Time-dependent spatial distribution of thermal stresses in the ice cover of a small reservoir

Petrich, Chris; Sæther, Irina Vasiljeva; Fransson, Lennart; Sand, Bjørnar; Arntsen, Bård

doi:10.1016/j.coldregions.2015.09.003

Cited by 16 publications

(33 citation statements)

References 9 publications

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“…Similarly, Nishio (1983) estimated that fracturing in dense glazed snow occurs at 40 kPa, which is lower than the tensile fracture strength of hard snow or firn (∼300 kPa). These observations confirm the idea that the local mechanical properties of ice and snow, in combination with the presence of defects, may lead to fracturing at relatively small stresses (e.g., thermal stresses; Lewis, 1993;Petrich et al, 2015) that are only ∼15% of the material strength.…”

Section: Introductionsupporting

confidence: 82%

“…Modeled stress profiles (elastic for debris and viscoelastic for ice; after Petrich et al, ; equation ) compared with the observed seismicity, expressed as noise power, at the four sites. The red and blue curves for the debris‐covered sites (C1 and C2) represent the average depth‐integrated stresses,

\overset{τ}{true}

, near the debris and ice surfaces, respectively.…”

Section: Resultsmentioning

confidence: 99%

“…This asymmetry means that the stresses during warm temperatures will be lower than those during cold temperatures. Petrich et al () reported that this temperature dependence of the creep rate is crucial for reproducing thermal stresses measurements in warm ice (above −10 °C).…”

Section: Thermal Stress Modelmentioning

confidence: 99%

“…Finally, we also compute the thermoviscoelastic stresses using an empirical model developed to estimate horizontal thermal stresses in the ice cover of a reservoir (Petrich et al, ):

\overset{τ}{true} = false(1 - C T false) ([], A \frac{\partial T}{\partial t} - sign false(τ false) B {((), \frac{T_{1}}{T_{1} - T})}^{m} {((), \frac{τ}{τ_{0}})}^{n}),

where A =131×10 3 Pa/°C and B =27∼24,000×10 3 Pa/day are the determined best fit parameters, τ 0 =100×10 3 Pa is an arbitrary reference for dimensional consistency, T 1 =−1 °C and m =1.92 are constants, C =0.012 °C −1 corresponds to the temperature dependence of Young's modulus, and sign ( τ ) is used to preserve the sign, which is independent of n ( n =3 for the current set of parameters). Contrary to all the other spatially independent parameters, B is known to include spatially dependent effects that are potentially due to the boundary conditions and crack patterns (Petrich et al, ). Extensive modeling and a literature review by Petrich et al () indicated that B decreased toward the center of a small, 30‐m‐wide reservoir (from 24,000 to 340 kPa/day), while B was significantly smaller (27 kPa/day) for an essentially laterally unconstrained setting.…”

Section: Thermal Stress Modelmentioning

confidence: 99%

“…Thermal strains induce near-surface thermal stresses, which are recognized as an important agent in various processes. For example, the thermal stress in ice cover is important for dam design (Petrich et al, 2015), can cause large-scale fractures in sea ice (Bazant, 1992;Evans & Untersteiner, 1971;Lewis, 1994;Xie & Farmer, 1991) and lake ice (Carmichael et al, 2012), is responsible for polygon formation in permafrost Journal of Geophysical Research: Earth Surface 10.1029/2018JF004848 on Earth and Mars (Lachenbruch, 1962;Levy et al, 2009;Mellon, 1997;O'Neill & Christiansen, 2018), and is suggested to be an important erosion process on cometary surfaces and the Moon (e.g., Attree et al, 2017). Sanderson (1978) conducted analytic investigations of thermal stresses near glacial surfaces and concluded that (i) in the upper 3 m of the ice, thermal stresses dominate those originating from the overburden pressure and from the gross deformation; (ii) tensile fracture cannot develop in pure ice due to its high tensile strength, unless assisted by stress concentrations at heterogeneities; and (iii) such fractures are more likely to form in weaker firn and snow.…”

Section: Introductionmentioning

confidence: 99%

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Viscoelastic Modeling of Nocturnal Thermal Fracturing in a Himalayan Debris‐Covered Glacier

et al. 2019

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Recent observations suggest that the nocturnal thermal fracturing of ice occurs at relatively warm temperatures (above −15 °C) at a high‐altitude Himalayan glacier system unless the ice is shielded by a debris mantle. Here we estimate the stresses induced by diurnal temperature variations using viscous, elastic, and two viscoelastic models, and various thicknesses of the debris mantle. Only the elastic and visco‐elastic models are in agreement with the observations. The timing and amplitudes of the stresses in the upper 15 cm of the glacier are different among the models despite the ability of each approach to predict a diurnal increase in tension exceeding the critical threshold proposed for crevasse formation. For example, the elastic stress is several times larger than the viscous stress at the ice surface (650 vs. 250 kPa) and reaches its peak up to 5–6 hr later in the night. The time lag is in line with the seismic records, suggesting that the viscous model is not appropriate. Furthermore, a debris layer of ≥50 cm in thickness suppresses the diurnal fluctuations in thermal stress and therefore protects the ice from mechanical damage. We suggest that high‐amplitude diurnal cooling and weak ice properties due to weathering are essential factors that influence thermal fracturing in the Himalayan environment. The ongoing expansion of seismic networks into cryospheric regions, which will be capable of detecting local thermal‐contraction‐induced cracks, in combination with the fact that such cracks can erode and weaken the ice, and thereby serve as meltwater and heat channels, warrants further research to better understand these near‐surface processes and to monitor ice properties.

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Section: Introductionsupporting

confidence: 82%

\overset{τ}{true}

, near the debris and ice surfaces, respectively.…”

Section: Resultsmentioning

confidence: 99%

Section: Thermal Stress Modelmentioning

confidence: 99%

“…Finally, we also compute the thermoviscoelastic stresses using an empirical model developed to estimate horizontal thermal stresses in the ice cover of a reservoir (Petrich et al, ):