Measuring the Elastic Modulus of Snow

Gerling, Bastian; Löwe, Henning; Herwijnen, A. van

doi:10.1002/2017gl075110

Cited by 48 publications

(80 citation statements)

References 42 publications

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“…Hence, the single fibers should be viewed as small discrete snow cells. The elastic modulus E = 19 MPa we used for the FBM simulations is in agreement with the reported literature values (Gerling et al, 2017). In addition, the measurement method has a strong influence on the reported values.…”

Section: Model Calibrationsupporting

confidence: 88%

“…The method providing best results for the elastic properties of snow is based on measuring the propagation speed of acoustic waves, which induce deformations that are small and fast enough to be in the elastic range (Capelli et al, 2016). Gerling et al (2017) reported values of the elastic modulus in the range of 10-20 MPa for the density range of the weak layers of our samples (~170 kg/m 3 ). The elastic modulus E = 19 MPa we used for the FBM simulations is in agreement with the reported literature values (Gerling et al, 2017).…”

Section: Model Calibrationmentioning

confidence: 91%

“…We determined the elastic modulus and the viscosity fitting the stress strain relation and strain rate of the model to the measured curves for the lowest and fastest loading rate (see Figure 1) obtaining the best results with a characteristic relaxation time t r ¼ η E ¼ 2 s: Moreover, we compared the elastic modulus and viscosity used within the model with literature values of snow rather than ice since the strongly simplified structure of the FBM (unidirectional fibers) cannot reproduce the complexity of the ice structure of snow (Kirchner et al, 2001). Gerling et al (2017) reported values of the elastic modulus in the range of 10-20 MPa for the density range of the weak layers of our samples (~170 kg/m 3 ). Literature values of the elastic modulus of snow span over several orders of magnitude depending on snow density and type (e.g., Mellor, 1975).…”

Section: Model Calibrationmentioning

confidence: 99%

See 2 more Smart Citations

Modeling Snow Failure Behavior and Concurrent Acoustic Emissions Signatures With a Fiber Bundle Model

Capelli¹,

Reiweger

Schweizer³

2019

Geophysical Research Letters

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Snow failure is the result of gradual damage accumulation culminating in macroscopic cracks. The failure type strongly depends on the rate of the applied load or strain. Our aim was to study the microstructural mechanisms leading to the macroscopic loading rate dependence. We modeled snow failure and the concurrent acoustic emissions for different loading rates with a fiber bundle model and compared the model results to laboratory experiments. The fiber bundle model included two time‐dependent healing mechanisms opposing the loading‐induced damage process: (a) sintering of broken fibers and (b) relaxation of load inhomogeneities due to viscous deformation. The experimental acoustic emissions features could only be reproduced correctly if both healing mechanisms were included in the model. We conclude that both sintering and viscous deformation at a microscopic level essentially contribute to the macroscopic loading‐ and strain‐rate dependent behavior of snow.

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Section: Model Calibrationsupporting

confidence: 88%

Section: Model Calibrationmentioning

confidence: 91%

Section: Model Calibrationmentioning

confidence: 99%

See 1 more Smart Citation

Modeling Snow Failure Behavior and Concurrent Acoustic Emissions Signatures With a Fiber Bundle Model

Capelli¹,

Reiweger

Schweizer³

2019

Geophysical Research Letters

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“…In the prefailure stage, the elastic properties of snow have been subject to numerous experimental investigations (Gerling et al, ; Mellor, ; Narita, ) and were shown to be controlled by density as well as microstructural anisotropy. Failure of snow is generally considered to be governed by the Mohr‐Coulomb criterion (Chiaia et al, ; Fyffe & Zaiser, ; Gaume et al, ; McClung, ), where the shear strength increases linearly with the normal load.…”

Section: Introductionmentioning

confidence: 99%

Snow Failure Modes Under Mixed Loading

Mede

Chambon

Hagenmuller

et al. 2018

Geophysical Research Letters

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The mechanical response of snow to mixed‐mode shear and normal loading is the key ingredient for snow avalanche modeling and strongly depends on microstructural characteristics. A discrete element numerical model was developed, which enables the simulation of large‐strain response of snow samples directly described by their full microstructure obtained through X‐ray microtomography. The model offers new insights into the failure mechanism as well as postfailure response of snow in mixed‐mode loading. Three distinct failure modes are identified, depending on the value of applied normal stress. Above a certain threshold normal stress, the failure is characterized by a structural collapse that decomposes the snow sample into a set of cohesionless grains. It is shown that the collapse is a dynamic process, which, once initiated, develops independently of shearing. This behavior was consistently observed for different snow types, including faceted crystals typically composing weak layers.

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“…Our assumption is justifiable, since the formation of initial bonds between ice crystals in snow takes place almost immediately [29,30]. The further increase of bond strength in snow (resulting in an increase of strength and elastic modulus) occurs at a time scale beyond the time scale of the failure process we consider in the model [31,32].…”

Section: A Sinteringmentioning

confidence: 99%

Fiber-bundle model with time-dependent healing mechanisms to simulate progressive failure of snow

et al. 2018

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Snow is a heterogeneous material with strain-and/or load-rate-dependent strength. In particular, a transition from ductile-to-brittle failure behavior with increasing load rate is observed. The rate-dependent behavior can partly be explained with the existence of a unique healing mechanism in snow that stems from its high homologous temperature (temperature close to melting point). As soon as broken elements in the ice matrix get in contact, they start sintering and the structure may regain strength. Moreover, the ice matrix is subjected to viscous deformation, inducing a relaxation of local load concentrations and, therefore, further counteracting the damage process. Ideal tools for studying the failure process of heterogeneous materials are the fiber-bundle models (FBMs), which allow investigating the effects of basic microstructural characteristics on the general macroscopic failure behavior. We present an FBM with two concurrent time-dependent healing mechanisms: sintering of broken fibers and relaxation of load inhomogeneities. Sintering compensates damage by creating additional intact, load-supporting fibers which lead to an increase of the bundle strength. However, the character of the failure is not changed by sintering alone. With combined sintering and load relaxation, load is distributed from old stronger fibers to new fibers that carry fewer load. So as we additionally incorporated load redistribution to the FBM, the failure occurred suddenly without decrease of the order parameter-describing the amount of damage in the bundle-and without divergence of the fiber failure rate. Moreover, the b value, i.e., the power-law exponent of frequency-magnitude statistics of fibers breaking in load redistribution steps, at failure converged to b ≈ 2, a value higher than that of a classical FBM without healing (b = 3 2 ). These results indicate that healing, as the combined effect of sintering and load relaxation, changes the type of the phase transition at failure. This change of the phase transition is important for quantifying or predicting the failure (e.g., by monitoring acoustic emissions) of snow or other materials for which healing plays an important role.

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Measuring the Elastic Modulus of Snow

Cited by 48 publications

References 42 publications

Modeling Snow Failure Behavior and Concurrent Acoustic Emissions Signatures With a Fiber Bundle Model

Modeling Snow Failure Behavior and Concurrent Acoustic Emissions Signatures With a Fiber Bundle Model

Snow Failure Modes Under Mixed Loading

Fiber-bundle model with time-dependent healing mechanisms to simulate progressive failure of snow

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