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Hydraulic Conductivity Estimation via Fuzzy Analysis of Grain Size Data James Ross · Metin Ozbek · George F. Pinder

Received: 24 October 2005 / Accepted: 8 February 2007 / Published online: 3 October 2007 © International Association for Mathematical Geology 2007

Abstract A measure of hydraulic conductivity is arguably the most important variable to practicing hydrogeologists. However, the amount of readily available hydraulic conductivity data at any site is generally small, given the resources required to adequately sample a spatial domain. However, other hydrogeologic data, such as grain size distributions and soil descriptions, are often rather easy to obtain. A fuzzy reasoning algorithm is used to define a relationship between soil grain size and hydraulic conductivity. By introducing soil grain distributions and qualitative borehole log descriptions into this fuzzy inference system, hydraulic conductivity can be estimated. The theory is defined, and an application to data from a Superfund site is provided, where the inference procedure produces accurate hydraulic conductivity estimates. Keywords Fuzzy sets · Approximate reasoning · Grain size distributions · Borehole logs · Qualitative data Introduction Large amounts of information often result from a hydrogeologic investigation, whereas hydraulic conductivity data comprise a relatively small subset because the tests required to determine conductivity are generally both time consuming and expensive. Consequently, regional estimates of hydraulic conductivity are inherently uncertain. Since significant uncertainty in hydraulic conductivity estimates lead to uncertainty in groundwater flow and transport models, less costly means of acquiring hydraulic conductivity data have been explored. Specifically, several attempts J. Ross () · M. Ozbek · G.F. Pinder Research Center for Groundwater Remediation Design, Civil and Environmental Engineering Program, College of Engineering and Math, University of Vermont, 33 Colchester Avenue, Burlington, VT 05446, USA e-mail: [email protected]

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Math Geol (2007) 39: 765–780

have been made to relate other more easily measured hydrogeologic parameters to hydraulic conductivity. Porosity, particle sorting, texture and soil type have all been related to hydraulic conductivity. These relationships have intuitive appeal. The determination of porosity requires little effort and expense when compared to that of hydraulic conductivity, and relationships between porosity and hydraulic conductivity have been modeled (Selley 1985). The degree of sorting can be evaluated from the soil’s grain size distribution curve and related to hydraulic conductivity through an empirical equation (Demmico and Klir 2004). Textural characteristics (grain size, ductility) are determined by the examination of a soil sample and have been related to hydraulic conductivity in sandstone through fuzzy relations (Fang and Chen 1997). In a very general sense, an understanding of the ranges of likely hydraulic conductivity values for various soil types has been us