Multivariate model for soil parameters based on Johnson distributions

Abstract

The objective of this paper is to demonstrate the practical construction of a multivariate probability distribution function using an actual soil database containing su(CIUC), OCR, and four piezocone parameters. Five hundred and thirty-five multivariate data points were compiled from 40 clay sites around the world (Brazil, Canada, Hong Kong, Italy, Malaysia, Norway, Singapore, Sweden, UK, USA, and Venezuela). It was found that a multivariate probability distribution can be constructed by transforming each component of a multivariate normal distribution to a Johnson distribution. Existing bivariate regression equations focus on strong correlations. Weak correlations are typically discarded. Site investigation is a costly exercise, and, ideally, one should exploit all measured geotechnical data for design. The multivariate distribution is a concise model to summarize all available information. Conditional distributions can be easily derived to update the marginal distribution of any one parameter or the multivariate distribution of any group of parameters given information from other parameters. One of the objectives of site investigation is to perform cost-effective field tests and to evaluate design parameters based on these field measurements. Clearly, conditioning involving updating one or more design parameters using one or more field measurements is a natural probabilistic generalization of the current soil property evaluation methodology. © 2013 American Society of Civil Engineers.