Quantifying the three-dimensional shapes of spheroidal objects in rocks imaged by tomography (original) (raw)
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In previous work we have described and validated robust techniques for partitioning the pore space of a porous material into simple regions, thereby allowing it to be represented by a network of simple building blocks. The primary purpose of this analysis is the generation of a pore-throat network for modelling immiscible multi-phase fluid displacements. However, combining our partitioning algorithms with recently developed methods for studying complex and disordered networks, and geometric studies of the building blocks themselves, results in powerful tools for characterising rock microstructure.
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The shape of aggregates used in concrete is an important parameter that helps determine many concrete properties, especially the rheology of fresh concrete and early-age mechanical properties. This paper discusses the sample preparation and image analysis techniques necessary for obtaining an aggregate particle image in 3-D, using X-ray computed tomography, which is then suitable for spherical harmonic analysis. The shapes of three reference rocks are analyzed for uncertainty determination via direct comparison to the geometry of their reconstructed images. A Virtual Reality Modeling Language technique is demonstrated that can give quick and accurate 3-D views of aggregates. Shape data on several different kinds of coarse aggregates are compared and used to illustrate potential mathematical shape analyses made possible by the spherical harmonic information.
Three dimensional least-squares fitting of ellipsoids and hyperboloids
Journal of Physics: Conference Series, 2017
Spatial continuity can be described as a variogram model that has an ellipsoid anisotropy. In previous research, two-dimensional least-square ellipse fitting method by Fitzgibbon, Pilu and Fisher has been applied to the analysis of spatial continuity for coal deposits. However, it is not easy to generalize their method to three-dimensional least-square ellipsoid fitting. In this research, we obtain a three-dimensional least-square fitting for ellipsoids and hyperboloids by generalizing two-dimensional least-square ellipse fitting method introduced by Gander, Golub and Strebel.
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Linear elastic properties of granular rocks derived from X‐ray‐CT images
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The elastic response of clastics rocks and grain packs is controlled to a large extend by the arrangements of grains and the strength of the contacts between them. For well-cemented rocks like Fontainebleau sandstone, the elastic moduli of the grains and the contact moduli can be taken as the one of quartz with good agreement to experimental data. In general, and in particular for less well cemented granular rocks, this is not the case, the contact moduli typically being weaker than the surrounding grains. In this study, we utilize microtomographic images and grain-partitioning techniques to assign grain moduli, and employ effective medium theories based on a relation between Xray-CT density and porosity to assign contact moduli between grains. We numerical derive the macroscopic effective elastic moduli of several reservoir rocks, and study their sensitivity to variations of contact moduli between grains in a parametric study.
Grain-size distribution of volcaniclastic rocks 1: A new technique based on functional stereology
Journal of Volcanology and Geothermal Research, 2012
The power of explosive volcanic eruptions is reflected in the grain size distribution and dispersal of their pyroclastic deposits. Grain size also forms part of lithofacies characteristics that are necessary to determine transport and depositional mechanisms responsible for producing pyroclastic deposits. However, the common process of welding and rock lithification prevents quantification of grain size by traditional sieving methods for deposits in the rock record. Here we show that functional stereology can be used to obtain actual 3D volume fractions of clast populations from 2D cross-sectional images. Tests made on artificially consolidated rocks demonstrate successful correlations with traditional sieving method. We show that the true grain size distribution is finer grained than its representation on a random 2D section. Our method allows the original size of vesicular pumice clasts to be estimated from their compacted shapes. We anticipate that the original grain-size distribution of welded ignimbrites can also be characterized by this method. Our method using functional stereology can be universally applied to any type of consolidated, weakly to non-deformed clastic material, regardless of grain size or age and therefore has a wide application in geology.