Identifying Material Parameters for a Micro-Polar Plasticity Model Via X-Ray Micro-Computed Tomographic (Ct) Images: Lessons Learned from the Curve-Fitting Exercises

Abstract: Unlike a conventional first-order continuum model, the material parameters of which can be identified via an inverse problem conducted at material point that exhibits homogeneous deformation, a higher-order continuum model requires information from the derivative of the deformation gradient. This study concerns an integrated experimental-numerical procedure designed to identify material parameters for higher-order continuum models. Using a combination of microCT images and macroscopic stress–strain curves as the database, we construct a new finite element inverse problem which identifies the optimal value of material parameters that matches both the macroscopic constitutive responses and the meso-scale micropolar kinematics. Our results indicate that the optimal characteristic length predicted by the constrained optimization procedure is highly sensitive to the types and weights of constraints used to define the objective function of the inverse problems. This sensitivity may in return affect the resultant failure modes (localized vs. diffuse), and the coupled stress responses. This result signals that using the mean grain diameter alone to calibrate the characteristic length may not be sufficient to yield reliable forward predictions. Key words: micro-CT imaging, micro-polar plasticity, critical state, higher-order continuum, Hostun San

Morphological transitions for pore water and pore air during drying and wetting processes in partially saturated sand

Water retention characteristics are important for modeling the mechanical and hydraulic behavior of partially saturated sand. It is well known that the soil water characteristic curve shows hysteresis during drying and wetting processes. For a better understanding of the water retention characteristics of partially saturated soil, a microscopic investigation of the morphological transitions for the pore water phase and the pore air phase, such as volume distribution, spatial distribution and continuity during drying and wetting processes, is crucial. In the present study, different water retention states of a partially saturated sand were visualized during water retention tests using microfocus X-ray computed tomography (CT). The CT images obtained from the tests were segmented into the soil particle phase, the pore water phase and the pore air phase. Then, a series of image processing, erosion, dilation and cluster labeling was applied to the images in this order to quantify the cluster volume distributions, the number of clusters and the continuity of both the pore water phase and the pore air phase. The morphological transitions for the pore air phase and the pore water phase, subjected to decreasing and increasing degrees of saturation, were revealed using the results of the image processing, and then, the water retention states were characterized based on the morphologies for the two phases. The influence of the morphologies on the hysteresis was discussed

La caractérisation multi-échelle du comportements hydro-mécanique d'un sable non saturé : la réponse de rétention d'eau et triaxial

With the recent developments of full field measurements, it has become possible to do experiments on a soil specimen, and perform measurements at different scales. This progress has allowed greater understanding for all the processes that occur within the soil, and also created better environment to observe these mechanisms in 3D. This PhD work aims to characterize water retention and hydro-mechanical behaviours of unsaturated Hostun sand at the grain scale. To achieve this goal, water retention and triaxial tests were performed and a set of experimental and image processing tools was developed and used for the two series of tests. X-ray computed tomography set up available at 3SR Laboratory in Grenoble University was used to generate 3D images of the unsaturated soil microstructure non-destructively. A developed region growing systematic technique (trinarization technique) was used to allow the separation of the phases (i.e., grains, water and air) in the 3D images, and performing different measurements at the grain scale. Porosity and degree of saturationwere measured macroscopically using the trinarized images and microscopically using a developed mapping code. The microscopic measurements were performed over an REV, whose size was determined using a developed analysis based on statistical tools. Several microscopic-discrete analyses were developed to investigate the evolution of fluid phase (water and air) with loading (suction and mechanical loading). Digital Image Correlation was performed for the two tests.To analyze water retention behaviour of Hostun sand during drying and wetting processes, a pressure plate apparatus was developed. Suction was applied using tensiometry technique. The specimen (cylindrical 1x1cm) was prepared using water pluviation technique and scanned with a resolution 7.5micron. As a result, water retention curve, surface and domains were obtained and hysteresis phenomenon and soil cohesion were analyzed at the grain scale.For the mechanical behaviour of unsaturated soils, triaxial test were performed at three conditions: saturated drained, unsaturated drained and unsaturated undrained. A triaxial apparatus that can be placed inside the x-ray cabinet was developed in order to facilitate monitoring the changes in sand microstructure and water distribution when subjecting the soil specimen to loading. The specimen (cylinder of hxd=2x1cm) was prepared using water pluviation technique (completely saturated at the beginning of the three tests), loaded then scanned with a resolution 13micron, repeatedly till reaching 21% axial strain forthe three tests.Consequently, stress-strain curves, volumetric response and deformations measurements were obtained and deformation pattern, specimen heterogeneity, cohesion and water distribution were analyzed.Avec les récents développements des mesures de champs, il est devenu possible deréaliser des expériences sur un échantillon de sol en effectuant des mesures simultanémentaux différentes échelles pertinentes : celle de l'échantillon, et celle des grains, et ceci en3D volumique. Ces progrès ont permis une meilleure compréhension des processus qui seproduisent dans le sol, en les observant au cœur même des échantillons.Cette thèse vise à caractériser les comportements de rétention d'eau et hydro-mécaniquedu sable d'Hostun non saturé à l'échelle du grain. Pour ce faire, des essais de rétentiond'eau et des essais triaxiaux ont été effectués, qui ont nécessité le développement d'outils detraitement d'image et des montages expérimentaux spécifiques. L'installation de tomographie à rayons X du Laboratoire 3SR de l'Université des Grenoble a été utilisée pour générer des images en 3D de la microstructure du sol non saturé. Une technique de trinarization a été mise en œuvre pour permettre la séparation des phases (les grains, l'eau et l'air) dans les images 3D, et d'effectuer différentes mesures à l'échelle du grain. La porosité et le degré de saturation ont été mesurées macroscopiquement en utilisant les images segmentées, et microscopiquement en utilisant un code de cartographie spécialement développé. Les mesures microscopiques ont été réalisées sur un volume élémentaire représentatif (VER), dont la taille a été déterminée en utilisant une analyse développée sur la base d'outils statistiques. Plusieurs analyses discrets ont été développées pour étudier l'évolution de la phase fluide (l'eau et l'air) avec le chargement (succion, et chargement mécanique). La corrélation d'images numérique 3D volumique a été mise en œuvre systématiquement pour ces deux types d'essais.Pour analyser le comportement de rétention d'eau du sable d'Hostun pendant les processus de séchage et de mouillage, une cellule spécifique a été développée. La succion a été appliquée en utilisant la technique de tensiomètre. L'échantillon (cylindrique 1x1cm) a été préparé en utilisant la technique de la pluviation sous l'eau et scanné avec une résolution de 7,5micron. La courbe de rétention d'eau, surface et les domaines hydriques ont été obtenus et le phénomène d'hystérésis et la cohésion du sol ont été analysés à l'échelle du grain.Pour le comportement hydro-mécanique des sols non saturés, des essais triaxiaux ontété effectué sous trois conditions: saturé drainé, non saturé drainé et non saturé non drainé. Un appareil triaxial que l'on peut placer à l'intérieur de la cabine du tomographe à rayons X a été développé afin de permettre le suivi des changements dans la microstructure du sable et la distribution de l'eau lorsque l'on soumet l'échantillon à chargement mécanique. L'échantillon (cylindre de dimensions hxd=2x1cm) a été préparé en utilisant la technique de la pluviation sous l'eau (complétement saturé au début des trois tests), amené ensuite au niveau de saturation désiré (dans le cas des essais non saturés), puis chargé par étapes successives avec scan à chaque étape avec une résolution de 13micron, jusqu'à arriver à 21% de déformation axiale pour les trois types d'essai. Les courbes contrainte-déformation, la réponse volumétrique et les déformations ont été obtenus et le profil de déformation, l'hétérogénéité de l'échantillon, la cohésion et la distribution de l'eau ont été analysés

Grain-scale characterization of water retention behaviour of sand using X-ray CT

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A tomographic imagery segmentation methodology for three-phase geomaterials based on simultaneous region growing

X-Ray Computed Tomography (X-Ray CT) is a powerful non-destructive technique used in many domains to obtain the three-dimensional representation of objects, starting from the reconstitution of two-dimensional images of radiographic scanning. This technique is now able to analyze objects within a few microns resolution. Consequently, X-Ray micro-computed tomography (X-Ray μCT) opens perspectivesfor the analysis of the fabric of multi-phase geomaterials such as soils, concretes, rocks or ceramics. To be able to characterize the spatial distribution of the different phases in such complex and disordered materials, automated phase recognition has to be implemented through image segmentation. A crucial difficulty in segmenting images lies in the presence of noise in the obtained tomographic representation, making it difficult to assign a specific phase to each voxel (vx) of the image. In the present study, simultaneous region growing is used to reconstitute the three-dimensional segmented image of granular materials. First, based on a set of expected phases in the image, regions where specific phases are sure to be present are identified, leaving uncertain regions of the image unidentified. Subsequently, the identified regions are grown until growing phases meet each other with vanishing unidentified regions. The methodrequires a limited number of manual parameters that are easily determined. The developed method is illustrated based on three applications on granular materials, comparing the phase volume fractions obtained by segmentation with macroscopic data. It is demonstrated that the algorithm rapidly converges and fills the image after a few iterations.SCOPUS: ar.jinfo:eu-repo/semantics/publishe