Thermal stress weathering and the spalling of Antarctic rocks · 2017-04-05 · Thermal stress...

Thermal stress weathering and the spallingof Antarctic rocksJ. L. Lamp1 , D. R. Marchant1, S. L. Mackay1, and J. W. Head2

1Department of Earth and Environment, Boston University, Boston, Massachusetts, USA, 2Department of Earth,Environmental and Planetary Sciences, Brown University, Providence, Rhode Island, USA

Abstract Using in situ field measurements, laboratory analyses, and numerical modeling, we test thepotential efficacy of thermal stress weathering in the flaking of millimeter-thick alteration rinds observed oncobbles and boulders of Ferrar Dolerite on Mullins Glacier, McMurdo Dry Valleys (MDV). In particular, weexamine whether low-magnitude stresses, arising from temperature variations over time, result in thermalfatigue weathering, yielding slow crack propagation along existing cracks and ultimate flake detachment. Ourfield results show that during summermonths clasts of Ferrar Dolerite experience large-temperature gradientsacross partially detached alteration rinds (>4.7°Cmm�1) and abrupt fluctuations in surface temperature(up to 12°Cmin�1); the latter are likely due to the combined effects of changing solar irradiation and coolingfrom episodic winds. The results of our thermal stress model, coupled with subcritical crack growth theory,suggest that thermal stresses induced at the base of thin alteration rinds ~2mm thick, common on rocksexposed for ~105 years, may be sufficient to cause existing cracks to propagate under present-daymeteorological forcing, eventually leading to rind detachment. The increase in porosity observed withinalteration rinds relative to unaltered rock interiors, as well as predicted decreases in rind strength based onallied weathering studies, likely facilitates thermal stress crack propagation through a reduction of fracturetoughness. We conclude that thermal stress weathering may be an active, though undervalued, weatheringprocess in hyperarid, terrestrial polar deserts such as the stable upland region of the MDV.

1. Introduction

The spalling or detachment of thin flakes from exposed rock surfaces is an important erosional process oper-ating across a range of rock types and climatic settings. Understanding the precise mechanisms responsiblefor spalling helps elucidate rates of long-term erosion and landscape evolution [Marchant et al., 2013]; assistsin the development of process models used to interpret the inventory of cosmogenic nuclides in surfacerocks [Gordon and Dorn, 2005; Gunnell et al., 2013; Mackay and Marchant, 2016; Muzikar, 2008, 2009]; anddocuments the potential for degradation of building stones, rock art, and monuments [Benito et al., 1993;Cardell et al., 2003; Hall et al., 2007; McCabe et al., 2013; Mol and Viles, 2010].

Although the primary geomorphic processes that lead to spalling vary with target lithology and local climate,candidate processes typically include oscillations in near-surface moisture and rock-surface temperature. Forporous rocks located in temperate regions, spalling may be facilitated through the freezing of pore water, thehydration of clays, the crystallization, and subsequent hydration of salts [Matsuoka, 2008; Matsuoka andMurton, 2008] or thermal stresses [Aldred et al., 2016; Collins and Stock, 2016; Eppes et al., 2016; McFaddenet al., 2005;Walsh and Lomov, 2013]. In the polar desert environment of the Transantarctic Mountains, wherethe climate is exceedingly cold and dry, the detachment of millimeter-thick flakes from exposed rock surfacesis thought to arise in part from thermal stress weathering [Campbell and Claridge, 1987; Hall, 1999], althoughno detailed quantitative studies have yet examined the process in this end-member environment.

Thermal stress weathering is defined as rock breakdown that occurs via expansion and/or contractioninduced by heating and/or cooling. In geomorphology, the Sun [e.g., Eppes et al., 2010; Eppes et al., 2016;McFadden et al., 2005; Molaro et al., 2015], forest fires [e.g., Blackwelder, 1927; Dorn, 2003; Kendrick et al.,2016], and lightning strikes [e.g., Knight and Grab, 2014; Wakasa et al., 2012] are the most commonly citedagents of rock surface heating; additional processes including wind and cloud cover act to cool rock surfaces[Molaro and McKay, 2010] and have been observed to cause cracking [Eppes et al., 2016]. The breakdown ofrock via thermal stress weathering is frequently attributed to one of two mechanisms [Hall and Thorn, 2014]:thermal shock, which causes rapid failure as the result of a sudden, high-amplitude temperature event or

LAMP ET AL. THERMAL SPALLING OF ANTARCTIC ROCKS 3

PUBLICATIONSJournal of Geophysical Research: Earth Surface

RESEARCH ARTICLE10.1002/2016JF003992

Key Points:• Antarctic dolerite clasts experiencelarge temperature gradients and fastfluctuations in surface temperature

• Thermal fatigue weathering likelycontributes to the spalling and flakingof dolerite boulders in Antarctica

• Alteration rinds on dolerite clastsallow for local weakening andsubcritical crack propagation underthermal stress

Supporting Information:• Supporting Information S1

Correspondence to:J. L. Lamp,[email protected]

Citation:Lamp, J. L., D. R. Marchant, S. L. Mackay,and J. W. Head (2017), Thermal stressweathering and the spalling of Antarcticrocks, J. Geophys. Res. Earth Surf., 122,3–24, doi:10.1002/2016JF003992.

Received 15 JUN 2016Accepted 13 DEC 2016Accepted article online 15 DEC 2016Published online 3 JAN 2017

©2016. American Geophysical Union.All Rights Reserved.

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http://dx.doi.org/10.1002/2016JF003992

http://dx.doi.org/10.1002/2016JF003992

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thermal fatigue, a process of subcritical crack growth, which arises from slow crack propagation alongpreexisting planes of weakness due to the long-term effects of low-magnitude, cyclic thermal loading.Here, we focus on rock weathering due to solar-induced thermal stresses via the process of thermal fatigue.Due to the scarcity of liquid water in inland regions of the McMurdo Dry Valleys (MDV), TransantarcticMountains [Kowalewski et al., 2006; Kowalewski et al., 2011; Marchant and Head, 2007; Fountain et al., 2010],thermal fatigue weathering may be an important but undervalued process in the mechanical breakdownof surface rocks.

In detail, we examine the question of whether thermal fatigueweathering plays a role in the detachment of thin(1–4mm) alteration rinds observed on exposed clasts of Ferrar Dolerite at the surface of the Mullins Valleydebris-covered glacier (hereafter Mullins Glacier) in the MDV. Our approach employs a finite element modelof thermal stresses generated at the base of a single alteration rind with boundary conditions based on (1)high-frequency micrometeorological data recorded in the field and (2) measured and inferred material proper-ties for Ferrar Dolerite. We then examine the results of our thermal stress model in the context of general frac-ture mechanics theory to determine if subcritical crack propagation (and the eventual spalling of alterationrinds) is likely to occur under thermal stresses induced via present-day meteorological forcing. Throughoutthe manuscript we use the terms “spalling” and “flaking” interchangeably to describe the surface-paralleldetachment of cohesive, millimeter-scale thick alteration rinds from exposed clasts of Ferrar Dolerite.

2. Background and Physical Setting

Mullins Glacier is centered at ~77.9°S, 160.5°E and lies at the southwestern corner of the stable upland zonein the MDV (Figure 1). Due to hyperarid, cold-desert conditions [Marchant and Head, 2007], rock erosion

Figure 1. Overview of the McMurdo Dry Valleys. Mullins Glacier occurs in the region outlined by the white box; the ice-free regions of the stable upland zone (SUZ),which represent the coldest and driest portions of the MDV, are highlighted in red and outlined in yellow.

Journal of Geophysical Research: Earth Surface 10.1002/2016JF003992


rates in this environment are among the lowest on Earth, ~5–50 cmMyr�1 [Margerison et al., 2005;Nishiizumi et al., 1991; Schäfer et al., 1999; Summerfield et al., 1999]. Mullins till rests directly on top ofMullins Glacier—a slow-moving, debris-covered alpine glacier that has been the subject of considerablestudy (Figure 2) [Kowalewski et al., 2011; Mackay et al., 2014; Mackay and Marchant, 2016; Shean et al.,2007; Shean and Marchant, 2010; Yau et al., 2015]. Mullins till is derived entirely from rockfall at the head ofMullins Valley; additional entrainment from basal regelation or intermittent rockfall from valley sidewalls ontoMullins Glacier is unlikely, as modeled basal-ice temperatures are well below the pressure-melting point andlarge topographic depressions separate Mullins Glacier from adjacent valley sidewalls [Mackay et al., 2014].The age of Mullins till increases with transport distance from the valley headwall; at our study location,cosmogenic 3He exposure ages for dolerite clasts on the till surface are ~1.5 × 105 years [Mackay andMarchant, 2016].

Modern mean annual and mean summertime atmospheric temperatures at the study site (~1650m ele-vation) are �23°C and �11°C, respectively, with a mean annual relative humidity (RH) of ~45%[Kowalewski et al., 2011]; annual snowfall is <50mm [water equivalent Fountain et al., 2010]. As a conse-quence, Mullins till is exceptionally dry, with <5% gravimetric water content [Kowalewski et al., 2011].Ablation of underlying glacier ice is entirely by sublimation [Mackay et al., 2014]. Saturated active-layercryoturbation, vertical mixing, and extensive soil creep within Mullins and adjacent Beacon valleys areessentially nonexistent as shown by cosmogenic nuclide depth profiles through near-surface debris[Morgan et al., 2010; Marchant et al., 2002]. Clasts at the ground surface tend to stay at the surface; theyare not subjected to repeated episodes of burial and reexposure as is typical of saturated active layers in

Figure 2. Oblique aerial view of the study region. Mullins Glacier descends from steep cliffs at the headwall of Mullins Valley and flows out onto the floor of upper andcentral Beacon Valley (foreground).



the Arctic [Hallet and Waddington, 1991] or even within the relatively warm soils in low-elevation coastalregions adjacent to McMurdo Sound [Marchant and Head, 2007]. The implication is that small-scaleweathering features on exposed rock surfaces are most probably related to atmospheric processes,rather than to impacts, collisions, or physical/chemical weathering associated with clast movement andburial/reexposure via cryoturbation [Marchant et al., 2013].

Dolerite clasts freshly fallen from the headwall onto the surface of Mullins Glacier are unweathered in appear-ance (Figure 3a). However, during downvalley rafting on the surface of Mullins Glacier, exposed clastsundergo slight chemical alteration, visible as a progressive darkening of the rock surface and, in cross section,as a slight discoloration within the outermost 1–4mm of the rocks (Figures 3b–3d). Although subtle, thesechanges in rock-surface chemistry are apparent in visible/near-infrared reflectance andmid-infrared emissionspectroscopy and by discrete zones of yellow-to-red discoloration that coincide with increased Fe3+/Fe2+

ratios [Salvatore et al., 2013]; the latter is likely due to an oxidation potential that drives the migration ofdivalent cations (Mg2+ and Ca2+) from the altered rind to the rock surface. In contrast, X-ray diffraction ana-lyses reveal no definitive changes in mineralogy between clast interiors and altered rinds [Salvatore et al.,2013]. Evidence for microbial weathering or other biological processes, present at lower elevations in theMDV (e.g., lichens), are not seen on dolerites in this upland region.

3. Approach

To test the potential efficacy for thermal fatigue weathering in the detachment of alteration rinds onexposed clasts of Ferrar Dolerite, we measured variations in temperature at the surface and undersideof partially detached flakes, as well as coeval, local variations in atmospheric temperature, RH, windspeed/direction, and solar irradiance during the 2010 and 2012 austral summers. Further, we measuredchanges in rock-surface albedo related to rind formation and spall development, as well as material prop-erties of Ferrar Dolerite samples. A subset of these data were used as input into a COMSOL Multiphysicsfinite element model to calculate the maximum thermal stresses achieved at the base of a 2mm thickalteration rind on a representative dolerite clast. The heat transfer boundary conditions for the modeledclast were provided by the recorded field data (solar irradiance, air temperature, and wind speed) coupledwith the measured albedo, and mechanical properties (modulus of elasticity, Poisson’s ratio, and tensilestrength) were determined by measurements of Ferrar Dolerite samples. The model results were thencoupled with calculations for the mode I stress intensity factor, and the threshold stress intensity factorfor subcritical crack growth, in order to determine whether thermal fatigue weathering could be contri-buting to crack propagation (and hence, forming spalls and partially detached flakes) at the base ofalteration rinds on dolerite clasts.

Figure 3. Progressive changes in surface characteristics of Ferrar Dolerite on Mullins Glacier. (a) Rockfall debris near the glacier head is visibly unweathered, (b) butthereafter begins to develop a thin reddish-brown, alteration rind, (c) which increases in maturity and thickness until it detaches from the rock. (d) Typically, clastsdisplay multiple generations of alteration rinds. Based on cross-cutting relationships, the darkest portion in Figure 3d, denoted via number 1, is likely the oldest rind,with surface number 3 being the youngest; surface 2 is intermediate in age. Although major changes in color and morphology occur as a function of exposure age,available data suggest minimal concomitant changes in rock-surface chemistry (see text and Salvatore et al. [2013]).



4. Field and Analytical Methods4.1. Field Measurements: Rock Temperatures

We instrumented two dolerite clasts (JKC-1 and JKC-2) with 0.003-inch diameter, fine-wire thermocouples(Campbell Scientific, FW3) to measure temperature change, both at the surface and underside of partiallydetached alteration rind flakes (Figure 4). These clasts were chosen because they (1) exhibited partiallydetached rind flakes on their uppermost surface, (2) were not shielded from sunlight by large nearby clastsor self-shielding, and (3) were morphologically representative of surrounding dolerite clasts (e.g., expressingsimilar grain sizes, weathering states, and flake thicknesses). The instrumented flake on JKC-1 was 1.89mmthick and ~30 cm above the till surface, and 1.90mm thick and ~50 cm above the till surface for JKC-2. A thirdthermocouple was placed on a light-colored region interpreted as the location of a recent flake detachmenton JKC-1. On exposed flake surfaces, the sensing tips of the thermocouples were positioned to maintain con-tact with the flake exterior. Thermocouples placed underneath the flakes were positioned as far into opencracks as possible, so that sensors record temperatures at the interface of partially detached flakes and therest of the rock underneath. Where needed, duct tape was used to secure sensor housing/rods to rock sur-faces to prevent movement of the sensing tip (which was not in contact with tape); the sensors were checkeddaily to ensure contacts between sensing tips and flakes were maintained.

To capture coeval changes in micrometeorological conditions at the study site, we deployed several OnsetComputer Corporation Smart Sensors connected to HOBO® data loggers. A dual air temperature/RH sensorwas housed in a radiation shield 10 cm from the ground surface, and a pyranometer recorded local solar irradi-ance at the till surface, bothwithin 0.5m of JKC-1. Additionally, an anemometer was deployed on a 2m tripod tomeasure wind speed and wind direction. Given the proximity of the two monitored clasts (<50m), the air tem-perature, RH, solar irradiance, and wind data apply equally to both JKC-1 and JKC-2. All sensors recorded mea-surements at 15 s intervals between 13 November and 10 December 2010 (28days); we chose high-frequencymeasurements (15 s intervals) as recommended in previous studies [e.g., Hall, 2003; Hall and Andre, 2001].

In order to investigate the influence of aspect on rock-surface temperature, we instrumented three partiallydetached flakes with different cardinal exposure orientations and surface slopes in the same manner asdescribedabove. The instrumentedflakesoccuron two separatedolerite clasts, JKC-3and JKC-4,whichare locatedwithin3mofoneanother at 77.87442°S, 160.54042°E. The setofflakes include (1) a southeastexposure: strike 57°E,dip 85°SE, 3.02mm thick, and 5 cm from the till surface on JKC-3; (2) a northwest exposure: strike 76°E, dip 72°NW,2.55mmthick,and8cmfromthetillsurfaceonJKC-4;and(3)ahorizontalexposure (e.g., on the top, horizontal surfaceof the rock): 1.75mm thick and 31 cm from the till surface on JKC-3. To track solar irradiance on these faces,we installed three silicon pyranometers, each oriented nearby and perpendicular to flake surfaces: SE, NW,and horizontal (Figure 4b). Data were collected every 15 s for 10days, from 30 December 2012 to 08January 2013.

Figure 4. Field setup tomeasure temperature variation on clasts JKC-1 and JKC-4. (a) Clast JKC-1. For clarity, the tips of two thermocouples are indicatedwith a yellowdot; the black arrow shows the orientation of the “buried” thermocouple recording the temperature at the underside of a partially detached flake. The lone ther-mocouple (vertical orientation in photograph) registers the surface temperature in a region inferred to have undergone recent spalling (see text). (b) Example fieldsetup to study the influence of aspect on flake temperatures. Pictured is JKC-4, with a partially detached flake on the northwest face. The red box and arrow indicatethe flake and pyranometer, respectively.



4.2. Laboratory Measurements:Surface Albedo, Chemical Alteration,Surface Morphology, and RindPorosity/Crack Density4.2.1. Surface AlbedoAs noted above, many dolerite rockswithin the study region display multiplegenerations of spalls, each with conco-mitant changes in rock color and sur-face albedo (Figure 3d); variation inrock-surface albedo has been impli-cated in spalling [e.g., Gomez-Heraset al., 2008]. To quantify better therange of surface albedo associated withmultiple generations of spalls, we mea-sured reflectance values for sampledrocks at Boston University with (1) visi-bly unweathered (fresh) surfaces, (2)mature alteration rinds, and (3) rocksurfaces inferred to have undergone

relatively recent spalls (based on the observation of relatively immature weathering rinds in comparison tothe rest of the rock surface; Figure 3d). Using a field spectrometer (ASD Inc.), reflectance in the 350–2500 nm range was measured 10 times on an ~2.5 cm diameter area on each sample (11 samples in total);values were averaged for a single reflectance at each wavelength. We generated a reference solar spectrumfor the MDV using the Simple Model of the Atmospheric Radiative Transfer of Sunshine (SMARTS) [Gueymard,1995, 2001]. The power at each wavelength (Pi) in the reference solar spectrum was coupled with the reflec-tance data (Ri) to estimate an overall albedo in the 350–2500 nm range as

Albedo ¼X2500 nm

i¼350 nmRi Pi (1)

4.2.2. Chemical AlterationIn order to qualitatively determine chemical changes between the altered surfaces and unaltered interiors ofdolerite clasts on Mullins Glacier, we conducted electron microprobe analyses on thin sections of multipledolerite clasts from the study area. We used a JEOL-JXA-8200 Superprobe at the Massachusetts Institute ofTechnology Electron Microprobe Facility (energy and wavelength dispersive spectroscopies (EDS andWDS)) to create detailed elemental maps of Al, Ca, Cl, Fe, K, Mg, Na, S, Si, and Ti across the outer 4mm ofone representative thin section. We also analyzed the chemistry of alteration rinds using a Phenom ProXdesktop scanning electron microscope (SEM) and Rigaku MiniFlex Powder X-ray diffractometer (XRD) atBoston University. Diffraction patterns were determined using the Jade 9 data analysis program.4.2.3. Surface MorphologyWe examined the morphology of dolerite alteration rinds and distribution of microcracks via optical micro-scope and SEM analyses across the outermost 1–2 cm of rock surfaces and detached flake fragments.While most samples (>10) were examined without pretreatment, the outer surfaces of two samples wereimpregnated with low-viscosity epoxy before cutting in order to ensure that the documented fractures inthe rinds were not caused by the cutting procedure. Changes in porosity/crack density within the outerfew millimeters of two representative clasts of Ferrar Dolerite with visibly mature rinds were calculated usingImageJ software and SEM and optical microscope images.

5. Results5.1. Surface Albedo

Reflectance data for the three categories of dolerite clast surfaces (visibly unweathered, minor alteration, andmature alteration) are provided in Figure 5. Our calculated values for albedo over wavelengths 350–2500 nmare 0.10 for mature alteration rinds, 0.15 for surfaces exposed due to recent spalling or flaking (minoralteration), and 0.10 for dolerite rockfall lacking any visible rind or surface alteration at the valley head (i.e.,

Figure 5. Reflectance data for Ferrar Dolerite samples. Black, recent rockfall (visibly unweathered surfaces); blue, minor alteration associated withsurface exposed due to recent spalling; red, mature surface alteration.



unweathered). These data imply that lighter-colored surfaces indicative of either recent spalls or immaturerind alteration reflect 50% more solar energy than darker, mature rind surfaces.

5.2. Microscopic and Geochemical Analyses

Three major findings arise from detailed microscopic and geochemical analyses. First, porosity associatedwith microfractures is highest near rock surfaces; second, millimeter-scale surface roughness varies in concertwith albedo; and third, alteration-rind flakes show minimal chemical alteration.

Figure 6 shows the optical and SEM images of alteration rinds and subhorizontal fractures that typically occurat, or just stratigraphically above, the transition from unweathered dolerite interiors to altered near-surfacerinds. Using ImageJ image analysis software to map voids in alteration rinds, we find that surface-parallelcracks increase rock porosity from <1% in unaltered clast interiors to >6% in the outer few millimeters ofdolerite clasts. Additional SEM images of dolerite rinds in Figure 7 show that cracks exist both alongsideand across crystals of plagioclase and clinopyroxene and that well-developed alteration rinds areexceptionally smooth.

Consistent with findings in Salvatore et al. [2013], the alteration rinds lack evidence for accretionary layers,oxides, or clay mineral development. XRD analyses established no resolvable mineralogical differencesbetween the upper and lower ~1mm of alteration rinds. EDS and WDS elemental maps failed to detectvariations in Al, Ca, Cl, Fe, K, Mg, Na, S, Si, or Ti between dolerite rinds and clast interiors (seesupporting information).

5.3. Rock-Surface Temperature and Micrometeorological Data Measurements

Table 1 provides an overview of the surface-temperature data collected for clasts JKC-1 and JKC-2 (the fullsuite of measured meteorological data is provided in the supporting information). The change in rock-surfacetemperature, dT/dt, at the top and underside of partially detached flakes, calculated using 1min moving

Figure 6. Microfracture patterns in mature dolerite alteration rinds from Mullins Glacier. (a) Backscattered electron (BSE)image showing fractures typical of mature alteration rinds in the study region. (b) Optical microscopic view (60X) show-ing major fractures within a typical alteration rind. For Figures 6a and 6b, the bottom plots show the distribution andrelative thickness of fractures and pores (ImageJ analysis) within the white boxed areas of the overlying images. The por-osity, determined by analyzing the percent area of the pores and open fractures in the bottom plots, is ~6% in bothFigures 6a and 6b.



windows, reached as much as 12°Cmin�1 and 8.9°Cmin�1, respectively, and the daily temperature range(Tmax� Tmin) on rock surfaces surpassed 42°C. Temperature gradients across the flakes reached ~4.7°Cmm�1

(i.e., 8.9°C across the 1.9mm thick flake on JKC-2). When combined with measured solar irradiance and winddata, the results show that wind gusts produce the most rapid temperature fluctuations across the surfaceand underside of flakes, especially during periods when rock-surface temperatures are warmest (Figure 8);at times, the underside of flakes can be either colder or warmer than the exposed, top surface.

The legacy of surface spalling also appears to play a critical role in rock-surface temperature. For example,temperatures measured at the surface of a recent spall location on JKC-1 consistently showed cooler tem-peratures than on other regions of the rock surface, likely reflecting the relatively higher albedo of recently

Figure 7. SEM images of dolerite alteration rinds. (a) The edge of a partially detached flake; note the smooth surface versus the rough flake edge where individualmineral grains are visible. (b) Close-up view of a near-surface crack within a vertical section of an alteration rind. Plagioclase (plag) and pyroxene (cpx) crystals arevisible, as well as transgranular and intergranular (white arrows) cracks. No modifications or pretreatments were applied to the samples before analysis.

Table 1. Measured Rock-Surface Temperatures

Flake Study Flake Aspect Study

JKC-1 JKC-2 Hor.a (JKC-3) SE (JKC-3) NW (JKC-4)

Fsb Fb

c Spalled Surface Fs Fb Fs Fb Fs Fb Fs Fb

Maximum|T-Tambient| (°C) 28.0 25.1 23.8 21.4 19.8 15.5 14.5 28.6 20.3 33.3 30.3Absolute T range 46.8 42.8 41.5 39.1 37.9 26.0 24.2 35.7 26.4 41.3 37.2Maximum daily T range 42.3 38.2 35.6 34.4 31.7 24.6 22.9 32.1 22.5 38.5 33.7Average daily T range 30.5 27.1 26.2 24.0 22.2 20.3 18.5 24.4 17.4 33.0 29.0Maximum dT/dt rated (°Cmin�1)Heating 6.6 2.8 5.0 8.7 7.9 2.2 4.3 3.6 1.8 7.1 3.0Cooling 8.6 3.4 6.6 12.0 8.9 2.5 5.5 4.0 1.9 9.3 3.2Average solar irradiance (Wm�2) 232 278 263 302Average Tambient (°C) �15.2 �4.5Average ambient RH (%) 48.3 41.7Average wind speed (m s�1)e 4.17 -

aHor. = horizontal surface.bFs = flake surface.cFb = flake bottom/underside.dCalculated using 1min moving windows.eMeasured at 2m.



Figure 8. Results from field temperaturemeasurements. Figures 8a–8c show data from the top of clast JKC-1. (a) A 2 day subsetshowing temperature data from the surface (dark blue) and underside (red) of a horizontal, partially detached flake on JKC-1 (seeFigure 4a for the location). (b) The same data set as in Figure 8a but with the addition of surface temperatures at the site ofa recent spall on JKC-1 in light blue. (c) An ~2 h subset of the data in Figure 8b (time period shown as vertical gray bar inFigure 8b). Note that surface temperatures at the recent spall site (light blue) do not reach those of the adjacent mature flakeand are cooler than the underside of the flake after peak solar heating. Figures 8d–8f show solar irradiance and rock tempera-tures as a function of aspect on JKC-3 and JKC-4. (d) Solar irradiance (Wm�2) derived from HOBO pyranometers mountedapproximately perpendicular to eachmonitored surface on JKC-3 and JKC-4 (see Figure 3b for details): horizontal surface on JKC-3 shown in blue, southeast facing surface shown in red, and northwest facing surface on JKC-4 shown in yellow. (e) Flake-surfacetemperatures. (f) Temperatures at the underside of flakes. A snowfall event on 7 and 8 January is visible in the data as a dis-turbance to both the solar irradiance and temperature patterns. The spike in irradiance on late 7 January is likely due to theeffects of passing clouds reflecting an increased amount of solar radiation to the pyranometer.



spalled surfaces compared to that ofmature alteration rinds. Results of theaspect study show that the NW facingflake consistently reached higher tem-peratures than the horizontal and SEfacing flakes (Figure 8 and Table 1).

The monitored clasts do not showcrack patterns indicative of thermalshock weathering, in which the surfaceof the clast would undergo instanta-neous fracture [Hall and Thorn, 2014];this leads us to believe that if thermalstresses are playing a role in alterationrind detachment, it is likely due to theaction of thermal fatigue weathering.

6. Modeling the Potential forThermal Stress Weathering

We now evaluate quantitatively thepotential for thermal fatigue weather-ing on Mullins Glacier using a combi-nation of finite element modelingand subcritical crack growth theory.First, we use COMSOL Multiphysics tomodel the thermal stresses over a24 h period in a model 3-D doleriteblock with an alteration rind on its sur-face. Thermal boundary conditions for

the model are based on the ambient field data recorded during the study of partially detached flakes onJKC-1 and JKC-2 (e.g., solar irradiance, air temperature, and wind speed); the wind speed at the modeled rockheight (30 cm) is estimated by converting our field-recorded values at 2m height using a logarithmic profileassumption and measured value of aerodynamic surface roughness. Next, we determine the maximum nor-mal tensile stress at the base of the alteration rind (i.e., the interface between the alteration rind and under-lying rock where we would expect detachment) from the model data. We then use measured mechanicalproperties of Ferrar Dolerite along with empirical relationships from existing literature to estimate a rangeof fracture toughness values (a measure of the stress required to induce catastrophic crack propagation fora particular material and initial crack length) expected in Ferrar Dolerite alteration rinds. Using these valuesalong with basic linear elastic fracture mechanics theory and our modeled thermal tensile stresses, we deter-mine whether subcritical crack propagation, which here represents crack propagation due to thermal fatigueweathering, is likely for dolerite clasts at the modeled conditions.

6.1. Model Setup

We simulate thermal stresses for a typical dolerite clast exposed on Mullins till by modeling the thermal stres-ses in a 3-D, elastic, homogenous, and isotropic solid using COMSOL Multiphysics. The thermal response ofthe dolerite clast is forced by meteorological field data recorded near JKC-1 (section 5.3). We chose a repre-sentative 24 h subset of these data that corresponds to a typical sunny, summer day (see supporting informa-tion). Measurements of air temperature, wind speed, and solar irradiance, collected at 15 s intervals, wereinterpolated linearly and an internal solar-position model in COMSOL allowed for realistic transient solarmovement throughout the modeled period.

Our model geometry consists of the upper 2 cm of a 30 cm tall, 40 cm long dolerite block capped by an inci-pient spall modeled as a circular pedestal 36 cm in diameter; the incipient spall stands 2mm above the sur-rounding rock surface (Figure 9). We envision this upstanding pedestal as a mature alteration rind surfacethat has not yet spalled and is assigned a low albedo of 0.10. Surrounding the pedestal is an immature surface

Figure 9. Schematic of COMSOL model. (a) The general COMSOL setup,with imposed boundary conditions. The block surface is 30 cm from theground. (b) The model mesh with resultant degrees of freedom of 86,710.The geometry is composed of a tetrahedral mesh, with a maximum ele-ment size of 0.06m, a minimum element size of 0.0112m, a maximumelement growth rate of 1.6, a resolution of curvature of 0.7, and a resolutionof narrow regions of 0.4.



with albedo characteristics matching those of surfaces exposed by recent spalls (0.15). The base of the blockis set as a heat outflow boundary, chosen to help minimize the size of the model and to prevent excess heatfrom building up in the model geometry that would occur with the application of an insulated boundary con-dition, with a prescribed zero displacement in the z direction. All other surfaces (i.e., all exposed sides of theblock) were coupled with radiative and convective heat transfer physics to model temperature changes andallowed to freely expand. Themodel block was heated by radiation from the Sun, with irradiance set to valuesmeasured in the field. The model block was cooled by externally forced convection. The air temperature wasset to the field-measured values, and the wind speed was determined via adjusting our measured values at2m height according to a logarithmic wind profile assumption (see section 6.2).

The radiative heat flux (Wm�2) is calculated as

qrad ¼ A qs � sT4rockFEPs� �þ ε ql � sT4rockFEPl

� �(2)

where A is the absorptivity of the rock surface, ε is the emissivity, qs is the incoming shortwave radiation(wavelengths from 0 to 2.5μm), ql is the incoming longwave radiation (wavelengths >2.5μm), s is theStefan-Boltzmann constant, Trock is the temperature of the rock surface, and FEP is the fractional emissivepower for each wavelength interval (FEPs+ FEPl= 1). The absorptivity of each surface is approximated as1-albedo, and the incoming solar radiation is calculated using the field-measured solar irradiance values.

The convective heat flux (Wm�2) for each boundary is

qconv ¼ h Tambient � T rockð Þ (3)

where Tambient is the air temperature and h is the heat transfer coefficient calculated as

h ¼ 2kL

0:3387 Pr1=3Re1=2

1þ 0:0468=Prð Þ2=3� �1=4

for Re ≤ 5�105 (4)

h ¼ 2kLPr1=3 0:037Re4=5 � 871

� �for Re > 5�105 (5)

where

Pr ¼ μ cpk

(6)

Re ¼ ρUextLμ

(7)

and where k is the thermal conductivity, μ is the dynamic viscosity, cp is the specific heat, ρ is the density, Uextis the external air speed (i.e., the wind speed), and L is the plate length. The Prandtl number (Pr) is a dimen-sionless number that calculates the ratio of viscous to thermal diffusivity of the fluid (in our case, air); theReynolds number (Re) represents the ratio of inertial to viscous forces.

The outflow boundary condition at the base of the model geometry allows the heat that reaches the base ofthe geometry to be transferred away from the boundary (i.e., deeper into the rock). This boundary conditionwas chosen to help minimize the size of the model and to prevent excess heat from building up in themodel geometry.

The general equation for conductive heat transfer inside the rock is

ρc∂T∂t

� ∇� k∇Tð Þ ¼ Q (8)

where Q accounts for a volumetric heat source. The equation of motion for linear elasticity is

ρ∂2u∂t2

� ∇ �σ ¼ F (9)

where u is the displacement vector, σ is the Cauchy stress tensor, and F is the body force per volume. Hooke’slaw relates the stress and strain tensors as

σ ¼ σ0 þ C : ∈�∈0 � ∈thermalð Þ (10)



and infinitesimal strain theory relates the strain tensor and displacement vectors as

∈ ¼ 12

∇uþ ∇uT� �

(11)

∈thermal ¼ α T � T refð Þ (12)

where C is the stiffness or elasticity matrix, ϵ is the infinitesimal strain tensor, ϵ0 and σ0 are the initial strain andstress, ϵthermal is the thermal strain tensor, α is the thermal expansion tensor, and Tref is a reference tempera-ture. Infinitesimal strain theory holds when the displacements due to deformation of an elastic solid body aremuch less than the size of the solid, such that the properties at each point can be assumed to be unchangeddue to the deformation.

The COMSOL model uses PARallel DIrect SOlver (PARDISO) to solve the model in two segregated steps: firstsolving for the temperature in the model and then the displacement field, from which the thermal stressesare derived. The model time steps were large (600–1000 s) between time 0 and 20,000 s and 5 and 15 s forthe remainder of the model duration. Details of the model mesh are given in Figure 9b.

6.2. Determination of Wind Speed near the Rock Surface

Wind speed, used in the model (e.g., Uext) to calculate the convective heat flux, varies with height aboveground, z, according to a logarithmic profile law, as

Uz ¼ U�κ

lnz � dz0

� �(13)

where Uz is the wind speed at height z, U* is the wind shear, κ is the dimensionless von Kármán constant(=0.4), d is the zero-plane displacement (assumed to be 0 here), and z0 is the aerodynamic surface roughness.For a measured wind speed at a known height above ground, we can approximate the wind speed at anyheight (in this case near the rock surface) in the profile as

Uz ¼ Uz1ln z=z0ð Þln z1=z0ð Þ (14)

where measured Uz1 is the wind speed at height z1 and Uz is the wind speed at height z.

Local aerodynamic surface roughness, z0, was determined using measured wind speed data from a verticalarray of four Onset Computer Corporation cup-style anemometers, spaced vertically at approximately logarith-mic heights of 0.28m, 0.66m, 1.34m, and 2.2m, installed at our field site over the period of 25 to 30 December2010. After processing with a 15min running average to reduce noise, wind velocity for each time step wasiteratively fit to a logarithmic profile to determine z0, computed from the ordinal intercept of the best fitting lineof ln(z� d) versus Uz, where z is themeasurement height, d is the displacement height (~0m), andUz is thewindvelocity at height z. In calculating the average z0, only data for which the wind speed at the lowest anemometerwas >2ms�1 were included. This segregation was done to minimize the potential errors associated with thethermal instability of the atmosphere and to use only data for wind speeds at which mechanical turbulencelikely exceeded buoyancy effects [Bauer et al., 1992; Lancaster, 2004; Wolfe and Nickling, 1996].

This analysis resulted in a computed mean aerodynamic roughness of z0 = 0.051m. Due to a lack ofco-located temperature profile measurements with the wind-profile measurements, we are unable to applycorrections for atmospheric stability in the z0 estimate and have thus implicitly assumed neutral stabilityduring the measurement period. This assumption requires that our mean z0 estimate should be considereda maximum estimate.

Finally, the wind speed (Uz=Uext,z) for the convective heat transfer coefficient, h, at each height, z, on thedolerite block boundary in the COMSOL model is calculated as

Uext;z ¼ U2mln z=0:051� �

ln 2=0:051� � (15)

where U2m is the field-recorded wind speed at a height of 2m.



6.3. Material Properties and Model Simulations

The elastic modulus (E), Poisson’s ratio (ν), and tensile strength (σt) were determined from analyses ofFerrar Dolerite samples at the University of British Columbia’s Norman B. Keevil Institute of MiningEngineering (Tables 2 and 3). Three of these rock samples were morphologically typical of medium-grained dolerites exhibiting detached weathering rinds, and one (JKC-11-019) was coarser grained.Additional material properties used in the thermal stress model were derived from previous studies onsimilar rock types (Table 4).

The material properties of rocks and minerals change with variations in weathering and porosity [Basu et al.,2009; Goh et al., 2011; Schön, 1996]; for example, dolerite clasts can lose >50% of their strength withmoderate weathering [Bell and Jermy, 2000; Gu et al., 2008; Kilic, 1995]. In order to capture this effect, weran two versions of the COMSOL model, one (COMSOL Simulation 1) with consistent values of physical prop-erties equal to that of unweathered dolerite and a second (COMSOL Simulation 2), in which we include (1) alinear 50% reduction in the values of E and ν between the unaltered interior at 2 cm depth and the alterationrind and (2) a similar linear 20% decrease in ρ (see Table 4). The thermal properties used in our model (cp, α,and κ) also likely change between the alteration rind and unaltered rock. However, we keep these valuesconstant through our model geometry because we do not have measured values for Ferrar Dolerite; as such,we cannot predict with certainty how slight chemical alteration in the dolerite rinds would cause variationsin these parameters (if at all) in comparison to the underlying unweathered rock. Likely, however, the pre-sence of air-filled fractures in the rinds (seen in Figure 6) would result in an overall decrease in κ and α nearthe surface of the modeled dolerite clast [Clauser and Huenges, 1995; Cooper and Simmons, 1977; Robertsonand Peck, 1974]. Additionally, we do not take into consideration the changes in material properties as afunction of temperature [Robertson, 1988].

In order to investigate the role of aspect and surface slope on thermal stresses, a third model was run(COMSOL Simulation 3) using the material properties of Simulation 2 but with the rock surface inclined 45°to the northwest (i.e., the aspect with the highest measured temperatures in the field). The calculation of nor-mal stresses and the geometry of the modeled dolerite block in Simulation 3 are provided in thesupporting information.

Table 2. Specimen Geometry and Uniaxial Compressive Strength (UCS) Testing Results for Ferrar Dolerite Samples FromMullins Glacier

Sample ID Height (mm) Diameter (mm) UCS (MPa) Elastic Modulus (GPa) Poisson’s Ratio

JKC-09-B 75.29 36.93 251.5 77.73 naa

77.45 37.67 287.1 76.53 0.2773.01 37.69 283.7 84.03 0.38

JKC-10-044 73.56 37.06 269.1 70.22 naa

JKC-11-019b 78.24 37.27 64.7 57.7 naa

aUnable to determine from testing data results.bCoarse-grained sample.

Table 3. Specimen Geometry and Brazilian Tensile Strength Testing Results for Ferrar Dolerite Samples FromMullins Glacier

Sample ID Diameter (mm) Thickness (mm) Peak Load (kN) Tensile Strength (MPa) KIcra (MPam1/2)

JKC-09-B 37.52 19.96 15.77 13.41 1.9537.62 16.41 18.47 19.05 2.77

JKC-10-044 36.95 20.22 16.65 14.19 2.0637.13 17.54 15.99 15.63 2.27

JKC-10-045 37.23 18.81 19.93 18.12 2.6337.44 20.15 11.15 9.41 1.3737.32 19.32 17.71 15.64 2.27

JKC-11-019b 37.33 20.62 6.36 5.26 0.7637.44 21.43 6.64 5.27 0.77

aKIcr (fracture toughness) values estimated using the relationship: tensile strength = 6.88 KIcr [Zhang, 2002].bCoarse-grained sample.



6.4. Thermal Stress Model Results

A comparison between the field-recorded rind flake surface temperature from JKC-1 and the temperatureat a location on the modeled mature rind surface (located on the westernmost edge of the 2mm thickmature rind) is shown in Figure 10. While the model does not fully capture all of the rapid temperaturefluctuations seen in the field data, the trend and temperature reached by the surface of the modeleddolerite clast closely track that of the flake surface on JKC-1. Figure 11 shows the maximum value ofthe surface-normal tensile stress calculated at the base of the modeled 2mm thick alteration rind at eachtime step in the three COMSOL simulations. In Simulations 1 and 2, the maximum stress occurred alongthe perimeter of the rind-unweathered rock interface at t=27,410 s (~7.62 h), near the time of peak irra-diation on the surface of the clast; in Simulation 3, the maximum stress occurred slightly later att=32,130 s (~8.93 h), reflecting the delayed response as a function of the Sun’s movement and rock

Table 4. COMSOL Model Input Parametersa

Valueb

Parameter Symbol I R Units

Density ρ 2900 2610 kgm�3

Thermal conductivity k 1.8 1.8 Wm�1 K�1

Heat capacity (constant pressure) cp 730 730 J kg�1 K�1

Poisson’s ratioc ν 0.325 0.163 -Modulus of elasticityc E 77 38.5 GPaCoefficient of thermal expansion α 5.5 × 10�6 5.5 × 10�6 K�1

Surface propertiesAbsorptivityd (mature rinde) Amr 0.9 -Absorptivityd (immature rindf) Air 0.85 -Emissivity ε 0.95 -

aAll values are applied to the entire model geometry unless otherwise noted.bI = interior, R = rind; the values of E, α, and ρ were varied linearly between 2 cm depth in the rock interior to the rind

base in COMSOL Simulations 2 and 3 to account for weathering-induced weakening, and values listed under column Iwere used throughout the entire rock in COMSOL Simulation 1.

cEstimated from measurements on Ferrar Dolerite clast samples from Mullins Valley (see Table 2).dAbsorptivity is calculated as 1-albedo, assuming that transmissivity = 0 (opaque).eApplied to the 2mm thick circular rind pedestal on surface of modeled dolerite block.fApplied to all exposed rock surfaces other than the surface rind pedestal.

Figure 10. Comparison of field-measured and modeled rind surface temperatures. The plotted field-measured tempera-ture (gray line) is the flake surface temperature on JKC-1; the modeled temperature (black dots) is taken from the wes-tern edge of the mature rind surface in our model 3-D dolerite block at x = 0.2 and y = 0.38. Time t = 0 is 18 November 2010at 6:50 A.M. A larger time step (between 600 and 1000 s) was used for t ≤ 5.56 h to reduce modeling time; for t> 5.56 h, thetime step was between 5 and 15 s.



aspect. The maximum tensile stress during the model run was 0.251MPa for Simulation 1, 0.153MPa forSimulation 2, and 0.145MPa for Simulation 3 (Figure 11).

6.5. Crack Propagation

We now determine whether the modeled maximum tensile thermal stresses are sufficient to cause crack pro-pagation at the base of alteration rinds in Ferrar Dolerite clasts, a process that leads to the eventual detach-ment of the alteration rind as a flake or spall. According to linear elastic fracture mechanics, stresses nearexisting crack tips approach infinity; therefore, a material can undergo crack extension for values below itsultimate tensile strength. Assuming primarily mode I (tensional) opening, the stress intensity factor (KI) fora pressurized penny-shaped crack is

KI ¼ 2 Δσcπ

� �12

(16)

where c is the radius of the crack and Δσ is the driving stress for crack opening, which in our case is the tensilestress perpendicular to the crack at the interface between the rind and unweathered rock.

Theoretically, a crack will propagate unstably to failure when KI equals or exceeds a critical value known as thefracture toughness (KIcr) of the material. In practice, however, cracks in rocks have commonly been observedto undergo extension at values of KI that are lower than KIcr due to the effects of subcritical crack growth[Atkinson, 1984; Meredith and Atkinson, 1985]. The threshold value of the stress intensity factor below whichsubcritical crack growth will not occur is denoted as K0. Unfortunately, the value of K0 is uncertain, and arange of K0 values from 10% to 30% of KIcr, the material’s measured fracture toughness, has been usedpreviously in studies of rock crack extension [e.g., Segall, 1984; Shen, 2013;Walder and Hallet, 1985]; therefore,we use a range of K0 values from 0.1 KIcr to 0.3 KIcr in our calculations.

As we do not have measured values of the fracture toughness of Ferrar Dolerite, we use an empirically deter-mined relationship between rock tensile strength and mode I fracture toughness from Zhang [2002], which isdetermined using a range of rock types:

σt ¼ 6:88 K Icr (17)

where σt is the rock tensile strength in MPa and KIcr is in units of MPam1/2.

However, because the value of σt is derived from the analysis of intact, unweathered dolerite samples (Table 3), the resultant value of KIcr is not indicative of the fracture toughness in the weakened alteration rind.

Figure 11. Maximum surface-normal tensile stress at the base of the alteration rind during COMSOL Simulations 1, 2,and 3. Simulation 1 models the entire rock (interior and the rind) as having consistent material properties (see data inTable 4). Simulation 2 models the decrease in mechanical properties between an unweathered interior and weatheredalteration rind. Simulation 3 models a rock with similar material properties as Simulation 2 but with a dip (surfaceslope) of 45° to the NW.



In order to determine the appropriatevalue of KIcr in the alteration rind, werequire a method to estimate the ten-sile strength of small samples. TheVickers hardness test can be used toapproximate the tensile strength ofsmall, microscale regions of rock. Astudy of weathering rinds on andesiteby Oguchi [2001] found that theVickers hardness number (VHN) of theouter 3mm of an andesite weatheringrind was <100Nm�2, whereas at loca-tions deeper than ~10mm, where therock was relatively unweathered, the

VHN was ~5000Nm�2. These values correspond to a >98% loss in strength between the inner,unweathered rock and the outer weathering rind. There is a general linear relationship between hard-ness measurements and material tensile strength [Kahraman et al., 2012; Szlavin, 1974; Rice and Stoller,2000] and therefore a corresponding similar decrease in tensile strength between unaltered rock interiors andthe outer weathering rind. As we do not have similar VHN values for Ferrar Dolerites, and with the understandingthat the difference in lithology and weathering history may influence the applicability of such a comparison, weestimate the reduction in strength for our samples by applying the Vickers hardness test results from Oguchi[2001], i.e., a 98% loss in strength between unweathered rock and the rind: this would result in a decrease inthe range of tensile strengths from 9.4MPa–19.1MPa (the range of tensile strengths measured on dolerite sam-ples in this study; Table 3) down to ~0.19MPa–0.38MPa in the outer alteration rind. Converting these values tofracture toughness via equation (17) gives a KIcr range of 0.028MPam1/2 to 0.055MPam1/2 for alteration rinds.The critical stress intensity factor for subcritical crack propagation (K0) in the rind, assuming K0 =0.1 KIcr, isbetween 0.0028MPam1/2 and 0.0055MPam1/2; assuming that K0 =0.3 KIcr, this range becomes0.0084MPam1/2–0.017MPam1/2. Taking into account the range of dolerite tensile strengths and the uncer-tainty in the relationship between KIcr and K0, we examine a range of possible alteration rind K0 valuesbetween 0.0028MPam1/2 and 0.017MPam1/2.

In Table 5, we show the results of combining this approach with the maximum tensile stresses determinedby our thermal stress models and equation (16) to find the initial crack lengths required for crack propaga-tion in the weakened alteration rind for the range of possible K0 values. The crack lengths range from0.05 cm (for Simulation 2 and a K0 value of 0.0028MPam1/2) to 2.2 cm (for Simulation 3 and a K0 value of0.017MPam1/2). Using the average tensile strength of the dolerite samples measured in Table 3(~15MPa) and K0 = 0.2 KIcr (a median estimate), we find that crack propagation due to calculated thermalstresses may occur when the initial crack lengths are greater than ~0.51 cm for Simulation 2 or ~0.57 cmfor Simulation 3; these crack lengths are observed in our microscopic and macroscopic investigations ofalteration rinds (e.g., Figure 6). For comparison, the required crack lengths for thermal stress-induced subcri-tical crack propagation in a dolerite with no weakened alteration rind (i.e., Simulation 1, with a maximumtensile stress of 0.251MPa), using the average measured dolerite tensile strength of 15MPa, would be~1.2m for K0 = 0.1 KIcr and ~10.7m for K0 = 0.3 KIcr.

7. Discussion7.1. Study Limitations and Applicability

We examined the likelihood of alteration rind detachment due to thermal fatigue weathering on exposedclasts of Ferrar Dolerite in an upland region of the McMurdo Dry Valleys. We modeled the thermal stressesin a 3-D idealized dolerite clast with boundary conditions based on a 24 h period (a necessary time restric-tion due to computing requirements for each model run) of solar irradiance, air temperature, and windspeed recorded in Mullins Valley during the austral summer. Using the model results, coupled with subcri-tical crack growth theory, we found that thermal fatigue weathering may be operating to promote crackextension in weakened alteration rinds. Our results are best interpreted as evidence that thermal fatigue

Table 5. Initial Crack Lengths Required for Subcritical CrackPropagation in Dolerite Alteration Rinds

Initial Crack Length (cm)b

K0a Simulation 2 Simulation 3

0.0028 0.05 0.060.005 0.17 0.190.008 0.43 0.480.01 0.67 0.750.013 1.13 1.260.015 1.51 1.680.017 1.94 2.16

aCrack propagation occurs when KI (see equation (16)) = K0.bRequired crack length = 2 × c (equation (16)).



weathering is contributing to the detachment of Ferrar Dolerite alteration rinds during portions of thepresent-day austral summer; however, quantifying the magnitude of this process relative to other potentialweathering agents, or predicting exactly when and if a single dolerite clast will undergo thermal fatigueweathering, is not possible with our current data set.

Additionally, while our 3-D model is novel in that it is forced by field-recorded meteorological data and usesmaterial properties based on measurements of Ferrar Dolerite from the study site, it has some limitations. First,while it does reproduce well the trend in mature alteration rind surface temperature, it does not fully captureabrupt changes in rock-surface temperature observed in the field (Figure 10). This is likely because (1) our modelis an idealized parameterization of a dolerite clast with no surface roughness and a flat rind surface (i.e., no par-tially detached flakes or curvature), (2) we model the influence of wind using simple plate-averaged convectionand not a complete fluid dynamics treatment, and (3) we do not include the influence of temperature and RHchanges on material properties (in order to capture the dynamics of thermal fatigue in better fashion, a compu-tationally intensivemodel coupling heat transfer, solid mechanics, and fluid dynamics, with a 3-D scannedmodelof an actual clast including detailed surface characteristics, would be required). Second, our resulting thermalstresses are calculated assuming a homogenous rock and do not take into consideration the effects of grain-scaleprocesses and the influence of the mismatch in thermal and mechanical properties [e.g., Hall et al., 2008;Molaroet al., 2015; Walsh and Lomov, 2013] between plagioclase and pyroxene crystals that make up Ferrar Dolerite;including these effects would likely increase the maximum thermal stresses in the rind. Third, the uncertaintyin physical properties for dolerite clasts on Mullins Glacier (Tables 2–4), the unknown degree of weakening inthe alteration rind, and the uncertain estimation of subcritical crack propagation parameters all introduce somelevel of uncertainty to our results. A better parameterization of wind action over rough, uneven rock surfaces(which likely causes the fast temperature fluctuations seen in the field data) would also improve model accuracy.Notwithstanding the above, we believe that our resultant modeled stresses are likely minimum values.

Our results show that for a flat (no dip) dolerite surface, the maximum stress at the base of the alteration rindoccurs near the time of maximum solar irradiance. If the maximum stress at the base of the alteration rind isindeed tied to the daily peak solar irradiance at the rock surface, we would expect the maximum stress toincrease or decrease depending on (1) the solar luminosity, which changes on decadal [Foukal et al., 2006]to billion-year time scales [Gough, 1981; Newman and Rood, 1977]; (2) the solar angle, which changesthroughout the year; and (3) the amount of cloud or snow cover, which changes on a daily basis. Rock aspectis certainly important in generating thermal stresses [e.g., Eppes et al., 2010; McFadden et al., 2005], but ourresults over this short modeling period do not capture a significant difference in stresses between a flatalteration rind and one with a NW aspect. Additionally, Eppes et al. [2016] found that acoustic emission eventsindicative of crack opening are concentrated during periods of high irradiation when weather events perturbthe normal daily temperature field on a rock surface.

7.2. The Influence of Porosity, Chemical Alteration, and Albedo in Promoting Spalling

In our study, we determined a reduction in fracture toughness for alteration rinds by first assigning a reducedtensile strength and then converting this reduced strength to an appropriate fracture toughness (via equa-tion (17)). This decrease in fracture toughness (relative to unaltered dolerite interiors) is expected due todecreases in rock strength [Oguchi, 2001; Thomson et al., 2014] and increases in rock porosity [Navarre-Sitchler et al., 2015; Navarre-Sitchler et al., 2009; Oguchi, 2001, 2004; Oguchi and Matsukura, 2000], both ofwhich typically accompany the formation of alteration rinds (see Figure 6).

The increased porosity and fracture density in the rind also aids subcritical crack growth by allowing waterfrom snowmelt to enter the rind and facilitate processes like stress corrosion. Stress corrosion in silicateminerals arises due to strained Si-O bonds (i.e., a reduction in atomic orbital overlap) at the tips of preexistingcracks, where environmental agents such as water or brine may react more readily than at sites of unstrainedbonds. These reactions weaken the Si-O bonds and allow them to break at stresses less than they wouldotherwise [Atkinson, 1984; Michalske and Freiman, 1982]. Additionally, the oxidative-driven cation diffusionthat Salvatore et al. [2013] argues is responsible for the minor chemical variations in dolerite rinds, results in adisrupted crystal atomic structure through the loss of divalent cations from, and an increased Fe3+/Fe2+ in,the rind layer. This process weakens the mineral grains in the rind and decreases their ability to withstand crackextension, making them more likely to undergo subcritical crack propagation.



The formation of the Ferrar Dolerite alteration rinds also causes changes in surface albedo, with albedodecreasing as the rinds mature (Figure 5). This lower albedo raises the surface temperature of the rock andcan lead to an increase in meltwater entering the rinds from albedo-induced melting of snow, increasingthe likelihood of stress corrosion. Additionally, previous studies have shown that increases in rock tempera-ture and relative humidity decrease the fracture toughness of rocks [Dwivedi et al., 2000; Nara et al., 2012;Nara et al., 2013]. And, as noted above, near-surface values for RH and air temperature are both a functionof albedo and its control on snowmelt at the margin of localized pockets of snow. Given this, we shouldexpect subcritical crack extension via thermal stress weathering to be most important at the peak of the aus-tral summer when insolation is the highest and when local relative humidity near crack tips is high—forinstance, after the melting or sublimation of snow from dolerite surfaces.

An interesting observation is that unweathered, freshly fallen dolerite clasts do not appear to exhibit surfacespalls, even though they share similar albedo values with dolerite exhibiting mature alteration rinds. At facevalue, one would expect that both types of rock would achieve similar thermal stresses under identicalmeteorological forcing, yet the results of model Simulations 1 and 2, in which the outer rock surface is wea-kened in Simulation 2, show that thermal stresses are actually higher near the surface of strong, unweathereddolerite clasts. However, due to the strength of unweathered dolerite, subcritical crack propagation requireslarger preexisting cracks, whereas smaller cracks may be propagated due to thermal stresses in weakenedrock. These results imply that alteration rind development, including changes in rind strength and porosity,is critical to the formation of spalls on clasts of Ferrar Dolerite in Mullins Valley.

7.3. Other Factors That May Influence Spalling at the Surface of Ferrar Dolerite7.3.1. Grain SizeDuring our field investigations, we found that spalled rinds form primarily on dolerite clasts with plagioclasecrystals ~0.3–0.5mm in width. In the field, dolerite clasts with either finer- or coarser-grained plagioclase crys-tals (greater than or less than ~0.3–0.5mm in width) do not show widespread evidence of flakes (Figure 12).

Figure 12. Ferrar Dolerite in thin section. Alteration rinds typically occur in clasts with (a and b) medium-grained plagio-clase crystals (0.3–0.5mm in width) but not in (c and d) fine-grained dolerites. All images are 14mm across.



Typically, strength and fracture toughness decrease as grain size increases, with rocks composed of fine-grained crystals tending to be strongest [Lindqvist et al., 2007]. Experiments by Eberhardt et al. [1999] showedthat intergranular cracks can propagate most easily and quickly along long, straight-line crystal boundariestypical of coarse-grained rocks. Cracks may also propagate more easily in minerals that have strong cleavageplanes [Schultz et al., 1994], like pyroxene and plagioclase. This faster rate of crack opening likely allows cracksto coalesce faster, resulting in macroscopic failure and the grain-to-grain disintegration of rock. If correct, theassertion is that coarse-grained dolerite clasts do not exhibit rind flaking because they break down tooquickly by grussification. On the other hand, the finest-grained dolerites may not produce rind spalls becausethey are too resistant to weathering and fracture propagation due to their higher strength and KIcr values.7.3.2. MicrocracksOur model results show that for the highest tensile stresses achieved at the base of a 2mm thick rind duringthe study period, crack propagation may occur along preexisting cracks>0.05 cm (see Table 5). Cracks of thislength are common and may have been formed by the extension of microcracks by thermal stresses undermore extreme climates, or from other processes, including rock formation and subsequent cooling, unload-ing due to erosion of overburden [Nur and Simmons, 1970], or higher stress concentrations at twin lamellaeand crystal kink band boundaries [Kranz, 1983]. Additionally, cracks may form in the outer portions of doleriteclasts due to initial rockfall deposition near the valley head and during subsequent transport.7.3.3. Surface MorphologyOur model assumes a planar rock surface and does not take into account how a more complex, irregular sur-face may influence thermal stresses. For example, recent work has shown that surface curvature can exacer-bate surface-normal tensile stresses [Martel, 2006, 2011; Stock et al., 2012]. Generally, dolerite clasts on MullinsGlacier are tabular and flat, but the presence of rounded surfaces will promote spalling. Additionally,submillimeter-scale surface roughness may lead to a wider range of stresses at the rock surface than we cal-culate assuming a smooth, planar surface.

8. Conclusions

Thermal fatigue weathering is likely a key weathering process in hyperarid, cold-desert environments wherethe action of liquid water does not overshadow its geomorphic impact [Eppes et al., 2010; Eppes et al., 2016;Hall, 1999; McFadden et al., 2005; Molaro et al., 2015; Vasile and Vespremeanu-Stroe, 2016; Viles et al., 2010]. Inthis study, we use a combination of field measurements, laboratory analyses, and numerical modeling to testthe potential efficacy of thermal fatigue weathering in the spalling of thin (~2mm) alteration rinds observedon clasts of Ferrar Dolerite on Mullins Glacier, located in the upland McMurdo Dry Valleys. Field measure-ments show that mature alteration rinds undergo abrupt changes in surface temperature and experiencelarge-temperature gradients over their millimeter-scale thicknesses during the austral summer. Our modelingresults suggest that thermal stresses at the tip of microcracks in weakened alteration rinds likely play a keyrole in generating spalls under present-day meteorological forcing. The increase in porosity and decreasein strength of alteration rinds relative to unaltered rock interiors facilitate crack propagation. Additionally,the limited cryoturbation and longevity of clasts at the surface of Mullins till [Marchant and Denton, 1996;Marchant and Head, 2007] allow for cracks to propagate over thousands to millions of years, so that even veryslow crack growth may lead to eventual flake detachment/spalling.

ReferencesAldred, J., M. C. Eppes, K. Aquino, R. Deal, J. Garbini, S. Swami, A. Tuttle, and G. Xanthos (2016), The influence of solar-induced thermal stresses

on the mechanical weathering of rocks in humid mid-latitudes, Earth Surf. Process. Landforms, 41(5), 603–614, doi:10.1002/esp.3849.Atkinson, B. K. (1984), Subcritical crack-growth in geological materials, J. Geophys. Res., 89(Nb6), 4077–4114, doi:10.1029/JB089ib06p04077.Basu, A., T. B. Celestino, and A. A. Bortolucci (2009), Evaluation of rock mechanical behaviors under uniaxial compression with reference to

assessed weathering grades, Rock Mech. Rock Eng., 42(1), 73–93, doi:10.1007/s00603-008-0170-2.Bauer, E., S. Hasselmann, K. Hasselmann, and H. C. Graber (1992), Validation and assimilation of Seasat altimeter wave heights using theWam

wave model, J. Geophys. Res., 97(C8), 12,671–12,682, doi:10.1029/92JC01056.Bell, F. G., and C. A. Jermy (2000), The geotechnical character of some South African dolerites, especially their strength and durability, Quart. J.

Eng. Geol. Hydrogeol., 33, 59–76.Benito, G., M. J. Machado, and C. Sancho (1993), Sandstone weathering processes damaging prehistoric rock-paintings at the Albarracin-

Cultural-Park, NE Spain, Environ. Geol., 22(1), 71–79.Blackwelder, E. (1927), Fire as an agent in rock weathering, J. Geol., 35(2), 134–140, doi:10.2307/30056951.Campbell, I. B., and G. G. C. Claridge (1987), Antarctica: Soils, Weathering Processes, and Environment, Elsevier, Amsterdam.



AcknowledgmentsThis material is based upon work sup-ported by a National ScienceFoundation (NSF) Graduate ResearchFellowship Program grant awarded to J.Lamp, as well as NSF grants PLR-1043706 and PLR-0944702 awarded toD. Marchant. The authors would like tothank A. Hayden, G. Wissink, and A. Yaufor their help in the field; A. Christ forreviewing and editing themanuscript; S.Martel for the insights into rock fracturemechanisms; D. Elmo for the analyses ofdolerite properties; N. Chatterjee for thehelp with EDS/WDS measurements; andJ. Sparks for the help with XRD mea-surements. This manuscript was greatlyimproved by reviews from M. Eppes, K.Hall, H. Viles, and an anonymousreviewer. The data used in this study arelisted in the tables, supporting informa-tion, and at http://people.bu.edu/marchant/databases/index.html.

http://doi.org/10.1002/esp.3849

http://doi.org/10.1029/JB089ib06p04077

http://doi.org/10.1007/s00603-008-0170-2

http://doi.org/10.1029/92JC01056

http://doi.org/10.2307/30056951

http://people.bu.edu/marchant/databases/index.html

http://people.bu.edu/marchant/databases/index.html

Cardell, C., F. Delalieux, K. Roumpopoulos, A. Moropoulou, F. Auger, and R. Van Grieken (2003), Salt-induced decay in calcareous stone monu-ments and buildings in a marine environment in SW France, Constr. Build. Mater., 17(3), 165–179, doi:10.1016/S0950-0618(02)00104-6.

Clauser, C., and E. Huenges (1995), Thermal conductivity of rocks and minerals, in Rock Physics & Phase Relations: A Handbook of PhysicalConstants, edited by T. J. Ahrens, pp. 105–126, AGU, Washington, D. C., doi:10.1029/RF003p0105.

Collins, B. D., and G. M. Stock (2016), Rockfall triggering by cyclic thermal stressing of exfoliation fractures, Nat. Geosci., 9(5), 395–400,doi:10.1038/Ngeo2686.

Cooper, H. W., and G. Simmons (1977), The effect of cracks on the thermal expansion of rocks, Earth Planet. Sci. Lett., 36(3), 404–412,doi:10.1016/0012-821X(77)90065-6.

Dorn, R. I. (2003), Boulder weathering and erosion associated with a wildfire, Sierra Ancha Mountains, Arizona, Geomorphology, 55(1–4),155–171, doi:10.1016/S0169-555X(03)00138-7.

Dwivedi, R. D., A. K. Soni, R. K. Goel, and A. K. Dube (2000), Fracture toughness of rocks under sub-zero temperature conditions, Int. J. RockMech. Min., 37(8), 1267–1275.

Eberhardt, E., B. Stimpson, and D. Stead (1999), Effects of grain size on the initiation and propagation thresholds of stress-induced brittlefractures, Rock Mech. Rock Eng., 32(2), 81–99.

Eppes, M. C., L. D. McFadden, K. W. Wegmann, and L. A. Scuderi (2010), Cracks in desert pavement rocks: Further insights into mechanicalweathering by directional insolation, Geomorphology, 123(1–2), 97–108, doi:10.1016/j.geomorph.2010.07.003.

Eppes, M. C., B. Magi, B. Hallet, E. Delmelle, P. Mackenzie-Helnwein, K. Warren, and S. Swami (2016), Deciphering the role of solar-inducedthermal stresses in rock weathering, Geol. Soc. Am. Bull., doi:10.1130/b31422.1.

Foukal, P., C. Frohlich, H. Spruit, and T. M. L. Wigley (2006), Variations in solar luminosity and their effect on the Earth’s climate, Nature,443(7108), 161–166, doi:10.1038/nature05072.

Fountain, A. G., T. H. Nylen, A. Monaghan, H. J. Basagic, and D. Bromwich (2010), Snow in the McMurdo Dry Valleys, Antarctica, Int. J. Climatol.,30(5), 633–642, doi:10.1002/Joc.1933.

Goh, T. L., A. G. Rafek, A. R. Samsudin, M. H. Ariffin, and N. B. Yunus (2011), Rock mass geomechanical characterization by seismic methods:Poisson’s ratio, Sains Malays, 40(6), 561–568.

Gomez-Heras, M., B. J. Smith, and R. Fort (2008), Influence of surface heterogeneities of building granite on its thermal response and itspotential for the generation of thermoclasty, Environ. Geol., 56(3–4), 547–560, doi:10.1007/s00254-008-1356-3.

Gordon, S. I., and R. I. Dorn (2005), In situ weathering rind erosion, Geomorphology, 67(1–2), 97–113, doi:10.1016/j.geomorph.2004.06.011.Gough, D. O. (1981), Solar interior structure and luminosity variations, Sol. Phys., 74(1), 21–34, doi:10.1007/Bf00151270.Gu, D. X., W. Tamblyn, I. Lamb, and N. Ramsey (2008), Effect of weathering on strength and modulus of basalt and siltstone, in 42nd US Rock

Mechanics Symposium, San Francisco, Calif.Gueymard, C. A. (1995), SMARTS, A Simple Model of the Atmospheric Radiative Transfer of Sunshine: Algorithms and Performance Assessment

Professional Paper FSEC-PF-270-95, Florida Solar Energy Center, 1679 Clearlake Rd., Cocoa, Fla.Gueymard, C. A. (2001), Parameterized transmittancemodel for direct beam and circumsolar spectral irradiance, Solar Energy, 71(5), 325–346,

doi:10.1016/S0038-092x(01)00054-8.Gunnell, Y., D. Jarman, R. Braucher, M. Calvet, M. Delmas, L. Leanni, D. Bourles, M. Arnold, G. Aumaitre, and K. Keddaouche (2013), The granite

tors of Dartmoor, Southwest England: Rapid and recent emergence revealed by late Pleistocene cosmogenic apparent exposure ages,Quat. Sci. Rev., 61, 62–76, doi:10.1016/j.quascirev.2012.11.005.

Hall, K. (1999), The role of thermal stress fatigue in the breakdown of rock in cold regions, Geomorphology, 31(1–4), 47–63.Hall, K. (2003), Micro-transducers and high-frequency rock temperature data: Changing our perspectives on rock weathering in cold regions,

Permafrost, 1(2), 349–354.Hall, K., and M. F. Andre (2001), New insights into rock weathering from high-frequency rock temperature data: An Antarctic study of

weathering by thermal stress, Geomorphology, 41(1), 23–35.Hall, K., and C. E. Thorn (2014), Thermal fatigue and thermal shock in bedrock: An attempt to unravel the geomorphic processes and pro-

ducts, Geomorphology, 206, 1–13, doi:10.1016/j.geomorph.2013.09.022.Hall, K., I. Meiklejohn, and J. Arocena (2007), The thermal responses of rock art pigments: Implications for rock art weathering in southern

Africa, Geomorphology, 91(1–2), 132–145, doi:10.1016/j.geomorph.2007.02.002.Hall, K., M. Guglielmin, and A. Strini (2008), Weathering of granite in Antarctica: II. Thermal stress at the grain scale, Earth Surf. Process.

Landforms, 33(3), 475–493, doi:10.1002/Esp.1617.Hallet, B., and E. D. Waddington (1991), Buoyancy forces induced by freeze-thaw in the active layer—Implications for diapirism and soil

circulation, Periglac. Geomorphol., 251–279.Kahraman, S., M. Fener, and E. Kozman (2012), Predicting the compressive and tensile strength of rocks from indentation hardness index, J. S.

Afr. I Min. Metall., 112(5), 331–339.Kendrick, K. J., C. A. Partin, and R. C. Graham (2016), Granitic boulder erosion caused by Chaparral wildfire: Implications for cosmogenic

radionuclide dating of bedrock surfaces, J. Geol., 124(4), 529–539, doi:10.1086/686273.Kilic, R. (1995), The degree of alteration and geomechanical properties of diabase in the Ankara Ophiolitic Mélange, Turkey, Environ. Eng.

Geosci., I(3), 341–351, doi:10.2113/gseegeosci.I.3.341.Knight, J., and S. W. Grab (2014), Lightning as a geomorphic agent on mountain summits: Evidence from southern Africa, Geomorphology,

204, 61–70, doi:10.1016/j.geomorph.2013.07.029.Kowalewski, D. E., D. R. Marchant, J. S. Levy, and J. W. Head (2006), Quantifying low rates of summertime sublimation for buried glacier ice in

Beacon Valley, Antarctica, Antarct. Sci., 18(3), 421–428, doi:10.1017/S0954102006000460.Kowalewski, D. E., D. R. Marchant, K. M. Swanger, and J. W. Head (2011), Modeling vapor diffusion within cold and dry supraglacial tills of

Antarctica: Implications for the preservation of ancient ice, Geomorphology, 126(1–2), 159–173, doi:10.1016/j.geomorph.2010.11.001.Kranz, R. L. (1983), Microcracks in rocks—A review, Tectonophysics, 100(1–3), 449–480.Lancaster, N. (2004), Relations between aerodynamic and surface roughness in a hyper-arid cold desert: Mcmurdo dry valleys, Antarctica,

Earth Surf. Process. Landforms, 29(7), 853–867, doi:10.1002/esp.1073.Lindqvist, J. E., U. Akesson, and K. Malaga (2007), Microstructure and functional properties of rock materials, Mater. Charact., 58(11–12),

1183–1188, doi:10.1016/j.matchar.2007.04.012.Mackay, S. L., and D. R. Marchant (2016), Dating buried glacier ice using cosmogenic He-3 in surface clasts: Theory and application to Mullins

Glacier, Antarctica, Quat. Sci. Rev., 140, 75–100, doi:10.1016/j.quascirev.2016.03.013.Mackay, S. L., D. R. Marchant, J. L. Lamp, and J. W. Head (2014), Cold-based debris-covered glaciers: Evaluating their potential as climate

archives through studies of ground-penetrating radar and surface morphology, J. Geophys. Res. Earth Surf., 119, 2505–2540, doi:10.1002/2014JF003178.



http://doi.org/10.1016/S0950-0618(02)00104-6

http://doi.org/10.1029/RF003p0105

http://doi.org/10.1038/Ngeo2686

http://doi.org/10.1016/0012-821X(77)90065-6

http://doi.org/10.1016/S0169-555X(03)00138-7

http://doi.org/10.1016/j.geomorph.2010.07.003

http://doi.org/10.1130/b31422.1

http://doi.org/10.1038/nature05072

http://doi.org/10.1002/Joc.1933

http://doi.org/10.1007/s00254-008-1356-3


http://doi.org/10.1007/Bf00151270

http://doi.org/10.1016/S0038-092x(01)00054-8

http://doi.org/10.1016/j.quascirev.2012.11.005



http://doi.org/10.1002/Esp.1617

http://doi.org/10.1086/686273

http://doi.org/10.2113/gseegeosci.I.3.341


http://doi.org/10.1017/S0954102006000460



http://doi.org/10.1016/j.matchar.2007.04.012

http://doi.org/10.1016/j.quascirev.2016.03.013

http://doi.org/10.1002/2014JF003178

http://doi.org/10.1002/2014JF003178

Marchant, D. R., and G. H. Denton (1996), Miocene and Pliocene paleoclimate of the Dry Valleys region, southern Victoria Land: A geomor-phological approach, Mar. Micropaleontol., 27(1–4), 253–271.

Marchant, D. R., and J. W. Head (2007), Antarctic dry valleys: Microclimate zonation, variable geomorphic processes, and implications forassessing climate change on Mars, Icarus, 192(1), 187–222.

Marchant, D. R., A. R. Lewis, W. M. Phillips, E. J. Moore, R. A. Souchez, G. H. Denton, D. E. Sugden, N. Potter, and G. P. Landis (2002), Formation ofpatterned ground and sublimation till over Miocene glacier ice in Beacon Valley, southern Victoria Land, Antarctica, Geol. Soc. Am. Bull.,114(6), 718–730, doi:10.1130/0016-7606(2002)114<0718:fopgas>2.0.co;2.

Marchant, D. R., S. L. Mackay, J. L. Lamp, A. T. Hayden, and J. W. Head (2013), A review of geomorphic processes and landforms in the DryValleys of southern Victoria Land: Implications for evaluating climate change and ice-sheet stability, Geol. Soc. Lond. Spec. Publ., 381,doi:10.1144/sp381.10.

Margerison, H. R., W. M. Phillips, F. M. Stuart, and D. E. Sugden (2005), Cosmogenic He-3 concentrations in ancient flood deposits from theCoombs Hills, northern Dry Valleys, East Antarctica: Interpreting exposure ages and erosion rates, Earth Planet. Sci. Lett., 230(1–2), 163–175,doi:10.1016/j.epsl.2004.11.007.

Martel, S. J. (2006), Effect of topographic curvature on near-surface stresses and application to sheeting joints, Geophys. Res. Lett., 33, L01308,doi:10.1029/2005GL024710.

Martel, S. J. (2011), Mechanics of curved surfaces, with application to surface-parallel cracks, Geophys. Res. Lett., 38, L20303, doi:10.1029/2011GL049354.

Matsuoka, N. (2008), Frost weathering and rockwall erosion in the southeastern Swiss Alps: Long-term (1994–2006) observations,Geomorphology, 99(1–4), 353–368, doi:10.1016/j.geomorph.2007.11.013.

Matsuoka, N., and J. Murton (2008), Frost weathering: Recent advances and future directions, Permafrost Periglac. Process., 19(2), 195–210,doi:10.1002/Ppp.620.

McCabe, S., B. J. Smith, J. J. McAlister, M. Gomez-Heras, D. McAllister, P. A. Warke, J. M. Curran, and P. A. M. Basheer (2013), Changing climate,changing process: Implications for salt transportation and weathering within building sandstones in the UK, Environ. Earth Sci., 69(4),1225–1235, doi:10.1007/s12665-013-2278-2.

McFadden, L. D., M. C. Eppes, A. R. Gillespie, and B. Hallet (2005), Physical weathering in and landscapes due to diurnal variation in thedirection of solar heating, Geol. Soc. Am. Bull., 117(1–2), 161–173, doi:10.1130/B25508.1.

Meredith, P. G., and B. K. Atkinson (1985), Fracture-toughness and subcritical crack-growth during high-temperature tensile deformation ofwesterly granite and black gabbro, Phys. Earth Planet. Inter., 39(1), 33–51, doi:10.1016/0031-9201(85)90113-X.

Michalske, T. A., and S. W. Freiman (1982), A molecular interpretation of stress-corrosion in silica, Nature, 295(5849), 511–512, doi:10.1038/295511a0.

Mol, L., and H. A. Viles (2010), Geoelectric investigations into sandstone moisture regimes: Implications for rock weathering and the dete-rioration of San Rock Art in the Golden Gate Reserve, South Africa, Geomorphology, 118(3–4), 280–287, doi:10.1016/j.geomorph.2010.01.008.

Molaro, J. L., and C. P. McKay (2010), Processes controlling rapid temperature variations on rock surfaces, Earth Surf. Process. Landforms, 35(5),501–507, doi:10.1002/Esp.1957.

Molaro, J. L., S. Byrne, and S. A. Langer (2015), Grain-scale thermoelastic stresses and spatiotemporal temperature gradients on airless bodies,implications for rock breakdown, J. Geophys. Res. Planet., 120, 255–277, doi:10.1002/2014JE004729.

Morgan, D., J. Putkonen, G. Balco, and J. Stone (2010), Degradation of glacial deposits quantified with cosmogenic nuclides, QuartermainMountains, Antarctica, Earth Surf. Process. Landforms, 36(2), 217–228, doi:10.1002/Esp.2039.

Muzikar, P. (2008), Cosmogenic nuclide concentrations in episodically eroding surfaces: Theoretical results, Geomorphology, 97(3–4),407–413, doi:10.1016/j.geomorph.2007.08.020.

Muzikar, P. (2009), General models for episodic surface denudation and its measurement by cosmogenic nuclides, Quat. Geochronol., 4(1),50–55, doi:10.1016/j.quageo.2008.06.004.

Nara, Y., K. Morimoto, N. Hiroyoshi, T. Yoneda, K. Kaneko, and P. M. Benson (2012), Influence of relative humidity on fracture toughness ofrock: Implications for subcritical crack growth, Int. J. Solids Struct., 49(18), 2471–2481, doi:10.1016/j.ijsolstr.2012.05.009.

Nara, Y., H. Yamanaka, Y. Oe, and K. Kaneko (2013), Influence of temperature and water on subcritical crack growth parameters and long-term strength for igneous rocks, Geophys. J. Int., 193(1), 47–60, doi:10.1093/gji/ggs116.

Navarre-Sitchler, A., C. I. Steefel, L. Yang, L. Tomutsa, and S. L. Brantley (2009), Evolution of porosity and diffusivity associated with chemicalweathering of a basalt clast, J. Geophys. Res. Earth, 114, F02016, doi:10.1029/2008JF001060.

Navarre-Sitchler, A., S. L. Brantley, and G. Rother (2015), How porosity increases during incipient weathering of crystalline silicate rocks, Rev.Mineral. Geochem., 80, 331–354, doi:10.2138/rmg.2015.80.10.

Newman, M. J., and R. T. Rood (1977), Implications of solar evolution for the Earth’s early atmosphere, Science, 198(4321), 1035–1037,doi:10.1126/science.198.4321.1035.

Nishiizumi, K., C. P. Kohl, J. R. Arnold, J. Klein, D. Fink, and R. Middleton (1991), Cosmic-ray produced Be-10 and Al-26 in Antarctic rocks—Exposure and erosion history, Earth Planet. Sci. Lett., 104(2–4), 440–454, doi:10.1016/0012-821x(91)90221-3.

Nur, A., and G. Simmons (1970), Origin of small cracks in igneous rocks, Int. J. Rock Mech. Min., 7(3), 307–314, doi:10.1016/0148-9062(70)90044-6.

Oguchi, C. T. (2001), Formation of weathering rinds on andesite, Earth Surf. Process. Landforms, 26(8), 847–858, doi:10.1002/esp.230.Oguchi, C. T. (2004), A porosity-related diffusion model of weathering-rind development, Catena, 58(1), 65–75, doi:10.1016/j.

catena.2003.12.002.Oguchi, C. T., and Y. Matsukura (2000), Effect of porosity on the increase in weathering-rind thicknesses of andesite gravel, Eng. Geol., 55(1–2),

77–89, doi:10.1016/S0013-7952(99)00108-8.Rice, P. M., and R. E. Stoller (2000), Correlation of nanoindentation and conventional mechanical property measurements, paper presented at

Fundamentals of Nanoindentation and Nanotribology II, Materials Research Society, Boston, Mass.Robertson, E. C. (1988), Thermal properties of rocks, Report Rep., 88–441.Robertson, E. C., and D. L. Peck (1974), Thermal conductivity of vesicular basalt from Hawaii, J. Geophys. Res., 79(32), 4875–4888, doi:10.1029/

JB079i032p04875.Salvatore, M. R., J. F. Mustard, J. W. Head, R. F. Cooper, D. R. Marchant, and M. B. Wyatt (2013), Development of alteration rinds by

oxidative weathering processes in Beacon Valley, Antarctica, and implications for Mars, Geochim. Cosmochim. Acta, 115, 137–161,doi:10.1016/j.gca.2013.04.002.

Schäfer, J. M., S. Ivy-Ochs, R. Wieler, J. Leya, H. Baur, G. H. Denton, and C. Schluchter (1999), Cosmogenic noble gas studies in the oldestlandscape on earth: Surface exposure ages of the Dry Valleys, Antarctica, Earth Planet. Sci. Lett., 167(3–4), 215–226.



http://doi.org/10.1130/0016-7606(2002)114%3c0718:fopgas%3e2.0.co;2



http://doi.org/10.1144/sp381.10

http://doi.org/10.1016/j.epsl.2004.11.007

http://doi.org/10.1029/2005GL024710

http://doi.org/10.1029/2011GL049354

http://doi.org/10.1029/2011GL049354


http://doi.org/10.1002/Ppp.620

http://doi.org/10.1007/s12665-013-2278-2

http://doi.org/10.1130/B25508.1

http://doi.org/10.1016/0031-9201(85)90113-X

http://doi.org/10.1038/295511a0

http://doi.org/10.1038/295511a0




http://doi.org/10.1002/2014JE004729



http://doi.org/10.1016/j.quageo.2008.06.004

http://doi.org/10.1016/j.ijsolstr.2012.05.009

http://doi.org/10.1093/gji/ggs116

http://doi.org/10.1029/2008JF001060

http://doi.org/10.2138/rmg.2015.80.10

http://doi.org/10.1126/science.198.4321.1035

http://doi.org/10.1016/0012-821x(91)90221-3

http://doi.org/10.1016/0148-9062(70)90044-6

http://doi.org/10.1016/0148-9062(70)90044-6


http://doi.org/10.1016/j.catena.2003.12.002

http://doi.org/10.1016/j.catena.2003.12.002

http://doi.org/10.1016/S0013-7952(99)00108-8

http://doi.org/10.1029/JB079i032p04875

http://doi.org/10.1029/JB079i032p04875

http://doi.org/10.1016/j.gca.2013.04.002

Schön, J. R. (1996), Physical Properties of Rocks : Fundamentals and Principles of Petrophysics, vol. 16, 1st ed., 583 pp., Pergamon, Oxford, OX,UK; Tarrytown, New York.

Schultz, R. A., M. C. Jensen, and R. C. Bradt (1994), Single-crystal cleavage of brittle materials, Int. J. Fract., 65(4), 291–312, doi:10.1007/Bf00012370.

Segall, P. (1984), Rate-dependent extensional deformation resulting from crack growth in rock, J. Geophys. Res., 89(B6), 4185–4195,doi:10.1029/JB089iB06p04185.

Shean, D. E., and D. R. Marchant (2010), Seismic and GPR surveys of Mullins Glacier, McMurdo Dry Valleys, Antarctica: Ice thickness, internalstructure and implications for surface ridge formation, J. Glaciol., 56(195), 48–64.

Shean, D. E., J. W. Head, and D. R. Marchant (2007), Shallow seismic surveys and ice thickness estimates of the Mullins Valley debris-coveredglacier, McMurdo Dry Valleys, Antarctica, Antarct. Sci., 19(4), 485–496, doi:10.1017/S0954102007000624.

Shen, B. (2013), Modelling Rock Fracturing Processes: A Fracture Mechanics Approach Using FRACOD, vol. 173, Springer, New York.Stock, G. M., S. J. Martel, B. D. Collins, and E. L. Harp (2012), Progressive failure of sheeted rock slopes: The 2009–2010 Rhombus Wall rockfalls

in Yosemite Valley, California, USA, Earth Surf. Process. Landforms, 37(5), 546–561, doi:10.1002/esp.3192.Summerfield, M. A., F. M. Stuart, H. A. P. Cockburn, D. E. Sugden, G. H. Denton, T. Dunai, and D. R. Marchant (1999), Long-term rates of

denudation in the Dry Valleys, Transantarctic Mountains, southern Victoria Land, Antarctica based on in-situ-produced cosmogenicNe-21, Geomorphology, 27(1–2), 113–129.

Szlavin, J. (1974), Relationships between some physical properties of rock determined by laboratory tests, Int. J. Rock Mech. Min. Sci. Geomech.Abstr., 11(2), 57–66, doi:10.1016/0148-9062(74)92649-7.

Thomson, B. J., J. A. Hurowitz, L. L. Baker, N. T. Bridges, A. M. Lennon, G. Paulsen, and K. Zacny (2014), The effects of weathering on thestrength and chemistry of Columbia River Basalts and their implications for Mars Exploration Rover Rock Abrasion Tool (RAT) results, EarthPlanet. Sci. Lett., 400, 130–144, doi:10.1016/j.epsl.2014.05.012.

Vasile, M., and A. Vespremeanu-Stroe (2016), Thermal weathering of granite spheroidal boulders in a dry-temperate climate, northernDobrogea, Romania, Earth Surf. Process. Landforms, doi:10.1002/esp.3984.

Viles, H., B. Ehlmann, C. F. Wilson, T. Cebula, M. Page, and M. Bourke (2010), Simulating weathering of basalt on Mars and Earth by thermalcycling, Geophys. Res. Lett., 37, L18201, doi:10.1029/2010GL043522.

Wakasa, S. A., S. Nishimura, H. Shimizu, and Y. Matsukura (2012), Does lightning destroy rocks?: Results from a laboratory lightning experi-ment using an impulse high-current generator, Geomorphology, 161–162, 110–114, doi:10.1016/j.geomorph.2012.04.005.

Walder, J., and B. Hallet (1985), A theoretical-model of the fracture of rock during freezing, Geol. Soc. Am. Bull., 96(3), 336–346.Walsh, S. D. C., and I. N. Lomov (2013), Micromechanical modeling of thermal spallation in granitic rock, Int. J. Heat Mass Trans., 65, 366–373,

doi:10.1016/j.ijheatmasstransfer.2013.05.043.Wolfe, S. A., and W. G. Nickling (1996), Shear stress partitioning in sparsely vegetated desert canopies, Earth Surf. Process. Landforms, 21(7),

607–619.Yau, A. M., M. L. Bender, D. R. Marchant, and S. L. Mackay (2015), Geochemical analyses of air from an ancient debris-covered glacier,

Antarctica, Quat. Geochronol., 28, 29–39, doi:10.1016/j.quageo.2015.03.008.Zhang, Z. X. (2002), An empirical relation between mode I fracture toughness and the tensile strength of rock, Int. J. Rock Mech. Min., 39(3),

401–406, doi:10.1016/S1365-1609(02)00032-1.



http://doi.org/10.1007/Bf00012370

http://doi.org/10.1007/Bf00012370

http://doi.org/10.1029/JB089iB06p04185

http://doi.org/10.1017/S0954102007000624


http://doi.org/10.1016/0148-9062(74)92649-7

http://doi.org/10.1016/j.epsl.2014.05.012


http://doi.org/10.1029/2010GL043522


http://doi.org/10.1016/j.ijheatmasstransfer.2013.05.043

http://doi.org/10.1016/j.quageo.2015.03.008

http://doi.org/10.1016/S1365-1609(02)00032-1

Thermal stress weathering and the spalling of Antarctic rocks · 2017-04-05 · Thermal stress...

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