Sugar as Snow Analog in Penetration Testing: History
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Adrian McCallum

Understanding the mechanical properties of snow and ice is necessary for the efficient design and construction of cold regions infrastructure. Testing and evaluation is most commonly undertaken in situ or using samples within cold labs. However, there is an inevitable uncertainty as to the accuracy of results obtained from ex situ testing. Therefore, development of suitable proxies for snow, such as sugar or foam, is valuable, potentially enabling further research in this field.

  • snow
  • sugar
  • penetration testing

1. Introduction

Understanding the mechanical properties of snow and ice is necessary for the efficient design and construction of cold regions infrastructure. Testing and evaluation is most commonly undertaken in situ or using samples within cold labs. However, there is an inevitable uncertainty as to the accuracy of results obtained from ex situ testing. Therefore, development of suitable proxies for snow, such as sugar or foam, is valuable, potentially enabling further research in this field. Snow has been specifically considered as a foam or a cellular solid by Brown [1], Petrovic [2] and others including Johnson [3]; Kirchner et al. [4] particularly examined the use of foam as a mechanical proxy for snow. Sugar is a crystalline particulate that sinters or bonds within different humidity environments, and fractures upon penetration; could sugar be a viable analogue for snow, for the purposes of mechanical testing?

2. Background

Blackford [5], in her review of ice, defined sintering as a thermal treatment for bonding particles into a coherent, predominantly solid structure via mass transport events that often occur on the atomic scale and Paterson [6] said that sintering of ice and snow is driven by the thermodynamical requirement to decrease surface energy, inducing an increase in both density and strength. The initial stages involve the transformation of the snow ice crystals into a spherical form. Because the radius of an ice particle is larger than the concave radius of the bond joining it to an adjacent ice particle, there is a driving force to move mass to this concave neck area. Two previously spherical particles start tending towards a dumb-bell shaped particle joined by a neck; this bonding leads to improved strength and a lower energy system [7].
This process of mass distribution occurs throughout the sintering process. When this process occurs under additional pressure such as when snow is buried owing to accumulation, it is termed pressure sintering, and the rate of sintering is increased. Material densification results from the sintering process; however, Alley [8] clarifies that although numerous processes occur throughout the pressure sintering process, not all contribute to densification. Herron and Langway [9] identified three main phases in the densification process: settling and packing of particles, pore-space reduction, then pore-space closure. In snow, the densification process slows down in each stage, and also occurs intermittently throughout the year, depending on accumulation rates [10]. This process of intermittent densification was recently demonstrated by Einav and Guillard [11] using rice crispies and was previously described as self-organised criticality by Sammonds [12].
The primary mechanical observation to be drawn from this discussion is that the strength of snow is controlled by the size of the bonds formed between grains through sintering [13] and that the rate and amount of sintering occurs at different rates under varying environmental conditions.
The increase in snow strength attained over time can be assessed in various ways [14]. One of the most efficient means is penetration testing. Schneebeli [15] has extensively examined the strength of snow undergoing penetration with a micro-penetrometer and McCallum [16] has examined such behaviour using a friction-sleeve-equipped cone penetrometer. More recently, Peinke et al. [17] examined snow sintering at microscopic and macroscopic scales with high-resolution cone penetration tests. They showed that macroscopic penetration force increased over time due to microstructural bond strengthening.
In the absence of snow, other analogues have served as a proxy to describe the behaviour of snow under mechanical testing; these include:
  • Sintered metal. Snow can be considered as a sintered material such as a metal, where, under stress, the usual fracture of the sintered necks takes place, as for most porous material [18]. This behaviour is consistent with the failure mechanism for snow described by Mellor [19].
  • Geomaterials. Leroueil and Vaughan [20] showed that deposits normally treated as soils usually have characteristics due to bonded structure which are similar to those of porous weak rock, resulting in mechanically stiff behaviour followed by yield. They showed that such characteristics are common in natural geological materials and that it is the structure of weak rock and cemented sands that gives them their strength. This structure, arising from different causes, gives similar behaviour in many different materials including snow [20].
  • Sedimentary material. Snow has historically been viewed specifically as a sedimentary material (Benson [21], Pielmeier and Schneebeli [22] and Schweizer et al. [23] amongst others) that ultimately may develop structure and thus behave in accordance with Leroueil and Vaughan’s supposition [20] above.
  • Porous Rock. Leite and Ferland [24], in their work on the indentation of porous material, note linear elasticity, yielding and structural collapse at a critical value, and strain hardening as the crushed material is compacted; all these behaviours are observed in the penetration of snow (of certain density). Tharp [25], in his work on polyphase rocks, suggests that incompetent phases (essentially non-load-bearing phases such as air) within a material result in the load-carrying framework behaving much like a porous solid, and snow has been considered as such by numerous authors including Brown [1], Kirchner et al. [4], and Petrovic [2].
  • Foam. Snow has been specifically considered as a foam or a cellular solid by Brown [1], Kirchner et al. [4], Petrovic [2] and others including Johnson [3]. In his work on a statistical micromechanical theory for penetration in granular materials, Johnson [3] draws upon initial work presented by Gibson and Ashby [26], who examine the behaviour of foam under penetration in their review of the behaviour of cellular solids. Examination of Gibson and Ashby’s work [26] suggests that below the pore close-off density of ∼840 kg m−3, snow might be regarded as an open-cellular foam, whilst above this density, description as a closed-cellular foam may be appropriate.
  • Polycrystalline ice. The main constituent of dry snow is ice, thus snow’s behaviour must tend towards that of polycrystalline ice as density increases. Nicot [27] states that on the microscopic scale, the behaviour of grain bonds (within snow) is governed by the behaviour of ice, Gubler [28] describes the load-bearing capacity of snow in terms of ice chains, and Bartelt and von Moos [29] note the straining of the ice lattice within snow during triaxial testing. Graphs of stress versus strain rate generated by Kinosita [30] through loading of snow are almost identical in form to those presented by Schulson [31] for polycrystalline ice.

3. Sugar as an Analogue for Snow?

Sugar is a synthesised organic material available in several shapes and sizes [32]. Raw sugars are refined and softened by removing the molasses coating through the process of affination [33]. The resulting syrup is then processed by precipitating and filtering solids in the syrup, then the liquor is spun using a centrifuge, separating the white crystals from the solution. These white crystals are dried in hot air and can then be used or packaged [34].
When stored in a sealed container, bonding between sugar grains is not evident [35]. However, when stored in a high humidity environment, sugar crystals bond; Bagster [36] speculated that these intergranular bonds form via crystalline bridging. Bagster [35] demonstrated an increase in raw sugar shear strength over time (out to ∼100 days), in a constant humidity environment. Zafar et al. [37] showed that sintering in a ’powder’ such as sugar is influenced by time, temperature and moisture, and that increased bonding will result in an increase in material strength, similar to what is observed in dry snow.

This entry is adapted from the peer-reviewed paper 10.3390/powders1010004

References

  1. Brown, R.L. A Volumetric Constitutive Law for Snow Subjected to Large Strains and Strain Rates; Technical Report 79-20; US Army Cold Regions Research and Engineering Laboratories: Hanover, Germany, 1979.
  2. Petrovic, J.J. Mechanical properties of ice and snow. J. Mater. Sci. 2003, 38, 1–6.
  3. Johnson, J.B. A Statistical Micromechanical Theory of Cone Penetration in Granular Materials; Technical Report ERDC/CRREL TR-03-3; Cold Regions Research and Engineering Laboratory: Hanover, Germany, 2003.
  4. Kirchner, H.O.K.; Michot, G.; Narita, H.; Suzuki, T. Snow as a foam of ice: Plasticity, fracture and the brittle-to-ductile transition. Philos. Mag. A 2001, 81, 2161.
  5. Blackford, J.R. Sintering and microstructure of ice: A review. J. Phys. D Appl. Phys. 2007, 40, R355–R385.
  6. Paterson, W. The Physics of Glaciers, 3rd ed.; Elsevier Science Ltd.: Oxford, UK, 1994.
  7. German, R.M. Sintering Theory and Practice; Wiley Interscience: New York, NY, USA, 1996.
  8. Alley, R.B. Firn Densification by Grain-boundary sliding: A 1st Model. J. Phys. 1987, 48, 249–256.
  9. Herron, M.M.; Langway, C.C. Firn densification—An empirical-model. J. Glaciol. 1980, 25, 373–385.
  10. Mellor, M. A Review of Basic Snow Mechanics. In International Symposium on Snow Mechanics; International Association of Hydrological Sciences Publication 114, International Association of Hydrological Sciences: Grindewald, Switzerland, 1975; pp. 251–291.
  11. Einav, I.; Guillard, F. Tracking time with ricequakes in partially soaked brittle porous media. Sci. Adv. 2018, 4, eaat6961.
  12. Sammonds, P.R. Deformation dynamics: Plasticity goes supercriticial. Nat. Mater. 2005, 4, 425–426.
  13. Colbeck, S.C. Sintering in a dry snow cover. J. Appl. Phys. 1998, 84, 4585–4589.
  14. Abele, G. Snow Roads and Runways; Technical Report 90-3; US Army Cold Regions Research and Engineering Laboratory: Hanover, Germany, 1990.
  15. Schneebeli, M.; Pielmeier, C.; Johnson, J.B. Measuring snow microstructure and hardness using a high resolution penetrometer. Cold Reg. Sci. Technol. 1999, 30, 101.
  16. McCallum, A.B. Direct estimation of snow density from CPT. In 3rd International Symposium on Cone Penetration Testing; Robertson, P.K., Cabal, K.I., Eds.; ISSMGE Technical Committee TC 102: Las Vegas, NV, USA, 2014; pp. 583–590.
  17. Peinke, I.; Hagenmuller, P.; Chambon, G.; Roulle, J. Investigation of snow sintering at microstructural scale from micro-penetration tests. Cold Reg. Sci. Technol. 2019, 162, 43–55.
  18. Tancret, F.; Osterstock, F. Modelling the toughness of porous sintered glass beads with various fracture mechanisms. Philos. Mag. 2003, 83, 137–150.
  19. Mellor, M. Snow mechanics. Appl. Mech. Rev. 1966, 19, 379–389.
  20. Leroueil, S.; Vaughan, P.R. The general and congruent effects of structure in natural soils and weak rocks. Geotechnique 1990, 41, 467–488.
  21. Benson, C.S. Stratigraphic Studies in the Snow and Firn of the Greenland Ice Sheet; Research Report 70; US Army Snow, Ice and Permafrost Research Establishment: Hanover, Germany, 1962.
  22. Pielmeier, C.; Schneebeli, M. Stratigraphy and changes in hardness of snow measured by hand, ramsonde and snow micro penetrometer: A comparison with planar sections. Cold Reg. Sci. Technol. 2003, 37, 393–405.
  23. Schweizer, J.; Heilig, A.; Bellaire, S.; Fierz, C. Variations in snow surface properties at the snowpack-depth, the slope and the basin scale. J. Glaciol. 2008, 54, 846–856.
  24. Leite, M.H.; Ferland, F. Determination of unconfined compressive strength and Young’s modulus of porous materials by indentation tests. Eng. Geol. 2001, 59, 267.
  25. Tharp, T.M. Analogies between the high-temperature deformation of polyphase rocks and the mechanical behavior of porous powder metal. Tectonophysics 1983, 96, T1–T11.
  26. Gibson, L.J.; Ashby, M.F. Cellular Solids—Structure and Properties, 2nd ed.; Cambridge University Press: Cambridge, UK, 1997.
  27. Nicot, F. Constitutive modelling of snow as a cohesive-granular material. Granul. Matter 2004, 6, 47–60.
  28. Gubler, H. Determination of the mean number of bonds per snow grain and of the dependence of the tensile strength of snow on stereological parameters. J. Glaciol. 1978, 20, 329–341.
  29. Bartelt, P.; von Moos, M. Triaxial tests to determine a microstructure-based snow viscosity law. Ann. Glaciol. 2000, 31, 457–462.
  30. Kinosita, S. Compression of snow at constant speed. Phys. Snow Ice Proc. 1967, 1, 911–927.
  31. Schulson, E.M. Brittle failure of ice. Eng. Fract. Mech. 2001, 68, 1839.
  32. Mao, B.; Zhang, F.L. Effect of granulated sugar as pore former on the microstructure and mechanical properties of the vitrified bond cubic boron nitride grinding wheels. Mater. Des. 2014, 60, 328–333.
  33. Rahman, A.; Kamel, A. New Trends in the Clarification Process in the Sugar Industry. In Proceedings of the International Conference on ‘Arab Region and Africa in the World Sugar Context’, Aswan, Egypt, 9–12 March 2003.
  34. Short, S.W.; Bocken, N.P.; Barlow, C.Y.; Chertow, M.R. From refining sugar to growing tomatoes. Ind. Ecol. Bus. Model Evol. 2014, 18, 603–618.
  35. Bagster, D.F. A Study of the Caking Behaviour of Raw Sugar under Storage. J. Bulk Solids Handl. 1985, 5, 437–441.
  36. Bagster, D.F. The anomalous flow properties of raw sugar under storage. In Proceedings of Australian Society of Sugar Cane Technologists (ASSCT), Townsville, Australia, 19–23 April 1982.
  37. Zafar, U.; Vivacqua, V.; Calvert, G.; Ghadiri, M.; Cleaver, J. A review of bulk powder caking. Powder Technol. 2017, 313, 389–401.
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