A 2D numerical study of the effect of particle shape and orientation on resistivity in shallow formations

Etienne Rey (1, 2) , Denis Jongmans (3)

1 CNAM - Conservatoire National des Arts et Métiers [CNAM]
2 LIRIGM - Laboratoire Interdisciplinaire de Recherche Impliquant la Géologie et la Mécanique
3 LGIT - Laboratoire de Géophysique Interne et Tectonophysique

Surficial heterogeneous soils such as till, alluvial fans or slope deposits are difficult to characterize by geotechnical tests due to the presence of decimeter to meter sized pebbles or rocks. The effective resistivity of such two-component medium composed of a percentage of resistive particles embedded in a conductive matrix is given by the Bussian's equation. The application of this equation allows the concentration of resistive particles to be determined if the resistivity values of each component and of the mixture, as well as the cementation exponent m, are known. However, previous theoretical and experimental studies have shown that the effective resistivity is affected by the shape of the particles. The objective of this study is to numerically determine the 2D effects of particle shape and orientation on the resistivity. Two configurations have been considered in the Finite Element modeling: laboratory like measurements and field layout. For circular particles, the numerical results fit the Bussian's equation with an exponent m of 2. Aligned elongated particles induce an anisotropy which can raise or diminish the exponent m, depending on the particle orientation and on the tortuosity of the current paths. Field experiment simulations showed that m varies 2 between 2.5 and 3.1 for an aspect ratio of 5 and that anisotropy resulting from the particle shape has little effect (m close to 2) when this ratio is lower than 2.5. This increase of m with the aspect ratio is in agreement with the theoretical model of Mendelson and Cohen and is consistent with the results of experimental studies. For laboratory measurement simulations, m values vary between 1.3 and 4 for a particle aspect ratio of 5, whatever the resistivity contrast between the particles and the matrix. The difference of results between the two configurations is explained by the paradox of anisotropy.

Mots clés: electrical resistivity; heterogeneous soil; anisotropy; particle shape; cementation exponent

Domaines: Géophysique [physics.geo-ph]

Etienne Rey, Denis Jongmans. A 2D numerical study of the effect of particle shape and orientation on resistivity in shallow formations. Geophysics, 2007, 72 (1), pp.F9-F17. ⟨10.1190/1.2399453⟩. ⟨hal-00196175⟩