Correlations among some clay parameters - the multivariate distribution

This paper constructs a 10-dimensional multivariate probability distribution covering 10 clay parameters. The parameters are the liquid limit, plasticity index (PI), liquidity index, effective vertical stress, undrained shear strength, sensitivity, and three piezocone test parameters. A CLAY/10/7490 database is compiled in a companion paper for this purpose. The database consists of 7490 data points from 251 studies. The number of data points associated with each study varies from 1 to 419 with an average 30 data points per study. The clay properties cover a wide range of overconsolidation ratios (but mostly 1 similar to 10), a wide range of sensitivity (S-t) (sites with S-t = 1 similar to tens or hundreds are fairly typical), and a wide range of PI (but mostly 8 similar to 100). The constructed multivariate probability distribution can be used as a prior distribution to derive the joint distribution of design parameters based on limited but site-specific field data. Note that the entire joint distribution of the 10 clay parameters is derived, not marginal distributions or simply means and coefficients of variation. These multiple design parameters can be updated from multiple field measurements, which is more useful than updating one design parameter using one field measurement that is typical in current practice. This paper also demonstrates that it is practical to build multivariate probability models by combining available bivariate models, which are prevalent in the geotechnical engineering correlation literature. The proposed approach circumvents the need to collect multivariate data, which are rarely found in typical site investigation programs.