Analytical and experimental studies to obtain electrical resistivity in a small-scaled laboratory test

Abstract

Electrical resistivity surveys have been used to investigate soil behavior at the microscale, and thus they require a method for obtaining accurate electrical resistivity. The previously suggested geometric factor ignores the dimensions of the electrode due to the scale effect present in field conditions, thus necessitating a more appropriate method to capture reliable electrical resistivity for laboratory tests. Our objective is to suggest an analytical solution to obtain reliable electrical resistivity in laboratory testing. Models are verified through laboratory tests and statistical methods. The relationship between electrical resistance and electrical resistivity is analytically defined by Ohm's law and Gauss's flux theorem. Consequently, the underlying importance of electrode capacitance including electrode length and diameter for estimating electrical resistivity is evaluated. In addition to the electrical resistivity estimated based on Ohm's law (EOL), capacitance based on the single-electrode model (CSM) and the multiple-electrode model (CMM), electrical resistivity based on the conventional calibration method is also addressed. Four-equally spaced electrode probe system is designed to measure the electrical resistance. The estimated electrical resistivity based on each model (EOL, CSM, CMM, and 2 pi sR) is compared with the electrical resistivity estimated from the conductivity meter to verify the suggested models. The electrical resistivity estimated from EOL shows high reliability. Our results underline the significance of EOL model in the conversion of measured electrical resistance into electrical resistivity in laboratory tests.