Thermal fracturing on comets

Abstract

We simulate the stresses induced by temperature changes in a putative hard layer near the surface of comet 67P/Churyumov-Gerasimenko with a thermo-viscoelastic model. Such a layer could be formed by the recondensation or sintering of water ice (and dust grains), as suggested by laboratory experiments and computer simulations, and would explain the high compressive strength encountered by experiments on board the Philae lander. Changes in temperature from seasonal insolation variation penetrate into the comet’s surface to depths controlled by the thermal inertia, causing the material to expand and contract. Modelling this with a Maxwellian viscoelastic response on a spherical nucleus, we show that a hard, icy layer with similar properties to Martian permafrost will experience high stresses: up to tens of MPa, which exceed its material strength (a few MPa), down to depths of centimetres to a metre. The stress distribution with latitude is confirmed qualitatively when taking into account the comet’s complex shape but neglecting thermal inertia. Stress is found to be comparable to the material strength everywhere for sufficient thermal inertia (≳50 J m−2 K−1 s−1∕2) and ice content (≳45% at the equator). In this case, stresses penetrate to a typical depth of ~0.25 m, consistent with the detection of metre-scale thermal contraction crack polygons all over the comet. Thermal fracturing may be an important erosion process on cometary surfaces which breaks down material and weakens cliffs.

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

“…Sanderson (1978) treated ice as a non-Newtonian fluid with a generalized Glen-Nye rheology when he calculated the thermal stresses in near-surface glacial ice. Contrary to more recent studies on Martian permafrost, comets (e.g., Attree et al, 2017;Mellon, 1997), and lake ice (Petrich et al, 2015), Sanderson (1978) omitted elasticity since some experimental evidence suggested that "ice responds elastically only over a time scale of 5 to 10 s." We argue that this assumption is invalid and may lead to incorrect stress calculations. Furthermore, Petrich et al (2015) demonstrated that the measured thermal stresses in the ice cover of a reservoir are well reproduced using a viscoelastic rheology.…”

“…These observations suggest that the thickness of the debris mantle has a major influence on the observed glacier seismicity, which the present study aims to elucidate, with a particular emphasis on exploring the constitutive behavior of ice in order to explain the observed behavior, and the thickness of debris mantle that is sufficient to protect the ice from contraction fracturing in a given environmental setting. This in situ experiment presents an interesting test case for validating the existing theory on ice fracture and crevasse formation with the ability to compare the data against two different approaches to ice constitutive behaviour: that is, with or without elasticity (e.g., Attree et al, 2017;Sanderson, 1978;Zhang et al, 2019).…”

“…where the superscript V indicates the viscous component, . i V is the strain rate tensor, A o is a prefactor of the creep parameter, Q is the temperature-dependent activation energy for creep, R is the gas constant, T is the temperature relative to the pressure melting point (in K; Greve & Blatter, 2009), E is the effective stress (with a creep exponent n = 3 as the most widely accepted preference over the range of 1-4.7; e.g., Attree et al, 2017;Cuffey & Paterson, 2010;Petrich et al, 2015), and ij is the stress deviator ( i = i − 1 3 kk i ). Sanderson (1978) assumed an infinite plain geometry to derive the thermal stresses, where the thermal volumetric changes were laterally restrained (a "rigid box"), employing only the stresses necessary to resist motion to address the observed expansion or contraction.…”

“…Several viscoelastic models were proposed to describe ice, including a Maxwell material, a Rivlin-Ericksen material, and an approach inspired by Fiber-Bundle models (e.g., Christmann et al, 2019;Keller & Hutter, 2014;Riesen et al, 2010). Here, we add an elastic term to the Maxwellian thermoviscoelastic model (e.g., Attree et al, 2017;Mellon, 1997) and omit the gross strain rate for simplicity, based on our previous arguments that they are negligible. The model assumes ice as a Maxwellian viscoelastic solid with its elastic and viscous behaviors acting in series (Mellon, 1997); this is reasonable since a "series" approach allows a purely viscous response to infinite strain.…”

“…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.…”