Generalized Archie's Law for Estimation of Soil Electrical Conductivity

Abstract

Archie's law, which is an empirical relationship between the electrical conductivity of rocks and their porosity, has been used widely for saturated rocks, while Archie's second law has been developed for unsaturated rocks. Both of these laws assume that the rock matrix is non-conducting and the conduction takes place through the pore-solution only. However, not many efforts have been made by the researchers to check suitability and applicability of Archie's law to the saturated or unsaturated states of the soils. Hence, a generalized Archie's law for soils, by incorporating their physical properties, volumetric moisture content, and bulk and pore-solution conductivities, was attempted in this study utilizing the data available in the literature. Further, to demonstrate the validity of this law, four soils with entirely different properties were used. These soils were characterized by conducting conventional laboratory tests, and their bulk and pore-solution conductivities were determined with the help of an impedance analyzer and a pressure membrane extractor.

Physical properties, electrical resistivity, and strength characteristics of carbonated silty soil admixed with reactive magnesia

“…It should also be noted that parameters s and m are equal to 1.81 and 1.33, for the uncarbonated specimens while they vary from 0.13 to 0.36 and 0.50 to 1.14, for the carbonated specimens, respectively. These parameters are noticed to be quite similar to those reported by Shah and Singh (2005). Figure 13 shows the relationship between the unconfined compressive strength (q u , in kPa) and w 0 /c and it can be noticed that q u decreases with an increase in w 0 /c at a given carbonation time (t = 1.5, 3.0, 4.5, 6.0 and 12 hr).…”

“…match very well. Figure 12 depicts the relationship between the ratio of the pore-water electrical resistivity to the bulk electrical resistivity (ρ w/ ρ) and the volumetric water content (θ), demonstrating the applicability of generalized Archie's law, proposed by Shah and Singh (2005) (Eq. (6)), to the soils tested in this study.…”

Electrical resistivity of compacted clay minerals

“…Shah and Singh (2005) indicated that pore water properties significantly affect the electrical conductivity of soil. An experimental programme was therefore developed for the characterisation of pore water of clay minerals.…”

“…However, little attention has been given to the influence of clay mineral types and their physico-chemical properties on electrical properties. Several studies have been conducted on the electrical mixing models and resistivity variations of soils (Abu-Hassanein et al 1996;Kibria and Hossain, 2012;Rinaldi and Cuestas, 2002;Shah and Singh, 2005); however, the electrical resistivity responses of clay minerals at different physico-chemical properties are not well documented. Kibria and Hossain (2014) The objective of this study was to determine the electrical resistivity responses of different clay minerals at three degrees of saturation (S r ) -that is, 40, 60 and 80% -and their relationships to pore water properties, activity, cation exchange capacity (C EC ) and porosity.…”

Methodology for determination of osmotic suction of soils

“…Details of the test setup for measuring w m are depicted in Figure 1 (Shah and Singh, 2005). The test setup mainly consists of a pressure membrane extractor (PME), manufactured by Eijkelkamp, Netherlands, as depicted in Figure 2.…”