This study investigates the underlying mechanisms causing necking instability in granular materials. Using a digital twin created with the level-set discrete element method (LS-DEM), we simulate triaxial compression and extension cycles on a Hostun sand specimen within an x-ray tomograph. The simulation accurately replicates experimental observations, including stress-strain behavior, deviatoric strain field evolution, and necking initiation and progression during triaxial extension.

This study investigates the microstructural response of a sand subjected to drained cyclic triaxial loading. Triaxial tests are performed within an x-ray tomograph to obtain grain scale measurements such as grain kinematics and grain contact orientations. Results are presented, indicating that the cycles causes changes in the contact network which may explain observed macro scale behaviour.

Background The DIC Challenge 2.0 follows on from the work accomplished in the first Digital Image Correlation (DIC) Challenge Reu et al. (Experimental Mechanics 58(7):1067, 1 ). The second challenge was required to better quantify the spatial resolution of 2D-DIC codes. Objective The goal of this paper is to outline the methods and images for the 2D-DIC community to use to evaluate the performance of their codes and improve the implementation of 2D-DIC. Methods This paper covers the creation of the new challenge images and the analysis and discussion of the results. It proposes a method of unambiguously defining spatial resolution for 2D-DIC and explores the tradeoff between displacement and strain noise (or measurement noise) and spatial resolution for a wide variety of DIC codes by a combination of the images presented here and a performance factor called Metrological Efficiency Indicator (MEI). Results The performance of the 2D codes generally followed the expected theoretical performance, particularly in the measurement of the displacement. The comparison did however show that even with fairly uniform displacement performance, the calculation of the strain spatial resolution varied widely. Conclusions This work provides a useful framework for understanding the tradeoff and analyzing the performance of the DIC software using the provided images. It details some of the unique errors associated with the analysis of these images, such as the Pattern Induced Bias (PIB) and imprecision introduced through the strain calculation method. Future authors claiming improvements in 2D accuracy are encouraged to use these images for an unambiguous comparison.

Reconstructed X-ray tomographies and python analysis scripts for the publication "Impacts into a porous graphite: an investigation on crater formation and ejecta distribution" Uses the spam python toolkit, which can probably be replaced by scipy.ndimage.center_of_mass if needed.

This paper presents an experimental study of concrete at meso-scale (aggregates, macro-pores and mortar matrix) in order to get a better understanding of the local failure mechanisms known to drive the macroscopic mechanical behaviour of the material. The main originality comes from conducting in-situ X-ray mechanical tests on micro-concrete samples of realistic composition (including cement, sand, aggregates and water), under uniaxial compression and, for the first time, under triaxial compression at 5 oa, 10 oa and 15 oa confining pressures. A timeseries analysis of the set of 3D images coming from each test allows for the measurement of the 3D kinematic fields (displacement and strain fields) throughout the experiments. The different failure patterns observed for each loading path are discussed, along with a quantification of the 3D fracturing processes at the scale of the largest heterogeneities (aggregates and macro-pores). With an increasing level of confinement, the transition from brittle to ductile response is observed, as well as an increase of the strength of the material. The pronounced impact of the meso-scale heterogeneities of concrete on their local failure mechanisms is highlighted. It is shown that strain localisation mainly originates between aggregates and mortar matrix, with the shape and location of the largest aggregates and macro-pores essentially driving the propagation of the cracking network.

The increased shear strength of soil bearing roots recently inspired researchers to assess the stability of vegetated slopes with continuum models and to design anchors by mimicking root system architectures. Yet, there is no clear understanding to date of why roots affect soil properties. This paper presents an experimental proof of concept based on X-ray tomography that addresses this issue by assessing soil microstructural changes induced by root growth. Root-soil interaction was investigated through the growth of maize roots in sand with two bulk densities. A 3D timeseries of the root-soil interaction was imaged using x-ray computed tomography for 7 days, allowing the root to be identified in each image. A local, total, finite strain tensor was computed from displacements measured with image correlation, and the first two strain invariants were studied. For the soil and plant under study, the proposed method highlights that the soil was sheared in the vicinity of the root system and did not evolve significantly after the root tip had passed. Additionally, the initial bulk density of the soil was found to significantly influence the response of soil to plant root growth. The sheared zone was larger when the bulk density was lower. In the sheared zone, the looser soil exhibited a slightly contractant behaviour, while the denser soil was purely dilatant. Soil dilation was predominant in the radial vicinity of the main root and below the tip. Further from the root system, no significant volume changes were measured for the denser specimen, whereas compaction was noted in the looser specimen. In contrast with previous works, results suggest that the high soil porosity near the root may result not only from steric exclusion, but also, from the constitutive soil response to a shear deformation.

Models that introduce rolling resistance at the contact are widely employed in simulations using the discrete element method (DEM) to indirectly represent particle shape effects. This approach offers substantial computational benefits at the price of increased calibration complexity. This work proposes a method to simplify calibration of rolling resistance. The key element is an empirical relation between a contact parameter (rolling friction) and a 3D grain shape descriptor (true sphericity). Values of true sphericity can be obtained by image analysis of the grains, either directly by 3D acquisition or by correlation with simpler-to-obtain 2D shape measures. Evaluation of rolling friction is thus made independent from that of other model parameters. As an extra benefit, the variability of grain shape in natural sands can be directly mapped into the discrete model. A mapping between rolling friction and true sphericity is calibrated using specimen-scale and grain scale results from two triaxial compression tests on Hostun sand and Caicos ooids. The mapping is validated using different triaxial tests from the same sands and from other reference sands (Ottawa, Ticino). In the case of Ticino grain-shape acquisition is made in 2D, using an ordinary table scanner. The results obtained support this direct calibration procedure.

Geotechnical parameters scatter in a wide range. On the one hand, this is due to the spatial variability of the subsoil, but also results of laboratory tests on reconstituted specimens of one sample scatter, as a completely homogeneous, reproducible specimen preparation is not feasible. For calculations according to the standards, characteristic shear parameters should be chosen as cautious estimate of the mean values. How this cautious estimate should be determined is not defined and therefore subjective. Often the results of shear tests are used as basis for the decision. In this paper, results of drained triaxial compression tests on a reconstituted, natural, widely graded soil are investigated. The specimens were prepared at same mean density but the results of the shear experiments scatter. The deviation of e.g. the peak strength is apparent. For the derivation of the Mohr-Coulomb parameter friction angle and cohesion according to the standards 3 or more stress levels have to be considered. The influence of the number of stress levels taken for the evaluation of the shear strength parameters is quantified. The evaluation of only three stress levels leads to a relatively large range of possible shear parameters. The two shear parameters friction angle and cohesion are statistically dependent - since they are two parameters of a linear regression. Therefore, they should be considered together. The scattering in the peak strength is probably caused by an inhomogeneous specimen construction. The influence of an inhomogeneous specimen preparation on the peak strength is investigated and proven in numerical simulations.

Strain localisation influences the behaviour of sheared soils in a way that the assumption of the continuum loses validity and may become inapplicable. This occurrence affects the interpretation of triaxial tests where samples are usually considered as representative elements of an equivalent continuum and a phenomenological interpretation is carried out to calibrate constitutive models. Considering the inherent and stress-induced heterogeneity of the material as a possible precursor of localisation, the evolution of porosity and strain fields is studied interpreting with statistical and geostatistical analyses, the results of X-ray computerised microtomography. The study is performed on sandy samples sheared in triaxial compression and extension. The analysis carried out before shearing shows a meaningful statistical heterogeneity of the porosity with correlation lengths to the order of a few grain diameters. The evolution on shearing reveals the onset of a second statistical population and of an anisotropic spatial variation dictated by strain localisation.

This paper explores the micro characteristics of unsaturated sand in triaxial shearing by using X-ray computed tomography (X-ray CT). To obtain higher resolution, a mini-triaxial set-up is designed in which the sample is miniaturised to 1 cm in diameter and 2 cm long, allowing scans with a pixel size of 9 μm. Samples are sheared in the mini-triaxial set-up at different constant suction levels (therefore, different degree of saturation). In the meanwhile, the samples are scanned by X-ray CT at various deformation stages, about 0, 2, 5, 10 and 15% axial strain. The three-dimensional (3D) reconstructed image is trinarised based on a region growing technique, which gives access to the microstructure of the solid, liquid and air phases. Then, the 3D image is subdivided into representative volume elements, with length ≈3·8D 50 , which gives local information of degree of saturation and porosity. It is observed that the sample dilates and water drains out during triaxial test under constant suction condition. The local study shows that the porosity increase and water desaturation are more significant in the middle part of the sample, especially for a higher suction value. This work allows the emphasis of the coupling between dilatancy on shearing (highlighted by the evolution of local porosity) and the evolution of the local degree of saturation in unsaturated granular materials.

The sphericity of a grain should measure the similitude of its shape with that of a sphere. Sphericity is a shape descriptor of long-standing interest for sedimentology. Now it has gained also interest to facilitate discrete element modelling of granular materials. True sphericity was initially defined by a surface ratio that requires three-dimensional (3D) grain surface measurement. That kind of measurement has been practically impossible until recently and, as a consequence, a number of alternative 3D measures and 2D proxies were proposed. In this work we present results from a study of grain shape based on x-ray tomography of two different sand specimens, containing more than 110.000 particles altogether. Sphericity measures were systematically obtained for all grains. 2D proxy measures were also obtained in samples of oriented and not-oriented grains. It is shown that the 2D proxy best correlated with true sphericity is perimeter sphericity, whereas the traditional Krumbein-Sloss chart proxy is poorly correlated. 2D measures acquired through minor axis projection are more closely related to 3D measures than those acquired using random projections.

Particle breakage of a granular material can cause significant changes in its microstructure, which will govern its macroscopic behaviour; this explains why the mechanisms leading to particle breakage have been a common subject within several fields, including geomechanics. In this paper, X-ray computed micro-tomography is used, to obtain three-dimensional images of entire specimens of sand, during high-confinement triaxial compression tests. The acquired images are processed and measurements are made on breakage, local variations of porosity, volumetric strain, maximum shear strain and grading. The evolution and spatial distribution of quantified breakage and the resulting particle size distribution for the whole specimen and for specific areas are presented here for the first time and are further related to the localised shear and volumetric strains. Before peak stress is reached, compaction is the governing mechanism leading to breakage; neither compressive strains nor breakage are significantly localised and the total amount of breakage is rather low. Post peak, in areas where strains localise and breakage is present, a dilative volumetric behaviour is observed locally, as opposed to the overall compaction of the specimen. Some specimens exhibited a compaction around the shear band at the end of the test, but there was no additional breakage at that point. From the grading analysis, it is found that mainly the grains with diameter close to the mean diameter of the specimen are the ones that break, whereas the biggest grains that are present in the specimen remain intact.

It is widely recognised that particle shape influences the mechanical response of granular materials. Rolling resistance elasto-plastic contact models are frequently used to approximate particle shape effects in simulations using the Discrete Element Method (DEM). Such contact models require calibration of several micro-parameters, most importantly a rolling resistance coefficient. In this work, the value of rolling resistance is directly linked to true sphericity, a basic measure of grain shape. When shape measurements are performed, this link enables independent evaluation of the rolling resistance coefficient. It does also allow the characteristic shape variability of natural soils to be easily taken into account. In this work, we explore the effect of shape variability on the triaxial response of sand. It is shown, using realistic values of shape distributions, that shape variability significantly affects observed triaxial strength.

Hydraulic fracturing, the creation of fractures by high-pressure fluid injection into a solid medium, is of interest to enhance the permeability of rocks. This complex three-dimensional hydro-mechanical process, however, has only been studied in the laboratory by boundary measurements or acoustic techniques with low spatio-temporal resolutions until now. In this paper, direct, high spatial resolution, and near real-time visualisation results of hydraulic fracture generation and propagation in prismatic specimens of Marcellus shale rock under in situ conditions (70 MPa, plane strain) are presented. Polymethyl methacrylate specimens are also tested under the same conditions to highlight the importance of rocks' internal structure on the response of the tested rock. The results reveal a complex interaction among the injected fluid, the pre-existing natural fractures in shale structure, and the hydraulically induced fracture highlighting the governing role of rock fabric even under high stresses. These measurements are possible due to the unique sensitivity of neutrons to water. Besides the intrinsic interest of the results presented, this exploratory investigation highlights the potential of neutron imaging in elucidating the evolution of fluid flow and fluid-driven fractures, as X-rays have done for the evolution of solid structure only. Further, understanding of the mechanics of fracking will lead to development of more accurate hydro-mechanical constitutive models thus enabling the design of field operations with higher efficiencies.

Grain breakage affects a number of geotechnical engineering problems. In this research study, the breakage of an artificial, porous granular material (light-expanded clay aggregate (LECA)) has been studied in one-dimensional compression with both standard laboratory techniques and in situ X-ray tomography during loading. X-ray tomography has revealed that there is a wide distribution of internal porosity among LECA particles, and particle tracking has been used, for the first time, to give an objective measurement of each particle's life expectancy. Links between micro- and macro-scale quantities are discussed.

The question of registering two images (or image volumes) acquired with different modalities, and thus exhibiting different contrast, at different positions is addressed based on an extension of global digital image (or volume) correlation. A specific comparison metric is introduced allowing the signature of the different phases to be related. A first solution consists of a Gaussian mixture to describe the joint distribution of gray levels, which not only provides a matching of both images, but also offers a natural segmentation indicator. A second 'self-adapting' solution does not include any postulated a priori model for the joint histogram and leads to a registration of the images based on their initial histograms. The algorithm is implemented with a pyramidal multiscale framework for the sake of robustness. The proposed multiscale technique is tested on two 3D images obtained from x-ray and neutron tomography respectively. The proposed approach brings the two images to coincidence with a sub-pixel accuracy and allows for a 'natural' segmentation of the different phases.

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.