The log-normal distribution for hydraulic conductivity of compacted clays: Two or three parameters? |
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Authors: | Huaming Zhai Craig H. Benson |
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Affiliation: | (1) Department of Civil and Environmental Engineering, University of Wisconsin, 2214 Eng. Hall, 1415 Engineering Drive, Madison, WI 53706, USA;(2) Vinya Capital LP, New York, NY, USA |
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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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Keywords: | clay liner hydraulic conductivity hypothesis test landfill lognormal distribution spatial variability |
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