Correlations among some parameters of coarse-grained soils - the multivariate probability distribution model

A multivariate probability distribution model for seven parameters of coarse-grained soils is constructed based on the SAND/7/2794 database that was compiled by the authors. It is shown that the multivariate probability distribution captures the correlation behaviors in the database among the seven parameters. This multivariate distribution model serves as a prior distribution model in the Bayesian analysis and can be updated into the posterior distribution of the design soil parameter when multivariate site-specific information is available. It is shown that this Bayesian analysis is conceptually similar to what is routinely carried out in practice, which utilizes information from comparable sites to supplement limited site-specific information. The resulting posterior distribution from Bayesian analysis merely combines different uncertainties associated with different sources of correlated information in a more consistent way. In this paper, the parameters for the posterior distribution of the design soil parameter are summarized into engineer-friendly tables (Tables 9 and 10) so that engineers do not need to conduct the actual Bayesian analysis. Caution should be taken in extrapolating the results of this paper to cases that are not covered by SAND/7/2794, because the resulting posterior distribution can be misleading. This caveat applies to conventional regression equations as well.