Quantitative relation between particle shape and archie's cementation exponent for coarse grains: A statistical analysis

Abstract

The estimation of the cementation exponent (m) in Archie's equation, which is pivotal for interpreting the electrical resistivity of soils and rocks, could be significantly enhanced by correlating it with particle shape characteristics. This study proposes a novel approach in which Archie's m-exponent for sand is estimated based on quantifiable particle shape parameters, including sphericity, convexity, elongation, slenderness, and roundness. The horizontal and vertical electrical resistivities of eight granular materials with varying particle shapes were measured. Correlation matrix scatter plot and multiple linear regression analyses were conducted to establish a quantitative relationship between Archie's m-exponents, electrical anisotropy, and particle shape parameters. The results indicate that all the investigated shape parameters exhibited strong correlations with m-exponents and electrical anisotropy. However, multiple linear regression analysis revealed that roundness (RD) is the most influential shape parameter, likely due to multicollinearity among the other shape parameters. Notably, m-exponents in both the vertical and horizontal directions were found to decrease linearly with increasing RD, as RD effectively captured the tortuosity of the electrical flow paths at a given porosity. These findings are supported by data from previous studies, further validating the observed relationship between RD and electrical properties.