Comparison of the anisotropic behaviour of undeformed sandstones under dry and saturated conditions

This article presents a systematic analysis of the anisotropic behaviours of the Bentheim and Rothbach sandstones using ultrasonic P-wave velocity, electrical conductivity and magnetic susceptibility measurements. For each sandstone, the data were obtained from three core samples drilled perpendicularly to each other and tested in dry- and water-saturated conditions. For acoustic and magnetic investigations, the same statistical analysis was applied in order to present the data on comparable stereoplots. Surprisingly, the Bentheim sandstone which appeared homogeneous at macroscopic scale showed a stronger elastic and electrical anisotropy than the Rothbach sandstone in which cross-laminations were clearly identified, as confirmed by a sedimentary magnetic fabric. A discussion on the velocity contrasts between dry and saturated samples led us to consider two different origins for the observed anisotropies. First, by comparing electrical and acoustic properties in the Bentheim sandstone, we conclude that the nature of the anisotropic behaviour is linked to the anisotropy of pore shape: the inclusion model developed by Kachanov (Kachanov, M., 1993. Elastic solids with many cracks and related problems. Advances in Applied Mechanics, vol. 30. Academic Press, Boston, MA, pp. 259–445) accounts for our observations if one considers that the pore space is made of parallel flat pores with moderate pore aspect ratio. Second, acoustic, electrical and magnetic properties indicate that the observed anisotropy in the Rothbach sandstone can be attributed to the matrix, and more specifically to cementation: we modified the Dvorkin and Nur (Geophysics 61 (5) (1996) 1363) model of cemented granular media by introducing a spatially variable contact length, and the model suggests that a very small variability of cemented contact length is enough to account for the observed P-wave velocity anisotropy. We emphasise the fact that combining several kinds of measurements is of great help in capturing the nature of the anisotropic behaviour of porous rocks.