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. INTRODUCTION When multivariate geotechnical data exist in sufficient amount, it is of significant practical usefulness to construct a multivariate probability distribution function. The applications include: (a) deriving the mean and coefficient of variation (COV) of any parameter given the information contained in a subset with possibly more than one parameter, and (b) evaluating if new strong pairwise correlations can be found either among the original components or some derived components. For the former, it is likely for the COV of a design parameter, say the undrained shear strength (su), to decrease when other parameters, say normalized cone tip resistance [(qtv)/ v] and overconsolidation (OCR), have been measured. This aspect is significant for reliability-based design. In fact, COV reduction can be viewed as a measure of the value of information and may eventually provide a sensible method for deciding if it is worthwhile to measure an additional parameter. For the latter, the ability to predict the existence of new correlations not included as part of model calibration provides a stronger scientific underpinning to correlation studies in geotechnical engineering. The reason is that these predictions can be falsified by taking new observations, which is the cornerstone of the scientific method. In other words, it is a lot harder to develop multivariate models, but if they do stand the test of time, they are usually more robust than bivariate models. 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