The log-normal distribution for hydraulic conductivity of compacted clays: Two or three parameters?

Author: Zhai Huaming   Benson Craig  

Publisher: Springer Publishing Company

ISSN: 0960-3182

Source: Geotechnical and Geological Engineering, Vol.24, Iss.5, 2006-10, pp. : 1149-1162

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Abstract

Risk and uncertainty assessments for waste containment systems employing clay barriers often include spatial variability in the hydraulic conductivity as part of the analysis. The two-parameter log-normal distribution is often used to describe the spatial variability, but for compacted clays the three-parameter form can be more appropriate. A statistical hypothesis test was developed that can be used to determine if the two- or three-parameter form of the log-normal distribution is more appropriate. The test is based on a likelihood ratio, comparing likelihood functions for the two- and three-parameter forms at their maximums. Likelihood functions are used assuming that a data set can be segregated into a set of distinct groups of hydraulic conductivities. A step-by-step calculation procedure is described and the test is applied to data collected from 45 sites.

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