Abstract
One of the elements that distinguishes geotechnical Reliability-Based Design (RBD) from the structural counterpart is the need to consider the multivariate nature of the data collected in a site investigation program. Multiple laboratory and field tests are commonly conducted and data are made available in a site investigation report for design. Although it is theoretically possible to couple data from different tests together using a multivariate probability model, it is not easy to do so in practice, because genuine multivariate data are rarely collected. The more common scenario is to collect multiple sets of bivariate data from different locations. This paper demonstrates that a multivariate probability model can be constructed using this more limited bivariate data type if a correlation matrix property called positive definiteness is satisfied. This conclusion is significant, because it would pave the way for characterization of geotechnical variability to advance beyond univariate data to more realistic multiple sets of bivariate data. Similar to the ubiquitous pairwise correlations in the geotechnical literature, a multivariate probability model is only applicable to the soil types represented in the calibration database.