Assessing Relations Between Electrical and Geotechnical Properties of Sand-Clay Mixtures Using Jonscher Fractal Power Law Model

Abstract

The geotechnical properties of unconsolidated geo-materials such as soils are influenced by modifications of their micro-structure, texture, mineralogy, water content and imposed effective stress levels. Fundamental relations between the characteristic electrical parameters describing the electrical responses soils based on a fractal power law model with scaling properties, and parameters influencing their geotechnical behavior are investigated. Low frequency electrical conductivity laboratory measurements were performed on sand and clay mixtures subjected to varying effective stress levels with concurrent measurements of their geotechnical properties. The conductivity spectra of the mixtures were described using a Jonscher fractal power law model characterized with three characteristic parameters, the dc conductivity ( σdc), the characteristic frequency ( fc) and an exponent ( n). Changes in effective stress, water content, clay content, and other engineering properties of the mixture such as dry density, porosity, pore size and intergranular void ratio are discussed with respect to changes in the electrical parameters. The dc conductivity and characteristic frequency decrease with an increase in effective stress levels. The exponent, however, has the opposite behavior and increases with an increase in effective stress. As the water content increases, σdc and fc increase while n decreases for all mixtures. With increasing stress levels, the average pore size of the mixtures decreases which results in a decrease in σdc and fc but an increase in the values of the exponent. An increase in dry density of the mixtures leads to a decrease in σdc and fc whilst n increases. Both σdc and fc increase with increase in the intergranular void ratio of the mixture whilst the exponent values decrease with an increase in the intergranular void ratio. This study serves as a contribution to our quest in utilizing electrical geophysical methods, to assess and monitor non-invasively, the geotechnical properties of the subsurface in a less expensive and faster manner.