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Modeling air transport through the entire firn column of polar ice sheets is needed to interpret climate archives. To this end, different regressions have been proposed in the past to estimate the effective coefficient of diffusion and permeability of firn. These regressions are often valid for specific depth or porosity ranges only. Also, they constitute a source of uncertainty as evaluations have been limited by the lack of reliable data of firn transport properties. To contribute with a new dataset, this study presents the effective coefficient of diffusion and the permeability at Dome C and Lock In, Antarctica, from the near-surface to the close-off (23 to 133 m depth). Also, microstructure is characterized based on density, specific surface area, closed porosity ratio, connectivity index, and structural anisotropy through the correlation lengths. All properties were estimated based on pore-scale computations from 3D tomographic images of firn samples. The normalized diffusion coefficient ranges from 1.9 × 10−1 to 8.3 × 10−5, and permeability ranges from 1.2 × 10−9 to 1.1 × 10−12 m2, for densities between 565 and 888 kg m−3. No or little anisotropy is reported. Next, we investigate the relationship of the transport properties with density over the firn density range (550–850 kg m−3), as well as over the entire density range encountered in the ice sheets (100–850 kg m−3), by extending the datasets with transport properties of alpine and artificial snow from previous studies. Classical analytical models and regressions from literature are evaluated against the estimates from pore-scale simulations. For firn, good agreements are found for permeability and the diffusion coefficient with two existing regressions of the literature based on open porosity despite the rather different site conditions (Greenland). Over the entire 100–850 kg m−3 density range, permeability is accurately reproduced by the Carman–Kozeny and self-consistent (spherical bi-composite) models when expressed in terms of a rescaled porosity, ϕres=(ϕ-ϕoff)/(1-ϕoff), to account for pore closure, where ϕoff is the close-off porosity. For the normalized diffusion coefficient, none of the evaluated formulas were satisfactory, so we propose a new regression based on the rescaled porosity that reads D/Dair=(ϕres)1.61.

Inside a snow cover, metamorphism plays a key role in snow evolution at different scales. This study focuses on the impact of temperature gradient metamorphism on a snow layer in its vertical extent. To this end, two cold-laboratory experiments were conducted to monitor a snow layer evolving under 100 K m−1 using X-ray tomography and environmental sensors. The first experiment shows that snow evolves differently in the vertical: at the end, coarser depth hoar are found in the center part of the layer, with covariance lengths about 50 % higher, compared to the top and bottom areas. We show that this heterogeneous grain growth could be related to the temperature profile and the associated crystal growth regimes, and to the profile of vapor supersaturation. In the second experiment, a non-disturbing sampling method was applied to enable a precise observation of the basal mass transfer in the case of dry boundary conditions. An air gap, characterized by a sharp drop in density, developed at the base and reached more than 3 mm after a month. The two reported phenomena, heterogeneous grain growth and basal mass loss, create heterogeneities in snow – in terms of density, grain and pore size, and ice morphology – from an initial homogeneous layer. Finally, we report the formation of hard depth hoar associated with an increase of SSA observed in the second experiment with higher initial density. These micro-scale effects may strongly impact the snowpack behavior, e.g. for snow transport processes or snow mechanics.

Water in jet fuels is an important concern for the aeronautical industry, especially at freezing temperatures, for which ice-clogging phenomena may occur in the fuel-feeding system, with a risk causing accidents. In this work, ice particles formed from water addition in jet A-1 fuel have been characterized by X-ray Micro-Computed Tomography (μCT) at −18±2 °C. For this purpose, an experimental sampling campaign was conducted in a fuel-icing test bench designed to characterize the properties of aeronautical filters. The samples were conditioned, transported, stored under cold-stable conditions and afterward preserved using a specific cryogenic cell during the X-ray scans. After image processing and analysis, the three dimensional (3D) images allowed us to access the shape complexity of the particles at a resolution of 5 μm. The different samples gave repeatable and coherent results, exhibiting wide size distributions of the ice particles, ranging from 20 to 970 μm with a peak between 100 and 400 μm. The increase of the water content volumetric fraction (C) as well as that of the time by which the ice particles were recirculating in the injection loop (τ), showed tendencies towards wider and smaller size distributions, respectively. The sphericity indexes (ψ) were higher than 0.7 for ~70% of particles, indicating a significant trend to rounded shapes. The mean curvature distributions of the agglomerates showed some displacements towards concave surfaces at high C, and towards convex surfaces at longer τ. This illustrates the occurrence of more complex structures for higher water contents and the “grinding effect” of the recirculating time.

A new experiment has been conducted to characterize experimentally heat and mass transport as well as metamorphism evolution during temperature gradient conditions. To be able to appreciate fine scale as well as larger scale processes, the experimentation lasted 3 weeks with a strong gradient of 100 K m-1 and a mean temperature of -9.5°C. The studied snow layer was 12 cm thick and had a horizontal surface of 0.5 m2. Temporal monitoring of the snow was made through 17 micro-tomographies at specific spots with a resolution of 8 μm and 9 micro-tomographies on full vertical profiles at 21 μm. The layer was also instrumented using 10 temperature and humidity sensors and 7 precise temperature sensors recording at different locations during the whole process. This experiment showed precisely the development of facets and depth hoar in the snow matrix, and leads to interesting results concerning the evolution of heat and mass fields during a strong temperature gradient. The results of this experiment are finally compared to numerical results predicted by coupled heat and mass transport models such as the one of Calonne et al., 2015.

Snow plays a crucial role in the climate system, as its high albedo is unique among the Earth’s surface materials. Several microstructural properties such as the snow specific surface area strongly modulate the optical properties of snow. Light penetration and scattering by ice particles are also impacted by other microstructural parameters, such as the grain shape. Nevertheless, most radiative transfer models still treat snow as a medium composed of idealized and simplified geometries, which limits the understanding of how the snow microstructure impacts the snow optical properties. Assuming geometric optics and weak ice absorption, only two parameters are needed to describe the snow grain shape in the diffusion regime. These are the absorption enhancement parameter B and the geometric asymmetry factor gG. Here we aim to understand the relationship between the snow microstructure properties and the shape parameters, B and gG. To do so, we combine ray-tracing Monte Carlo methods with 3D images of the actual microstructure of snow, obtained with X-ray imaging and computed microtomography (µCT). The existing Rough Surface Ray-Tracer (RSRT) model, originally designed to simulate snow albedo over rough surfaces, has been adapted to trace light propagation in microstructure 3D images. This approach allows getting rid of the simplified representation of snow in radiative transfer models, and benefits from the accurate ray-tracing calculations. We present here our initial findings and results, which compare well with the results of the advanced radiative transfer theories that relate snow optical properties to the chord length distribution in snow microstructure.

In this study, the microstructural evolution of a non-reactive porous model food (sponge cake) during freezing was investigated. Sponge cake samples were frozen at two different rates: slow freezing (0.3 °C min−1) and fast freezing (17.2 °C min−1). Synchrotron X-ray microtomography (µ-CT) and cryo-scanning electron microscopy (Cryo-SEM) were used to visualize and analyze the microstructure features. The samples were scanned before and after freezing using a specific thermostated cell (CellStat) combined with the synchrotron beamline. Cryo-SEM and 3D µ-CT image visualization allowed a qualitative analysis of the ice formation and location in the porous structure. An image analysis method based on grey level was used to segment the three phases of the frozen samples: air, ice and starch. Volume fractions of each phase, ice local thickness and shape characterization were determined and discussed according to the freezing rates.

Modeling air transport through the entire ice sheet column is needed to interpret climate archives. To this end, different regressions were proposed to estimate the effective coefficient of diffusion and permeability of firn. Such regressions are often valid for specific depth or porosity ranges and were little evaluated as data of these properties are scarce. To contribute with a new dataset, this study presents the effective coefficient of diffusion and the permeability at Dome C and Lock In, Antarctica, from the near-surface to the close-off (23 to 133 m depth). Also, microstructure is characterized based on density, specific surface area, closed porosity ratio, connectivity index and structural anisotropy through the correlation lengths. All properties were estimated based on pore-scale computations on 3D tomographic images of firn samples. Normalized diffusion coefficient ranges from 1.9 × 10−1 to 8.3 × 10−5 and permeability ranges from 1.2 × 10−9 to 1.1 × 10−12 m2, for densities between 565 and 888 kg m−3. No or little anisotropy is reported. Next, we investigate the relationship of the transport properties with density over the firn density range as well as over the entire density range encountered in ice sheets by including snow data. Classical analytical models and regressions from literature are evaluated. For firn (550–850 kg m−3), good agreements are found for permeability and diffusion coefficient with the regressions based on the open porosity of Freitag et al. (2002) and Adolph and Albert (2014), despite the rather different site conditions (Greenland). Over the entire 100–850 kg m−3 density range, permeability is accurately reproduced by the Carman-Kozeny and Self-Consistent (spherical bi-composite) model when expressed in terms of a rescaled porosity ϕres = (ϕ–ϕoff) / (1–ϕoff) to account for pore closure, with ϕoff the close-off porosity. For the normalized diffusion coefficient, none of the evaluated formulas were satisfactory so we propose a new regression based on the rescaled porosity that reads D/Dair = (ϕres)1.61.

Representing snow isothermal metamorphism is key to model the evolution and properties of the snow cover. Recently, a new phase-field model allowing to describe 3D microstructure induced by curvature effects has been proposed (Bretin et al, Esiam: M2an, 2019). In the present work, this model is used to simulate isothermal metamorphism of snow at the pore scale, considering the only process of moving interfaces by sublimation-deposition driven by curvatures. This model runs on real 3D microtomographic images and gives a temporal series of 3D images simulating isothermal metamorphism. To determine the condensation coefficient to use in the model, which shows complex dependencies and is still poorly known, we calibrated it by reproducing the time evolution of the specific surface area (SSA) measured during an isothermal experimental time-series at -2°C (Flin et al., Ann. Glaciol., 2004). This calibration has led to a value of the condensation coefficient of 9.9 ± 0.6 10−4. Using this calibration, we obtained a good agreement between simulations and an independent series of isothermal metamorphism at -2°C (Hagenmuller et al., The Cryosphere, 2019). Finally, 4 images representing different types of snow microstructure have been chosen as input to simulate isothermal metamorphism at -2°C during 75 days. The obtained temporal series of 3D images were then used to calculate microstructural (porosity, SSA, covariance lengths) and physical transport properties (thermal conductivity, effective diffusion, permeability) evolution. Comparing our numerical estimations of physical properties to current parameterizations gives overall good agreement. An interesting new result arising from the simulations is the conservation or enhancement of the structural anisotropy under isothermal conditions for the samples that were initially strongly anisotropic.

Snow stands out from materials at the Earth’s surface owing to its unique optical properties. Snow optical properties are sensitive to the snow microstructure, triggering potent climate feedbacks. The impacts of snow microstructure on its optical properties such as reflectance are, to date, only partially understood. However, precise modelling of snow reflectance, particularly bidirectional reflectance, are required in many problems, e.g. to correctly process satellite data over snow-covered areas. This study presents a dataset that combines bidirectional reflectance measurements over 500–2500 nm and the X-ray tomography of the snow microstructure for three snow samples of two different morphological types. The dataset is used to evaluate the stereological approach from Malinka (2014) that relates snow optical properties to the chord length distribution in the snow microstructure. The mean chord length and specific surface area (SSA) retrieved with this approach from the albedo spectrum and those measured by the X-ray tomography are in excellent agreement. The analysis of the 3D images has shown that the random chords of the ice phase obey the gamma distribution with the shape parameter m taking the value approximately equal to or a little greater than 2. For weak and intermediate absorption (high and medium albedo), the simulated bidirectional reflectances reproduce the measured ones accurately but tend to slightly overestimate the anisotropy of the radiation. For such absorptions the use of the exponential law for the ice chord length distribution instead of the one measured with the X-ray tomography does not affect the simulated reflectance. In contrast, under high absorption (albedo of a few percent), snow microstructure and especially facet orientation at the surface play a significant role in the reflectance, particularly at oblique viewing and incidence.

International audience; The cone penetration test is widely used to determine the mechanical properties of snow and to delineate snow stratigraphy. Precise knowledge of the snow stratigraphy is essential for many applications such as avalanche forecasting or estimating the snowpack energy budget. With the development of sophisticated, high-resolution digital penetrometers such as the SnowMicroPenetrometer, the cone penetration test remains one of the only objective methods to measure snow stratigraphy. An accurate interpretation of the measured hardness profiles requires to understand the interaction between the cone tip and the snow material. In this study, we measured the displacement induced by the penetration of a conic tip with a radius of 2.5 mm in eight different snow samples using X-ray tomography. The experiments were conducted at a temperature of −10°C. To recover the full three-dimensional displacements between the tomographic images measured before and after the test, we specifically designed a tracking algorithm which exploits the unique shape of each snow grain. The tracking algorithm enables to recover most of the granular displacements and accurately captures the volumetric strain directly derived from density changes. The measured displacements are shown to be oriented downwards below the tip apex, upwards close to the snow surface, and nearly only radially in between. We observed and quantified the development of a compaction around and below the tip. Surprisingly, we also observed dilation of the snow material close to the snow and tip surfaces in very high-density samples. The radial extent of the compaction zone ranged between 1.6 and 2.3 times the tip radius. These results were compared to existing interpretative models. Although limited to relatively small samples and short penetration depths, these results provide new insights on snow deformation during a cone penetration test, and the validity of these models.

Temperature ( θ ) and time are key factors in both nucleation and evolution of ice crystals in jet fuels occurring inside aircraft fuel systems. In this study, we followed the morphological evolution of an ice agglomerate in jet A-1 fuel using a specific dynamic cryogenic cell (CellDyM). An in vivo experiment was conducted, imposing temperatures between −45 ∘ C and −5 ∘ C, while performing X-ray scans throughout the experiment. Then, image processing and analysis provided access to the morphological evolution of the ice sample, at a resolution of 7.5 μ m. Three types of analyses were mainly computed: (i) cumulative evolution of the microstructure as a function of temperature and time intervals, (ii) evolution of the ice microstructure for isothermal conditions and (iii) evolution of the microstructure for different temperature jumps. Overall, the effect of temperature is minor in the θ interval of [−45, −10] ∘ C, with evolution rates between 1.6 and 4.6 μ m.h − 1 , compared to the θ interval of [−10, −5] ∘ C, during which a significant change in the morphology of the ice agglomerate was observed, with an evolution rate of 10.4 μ m.h − 1 . This study illustrates the key values of the temperature ranges that influence the ice microstructure in jet fuel and brings new insights on the physical mechanisms potentially involved.

The formation of ice crystals in aviation fuels at low temperatures is a major problem to the aviation industry. In this work, a fuel-icing bench from the Institut de la Filtration et des Techniques Seeparatives (IFTS) was used to develop two characterization methods for the ice particles in jet A-1 fuel: (i) a 3D ex-situ method using X-ray tomography at low temperature, giving full access to the geometric complexities of the ice particles at 5.5 μm resolution and (ii) a 2D in-situ method using high-speed imaging at 4 μm resolution, allowing real-time measurements of ice particles flowing at high velocity. A large set of process parameters was studied: the circulation time (τ), the water concentration (C) and the interfacial tension (γ) at fixed temperature (θ) ∼ -18±2 °C. Overall, both methods gave consistent results, with particle sizes not exceeding 1 mm and mean sizes between 100 to 300 μm. The shapes of the particles were mainly spherical in 3D (∼ 50%) and circular in 2D (≥ 60%). Same trends were observed with both methods in relation to the process parameters. The grinding effect induced by an increased τ seems to be the most influencing phenomenon in the process, leading to the decrease of the particle size. In contrast, the effect of C is not conclusive, given the detection limit of particles in 2D for high concentrations. This study highlights the specificities of both characterization methods and the influence of the process parameters on the properties of the ice particles in jet fuel.

Icing in aircraft fuel systems remains a serious issue for aviation safety and security. It is linked to the geometrical properties of the ice particles formed in situ, which are themselves highly sensitive to the operating parameters of the fuel system. In this work, an experimental campaign was conducted with a fuel-icing bench to explore the impact of the interfacial tension ( γ ), the sampling temperature ( θ ) as well as the recirculation time of the particles in the injection loop ( τ ). For this purpose, a new sampling method has been defined, tested and validated, using paraffin oil (PO) as an impregnation product for ice particles. The specimens were prepared, set up in a cryogenic cell and then scanned using X-ray Micro-Computed Tomography (μCT). Image processing and analyses allowed computation of the 3D properties at 5 μ m resolution. The impregnation with PO revealed satisfying results in terms of physical separation of ice particles (more than 66%), especially for the smallest ones ( ⩽ 200 μ m), thus limiting the sintering phenomenon over time. The decrease in γ values showed a slight tendency to form smaller particle size distributions widths ( PSD w ). The observed influence of θ was minor due to its interference with τ , which proved to have the strongest effect on particle size and morphology. Thus, the increase in τ promoted the formation of smaller PSD w with modes ~ 100 μ m. The elongation ( E e ) and flatness ( E f ) form factors showed significant tendencies ( ⩾ 40%) towards rounded and spherical shapes for all ice specimens. The mean curvature distributions showed a trend towards convexities either by decreasing γ or increasing τ values. This study illustrates the complex impact of process parameters on the geometric properties of ice particles in jet fuel. The obtained results may be useful for further testing of filter clogging phenomena or numerical simulation and modeling studies.

Several low-density crumpled paper-based materials were fabricated by varying both the volume fraction and the geometry and mechanical properties of paper sheets. Their 3D architecture was investigated using X-ray microtomography. Microstructure descriptors such as the pore size distribution, the mean curvature distribution and the volume fraction of ordered domains were finely analyzed. Their mechanical properties were also assessed using uniaxial compression tests. Our results showed that crumpled materials exhibited a particular porous microstructure with a reproducible mechanical behavior between foams and entangled fibrous materials. Their compressive behavior was characterized by successive elastic, strain-hardening and densification regimes. The effects of the geometry, microstructure and mechanical properties of the sheets on the process-induced microstructures and mechanical performances were discussed. In particular, a simple micromechanical approach was used to estimate analytically and from the 3D images the role of ridges and ordered domains on the mechanical properties of crumpled papers. The evolution of their Young's moduli and yield stresses were studied as a function of their relative densities and compared with experimental data available in the literature for other cellular materials, showing that crumpled papers are promising renewable alternatives to standard polymer foams for several engineering applications, due to the proper combination of mechanical properties, porosity, cost, and easy fabrication. Keywords: Crumpled sheets, Paper, Self-locked architecture, Core materials, Microstructure, Compression behavior, Structural applications, Sandwich panel

International audience; Estimating thermal conductivity of snow, firn, and porous ice is key for modeling the thermal regime of alpine and polar glaciers. Whereas thermal conductivity of snow was widely investigated, studies on firn and porous ice are very scarce. This study presents the effective thermal conductivity tensor computed from 64 3‐D images of microstructures of snow, antarctic firn, and porous ice at −3, −20, and −60°C. We show that, in contrast with snow, conductivity of firn and porous ice correlates linearly with density, is approximately isotropic, and is largely impacted by temperature. We report that performances of commonly used estimates of thermal conductivity vary largely with density. In particular, formulas designed for snow lead to significant underestimations when applied to denser ice structures. We present a new formulation to accurately estimate the thermal conductivity throughout the whole density range, from fresh snow to bubbly ice, and for any temperature conditions encountered in glaciers.

The deposition of light-absorbing particles (LAPs) such as mineral dust and black carbon on snow is responsible for a highly effective climate forcing, through darkening of the snow surface and associated feedbacks. The interplay between post-depositional snow transformation (metamorphism) and the dynamics of LAPs in snow remains largely unknown. We obtained time series of X-ray tomography images of dust-contaminated samples undergoing dry snow metamorphism at around −2 ∘C. They provide the first observational evidence that temperature gradient metamorphism induces dust particle motion in snow, while no movement is observed under isothermal conditions. Under temperature gradient metamorphism, dust particles can enter the ice matrix due to sublimation–condensation processes and spread down mainly by falling into the pore space. Overall, such motions might reduce the radiative impact of dust in snow, in particular in arctic regions where temperature gradient metamorphism prevails.

We used three-dimensional (3-D) images of snow microstructure to carry out numerical estimations of the full tensor of the intrinsic permeability of snow (K). This study was performed on 35 snow samples, spanning a wide range of seasonal snow types. For several snow samples, a significant anisotropy of permeability was detected and is consistent with that observed for the effective thermal conductivity obtained from the same samples. The anisotropy coefficient, defined as the ratio of the vertical over the horizontal components of K, ranges from 0.74 for a sample of decomposing precipitation particles collected in the field to 1.66 for a depth hoar specimen. Because the permeability is related to a characteristic length, we introduced a dimensionless tensor K*=K/res2, where the equivalent sphere radius of ice grains (res) is computed from the specific surface area of snow (SSA) and the ice density (ρi) as follows: res=3/(SSA×ρi. We define K and K* as the average of the diagonal components of K and K*, respectively. The 35 values of K* were fitted to snow density (ρs) and provide the following regression: K = (3.0 ± 0.3) res2 exp((−0.0130 ± 0.0003)ρs). We noted that the anisotropy of permeability does not affect significantly the proposed equation. This regression curve was applied to several independent datasets from the literature and compared to other existing regression curves or analytical models. The results show that it is probably the best currently available simple relationship linking the average value of permeability, K, to snow density and specific surface area.

At the microscopic scale, i.e., pore scale, dry snow metamorphism is mainly driven by the heat and water vapor transfer and the sublimation-deposition process at the ice-air interface. Up to now, the description of these phenomena at the macroscopic scale, i.e., snow layer scale, in the snowpack models has been proposed in a phenomenological way. Here we used an upscaling method, namely, the homogenization of multiple-scale expansions, to derive theoretically the macroscopic equivalent modeling of heat and vapor transfer through a snow layer from the physics at the pore scale. The physical phenomena under consideration are steady state air flow, heat transfer by conduction and convection, water vapor transfer by diffusion and convection, and phase change (sublimation and deposition). We derived three different macroscopic models depending on the intensity of the air flow considered at the pore scale, i.e., on the order of magnitude of the pore Reynolds number and the Peclet numbers: (A) pure diffusion, (B) diffusion and moderate convection (Darcy's law), and (C) strong convection (nonlinear flow). The formulation of the models includes the exact expression of the macroscopic properties (effective thermal conductivity, effective vapor diffusion coefficient, and intrinsic permeability) and of the macroscopic source terms of heat and vapor arising from the phase change at the pore scale. Such definitions can be used to compute macroscopic snow properties from 3-D descriptions of snow microstructures. Finally, we illustrated the precision and the robustness of the proposed macroscopic models through 2-D numerical simulations.

Monitoring the time evolution of snow microstructure in 3-D is crucial for a better understanding of snow metamorphism. We, therefore, designed a cryogenic cell that precisely controls the experimental conditions of a sample while it is scanned by X-ray tomography. Based on a thermoelectrical regulation and a vacuum insulation, the cell operates at room temperature. It is, thus, adaptable to diverse scanners, offering advantages in terms of imaging techniques, resolution, and speed. Three-dimensional time-lapse series were obtained under equitemperature and temperature gradient conditions at a 7.8 μm precision. The typical features of each metamorphism and the anisotropic faceting behavior between the basal and prismatic planes, known to occur close to −2°C, were observed in less than 30 h. These results are consistent with the temperature fields expected from heat conduction simulations through the cell. They confirm the cell's accuracy and the interest of relatively short periods to study snow metamorphism.

We carried out a study to monitor the time evolution of microstructural and physical properties of snow during temperature gradient metamorphism: a snow slab was subjected to a constant temperature gradient in the vertical direction for 3 weeks in a cold room, and regularly sampled in order to obtain a series of three-dimensional (3-D) images using X-ray microtomography. A large set of properties was then computed from this series of 3-D images: density, specific surface area, correlation lengths, mean and Gaussian curvature distributions, air and ice tortuosities, effective thermal conductivity, and intrinsic permeability. Whenever possible, specific attention was paid to assess these properties along the vertical and horizontal directions, and an anisotropy coefficient defined as the ratio of the vertical over the horizontal values was deduced. The time evolution of these properties, as well as their anisotropy coefficients, was investigated, showing the development of a strong anisotropic behavior during the experiment. Most of the computed physical properties of snow were then compared with two analytical estimates (self-consistent estimates and dilute beds of spheroids) based on the snow density, and the size and anisotropy of the microstructure through the correlation lengths. These models, which require only basic microstructural information, offer rather good estimates of the properties and anisotropy coefficients for our experiment without any fitting parameters. Our results highlight the interplay between the microstructure and physical properties, showing that the physical properties of snow subjected to a temperature gradient cannot be described accurately using only isotropic parameters such as the density and require more refined information. Furthermore, this study constitutes a detailed database on the evolution of snow properties under a temperature gradient, which can be used as a guideline and a validation tool for snow metamorphism models at the micro- or macroscale.

International audience; Rapid deformations in snow are mainly con- trolled by particle rearrangements and contact interactions. To study this deformation regime, the description of the snow microstructure in terms of grains, which could eventually be handled by discrete element models, is relevant. In practice, microtomography has become a standard method to image the three-dimensional distribution of ice and pores, as a set of binary voxels. Here, we propose a new method to directly identify individual snow grains defined as zones separated by regions of potential mechanical weakness, in the microtomo- graphic images. In general, these grains are not well sepa- rated but rather sintered together. Our new method, based on local geometrical criteria, is shown to detect contacts directly inferred from an explicit numerical mechanical experiment. The developed algorithm is tested on snow but is generic and applicable to various geomaterials with a granular-like microstructure.

International audience; Snow is an agglomerate of ice crystals. The details of its mechanical behavior are still controversially discussed: what is the relative importance of intragranular-viscoplastic deformation versus grain boundary sliding under mechanical loading? In order to understand how snow deforms at the grain scale, micro-mechanical compression tests on dry snow have been performed using X-ray diffraction contrast tomography (DCT). DCT is a non-destructive, 3D characterization technique which combines the principles of X-ray absorption and diffraction imaging. DCT reveals simultaneously the grain structure (in terms of 3D shape and crystallographic orientation) and the absorption microstructure of polycrystalline materials that fulfill specific requirements. Coupled with a sample environment that maintains the snow sample at sub-zero temperature and allows the application of a constant load, this technique allows us to follow at the grain scale the microstructural changes undergone by the sample. We briefly describe the principle of the DCT technique and then present and discuss the first results obtained during in situ compression experiments performed on large-grained snow samples.

The metamorphism of seasonal snow is classically considered as limited by vapour diffusion in the pore phase. To account for the lack of knowledge of the ice–vapour reaction coefficient near 0°C, the assumption of a reaction-limited metamorphism was first tested in three-dimensional simulations at low and very low temperature gradients; however, the validity of such results is difficult to verify experimentally. By a reasoned use of traditional iterative schemes, vapour diffusion is now simulated in three dimensions on tomographic snow data, mapping the gradient of vapour pressure near the grains. Repeating this process may provide a way to simulate the isothermal metamorphism without grain packing at a reasonable expense of computation time. Preliminary results are compared with existing computations made within the reaction-limited hypothesis.

A simple physical model describing the temperature-gradient metamorphism of snow is presented. This model, based on Kelvin’s equation and Fick’s law, takes into account the local variation of the saturating vapour pressure with temperature. It can determine locally whether the ice is condensing or subliming, depending on both the pressure and temperature fields in the snow structure. This model can also explain the formation of facets that occurs during the metamorphism. Using X-ray microtomographic images of snow samples obtained under low to moderate temperature-gradient conditions, this model has been tested and compared to the reaction-limited model proposed in a previous work.

International audience; The full 3-D macroscopic mechanical behavior of snow is investigated by solving kinematically uniform boundary condition problems derived from homogenization theories over 3-D images obtained by X-ray tomography. Snow is modeled as a porous cohesive material, and its mechanical stiffness tensor is computed within the framework of the elastic behavior of ice. The size of the optimal representative elementary volume, expressed in terms of correlation lengths, is determined through a convergence analysis of the computed effective properties. A wide range of snow densities is explored, and power laws with high regression coefficients are proposed to link the Young's and shear moduli of snow to its density. The degree of anisotropy of these properties is quantified, and Poisson's ratios are also provided. Finally, the influence of the main types of metamorphism (isothermal, temperature gradient, and wet snow metamorphism) on the elastic properties of snow and on their anisotropy is reported.

La neige, depuis sa chute jusqu’a sa fonte totale, subit des metamorphoses regies par les champs de temperature et de pression. Parmi les divers mecanismes possibles qui contribuent aux metamorphoses de neige, ceux dependant uniquement de la courbure sont les plus accessibles a la modelisation. Dans cet article, on s’interesse a la metamorphose d’un echantillon de neige seche place en conditions d’isothermie, pres de 0°C. A cette temperature, la pression de vapeur saturante de l’eau est elevee. On peut donc, en premiere approximation, considerer cette metamorphose comme entierement regie par la courbure. Ceci revient a negliger les effets d’orientation cristallographique et de limitation par la diffusion. A partir des lois de Kelvin et de Langmuir-Knudsen, une loi de croissance de la phase glace a ete obtenue de maniere analytique. Cette loi indique que la variation de la fraction volumique locale au cours du temps est proportionnelle a la difference entre les courbures locale et integrale. Un modele numerique simple a ete implemente en trois dimensions et applique a des images tomographiques de neige.

Snow, from its fall until its full melting, undergoes a structural metamorphism that is governed by temperature and humidity fields. Among the many possible mechanisms that contribute to snow metamorphism, those that depend only on curvature are the most accessible to modelling. In this paper, techniques of volume data analysis adapted to the complex geometry of snow are introduced and then applied to experimental tomographic data coming from the isothermal metamorphism of snow near 0°C. In particular, an adaptive algorithm of curvature computation is described. Present results on the evolution of specific surface area and anisotropy already show that such image-analysis methods are relevant tools for the characterization of real snow microstructures. Moreover, the evolution of the curvature distribution with time provides valuable information for the development of sintering models, in the same way as a possible quantitative calibration of snow-grain coarsening laws.

The new approaches in absorption X-ray microtomography allow snow-volume image acquisition in the cm3 range without destroying snow structure, and make it possible to perform micromechanical studies with the real geometry. The main objective of this paper is to introduce the development of a new three-dimensional (3-D) geometry modeling and finite-element analysis simulation package adapted to these scales. These new code modules and procedures are briefly described using an isothermal metamorphism snow experiment (–2°C, 3 months).This sample of aged snow (3.375mm3; 3003 voxels) allows simulation of a simple hypothetical uniaxial compressive stress experiment. The constitutive equations, boundary conditions, basic assumptions and the result showing the stress field over the 3-D data are discussed. The first qualitative results show a maximum stress of 6–9MPa in some small bonds, showing the potential of these codes to simulate the micromechanical behavior of complex materials.

Snow, from its fall until its full melting, undergoes a structure metamorphism governed by temperature and humidity fields. Among the many possible mechanisms that contribute to snow metamorphism, those that depend only on curvature are the most accessible to modelling. The isothermal metamorphism of a dry snow sample near 0uC is addressed in this paper. Near 0uC, the vapour pressure of water is high: the metamorphism can be considered, in first approximation, as fully curvature-driven. This corresponds to neglect crystallographic orientation and diffusion-limited effects. Based on Kelvin’s and Langmuir–Knudsen equations, a growth law of the ice phase can be analytically obtained. In this law, the variation of the local volume fraction is proportional to the difference between integral and local curvatures. A simple numerical model was implemented in three dimensions and applied on real tomographic images.

EnglishDry snow metamorphism refers to the evolutions of the snow microstructure mainly governed by processes of heat and vapor transport. This metamorphism leads to a variety of microstructures in terms of shape, size, proportion of air and ice, etc.The snow microstructure drives nearly all the macroscopic properties of the snow layer. It is thus crucial that the snow models, which are used to address different issues, from the avalanche risk prediction to climate studies, describe realistically dry snow metamorphism.We present here our work dedicated to improve this modeling. francaisLes metamorphoses de la neige seche correspondent a des transformations de la microstructure de la neige principalement regies par des processus de transport de chaleur et de vapeur. Elles aboutissent a des microstructures variees en termes de forme, de taille, de proportion d'air et de glace... La microstructure de la neige determine la quasi-totalite des proprietes macroscopiques de la couche qu'elle constitue. Ainsi, il est capital que les modeles macroscopiques de manteau neigeux, qui repondent a diverses problematiques, de la prevision du risque d'avalanche aux etudes climatiques, decrivent de maniere realiste les metamorphoses. On presente ici des travaux visant a ameliorer cette modelisation.

Snow density is commonly used to phenomenologically parameterize other snow properties such as strength or thermal conductivity. However, density is insufficient to fully characterize the variety of microstructures, as revealed by the existing scatter in the parameterizations. This can be explained by the role of bonds which are almost as important as grains to describe the macroscopic properties of snow. A quantification of the narrow constrictions or bonds between snow grains is thus essential to accurately parameterize snow properties. In order to characterize the reduced thickness of the ice matrix at bonds, we introduce a new microstructural indicator, the minimum cut density , ρ mc . This variable quantifies, on three-dimensional (3D) microtomographic images of snow, the minimal effective density of a surface that disconnects two opposite faces of the sample. The obtained minimum cut density values are surprisingly low, in the range [0.2, 35] kg m −3 for the tested samples with density in the range [100, 350] kg m −3 . This reveals the high variability and weak connectivity of the bonding system in snow. Structural anisotropy of faceted crystals and depth hoar is also well characterized by the minimum cut density. To evaluate the physical and mechanical relevance of this microstructural indicator, we estimate the thermal conductivity and the Young's modulus of the studied snow samples through microstructure-based simulations. An excellent correlation is found between the Young's modulus and the minimum cut density ( R 2 = 0.97). In particular, the minimum cut density well accounts for the anisotropy of the Young's modulus in faceted snow types. The correlation of thermal conductivity and minimum cut density is also highly significant ( R 2 = 0.88) but not better than the parameterization with density ( R 2 = 0.92). We show that this difference is mainly due to the role played by the thermal conduction of air.

Dry snow metamorphism, involved in several topics related to cryospheric sciences, is mainly linked to heat and water vapor transfers through snow including sublimation and deposition at the ice-pore interface. In this paper, the macroscopic equivalent modeling of heat and water vapor transfers through a snow layer was derived from the physics at the pore scale using the homogenization of multiple scale expansions. The microscopic phenomena under consideration are heat conduction, vapor diffusion, sublimation, and deposition. The obtained macroscopic equivalent model is described by two coupled transient diffusion equations including a source term arising from phase change at the pore scale. By dimensional analysis, it was shown that the influence of such source terms on the overall transfers can generally not be neglected, except typically under small temperature gradients. The precision and the robustness of the proposed macroscopic modeling were illustrated through 2D numerical simulations. Finally, the effective vapor diffusion tensor arising in the macroscopic modeling was computed on 3D images of snow. The self-consistent formula offers a good estimate of the effective diffusion coefficient with respect to the snow density, within an average relative error of 10%. Our results confirm recent work that the effective vapor diffusion is not enhanced in snow.

Pile foundations of offshore platforms, wind and water turbines are typically subjected to a variety of cyclic loading paths due to their complex environment. While many studies focus on global pile behaviour, the soil-pile interface is explored here by a micromechanical study of the soil layer in contact with the pile surface. This work is devoted to the analysis of frozen post-mortem silica sand samples recovered at the pile interface following installation and cyclic loading tests in a calibration chamber using x-ray tomography. An experimental procedure developed for three dimensional (3D) snow imaging was adapted for the recovery of the in-situ sand samples to preserve their structure during tomography scans. 3D images at a pixel size of 7 μm were then obtained using a cryogenic cell. Results confirm the presence of a shear band at the pile surface as well as void ratios changes in the direction of the pile’s radius.

X-ray microtomography has become an essential tool for investigating the mechanical and physical properties of snow, which are tied to its microstructure. To allow a quantitative characterization of the microstructure, the grayscale X-ray attenuation coefficient image has to be segmented into a binary ice/pore image. This step, called binary segmentation, is crucial and affects all subsequent analysis and modeling. Common segmentation methods are based on thresholding. In practice, these methods present some drawbacks and often require time-consuming manual post-processing. Here we present a binary segmentation algorithm based on the minimization of a segmentation energy. This energy is composed of a data fidelity term and a regularization term penalizing large interface area, which is of particular interest for snow where sintering naturally tends to reduce the surface energy. The accuracy of the method is demonstrated on a synthetic image. The method is then successfully applied on microtomographic images of snow and compared to the threshold-based segmentation. The main advantage of the presented approach is that it benefits from local spatial information. Moreover, the effective resolution of the segmented image is clearly defined and can be chosen a priori.

[1] We carried out numerical simulations of the conductivity of snow using microtomographic images. The full tensor of the effective thermal conductivity (keff) was computed from 30 three-dimensional images of the snow microstructure, spanning all types of seasonal snow. Only conduction through ice and interstitial air were considered. The obtained values are strongly correlated to snow density. The main cause for the slight scatter around the regression curve to snow density is the anisotropy of keff: the vertical component of keff of facetted crystals and depth hoar samples is up to 1.5 times larger than the horizontal component, while rounded grains sampled deeply in the snowpack exhibit the inverse behavior. Results of simulations neglecting the conduction in the interstitial air indicate that this phase plays a vital role in heat conduction through snow. The computed effective thermal conductivity is found to increase with decreasing temperature, mostly following the temperature dependency of the thermal conductivity of ice. The results are compared to experimental data obtained either with the needle-probe technique or using combined measurements of the vertical heat flux and the corresponding temperature gradient. Needle-probe measurements are systematically significantly lower than those from the two other techniques. The observed discrepancies between the three methods are investigated and briefly discussed.

Surface area of discrete objects is an important feature for model-based image analysis. In this article, we present a theoretical framework in order to prove multigrid convergence of surface area estimators based on discrete normal vector field integration. The paper details an algorithm which is optimal in time and multigrid convergent to estimate the surface area and a very efficient algorithm based on a local but adaptive computation.

Estimating the normal vector field on the boundary of discrete 3D objects is essential for rendering and image measurement problems. Most of the existing algorithms do not provide an accurate determination of the normal vector field for shapes that present edges. We propose here a new and simple computational method to obtain accurate results on all types of shapes whatever their degree of local convexity. The presented method is based on the analysis of the gradient vector field of the distance map of the object. Some results on simulated data and snow images from X-ray tomography are presented and discussed.

The main objective of the thesis is to improve our understanding of faceting occuring in dry snow metamorphism. The thesis focuses on the interplay between heat and mass diffusion and kinetic effects in the context of snow. For the first time,Diffraction Contrast Tomography (DCT) has been performed to monitor an experiment of temperature gradient metamorphism. The technique permits to retrieve the crystalline orientation of the grains constituting the microstructcure of the sample. Links between orientation of crystals and mass fluxres were analysed.The study shows that kinetic differences between basal and prismatic faces have effects on phase change fluxes at the ice/air interface.From a numerical modeling point of view, a highly anisotropic kinetic coefficient has been taken into account for the evolution of the ice/air interface. The model uses the phase-field approach and couples phase changes to heat and water vapor diffusion.The model was tested against an experiment of air cavity migration under temperature gradient in a monocrystalline ice block monitored with X-ray microtomography in one hand, and with the growth of a negative crystal during a pumping experiment followed with optical microscopy in the other hand.Such anisotropy permits to reproduce faceting as observed.Finally, the potential of the porposed model to describe snow metamorphism is highlighted.; L'objectif principal de la thèse est d'améliorer la compréhension des phénomènes de facettage observables lors des métamorphoses de la neige sèche.La thèse se concentre sur les couplages entre la cinétique de croissance cristalline et la diffusion de la vapeur et de la chaleur. Pour la première fois, la tomographie par contraste de diffraction (DCT) a été utilisée pour suivre l'évolution d'un échantillon de neige sous gradient de température contrôlé.La technique permet de mesurer l'orientation cristalline des grains constituant la microstructure de l'échantillon.Les relations entre l'orientation cristalline et les échanges de matière ont étés analysés. L'étude montre que les différences de cinétique entre les faces basales et prismatiques des cristaux de glace influencent les flux de matière à l'interface air/glace.Sur le plan de la simulation numérique, une forte anisotropie du coefficient cinétique a été prise en compte dans l'évolution de l'interface air/glace. Le modèle développé utilise la méthode du champ de phase et couple le changement de phase à la diffusion de la vapeur et de la chaleur.Le modèle a été comparé d'une part à une expérience de migration d'une cavité d'air dans un monocristal de glace sous gradient de température, observée par microtomographie à rayons X et d'autre part, à la croissance d'un cristal négatif de glace lors d'une expérience de pompage suivie par microscopie optique. L'anisotropie prise en compte permet de reproduire le facettage observé. Enfin, le potentiel du modèle numérique proposé pour décrire les métamorphoses de la neige est mis en évidence.

The main objective of the thesis is to improve our understanding of faceting occuring in dry snow metamorphism. The thesis focuses on the interplay between heat and mass diffusion and kinetic effects in the context of snow. For the first time,Diffraction Contrast Tomography (DCT) has been performed to monitor an experiment of temperature gradient metamorphism. The technique permits to retrieve the crystalline orientation of the grains constituting the microstructcure of the sample. Links between orientation of crystals and mass fluxres were analysed.The study shows that kinetic differences between basal and prismatic faces have effects on phase change fluxes at the ice/air interface.From a numerical modeling point of view, a highly anisotropic kinetic coefficient has been taken into account for the evolution of the ice/air interface. The model uses the phase-field approach and couples phase changes to heat and water vapor diffusion.The model was tested against an experiment of air cavity migration under temperature gradient in a monocrystalline ice block monitored with X-ray microtomography in one hand, and with the growth of a negative crystal during a pumping experiment followed with optical microscopy in the other hand.Such anisotropy permits to reproduce faceting as observed.Finally, the potential of the porposed model to describe snow metamorphism is highlighted., L'objectif principal de la thèse est d'améliorer la compréhension des phénomènes de facettage observables lors des métamorphoses de la neige sèche.La thèse se concentre sur les couplages entre la cinétique de croissance cristalline et la diffusion de la vapeur et de la chaleur. Pour la première fois, la tomographie par contraste de diffraction (DCT) a été utilisée pour suivre l'évolution d'un échantillon de neige sous gradient de température contrôlé.La technique permet de mesurer l'orientation cristalline des grains constituant la microstructure de l'échantillon.Les relations entre l'orientation cristalline et les échanges de matière ont étés analysés. L'étude montre que les différences de cinétique entre les faces basales et prismatiques des cristaux de glace influencent les flux de matière à l'interface air/glace.Sur le plan de la simulation numérique, une forte anisotropie du coefficient cinétique a été prise en compte dans l'évolution de l'interface air/glace. Le modèle développé utilise la méthode du champ de phase et couple le changement de phase à la diffusion de la vapeur et de la chaleur.Le modèle a été comparé d'une part à une expérience de migration d'une cavité d'air dans un monocristal de glace sous gradient de température, observée par microtomographie à rayons X et d'autre part, à la croissance d'un cristal négatif de glace lors d'une expérience de pompage suivie par microscopie optique. L'anisotropie prise en compte permet de reproduire le facettage observé. Enfin, le potentiel du modèle numérique proposé pour décrire les métamorphoses de la neige est mis en évidence.

The main objective of the thesis is to improve our knowledge about dry snow metamorphismand its physical description, at the microscopic (ice grains and pores) andmacroscopic (snow layer) scales. First, the homogenization method of multiple scaleexpansions is applied for the first time to the physics involved in dry snow metamorphism.This way, we present the equivalent macroscopic descriptions of heat and vaportransfers derived from the physical description at micro-scale. We consider at the grainscale diffusion, conduction, and forced convection, coupled to phase changes (sublimationand deposition). Second, the effective properties of transport arising in the macroscopicdescriptions (effective thermal conductivity, effective coefficient of vapor diffusion, andintrinsic permeability) are estimated from 3D images of snow spanning the whole range ofdensity and snow types. Finally, the monitoring of metamorphism with time is considered.The relationship between the microstructure and the effective properties of a snow layerare investigated during temperature gradient metamorphism using 3D images. We presentthen a new cryogenic cell that we developed to monitor the grain to grain evolution of asnow sample by time-lapse tomography during the metamorphism, and which operates atroom temperature.; L’objectif général de la thèse est de contribuer à l’amélioration de nos connaissances sur les métamorphoses de la neige sèche et sur sa description physique, à l’échelle microscopique (grains de glace et pores) et macroscopique (couche de neige). Dans un premier temps,la méthode d’homogénéisation basée sur les développements asymptotiques à échelles multiples est appliquée à la physique des métamorphoses de la neige sèche. On présente ainsi les descriptions macroscopiques équivalentes du transport de vapeur et de chaleur dérivées à partir de la description de la physique à micro-échelle. On considère à l’échelle des grains la diffusion, la conduction, et la convection forcée, couplées aux changements de phase (sublimation et déposition). Dans un second temps, les propriétés effectives de transport impliquées dans les descriptions macroscopiques (conductivité thermique effective, coefficient effectif de diffusion de vapeur et perméabilité intrinsèque) sont estimées à l’aide d’images 3D de neige couvrant toute la gamme de masse volumique et de types de neige. Enfin, on s’intéresse au suivi temporel des métamorphoses. Les liens entre la microstructure et les propriétés effectives d’une couche de neige sont mis en évidence au cours d’une métamorphose de gradient de température en utilisant des images 3D.On présente ensuite une cellule cryogénique que nous avons mise au point pour le suivi grains à grains par tomographie des évolutions d’un échantillon de neige au cours des métamorphoses, et qui s’utilise à température ambiante.