Site-specific probability distribution of geotechnical properties

Although the site-specific nature of soil variability has been well-recognized, it is difficult to obtain the site-specific probability distribution of geotechnical properties. Previous studies on soil variability were usually based on a large number of data that have been collected from many different sites in a large region, or even from different parts of the world. For geotechnical engineering practices in a specific project, it is the variability of geotechnical properties within this specific site, not the variability from many different sites, that geotechnical engineers are interested in and require. This leads to the questions of how to model the site-specific variability of geotechnical properties and how to estimate the site-specific probability distribution of geotechnical properties. This paper aims to address these questions using a statistic concept called mixture model and the Bayes' theorem. It is shown that the site-specific probability distribution of geotechnical properties can be considered as a weighted summation of a number of normal or lognormal distributions with different distribution parameters. Then, estimating site-specific probability distribution of geotechnical properties is equivalent to finding a suitable group of normal or lognormal distributions and their respective weights, based on the data available. The formulation and implementation procedure are illustrated and validated through an effective cohesion example and an example of estimating site-specific probability distribution of effective friction angle, based on a limited number of standard penetration test data (i.e., SPT N values) obtained for the project. The proposed methods perform satisfactorily in the examples.