Laurent Louis

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

Abstract 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.

Effects of bedding and foliation on mechanical anisotropy, damage evolution and failure mode

Abstract In this study we review recent advances in our understanding of anisotropy in rocks, focusing on dilatant and compactant failure in sandstones and in a foliated metamorphic rock. In sandstones, the anisotropy can be associated with bedding, as in the Rothbach sandstone, or it can also be due to shape anisotropy of the grains and/or the pores, as in the Bentheim sandstone. Two scenarios are proposed for the development of anisotropy in these two end members. In a metamorphic rock with strong foliation like the Four-mile gneiss, it has been commonly observed that the brittle strength is minimum at a foliation angle of about 30°–45°. A damage mechanics model is proposed that underscores the dominant role of biotite foliation in the development of microcracking. In contrast it is often observed in sandstones with strong bedding that the strength is minimum in the direction parallel to bedding. New results for the Rothbach sandstone showed that compared to parallel-to-bedding samples: (i) in the brittle faulting regime the perpendicular-to-bedding samples have both a higher strength and dilatancy stress; and (ii) in the cataclastic flow regime the compactive yield envelope for the perpendicular-to-bedding samples expands significantly towards higher stress values.

Characterization of pore-space heterogeneity in sandstone by X-ray computed tomography

Abstract In this study we review some of the recent advances in the application of X-ray computed tomography (X-ray CT) to geomaterials. This non-destructive technique based on density contrasts provides 2D images comparable with micrographs and 3D reconstructions at various resolutions depending on the acquisition setup. Synchrotron images with resolution of a few microns allow for 3D mapping of the pore space and can be used to perform 3D fluid flow simulations. ‘Industrial’ CT systems can provide images of centimetre-sized samples with a resolution of c. 50 µm. This resolution is suitable for studying centimetre-scale structural heterogeneities and compaction localization, as illustrated in recent studies. Starting from images taken at both synchrotron and industrial resolutions in intact samples of porous sandstones, we show that important conclusions on pore-space heterogeneity can be drawn from global and local analysis of the distributions of X-ray attenuation values. The global analysis is used in particular to identify relatively homogeneous materials in which compaction bands are likely to develop. Local analysis performed over small clusters of voxels appears to have more potential for the geometric description of the pore space. We show the existence of a resolution at which the local coefficient of variation of the X-ray distributions reaches a maximum. This resolution, which is about an order of magnitude lower than synchrotron resolution, appears to be related to the pore size, and the corresponding coefficient of variation to the porosity.