit a multi-modal nature cannot be well fitted using theoretical probability distributions such as normal, lognormal or beta distributions. Therefore, challenges may arise in sampling of such irregular probability distributions, which could hinder the subsequent geotechnical reliability analyses. To facilitate the geotechnical reliability analyses with limited data, an efficient sampling method that is based on a mixture of uniform distributions is proposed in this study. This sampling method is capable of drawing random samples from the irregular probability distribution of a single geotechnical parameter as well as the joint probability distribution of cross-correlated spatially varied geotechnical parameters. The proposed sampling method is first illustrated and validated using three examples that employ both simulated and real data. The results confirm that the proposed sampling method is accurate and highly efficient. Last, the proposed method is implemented to sample from the posterior distributions of two cross-correlated spatially varied geotechnical parameters obtained from the Bayesian updating of a soil slope. The results indicate that the proposed method can provide an effective and versatile tool for the random sampling of the joint probability distribution and posterior distributions of geotechnical parameters.