Relationship between hydraulic conductivity and formation factor of coarse-grained soils as a function of particle size H. Choo a , J. Kim a , W. Lee a , C. Lee b, ⁎ a School of Civil, Environmental, and Architectural Engineering, Korea University, Anam-dong 5-ga, Seoul 136-713, South Korea b Department of Marine and Civil Engineering, Chonnam National University, Yeosu 550-749, South Korea abstract article info Article history: Received 23 April 2015 Received in revised form 23 February 2016 Accepted 25 February 2016 Available online 27 February 2016 This theoretical and experimental study investigates the variations of both the hydraulic conductivity and the electrical conductivity of coarse-grained soils as a function of pore water conductivity, porosity, and median par- ticle size, with the ultimate goal of developing the relationship between the hydraulic conductivity (K) and the formation factor (F) in coarse-grained soils as a function of particle size. To monitor the variations of both the hy- draulic conductivity and electrical conductivity (formation factor) of six sands with varying particle sizes, a series of hydraulic conductivity tests were conducted using a modified constant head permeameter equipped with a four electrode resistivity probe. It is demonstrated that K of the tested coarse-grained soils is mainly determined by the porosity and particle size. In contrast, the effect of particle size on the measured electrical conductivity (or F) is negligible, and the variation of F of the tested soils is mainly determined by porosity. Because the porosity may act as a connecting characteristic between K and F, the relation between them in coarse-grained soils can be expressed as a function of particle size. Finally, simple charts are developed for estimating the hydraulic con- ductivity of coarse-grained soils from the measured particle sizes and formations factors. © 2016 Elsevier B.V. All rights reserved. Keywords: Hydraulic conductivity Electrical conductivity Formation factor Porosity Particle size Constant head test 1. Introduction The reliable estimation of hydraulic conductivity (K) in a porous media is a very important task in many areas of engineering, soil sci- ence, and industry because hydraulic conductivity is an essential prop- erty describing the ability of soils to conduct fluid through the pore space between soil particles (Alyamani and Sen, 1993; Costa, 2006; Mitchell and Soga, 2005). The K of soils has been measured in the field using various hydrogeological methods, including ring infiltrometers, two- or four-well methods, constant or falling head permeameters, and other methods (Daniel, 1989; Lee et al., 1985). However, these methods are laborious and expensive. Furthermore, the measured K resulting from these hydrogeological methods represents the average of a large volume of tested areas (Khalil and Santos, 2009; Sikandar and Christen, 2012; Slater and Lesmes, 2002). Consequently, the estima- tion of K using geophysical methods (i.e., electrical conductivity mea- surement) has attracted the attention of many researchers because the measurements of electrical properties of soils are nondestructive, continuous, reliable, and relatively inexpensive (Gomez et al., 2010; Kelly and Frohlich, 1985; Khalil and Santos, 2009; Mazac et al., 1985; Sikandar and Christen, 2012; Slater and Lesmes, 2002; Urish, 1981; Worthington, 1997). In particular, these previous studies demonstrated that there is a strong correlation between K and the formation factor F (F = σ w / σ mix , where σ w = pore water conductivity and σ mix = electri- cal conductivity of media) for coarse-grained soils because both hydrau- lic and electrical conductions in coarse-grained soils mainly occur through the pore space between soil particles (Milsch et al., 2008). Previous empirical relations between K and F showed debatable re- sults, with some investigations reporting a direct relationship between those two (Kelly and Frohlich, 1985; Perdomo et al., 2014; Sikandar and Christen, 2012; Urish, 1981), but the others showing an inverse re- lationship (Archie, 1942; Frohlich et al., 1996; Gomez et al., 2010; Heigold et al., 1979; Milsch et al., 2008). These previous empirical rela- tions between K and F were generally derived for local field conditions; therefore, each relation may be site-specific, resulting in debatable (or at least inconsistent) results. In contrast, previous studies using con- trolled laboratory tests with theoretical background showed that the re- lation between K and F can be either direct or inverse according to the results of the electrical property measurements (Khalil and Santos, 2009; Mazac et al., 1985; Worthington, 1997). When the measured electrical conductivity (or resistivity) can be captured by Archie's equa- tion (a decrease of electrical conductivity with a decrease in porosity), the relationship between K and F is inverse, while the relationship is di- rect in cases where the result is a non-Archie type. Additionally, previous empirical relations generally didn't consider the impact of particle size on the relation between K and F. In theory, the K of soils is determined by the pore size and the distribution of pore space. However, both parameters are not easy to measure; Journal of Applied Geophysics 127 (2016) 91–101 ⁎ Corresponding author. E-mail addresses: choohw@gmail.com (H. Choo), ksmart@korea.ac.kr (J. Kim), woojin@korea.ac.kr (W. Lee), changho@jnu.ac.kr (C. Lee). http://dx.doi.org/10.1016/j.jappgeo.2016.02.013 0926-9851/© 2016 Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Journal of Applied Geophysics journal homepage: www.elsevier.com/locate/jappgeo