Compression of snow at low strain rates governs the natural densification of snow and firn on Earth. Different deformation mechanisms (e.g., grain boundary sliding and dislocation creep) are widely ...employed in models and are mainly believed to change depending on relative density or snow type. To explore this picture, we conducted compression experiments with a nominally constant strain rate ɛ̇≈10−6s−1 and systematically varied snow type, density, and specific surface area. We used a micro-compression stage to enable X-ray micro-tomography imaging and microstructure characterization before and after the experiment. Using repeated load-relaxation cycles, we eliminate changes in the microstructure that occur during the first loading, allowing us to probe the viscoplastic behavior of the intact ice matrix. To evaluate the effective mechanical behavior of snow, we derived an implicit, analytical solution of a non-linear scalar model that characterizes loading and relaxation in terms of the stress exponent n in Glen’s law. Our results evidence a sharp transition of n as a function of the geometrical grain size, and rule out that this transition is caused by density or snow type. The derived values of n≈1.9 for small grains to n≈4.4 for large grains are consistent with a transition from grain boundary sliding to dislocation creep at a transition grain size of around 0.5-0.6 mm. Our results shed new light on the old discussion about deformation mechanisms in snow and firn.
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•Consecutive loading-relaxation experiments complemented by micro-CT were employed.•Experiments allow probing the viscoplastic behavior of the intact ice matrix in snow.•We evaluated experiments to estimate Glen’s law stress exponent and time scales.•The geometrical grain size drives transition in Glen’s law exponent n for snow.•n transits from n≈1.9 (fine grains) to n≈4.4 (coarse grains) in snow.•This transition is interpreted as a transition from GBS (n≈1.9) to DC (n≈4.4).
Through stochastic-numerical microstructure-based experiments, the plastic consolidation under compression of porous brittle solids, with porosities from 0.25 to 0.75 and a large variety of ...microstructural characteristics, has been investigated. This was made possible by generating microstructures from Gaussian random fields in order to obtain stochastic ensembles of structures with prescribed properties, which are then simulated within the material point method. Below a critical imposed strain rate, the consolidation behavior is found to be very weakly affected by the degree of heterogeneity and anisotropy. Structures where the solid phase takes up more space than the void phase have a consolidation response approximately independent of the structural geometry and dimensionality (comparing two- and three-dimensional structures). Finally, we show that the consolidation of two-dimensional structures collapses on a single master curve that can be described by a simple function similar to one presented for a completely different system, namely a system of interacting discrete cohesive disks. In this function, we report a universal parameter largely independent of material specifications.
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The Snow Microwave Radiative Transfer (SMRT) thermal emission and backscatter model was developed to determine uncertainties in forward modeling through intercomparison of different model ...ingredients. The model differs from established models by the high degree of flexibility in switching between different electromagnetic theories, representations of snow microstructure, and other modules involved in various calculation steps. SMRT v1.0 includes the dense media radiative transfer theory (DMRT), the improved Born approximation (IBA), and independent Rayleigh scatterers to compute the intrinsic electromagnetic properties of a snow layer. In the case of IBA, five different formulations of the autocorrelation function to describe the snow microstructure characteristics are available, including the sticky hard sphere model, for which close equivalence between the IBA and DMRT theories has been shown here. Validation is demonstrated against established theories and models. SMRT was used to identify that several former studies conducting simulations with in situ measured snow properties are now comparable and moreover appear to be quantitatively nearly equivalent. This study also proves that a third parameter is needed in addition to density and specific surface area to characterize the microstructure. The paper provides a comprehensive description of the mathematical basis of SMRT and its numerical implementation in Python. Modularity supports model extensions foreseen in future versions comprising other media (e.g., sea ice, frozen lakes), different scattering theories, rough surface models, or new microstructure models.
Porous brittle solids evidence complex mechanical behavior, where localized failure patterns originate from mechanical processes on the microstructural level. In order to investigate the failure ...mechanics of porous brittle solids, we outline a general stochastic and numerical microstructure-based approach. To this end, we generate random porous microstructures by level-cutting Gaussian random fields, and conduct numerical simulations using the material point method. This allows investigating both small and large deformation characteristics of irregular porous media where a segmentation into grains and bonds is ambiguous. We demonstrate the versatility of our approach by examining elasticity and failure as a function of a wide range of porosities, from 20% to 80%. Observing that onset of failure can be well described through the second order work, we show that the stress at failure follows a power law similar to that of the elastic modulus. Moreover, we propose that the failure envelope can be approximated by a simple quadratic fitting curve, and that plastic deformation appears to be governed by an associative plastic flow rule. Finally, large deformation simulations reveal a transition in the mode of localization of the deformation, from compaction bands for highly porous samples to shear bands for denser ones.
Abstract
Porous brittle solids have the ability to collapse and fail even under compressive stresses. In fracture mechanics, this singular behavior, often referred to as anticrack, demands for ...appropriate continuum models to predict the catastrophic failure. To identify universal controls of anticracks, we link the microstructure of a porous solid with its yield surface at the onset of plastic flow. We utilize an assembly method for porous structures, which allows to independently vary microstructural properties (density and coordination number) and perform discrete element simulations under mixed-mode (shear-compression) loading. In rescaled stress coordinates, the concurrent influence of the microstructural properties can be cast into a universal, ellipsoidal form of the yield surface that reveals an associative plastic flow rule, as a common feature of these materials. Our results constitute a constructive approach for continuum modeling of anticrack nucleation and propagation in highly porous brittle, engineering and geo-materials.
Precise measurements of snow structural parameters are crucial to understand the formation of snowpacks by deposition and metamorphism and to characterize the stratigraphy for many applications and ...remote sensing in particular. The area‐wide acquisition of structural parameters at high spatial resolution from state‐of‐the‐art methods is, however, still cumbersome, since the time required for a single profile is a serious practical limitation. As a remedy we have developed a statistical model to extract three major snow structural parameters: density, correlation length, and specific surface area (SSA) solely from the SnowMicroPen (SMP), a high‐resolution penetrometer, which allows a meter profile to be measured with millimeter resolution in less than 1 min. The model was calibrated by combining SMP data with 3‐D microstructural data from microcomputed tomography which was used to reconstruct full‐depth snow profiles from different snow climates (Alpine, Arctic, and Antarctic). Density, correlation length, and SSA were derived from the SMP with a mean relative error of 10.6%, 16.4%, and 23.1%, respectively. For validation, we compared the density and SSA derived from the SMP to traditional measurements and near‐infrared profiles. We demonstrate the potential of our method by the retrieval of a two‐dimensional stratigraphy at Kohnen Station, Antarctica, from a 46 m long SMP transect. The result clearly reveals past depositional and metamorphic events, and our findings show that the SMP can be used as an objective, high‐resolution tool to retrieve essential snow structural parameters efficiently in the field.
Key Points
Statistical model relating micro‐CT structure to SMP force for many snow data
New method to retrieve density, correlation length, and SSA in the field
Efficient retrieval of spatial variability and 2‐D stratigraphy of snow
The structural evolution of snow under metamorphism is one of the key challenges in snow modeling. The main driving forces for metamorphism are curvature differences and temperature gradients, ...inducing water vapor transport and corresponding crystal growth, which is detectable by the motion of the ice/air interface. To provide quantitative means for a microscopic validation of metamorphism models, a VTK-based image analysis method is developed to track the ice/air interface in time-lapse μCT experiments to measure local interface velocities under both, isothermal and temperature gradient conditions. Using estimates of local temperatures from microstructure-based finite element simulations, a quantitative comparison of measured interface velocities with theoretical expressions is facilitated. For isothermal metamorphism, the data are compared with a kinetics and a diffusion limited growth law. In both cases the data are largely scattered but consistently show a mean curvature dependency of the interface velocity. For temperature gradient metamorphism, we confirm that the main contribution stems from the temperature gradient induced vapor flux, accompanied by effects of mean curvature as a secondary process. The scatter and uncertainties are discussed in view of the present theoretical understanding, the experimental setup and complications such as mechanical deformations.
Despite being one of the most fundamental microstructural parameters of snow, the specific surface area (SSA) dynamics during temperature gradient metamorphism (TGM) have so far been addressed only ...within empirical modeling. To surpass this limitation, we propose a rigorous modeling of SSA dynamics using an exact equation for the temporal evolution of the surface area, fed by pore-scale finite-element simulations of the water vapor field coupled with the temperature field on X-ray computed tomography images. The proposed methodology is derived from the first principles of physics and thus does not rely on any empirical parameter. Since the calculated evolution of the SSA is highly sensitive to fluctuations in the experimental data, we quantify the impact of these fluctuations within a stochastic error model. In our simulations, the only poorly constrained physical parameter is the condensation coefficient α. We address this problem by simulating the SSA evolution for a wide range of α values and estimate optimal values by minimizing the differences between simulations and experiments. This methodology suggests that α lies in the intermediate range 10-3<α<10-1 and slightly varies between experiments. Also, our results suggest a transition of the value of α in one TGM experiment, which can be explained by a transition in the underlying surface morphology. Overall, we are able to reproduce very subtle variations in the SSA evolution with correlations of R2=0.95 and 0.99, respectively, for the two TGM time series considered. Finally, our work highlights the necessity of including kinetic effects and of using realistic microstructures to comprehend the evolution of SSA during TGM.
Snow appears as a granular material in most engineering applications. We examined the role of grain shape and cohesion in angle of repose experiments, which are a common means for the ...characterization of granular materials. The role of shape was examined by investigating diverse snow types with discernable shape and spherical ice beads. Two geometrical shape parameters were calculated from X-ray micro-computed-tomography images after a particle segmentation was performed with a watershed algorithm. Cohesion was examined by conducting experiments at six different temperatures between −40 and −2°C, assuming sintering as its cause, which accelerates with increasing temperature. As a cohesionless reference, experiments with glass beads were performed. We found that both shape and cohesion exerted about equally strong influence on the angle of repose. We utilized our results for an empirical model that describes the influence of shape and cohesion as additive corrections of the angle of repose of cohesionless spheres and explains all experiments with a correlation coefficient r2 = 0.95. With temperature and the chosen shape parameter as fitting variables, previous experiments with another snow type could be consistently included. The experiments highlight the relevance of these parameters in granular snow mechanics and can be used for model calibration.
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