Sébastien Brisard

Morphological quantification of hierarchical geomaterials by X-ray nano-CT bridges the gap from nano to micro length scales

Abstract Morphological quantification of the complex structure of hierarchical geomaterials is of great relevance for Earth science and environmental engineering, among others. To date, methods that quantify the 3D morphology on length scales ranging from a few tens of nanometers to several hundred nanometers have had limited success. We demonstrate, for the first time, that it is possible to go beyond visualization and to extract quantitative morphological information from X-ray images in the aforementioned length scales. As examples, two different hierarchical geomaterials exhibiting complex porous structures ranging from nanometer to macroscopic scale are studied: a flocculated clay water suspension and two hydrated cement pastes. We show that from a single projection image it is possible to perform a direct computation of the ultra-small angle-scattering spectra. The predictions matched very well the experimental data obtained by the best ultra-small angle-scattering experimental setups as observed for the cement paste. In this context, we demonstrate that the structure of flocculated clay suspension exhibit two well-distinct regimes of aggregation, a dense mass fractal aggregation at short distance and a more open structure at large distance, which can be generated by a 3D reaction limited cluster-cluster aggregation process. For the first time, a high-resolution 3D image of fibrillar cement paste cluster was obtained from limited angle nanotomography.

A numerical study of one-dimensional compression of granular materials: I. Stress-strain behavior, microstructure and irreversibility

The behavior of a model granular material, made of slightly polydisperse beads with Hertz-Mindlin elastic-frictional contacts, in oedometric compression (i.e., compression along one axis, with no lateral strain) is studied by grain-level numerical simulations. We systematically investigate the influence of the (idealized) packing process on the microstructure and stresses in the initial, weakly confined equilibrium state, and prepare both isotropic and anisotropic configurations differing in solid fraction Φ and coordination number z. Φ (ranging from maximally dense to moderately loose), z (which might vary independently of Φ in dense systems), fabric and force anisotropy parameters, and the ratio K_{0} of lateral stresses σ_{2}=σ_{3} to stress σ_{1} in the compression direction are monitored in oedometric compression in which σ_{1} varies by more than three orders of magnitude. K_{0} reflects the anisotropy of the assembling process and may remain nearly constant in further loading if the material is already oedometrically compressed (as a granular gas) in the preparation stage. Otherwise, it tends to decrease steadily over the investigated stress range. It is related to force and fabric anisotropy parameters by a simple formula. Elastic moduli, separately computed with an appropriate matrix method, may express the response to very small stress increments about the transversely isotropic well-equilibrated states along the loading path, although oedometric compression proves an essentially anelastic process, mainly due to friction mobilization, with large irreversible effects apparent upon unloading. While the evolution of axial strain ε_{1} and solid fraction Φ (or of the void ratio e=-1+1/Φ) with axial stress σ_{1} is very nearly reversible, especially in dense samples, z is observed to decrease (as previously observed in isotropic compression) after a compression cycle if its initial value was high. K_{0} relates to the evolution of internal variables and may exceed 1 in unloading. The considerably greater irreversibility of oedometric compression reported in sands, compared to our model systems, should signal contact plasticity or damage.

A numerical study of one-dimensional compression of granular materials. II. Elastic moduli, stresses and microstructure

The elastic moduli of a transversely isotropic model granular material, made of slightly polydisperse elastic-frictional spherical beads, in equilibrium along a one-dimensional (oedometric) compression path, as described in the companion paper [M. H. Khalili et al., Phys. Rev. E 95, 032907 (2017)]10.1103/PhysRevE.95.032907, are investigated by numerical simulations. The relations of the five independent moduli to stresses, density, coordination number, fabric and force anisotropies are studied for different internal material states along the oedometric loading path. It is observed that elastic moduli, as in isotropic packs, are primarily determined by the coordination number, with anomalously small shear moduli in poorly coordinated systems, whatever their density. Such states also exhibit faster increasing moduli in compression, and larger off-diagonal moduli and Poisson ratios. Anisotropy affects the longitudinal moduli C_{11} in the axial direction and C_{22} in the transverse directions, and the shear modulus in the transverse plane C_{44}, more than the shear modulus in a plane containing the axial direction C_{55}. The results are compared to available experiments on anisotropic bead packs, revealing, despite likely differences in internal states, a very similar range of stiffness level (linked to coordination), and semiquantitative agreement as regards the influence of anisotropy. Effective medium theory (the Voigt approach) provides quite inaccurate predictions of the moduli. It also significantly underestimates ratios C_{11}/C_{22} (varying between 1 and 2.2) and C_{55}/C_{44} (varying from 1 to 1.6), which characterize elastic anisotropy, except in relatively weakly anisotropic states. The bulk modulus for isotropic compression and the compliance corresponding to stress increments proportional to the previous stress values are the only elastic coefficients to be correctly estimated by available predictive relations. We discuss the influences of fabric and force anisotropies onto elastic anisotropy, showing in particular that the former dominates in sample series that are directly assembled in anisotropic configurations and keep a roughly constant lateral to axial stress ratio under compression.

Using Fractal Geometry to Recover the 3D Air Void, Scale-Independent, Microstructure Information From 2D Sections of Mortars

Advances in digital image analysis have allowed for rapid and detailed investigations of the microstructural topography of cementitious materials, and recent theoretical and analytical work have allowed for recovery of 3D information from 2D analyses. However, measurements of parameters such as the entrained air void size distribution and number density obtained from digital images of concrete are sensitive to the resolution of the image. To address this, an analytical model for recovering 3D information from 2D sections was applied to images of air-entrained mortar at different resolutions, and the results were interpreted in terms of fractal geometry. It is shown that there exists a “cutoff” resolution for scale independence, which is crucial for viewing stereological measurements in an absolute sense rather than relative to the resolution of the instrument used to acquire them. For the analysis of entrained air void structure, this cutoff resolution is around 3200 DPI; for such analyses, it is recommended that images be acquired at this resolution. Furthermore, the same analytical model was validated against full 3D X-ray microtomographic images.