Computer simulation of random parckings for self-similar particle size distributions in soil and granular materials: porosity and pore size distribution

A 2D computer simulation method of random packings is applied to sets of particles generated by a self-similar uniparametric model for particle size distributions (PSDs) in granular media. The parameter p which controls the model is the proportion of mass of particles corresponding to the left half of the normalized size interval [0,1]. First the influence on the total porosity of the parameter p is analyzed and interpreted. It is shown that such parameter, and the fractal exponent of the associated power scaling, are efficient packing parameters, but this last one is not in the way predicted in a former published work addressing an analogous research in artificial granular materials. The total porosity reaches the minimum value for p = 0.6. Limited information on the pore size distribution is obtained from the packing simulations and by means of morphological analysis methods. Results show that the range of pore sizes increases for decreasing values of p showing also different shape in the volume pore size distribution. Further research including simulations with a greater number of particles and image resolution are required to obtain finer results on the hierarchical structure of pore space.

Modelling of landslides propagation with SPH : effects of rheology and pore water pressure

El estudio desarrollado en este trabajo de tesis se centra en la modelización numérica de la fase de propagación de los deslizamientos rápidos de ladera a través del método sin malla Smoothed Particle Hydrodynamics (SPH). Este método tiene la gran ventaja de permitir el análisis de problemas de grandes deformaciones evitando operaciones costosas de remallado como en el caso de métodos numéricos con mallas tal como el método de los Elementos Finitos. En esta tesis, particular atención viene dada al rol que la reología y la presión de poros desempeñan durante estos eventos. El modelo matemático utilizado se basa en la formulación de Biot-Zienkiewicz v - pw, que representa el comportamiento, expresado en términos de velocidad del esqueleto sólido y presiones de poros, de la mezcla de partículas sólidas en un medio saturado. Las ecuaciones que gobiernan el problema son: • la ecuación de balance de masa de la fase del fluido intersticial, • la ecuación de balance de momento de la fase del fluido intersticial y de la mezcla, • la ecuación constitutiva y • una ecuación cinemática. Debido a sus propiedades geométricas, los deslizamientos de ladera se caracterizan por tener una profundidad muy pequeña frente a su longitud y a su anchura, y, consecuentemente, el modelo matemático mencionado anteriormente se puede simplificar integrando en profundidad las ecuaciones, pasando de un modelo 3D a 2D, el cual presenta una combinación excelente de precisión, sencillez y costes computacionales. El modelo propuesto en este trabajo se diferencia de los modelos integrados en profundidad existentes por incorporar un ulterior modelo capaz de proveer información sobre la presión del fluido intersticial a cada paso computacional de la propagación del deslizamiento. En una manera muy eficaz, la evolución de los perfiles de la presión de poros está numéricamente resuelta a través de un esquema explicito de Diferencias Finitas a cada nodo SPH. Este nuevo enfoque es capaz de tener en cuenta la variación de presión de poros debida a cambios de altura, de consolidación vertical o de cambios en las tensiones totales. Con respecto al comportamiento constitutivo, uno de los problemas principales al modelizar numéricamente deslizamientos rápidos de ladera está en la dificultad de simular con la misma ley constitutiva o reológica la transición de la fase de iniciación, donde el material se comporta como un sólido, a la fase de propagación donde el material se comporta como un fluido. En este trabajo de tesis, se propone un nuevo modelo reológico basado en el modelo viscoplástico de Perzyna, pensando a la viscoplasticidad como a la llave para poder simular tanto la fase de iniciación como la de propagación con el mismo modelo constitutivo. Con el fin de validar el modelo matemático y numérico se reproducen tanto ejemplos de referencia con solución analítica como experimentos de laboratorio. Finalmente, el modelo se aplica a casos reales, con especial atención al caso del deslizamiento de 1966 en Aberfan, mostrando como los resultados obtenidos simulan con éxito estos tipos de riesgos naturales. The study developed in this thesis focuses on the modelling of landslides propagation with the Smoothed Particle Hydrodynamics (SPH) meshless method which has the great advantage of allowing to deal with large deformation problems by avoiding expensive remeshing operations as happens for mesh methods such as, for example, the Finite Element Method. In this thesis, special attention is given to the role played by rheology and pore water pressure during these natural hazards. The mathematical framework used is based on the v - pw Biot-Zienkiewicz formulation, which represents the behaviour, formulated in terms of soil skeleton velocity and pore water pressure, of the mixture of solid particles and pore water in a saturated media. The governing equations are: • the mass balance equation for the pore water phase, • the momentum balance equation for the pore water phase and the mixture, • the constitutive equation and • a kinematic equation. Landslides, due to their shape and geometrical properties, have small depths in comparison with their length or width, therefore, the mathematical model aforementioned can then be simplified by depth integrating the equations, switching from a 3D to a 2D model, which presents an excellent combination of accuracy, computational costs and simplicity. The proposed model differs from previous depth integrated models by including a sub-model able to provide information on pore water pressure profiles at each computational step of the landslide's propagation. In an effective way, the evolution of the pore water pressure profiles is numerically solved through a set of 1D Finite Differences explicit scheme at each SPH node. This new approach is able to take into account the variation of the pore water pressure due to changes of height, vertical consolidation or changes of total stress. Concerning the constitutive behaviour, one of the main issues when modelling fast landslides is the difficulty to simulate with the same constitutive or rheological model the transition from the triggering phase, where the landslide behaves like a solid, to the propagation phase, where the landslide behaves in a fluid-like manner. In this work thesis, a new rheological model is proposed, based on the Perzyna viscoplastic model, thinking of viscoplasticity as the key to close the gap between the triggering and the propagation phase. In order to validate the mathematical model and the numerical approach, benchmarks and laboratory experiments are reproduced and compared to analytical solutions when possible. Finally, applications to real cases are studied, with particular attention paid to the Aberfan flowslide of 1966, showing how the mathematical model accurately and successfully simulate these kind of natural hazards.

Percolation in soils at Different Bulk Densities: Porosity, Connectivity and Grey Threshold.

To improve percolation modelling on soils the geometrical properties of the pore space must be understood; this includes porosity, particle and pore size distribution and connectivity of the pores. A study was conducted with a soil at different bulk densities based on 3D grey images acquired by X-ray computed tomography. The objective was to analyze the effect in percolation of aspects of pore network geometry and discuss the influence of the grey threshold applied to the images. A model based on random walk algorithms was applied to the images, combining five bulk densities with up to six threshold values per density. This allowed for a dynamical perspective of soil structure in relation to water transport through the inclusion of percolation speed in the analyses. To evaluate separately connectivity and isolate the effect of the grey threshold, a critical value of 35% of porosity was selected for every density. This value was the smallest at which total-percolation walks appeared for the all images of the same porosity and may represent a situation of percolation comparable among bulks densities. This criterion avoided an arbitrary decision in grey thresholds. Besides, a random matrix simulation at 35% of porosity with real images was used to test the existence of pore connectivity as a consequence of a non-random soil structure.

Nonequlibrium particle and energy currents in quantum chains connected to mesoscopic Fermi reservoirs

We propose a model of nonequilibrium quantum transport of particles and energy in a system connected to mesoscopic Fermi reservoirs (mesoreservoir). The mesoreservoirs are in turn thermalized to prescribed temperatures and chemical potentials by a simple dissipative mechanism described by the Lindblad equation. As an example, we study transport in monoatomic and diatomic chains of noninteracting spinless fermions. We show numerically the breakdown of the Onsager reciprocity relation due to the dissipative terms of the model.

Particle and energy transport in quantum disordered and quasi-periodic chains connected to mesoscopic Fermi reservoirs

We study a model of nonequilibrium quantum transport of particles and energy in a many-body system connected to mesoscopic Fermi reservoirs (the so-called meso-reservoirs). We discuss the conservation laws of particles and energy within our setup as well as the transport properties of quasi-periodic and disordered chains.

Computer simulation of the interplay between fractal structures and surrounding heterogeneous multifractal distributions. Applications

In a large number of physical, biological and environmental processes interfaces with high irregular geometry appear separating media (phases) in which the heterogeneity of constituents is present. In this work the quantification of the interplay between irregular structures and surrounding heterogeneous distributions in the plane is made For a geometric set image and a mass distribution (measure) image supported in image, being image, the mass image gives account of the interplay between the geometric structure and the surrounding distribution. A computation method is developed for the estimation and corresponding scaling analysis of image, being image a fractal plane set of Minkowski dimension image and image a multifractal measure produced by random multiplicative cascades. The method is applied to natural and mathematical fractal structures in order to study the influence of both, the irregularity of the geometric structure and the heterogeneity of the distribution, in the scaling of image. Applications to the analysis and modeling of interplay of phases in environmental scenarios are given.

Volume, Surface, Connectivity and Size Distribution of Soil Pore Space in CT Images: Comparison of Samples at Different Depths from Nearby Natural and Tillage Areas

The study of soil structure, i.e., the pores, is of vital importance in different fields of science and technology. Total pore volume (porosity), pore surface, pore connectivity and pore size distribution are some (probably the most important) of the geometric measurements of pore space. The technology of X-ray computed tomography allows us to obtain 3D images of the inside of a soil sample enabling study of the pores without disturbing the samples. In this work we performed a set of geometrical measures, some of them from mathematical morphology, to assess and quantify any possible difference that tillage may have caused on the soil. We compared samples from tilled soil with samples from a soil with natural vegetation taken in a very close area. Our results show that the main differences between these two groups of samples are total surface area and pore connectivity per unit pore volume.

Fractal parameters of pore space from CT images of soils under contrasting management practices

Soil structure plays an important role in flow and transport phenomena, and a quantitative characterization of the spatial heterogeneity of the pore space geometry is beneficial for prediction of soil physical properties. Morphological features such as pore-size distribution, pore space volume or pore?solid surface can be altered by different soil management practices. Irregularity of these features and their changes can be described using fractal geometry. In this study, we focus primarily on the characterization of soil pore space as a 3D geometrical shape by fractal analysis and on the ability of fractal dimensions to differentiate between two a priori different soil structures. We analyze X-ray computed tomography (CT) images of soils samples from two nearby areas with contrasting management practices. Within these two different soil systems, samples were collected from three depths. Fractal dimensions of the pore-size distributions were different depending on soil use and averaged values also differed at each depth. Fractal dimensions of the volume and surface of the pore space were lower in the tilled soil than in the natural soil but their standard deviations were higher in the former as compared to the latter. Also, it was observed that soil use was a factor that had a statistically significant effect on fractal parameters. Fractal parameters provide useful complementary information about changes in soil structure due to changes in soil management. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0218348X14400118?queryID=%24%7BresultBean.queryID%7D&

In situ acoustic methods to estimate the physical and mechanical aging of oriented strand board

Following the success achieved in previous research projects usin non-destructive methods to estimate the physical and mechanical aging of particle and fibre boards, this paper studies the relationships between aging, physical and mechanical changes, using non-destructive measurements of oriented strand board (OSB). 184 pieces of OSB board from a French source were tested to analyze its actual physical and mechanical properties. The same properties were estimated using acoustic non-destructive methods (ultrasound and stress wave velocity) during a physical laboratory aging test. Measurements were recorded of propagation wave velocity with the sensors aligned, edge to edge, and forming an angle of 45 degrees, with both sensors on the same face of the board. This is because aligned measures are not possible on site. The velocity results are always higher in 45 degree measurements. Given the results of statistical analysis, it can be concluded that there is a strong relationship between acoustic measurements and the decline in physical and mechanical properties of the panels due to aging. The authors propose several models to estimate the physical and mechanical properties of board, as well as their degree of aging. The best results are obtained using ultrasound, although the difference in comparison with the stress wave method is not very significant. A reliable prediction of the degree of deterioration (aging) of board is presented.

First results obtained using the CENBG nanobeam line: performances and applications

A high resolution focused beam line has been recently installed on the AIFIRA (“Applications Interdisciplinaires des Faisceaux d’Ions en Région Aquitaine”) facility at CENBG. This nanobeam line, based on a doublet–triplet configuration of Oxford Microbeam Ltd. OM-50™ quadrupoles, offers the opportunity to focus protons, deuterons and alpha particles in the MeV energy range to a sub-micrometer beam spot. The beam optics design has been studied in detail and optimized using detailed ray-tracing simulations and the full mechanical design of the beam line was reported in the Debrecen ICNMTA conference in 2008. During the last two years, the lenses have been carefully aligned and the target chamber has been fully equipped with particle and X-ray detectors, microscopes and precise positioning stages. The beam line is now operational and has been used for its firstapplications to ion beam analysis. Interestingly, this set-up turned out to be a very versatile tool for a wide range of applications. Indeed, even if it was not intended during the design phase, the ion optics configuration offers the opportunity to work either with a high current microbeam (using the triplet only) or with a lower current beam presenting a sub-micrometer resolution (using the doublet–triplet configuration). The performances of the CENBGnanobeam line are presented for both configurations. Quantitative data concerning the beam lateral resolutions at different beam currents are provided. Finally, the firstresults obtained for different types of application are shown, including nuclear reaction analysis at the micrometer scale and the firstresults on biological samples

Monte-Carlo dosimetry on a realistic cell monolayer geometry exposed to alpha particles

The energy and specific energy absorbed in the main cell compartments (nucleus and cytoplasm) in typical radiobiology experiments are usually estimated by calculations as they are not accessible for a direct measurement. In most of the work, the cell geometry is modelled using the combination of simple mathematical volumes. We propose a method based on high resolution confocal imaging and ion beam analysis (IBA) in order to import realistic cell nuclei geometries in Monte-Carlo simulations and thus take into account the variety of different geometries encountered in a typical cell population. Seventy-six cell nuclei have been imaged using confocal microscopy and their chemical composition has been measured using IBA. A cellular phantom was created from these data using the ImageJ image analysis software and imported in the Geant4 Monte-Carlo simulation toolkit. Total energy and specific energy distributions in the 76 cell nuclei have been calculated for two types of irradiation protocols: a 3 MeV alpha particle microbeam used for targeted irradiation and a 239Pu alpha source used for large angle random irradiation. Qualitative images of the energy deposited along the particle tracks have been produced and show good agreement with images of DNA double strand break signalling proteins obtained experimentally. The methodology presented in this paper provides microdosimetric quantities calculated from realistic cellular volumes. It is based on open-source oriented software that is publicly available.

Three dimensional (3D) microstructure-based modeling of interfacial decohesion in particle reinforced metal matrix composites

Modeling and prediction of the overall elastic–plastic response and local damage mechanisms in heterogeneous materials, in particular particle reinforced composites, is a very complex problem. Microstructural complexities such as the inhomogeneous spatial distribution of particles, irregular morphology of the particles, and anisotropy in particle orientation after secondary processing, such as extrusion, significantly affect deformation behavior. We have studied the effect of particle/matrix interface debonding in SiC particle reinforced Al alloy matrix composites with (a) actual microstructure consisting of angular SiC particles and (b) idealized ellipsoidal SiC particles. Tensile deformation in SiC particle reinforced Al matrix composites was modeled using actual microstructures reconstructed from serial sectioning approach. Interfacial debonding was modeled using user-defined cohesive zone elements. Modeling with the actual microstructure (versus idealized ellipsoids) has a significant influence on: (a) localized stresses and strains in particle and matrix, and (b) far-field strain at which localized debonding takes place. The angular particles exhibited higher degree of load transfer and are more sensitive to interfacial debonding. Larger decreases in stress are observed in the angular particles, because of the flat surfaces, normal to the loading axis, which bear load. Furthermore, simplification of particle morphology may lead to erroneous results.

Mathematical and Numerical Modeling in Maritime Geomechanics

A theoretical and numerical framework to model the foundation of marine offshore structures is presented. The theoretical model is composed by a system of partial differential equations describing coupling between seabed solid skeleton and pore fluids (water, air, oil,…) combined with a system of ordinary differential equations describing the specific constitutive relation of the seabed soil skeleton. Once the theoretical model is described, the finite element numerical procedure to achieve an approximate solution of the governing equations is outlined. In order to validate the proposed theoretical and numerical framework the seaward tilt mechanism induced by the action of breaking waves over a vertical breakwater is numerically reproduced. The results numerically attained are in agreement with the main conclusions drawn from the literature associated with this failure mechanism

Ion charge number and flux saturation effects in the corona of a laser-irradiated pellet

The quasisteady structure of the corona of a laser-irradiated pellet is completely determined for arbitrary Z, (ion charge number} and re/ra (ratio of critical and ablation radii), and for heat-flux saturation factor/above approximately 0.04. The ion-to-electron temperature ratio at rc grows sensibly with Z,; all other quantities depend weakly and nonmonotonically on Z,. For rc /ra close to unity, and all Z, of interest (Z, < 47}, the flow is subsonic at rc. For a given laser power W, flux saturation may decrease (low/) or increase (high/) the ablation pressure Pa relative to the value obtained when saturation is not considered; in some cases a decrease in/with W fixed increases Pa. For intermediate^ ~0.1), Pa cc (W/r* )2/3 p\n\pc = critical density), independently of rc/ra; for/~0.6, Pa «s larger by a factor of about [rc/raf13. For rjra > 1.2 roughly, the mass ablation rate is C{Z,) [{m/kZ.f^Kr^Pl) l,\ independent of pc and/, and barely dependent on Z,(m, is ion mass; k, Boltzmann's constant; K, conductivity coefficient; and C, a tabulated function).

Identification of pore spaces in 3D CT soil images using a PFCM partitional clustering

Recent advances in non-destructive imaging techniques, such as X-ray computed tomography (CT), make it possible to analyse pore space features from the direct visualisation from soil structures. A quantitative characterisation of the three-dimensional solid-pore architecture is important to understand soil mechanics, as they relate to the control of biological, chemical, and physical processes across scales. This analysis technique therefore offers an opportunity to better interpret soil strata, as new and relevant information can be obtained. In this work, we propose an approach to automatically identify the pore structure of a set of 200-2D images that represent slices of an original 3D CT image of a soil sample, which can be accomplished through non-linear enhancement of the pixel grey levels and an image segmentation based on a PFCM (Possibilistic Fuzzy C-Means) algorithm. Once the solids and pore spaces have been identified, the set of 200-2D images is then used to reconstruct an approximation of the soil sample by projecting only the pore spaces. This reconstruction shows the structure of the soil and its pores, which become more bounded, less bounded, or unbounded with changes in depth. If the soil sample image quality is sufficiently favourable in terms of contrast, noise and sharpness, the pore identification is less complicated, and the PFCM clustering algorithm can be used without additional processing; otherwise, images require pre-processing before using this algorithm. Promising results were obtained with four soil samples, the first of which was used to show the algorithm validity and the additional three were used to demonstrate the robustness of our proposal. The methodology we present here can better detect the solid soil and pore spaces on CT images, enabling the generation of better 2D?3D representations of pore structures from segmented 2D images.