Edward Andò

Water Retention Behaviour Explored by X-Ray CT Analysis

This study aims to experimentally characterise the link between partial water saturation and suction in a sand sample at the micro scale. The paper presents the first results of an experimental study in which high resolution (7.5μm/px) X-ray tomography has been performed on a small (10×10mm) cylindrical sample of Hostun HN31 sand at several different levels of imposed suction. A specialised cell allowing X-ray scanning as well as fine control of suction (imposed both by negative water pressure as well as by positive air pressure) has been developed for this study and is described herein. The 3D images resulting from X-ray tomography are treated in order to define each voxel in the image as either air, water or grain. From these “trinarised” 3D images, local and global values of porosity and degree of saturation are then measured. This method enables the study of water retention behaviour of sand at the grain scale, all the while allowing characterisation of water retention in the sample as a whole.

Shear bands as bottlenecks in force transmission

The formation of shear bands is a key attribute of degradation and failure in soil, rocks, and many other forms of amorphous and crystalline materials. Previous studies of dense sand under triaxial compression and two-dimensional analogues from simulations have shown that the ultimate shear band pattern may be detected in the nascent stages of loading, well before the bands known nucleation point (i.e., around peak stress ratio), as reported in the published literature. Here we construct a network flow model of force transmission to identify the bottlenecks in the contact networks of dense granular media: triaxial compression of Caicos ooid and Ottawa sand and a discrete element simulation of simple shear. The bottlenecks localise in the nascent stages of loading —in the location where the persistent shear band ultimately forms. This corroborates recent findings on vortices that suggest localised failure is a progressive process of degradation, initiating early in the loading history at sites spanning the full extent, yet confined to a subregion, of the sample. Bottlenecks are governed by the local and global properties of the sample fabric and the grain kinematics. Grains with large rotations and/or contacts having minimal load-bearing capacities per se do not identify the bottlenecks early in the loading history.

Application of microtomography and image analysis to the quantification of fragmentation in ceramics after impact loading

Silicon carbide ceramics are widely used in personal body armour and protective solutions. However, during impact, an intense fragmentation develops in the ceramic tile due to high-strain-rate tensile loadings. In this work, microtomography equipment was used to analyse the fragmentation patterns of two silicon carbide grades subjected to edge-on impact (EOI) tests. The EOI experiments were conducted in two configurations. The so-called open configuration relies on the use of an ultra-high-speed camera to visualize the fragmentation process with an interframe time set to 1 µs. The so-called sarcophagus configuration consists in confining the target in a metallic casing to avoid any dispersion of fragments. The target is infiltrated after impact so the final damage pattern is entirely scanned using X-ray tomography and a microfocus source. Thereafter, a three-dimensional (3D) segmentation algorithm was tested and applied in order to separate fragments in 3D allowing a particle size distribution to be obtained. Significant differences between the two specimens of different SiC grades were noted. To explain such experimental results, numerical simulations were conducted considering the Denoual–Forquin–Hild anisotropic damage model. According to the calculations, the difference of crack pattern in EOI tests is related to the population of defects within the two ceramics. This article is part of the themed issue ‘Experimental testing and modelling of brittle materials at high strain rates’.

Application of X-ray Tomography to the Characterisation of Grain-Scale Mechanisms in Sand

X-ray micro-tomography allows 3D imaging at sufficiently high spatial resolution to distinguish all the individual sand grains in a small sample (10mm diameter), as well as the distribution of air and/or water at this scale. Since this imaging technique is completely non-destructive, an imaged sample can be made to evolve by controlling some relevant variable (e.g., imposed deformation, suction), and can subsequently be re-imaged. This allows processes to be followed in 4 dimensions (3D + relevant variable). This paper shows the application of this technique and philosophy to the study of two different phenomena: localised deformation resulting from imposed triaxial compression, and the water retention behaviour of sand. The experimental techniques and setups for these two studies are detailed, and the fundamental steps of image treatment are outlined. Some key results are given to demonstrate the power of this “full-field” characterisation approach, such as rotations and displacements for each of the 50,000 grains of a sample in which a shear band occurs as well as the evolution of local measurements of porosity and degree of saturation in a sand where suction is being varied.

Localisation Precursors in Geomaterials

Strain localisation in soils and rocks has been studied extensively for the last 40 years or so. On the experimental side, a large number of these studies have been devoted to the experimental observation of localised deformation in laboratory element tests like biaxial (plane strain) and triaxial tests. 2D and 3D imaging techniques and image analysis methods have been used to characterize the onset and subsequent development of strain localisation. In the recent years, these techniques and methods have improved dramatically, allowing considerably more accurate measurement of displacement and strain field in the laboratory specimens. It is time to have a second look, with these new glasses, at some decades-old results, to assess what can be confirmed and what should be reconsidered.

3D fibre architecture of fibre-reinforced sand

The mechanical behaviour of fibre-reinforced sands is primarily governed by the three-dimensional fibre architecture within the sand matrix. In laboratory, the normal procedures for sample preparation of fibre-sand mixtures generally produce a distribution of fibre orientations with a preferential bedding orientation, generating strength anisotropy of the composite’s response under loading. While demonstrating the potential application of X-ray tomography to the analysis of fibre-reinforced soils, this paper provides for the first time a direct experimental description of the three-dimensional architecture of the fibres induced by the laboratory sample fabrication method. Miniature fibre reinforced sand samples were produced using two widely used laboratory sample fabrication techniques: the moist tamping and the moist vibration. It is shown that both laboratory fabrication methods create anisotropic fibre orientation with preferential sub-horizontal directions. The fibre orientation distribution does not seem to be affected by the concentration of fibres, at least for the fibre concentrations considered in this study and, for both fabrication methods, the fibre orientation distribution appears to be axisymmetric with respect to the vertical axis of the sample. The X-ray analysis also demonstrates the presence of an increased porosity in the fibre vicinity, which confirms the assumption of the “stolen void ratio” effect adopted in previous constitutive modelling. A fibre orientation distribution function is tested and a combined experimental and analytical method for fibre orientation determination is further validated.

Double-Scale Assessment of Micro-mechanics Based Constitutive Models for Granular Materials Undergoing Mechanical Degradation

The richness across the scales of geomaterials has long been known. Yet only recently, thanks to the development of new experimental techniques, it has been possible to study the micro (grain scale) origin of some of the phenomena observed at the macro (specimen) scale. This unprecedented insight calls for new models able to build rational links between these two scales. Some recently proposed models for cemented and uncemented granular materials take advantage of this understanding to conjugate the macroscopic irreversible strains with internal variables representing a statistically averaged evolution of the micro-structure. While these models have shown their capability to reproduce the macroscopic behavior of the geomaterials they were designed for, to fully assess them and to prioritize possible enhancements, a comparison between the predicted evolution of the micro-structure and appropriate experimental data is desirable. In this contribution we study the possibility of extracting robust and statistically meaningful measurements of microstructural evolution from X-ray computed tomography images which are then compared with the micro-scale predictions of the existing micro-mechanics based models.

Development of Image Analysis Tools to Evaluate In-Situ Evolution of the Grain Size Distribution in Sand Subjected to Breakage

Grain crushing is a phenomenon of pivotal importance in the inelastic deformation of granular materials. The progressive evolution of the grain size distribution is known to play a major role in a number of geotechnical engineering problems. There is, however, a lack of experimental work tackling the quantification of the three dimensional evolution of the grain size distribution of materials undergoing grain crushing. The technological advancements in X-ray computed tomography now allow in situ, 4 dimensional (3D + time) images of geomaterials to be obtained as they evolve. While recent investigations of the kinematics of persistent grains have allowed a deeper experimental understanding of some inelastic micro-mechanisms to be obtained, a further effort is required when interpreting tomographic images in which grains are not persistent (i.e., they can break). In this contribution, a novel image-analysis technique under development is proposed to quantify the evolution of the grain size distribution as grain crushing proceeds in an experiment. This technique is applied to the analysis of 3D tomographic images of sand sheared at high confinement.

Validation of Synthetic Images for Contact Fabric Generated by DEM

X-ray tomography can be used to acquire three-dimensional images of granular materials. In order to check the performance of image analysis tools to extract information from such images, a benchmarking strategy is presented.

Strain Localisation in Sand in Cycles of Triaxial Compression and Extension: Continuum and Grain-Scale Analysis

In this work we present selected results from a recent experimental programme where small sand specimens are subjected to cycles of triaxial compression and triaxial extension: the material is “yielded” in extension, after which the loading is reversed and the material is “yielded” in compression—a number of cycles are performed. The ways in which extension and compression-like localisation patterns (i.e., dilatant shear banding, and necking respectively) appear, get activated and disactivated on reversal of loading are measured, and discussed—in terms of both (continuum) strain fields and individual grain rotations.