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• The electrical conductivity tensor of a transversely isotropic material that contains inhomogeneities of arbitrary orientation is determined • Mudstone rock is modeled as a transversely isotropic multiphase composite. • Two sources of effective anisotropy of the conductivity tensor are considered, matrix anisotropy and shape, orientation distribution of inclusions. • In the case of low aspect ratio of inhomogeneity, contribution of inclusion phases to effective anisotropy may be significant. • Mori–Tanaka–Benveniste, Maxwell, and differential homogenization schemes are used to calculate electric conductivity and compared. This paper addresses the problem of the electrical conductivity tensor calculation for a transversely isotropic material that contains inhomogeneities of arbitrary orientation. For this goal, we first construct the electrical conductivity contribution tensor for an arbitrarily oriented isolated ellipsoidal anisotropic inhomogeneity embedded in a transversely isotropic matrix. The general case of an orthotropic ellipsoidal inhomogeneity unaligned in an anisotropic matrix with different classes of symmetry can be considered. This solution is used as the basic building block of various homogenization techniques: the Mori–Tanaka–Benveniste scheme, Maxwell scheme, and differential scheme. The approach is illustrated by an application to a transversely isotropic mudstone rock, composed of a clay matrix containing inhomogeneities of calcite and quartz. We analyse the origins of the extent of anisotropy of the effective conductivity tensor, distinguishing among the shape, orientation distribution, and anisotropy of the inhomogeneities on the one hand and the anisotropy of the matrix on the other hand. Numerical results show that the orientation distribution of the inhomogeneities significantly affects the overall anisotropy in the case of inhomogeneities with low aspect ratio(s). Limiting cases of aligned and randomly oriented inhomogeneities provide bounds of the extent of anisotropy for the overall conductivity tensor. [ABSTRACT FROM AUTHOR]

The Callovo-Oxfordian mudstone (Meuse/Haute-Marne, France) is currently considered as the host rock barrier for a deep geological repository. The intimate relationships between the porosity and mineralogy of this host rock were investigated at the small scale (μm–mm) and large scale (m–hm). At the small scale, we have adapted the 3 H-PMMA autoradiographic method to map the porosity of the Callovo-Oxfordian mudstone. The 3 H-PMMA autoradiographic method was improved in terms of its spatial resolution. 3 H-PMMA porosity maps were then compared to homologous mineral maps (clay minerals, carbonates and tectosilicates) built from scanning electron microscopy images (using back-scattered electron imaging). Based on an inversion procedure, the specific porosity of each mineral group was estimated from the mineral and porosity maps. We found that the spatial distribution of porosity at the small scale is mainly controlled by the spatial distribution of the clay matrix (the average porosity of the clay matrix is 40–45%), whereas quartz and carbonate mineral grains have low porosities (0–4%). At the geological formation scale, the porosity and mineralogy distributions were determined by logging tool techniques (nuclear magnetic resonance and spectral gamma-ray). The coupled evolution of clay content and porosity with depth was analyzed according to the porosity/mineralogy relationship defined at the small scale. Finally, we modeled the evolution of the porosity of the Callovo-Oxfordian mudstone with depth by considering the clay content and the effect of physical compaction during burial. [ABSTRACT FROM AUTHOR]