18 GEO NEWS

Frost HeaveBy Lorraine Manz

TherewasonceawidelyheldbeliefamongtheruralinhabitantsofseveralEnglishcountiesthatstonesgrewandmultiplied. Tothefarmersandlaborerswhoworkedthelandthisexplainedwhy,whenafieldwasclearedofstones,itwouldsoonbelitteredwithmore.Thecommonthoughtwasthatthestonesgrewfromsmallpebblesinthesoilandthensomehowrosetothesurface.Manypeopleevenwentsofarastobelievethatthepebblesthemselvesweretheoffspringofso-called“mother-”or“breeding-stones,”inreality chunksofanunusual siliceousflintconglomerate that isalsoknownlocallyas“puddingstone”becauseofitsresemblancetoanold-fashionedplumpudding(fig.1).

Mother-stones are still kept by some,but only as curiosities and conversationpieces.No-oneintheirrightmindtodaywould seriously bestow them with anyprocreative capability or believe thatpebblesarebabyrocks. Andthearrivalof yet anothermultitude of stones thatin years past country people could onlyattributetosomesortofmagic,wenowrecognize as nothing more than onemanifestationofanaturalprocesscalledfrostheave.Itisthesameprocess,oftenaggravated by flooding and/or heavy

traffic,thatruinsmilesofNorthDakota’sroadseveryspring:theobstaclecourseofbrokenpavement,potholes,andcarbuncle-likehumps(fig.2)thattheybecomeaswinterlosesitsgripandtheannualthawsetsinisprimarilytheresultoffrostheave.

Frostheaveisaformoffrostaction,aphysicalweatheringprocessinvolvingthecyclicfreezingandthawingofwaterinsoilorrock.Heaveinthiscontextreferstotheupwardmovementofthegroundsurfacethatoccursinresponsetotheseasonalformationoficeintheunderlyingsoil.Thedynamicsofthisostensiblysimpleprocessareexceedinglycomplexandstillnotfullyunderstood;yetdespiteits intricacies,the incidenceoffrostheaveisdependentonjustthreethings:besidesfreezingtemperatures,itonlyrequirestherightkindofsoilandanabundant,readilyavailablewatersupply.

Early investigators attributed frost heave to the expansion thatoccurswhenwaterfreezes,butthisdidnotexplainwhytheeffectsof frost heave are so frequentlymuch greater than frozen soilaloneiscapableofproducing.Thediscrepancyquicklybecomes

Figure1.Puddingstoneisatypeofconglomerateinwhichthecoloroftheclastscontrastssharplywiththatofthematrixgivingittheappearanceof an old-fashioned plum pudding. The photo shows an example ofHertfordshire puddingstone (named after the county of HertfordshireinsouthernEnglandwheremostof it isfound),whichconsistsofwell-rounded brown and dark gray flint pebbles distributed throughout astronglycemented,muchlighter-coloredsiliceousmatrix.InsomepartsofEnglandrockslikethiswereknownas“mother-stones”or“breeding-stones”inthebeliefthatpebblesweretheiroffspring.PhotocourtesyofD.M.GACFossilsandreleasedbythemintothepublicdomain.

Figure 2. Asphalt pavement on a Bismarckstreet damaged by frost heave. Severalchunks of the surface course have beendislodged by the wheels of local trafficexposing the underlying aggregate base.PhotobyLorraineManz.

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apparent if you consider that when water freezes its volumeincreasesbyabout9%.Thatbeingthecase,asoilwithawatercontentof50%(aboutasmuchastheaveragesoilcanhold)wouldonlyexpandbyhalfthisamount.Yetevenifthisexpansionwasunidirectional (theold theoryassumed itwasupwardsbecausethatwasthepathofleastresistance)itwouldonlyproduceabouthalfaninchofupliftperverticalfootoffrozensoil. InatypicalNorthDakotawinterthegroundfreezestoanaveragedepthofabout4.5feet(1.4m)(Jensen,Nodate),butasfigure3shows,heavingcanfarexceedthe1or2inches(2.5-5cm)thispremiseforecasts.Clearly,somethingelseisgoingon.

Theproblemwith the theory that frostheave is causedby theexpansion ofwaterwhen it freezes is that it was based on anerroneous assumption,whichwas that soils behaved as closedsystems(nothinginorout). EvidencetothecontraryremainedlargelyignoreduntilStephenTaber,ageologistattheUniversityofSouthCarolina,publishedtheresultsofaseriesofinvestigationsthat debunked the old theory once and for all (Taber, 1929,1930).Taberdemonstratedthatitwasnotexpansion,butrathertheformationoficelensesbysegregationofwaterfromthesoilasthegroundfreezesthat is theprincipalcauseof frostheave.Moreover,byexperimentingwith soilsasopensystemshewasabletoshowthatlensgrowthmaybesustainedbytheadditionofgroundwaterdrawnfromwarmerzonesbelowthefreezingfront,andalsothatliquidsotherthanwater(Taberusedbenzeneandnitrobenzene)caninducefrostheave.Thislastobservationclearlyconfirmedthatthevolumetricexpansionofwaterasitturnstoicecouldnotbethedrivingforcebehindtheverticaldisplacementoffrozensoilbecause,likealmostallliquidsbesideswater,benzeneandnitrobenzenecontractastheysolidify.

Ice lensesare lens-shapedmassesofalmostpure ice that formin frozensoilorrock. Lens formationtakesplaceat,orashortdistancebehind,thefreezingfrontatanydepthwhereconditionsare favorable and will continue until those conditions change.Becausetheyformperpendiculartothedirectionofheatflow,icelensestendtogrowwiththeirlongaxesorientedparalleltothe

groundsurface. Most lensingisperiodic,givingrisetomultiplelensesseparatedverticallyfromoneanotherbyalayeroffrozensoil. Single, thick lenses are rare in temperate climatic zonesbecause their formation depends on persistent, steady stateconditions.Icelensesrangeinsizefromhair-thinslivers,barelyvisible to the naked eye, to laterally very extensive structuresseveralfeetthick.

An up-close examination of an ice lens reveals a structurecomposedofamultitudeof thin,hair-likecrystals thatgivethelens what has been described as a “satiny” appearance. The

crystalsdevelop,andarethusoriented;paralleltothedirectionofheatflowanditistheirgrowth,notthepathofleastresistance,thatcontrolsthedirectionofheave.

Thegroundfreezesfromthesurfacedown,progressingalongafront parallel to the surface andperpendicular to thedirectionofheatflow,therebycreatingathermalgradientasthegroundlosesheattothecoldairabove it. An ice lensalsoformsfromthe topdownand growsby the additionofwater to its lower,warmersurface fromsoilbelowthefreezing front (fig.4). Thisis a far-from-straightforward process because it requires a setof conditions that will allowwater to (i) defy gravity and flowupwardsand(ii)co-existwithiceattemperaturesbelowfreezing.

Inaporousmediumlikesoil,gettingwatertoflowupwardsisnotdifficult because itwill rise naturally by capillary action. If thewater ismovingthroughunfrozensoil towardsthefreezefront,thenthisriseisaidedbyvirtueofthefactthatitismovingdownthethermalgradient.Waterinfreezingsoilsisalsomovedaroundbycryogenicsuction forces thatareproducedwithinapartiallyfrozenregion,orfrozenfringe,justbelowthebasalsurfaceofthe

Figure 3. Spring 2011.Frost heave on thisBismarck street has liftedparts of the road surfaceabout 18 inches (46 cm).The maximum freezedepth in the Bismarckarea for the winter of2010-2011 was about 40inches (100 cm)* (NorthDakota State ClimateOffice, 2011). Photo byLorraineManz.

*NodataavailableforBismarckweatherstations.ThisfigurewasestimatedusingdeepsoiltemperaturesfromthenearestNDAWNstation at Streeter in StutsmanCounty, approximately 65miles(100km)eastofBismarck.

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growing ice lens (fig. 5). Themicroscopic interactions betweensoilgrains, ice,andwaterthatareresponsibleforthesesuctionforcesarealsothefundamentalcontrollinginfluenceonicelensformation and growth, and thus, ultimately drive the wholeprocessoffrostheave.Theyarealsothereasonswhywatercansometimesremaininliquidformatsub-zero(0°C)temperatures.

Therearetwothermodynamicprocessesthatallowliquidwatertopersistatbelow-freezingtemperatures.ThefirstistheGibbs-Thomson effect, which is a surface phenomenon that causesmeltingpointdepression.Whenicefreezesinaporousmedium,solidificationtakesplacealongacurvedinterfacethatisconvex-outward with respect to the ice. Freezing progresses by thepenetrationofthissolid-liquidinterfaceintoincreasinglysmallerpore spaces; and in the sameway that the radius of curvatureof the meniscus formed by capillary action at a liquid-vaporboundary is proportional to the internal radius of the capillarytube,i.e.,thenarrowertheporespace,thehighertheconvexityof the icesurface. Ataparticularsub-zerotemperaturea levelofporespaceconfinementisreachedwheretheenergyrequiredto furtherreducethecurvatureof the ice-solid interfacewouldexceedtheamountrequiredtomaintainasmallvolumeofwaterinitsliquidform.Asthetemperaturecontinuestofall,iceisableto move into more confined spaces and the amount of liquidwaterdecreasesuntileventuallyitisallfrozen.

Liquidwatermayalsopersistatbelow-freezingtemperaturesasananometers-thick,“premelted”filmthatformsalongthesurfacecontactsbetweenindividualsoilgrainsandice.Premeltingisaneffect that is surprisingly common in nature, and besides frostheave is known to have a controlling influence on a numberof other natural phenomena including the electrification ofthunderclouds, the formationof sea ice, andpossibly even thedevelopment of planetary systems (Dash et al., 2006). Themolecular interactions that cause premelting are complex, butthereasonfortheliquidfilmsissimpleenough:theyareabarrier,set in place to attenuate the solid-solid electrostatic forces ofrepulsionbetweenthesurfacesoftheiceandsoilgrains.

Water istransportedalongthese liquidpathwaysfromthezeroisotherm to the base of the ice lens by pressure differencesgeneratedbythesameforcesthatproducepremeltedfilms.Theliquidfilmsurroundingasoilgrainwithinthefrozenfringeisthickeronits lower(warmer)side(fig.6). Thisvariationinthicknessisaccompaniedbyacorrespondingpressurechangewithinthefilm(Dash, 1989), which establishes a pressure gradient across thesoil grainparallel,but in theoppositedirection, to the thermalgradient.Thegrainisthuspushedawayfromtheicelenstowardswarmertemperaturesaswaterisdrawn(sucked)throughthefilmaroundthegraintofeedthegrowing lens(Rempel,2010). Theprocessissustainedbythecontinuoussupplyofliquidwaterfrom

Figure4.Formationoficelensesinfrozengroundoverlainbypavement.Freezing takes place from the surface down (white arrows). Whenconditions are favorable, an ice lens begins to form a short distancebehindthefreezingfront.Fedbyliquidgroundwaterfromwarmerzonesdeeper inthesoilprofile,the lenswillcontinuetogrowforas longasthecontrollingmechanismsallow. Multiple lenses reflectfluctuationsinthesecontrolsduetochangesinsurfacetemperature(whichaffectsthe rate of freezing), soil texture, andwater availability. The amountof vertical displacement (heave) is roughly equal to the combinedthicknessesoftheunderlyingicelenses.Heavingcausesthepavementtocrack,resultinginthekindofdamageshowninfigures2and3.

Figure5. The frozen fringebelowa growing ice lens (representedbythehazyareabelowthelowesticelensesinfigure4).Eventhoughthetemperaturehereisafewdegreesbelowfreezing,liquidwaterisabletoexistinequilibriumwithiceowingto(i)meltingpointdepressioncausedbytheGibbs-Thomsoneffectand(ii)premeltingattheice-soilinterface.ModifiedfromRempel,2010.

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belowthefrozenfringe,and isanexampleofpressure-inducedregelation.NotallsoilsaresusceptibletofrostheaveAtaboutthesametimethatTaberwasconductinghislaboratoryexperimentsinSouthCarolina,GunnarBeskow(1935),ageologistwith the Swedish Institute of Roads, launched an investigationtoaddress the costlyproblemof frostdamage to Scandinavia’stransportationnetwork.Inwhatwasthefirstin-depthfieldstudyoffrostheave,Beskownotedthatthemagnitudeofitseffectsislargelydeterminedbytheparticlesizeofthesoil,anobservationconsistentwithTaber’sexperimentalfindings.

They both found that the effects of frost heave are mostpronouncedinsoilsthatfacilitatecapillaryflow.Frost-susceptiblesoils thus tend to be fine-textured; with silts, loams, and veryfine sands providing the optimum balance of moisture affinity(favoredbyhighparticlesurfacetovolumeratios, i.e.smallsoilgrains),poresize,permeabilityandhydraulicconductivity.Manyglacialsoilsfallwithinthistexturalrange,whichisunfortunateforNorthDakotabecause theyquite literally covera lotof groundhere. Claysarehygroscopic,highlyporous,andpermeablebuthavelowhydraulicconductivitybecauseoftheirsmallvoidsize.The consequent reduction in capillary flow tends to lessen theseverity of heaving because it impedes lens formation. Frostheave is very rare in coarse-grained soils especially clean,well-drained sands and gravels. Their pore spaces are too large topermitcapillaryflowortheformationoficelenses,soanyporewatersimplyfreezesin-placewithnosegregation.

Differentialfrostheave,freeze-thawcyclesandfrostjackingFrostheave,iflaterallyuniform,iscomparativelybenignbecausethere is no surface deformation and thus no threat to theintegrityofpavementsandotherstructures.Mostfrostdamageiscausedbynon-uniformordifferentialheave.Thisoccursasa

result of lateral variations inthe conditions that controlice lens formation and otherfreezing behavior. The maininfluences are soil textureand the availability of water(i.e. the height of the watertable). Other factors suchas the presence or absenceof vegetation, fluctuationsin the thermal regime, andoverburden pressure arealso important but of lessersignificance.

Differentialfrostheaveiswhatturns our roads into rollercoasters every spring andcauses the kind of damage

shown in figures 2 and 3. Heaving ismore destructive at thattimeofyear,notonlybecausethefreezedepthisatornearitsmaximum,butalsobecauseitseffectsareintensifiedbyaninfluxofwaterfrommeltingsnowandice,andthewearandteartheroadhasbeensubjectedtoallwinter.

The ground thaws from the surface down,which can seriouslyimpedesoildrainage.Unlessthereissufficientgradienttoallowthroughflow,meltwaterwill accumulate and remain trapped intheupperpartofthesoiluntilthelayeroffrozengroundbeneathhascompletely thawed. A roadwithwater trappedunder it inthiswaycanlose50%ormoreofitsnormalloadbearingcapacity(Mokwa, 2004). This is why the North Dakota Department ofTransportation imposes load restrictions on certain roads foraboutamonthaftertheonsetofthespringthaw(fig.7),whichiswhentheyareattheirweakest.Refreezingafteratemporarythawalsoexacerbates frostheavebecause the increasedwatercontentofthenear-surfacesoilresultsinacorrespondinglyhigherdegreeofsegregation.

Shallowfootingsandfoundationscancrackunderthe influenceof differential frost heave, which may render the structurethey support unsound. Small buildings, especially if they areunheated, are particularly vulnerable to this problem, as aremany other lightweight constructions such as decks, retainingwalls,transmissiontowers,andsoon.

Theverticaldisplacementofanisolatedstructure(asopposedtopartofaroadorparkinglot,forexample)byfrostheaveisknownasfrostjacking,orfrostpull. Butwhereasaroadliftedbyfrostheavewillgraduallysubsidetoitsoriginallevelafterthegroundbeneathithasthawed,upliftcausedbyfrostjackingtendstobepermanent.Thesequenceofdrawingsinfigure8explainswhy.

Figure 6. Segregation of soil and ice by regelation. The thickness ofthepremeltedfilmsurroundingasoilgrainsubjectedtoatemperaturegradient is greater on its warmer side. Water in the premelted filmmigrates down the resulting pressure gradient (blue arrows) from thelower,warmersideofthegraintoitsupper,coolersidewherethewaterrefreezes,forcingthesoilgraindownwards(away)fromthegrowingicelens(redarrow).

Figure7.Loadrestrictionsareimposedtopreventdamagetoroadsweakenedbymeltwatersaturationduringthespringthaw.PhotobyLorraineManz.

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The effects of frost jacking are usually quite subtle but if theprocessisrepeatedoverseveralwinters,thecumulativedamagecan be significant. Properly observed, engineering guidelinesandbuildingcodesdesignedtomitigatefrostjacking(andotherformsof frost heave) haveprovenhighly successful; so reportsof foundationpilesbeing“jacked”24 inches inasingleyear,or11 feet over severalwinters (Péwé and Paige, 1963) should bea thing of the past. Nevertheless, there is no one-size-fits-allsolutiontofrostheave,andwhatworkswellinonesituationmayfailmiserablyinanother;sountilwehaveabetterunderstandingoftheprocess,therearenoguarantees.

LandformsassociatedwithfrostheaveFrost heave is indiscriminate and anything we put in or onthe ground, or which belongs there naturally (e.g. rocks and

vegetation), is fair game. Railroads, bridges (Péwé and Paige,1963), pipelines, utility poles, coffins (McFadden and Bennett,1991), unexploded ordnance (Henry et al., 2004), trash, smalltrees,fenceposts,lawnedging,thelistisendlessandbizarre.Asforthelanditself,itisnowplaintoseethattheannualappearancein spring of yetmore stones on farmland cleared of them thepreviousyearisdueprimarilytofrostpull,probablyaidedalittlebydifferentialheave(Washburn,1980).Thisseeminglyuncannyabilityoffrostheavetosortunconsolidatedmaterialbysizeistakentoawholenewlevelinregionsunderlainby permafrost, where intense cold, recurrent diurnal andseasonalfreeze-thawcycles,andpoorlydrainedsoilsallservetoenhancetheprocessesoffrostaction.Differentialheaveisakeymechanismintheformationofsometypesofpatternedground

Figure8.Across-sectionalviewofablockofconcretepartiallyburiedinamoist,frost-susceptiblesoil.(a)Beforetheonsetoffreezing.(b)Frozensoiladherestothesidesoftheblock,formingbondsthatbecomestrongenoughtoovercomethedownwardshearandotherresistantforces.Heavefromgrowingicelensesistransmittedtotheblockthroughthesebonds,whichliftstheblockalongwiththesurroundingsoil,leavingacavitythatmaycollapseorfillwithunfrozendebris.Frostjackinganddifferentialheavecommonlyworkintandem,causingtheblocktotiltasitrises.(c)Theblockisunabletoreturntoitsoriginalpositionwhenthegroundthaws.Ifthecycleisallowedtorepeatoverseveralwinters,theblockwillcontinuetobe“jacked”upwardsandpossiblyevenforcedcompletelyoutofthesoil.

Figure9.Twoexamplesofpatternedground.(a)StonecirclesintheSvalbardIslands,northernNorway.PhotobyHannesGrobe.(b)Frostboils(indicatedbythearrows)inAbiskoNationalPark,Lapland,Sweden.PhotobyDentrenaten.wikipedia

a b

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(KesslerandWerner,2003;PetersonandKrantz,2003,2008),thereorganizationofsurfacematerialsintoregulararrangementsofvariousgeometricshapes,commonlycircles(fig.9),polygonsandlines(stripes).Sortedpatternedground,suchasthestonecirclesinfigure9a,developsontillandotherdiamictons.Thestonesaremovedupward andoutward by repeated freezing and thawingleaving the finer-grained material in the center of the ring.Frost boils (fig. 9b) are a type of non-sorted patterned groundconsisting of circles of bare earth formed by a combination offrost heave and cryoturbation (soil disturbance causedby frost

action)(PetersonandKrantz,2008).Theyareusuallyseparatedbyareasofvegetationorpeatandarenotringedbystones.

The small ice-coredhills knownas pingos (from the Inuitwordpinguq, meaning “little hill”) are unique to the permafrostenvironmentand their relict forms inmodern temperate zonesare indicativeof an earlier,much colder climate. Viewed fromabove,pingosareeithercircularorellipticalinshapewithbasaldiametersrangingfromafewfeettomorethanathirdofamile(Washburn,1980).Upto200feet(70m)high,theyaregenerallyrounded inprofile although the summitsofmanyof the largeronesarecrateredandfractured,givingthemtheappearanceofasmallvolcaniccone(fig.10).Theserupturedsurfacesarecausedbytensilestressgeneratedbythegrowing,typicallymassiveicecore,whichisoftenexposedasthedisplacedoverburdenofsoilandvegetationslumpstolowerelevations.

Mostpingosmaybeclassifiedasoneoftwotypes,basedontheirorigin. Both types involve the formationof segregated ice, theprincipal difference between the two classes being the source

of thewater supply. Closed-systempingos develop in recentlydrainedshallowlakebasins,whereliquidgroundwaterpersistsinalayerofunfrozenground,ortalik,withintheformerlakebed.Strippedof its insulatingcoverof lakewater, thesurfaceof thetalikbeginstofreeze,completelyenclosingtheremainingwaterin permafrost. Hydrostatic pressure from the encroaching iceforcesthewaterupwarduntilit,too,eventuallybeginstofreezeandheavethefrozenoverburdenintoamound.Closed-systempingosaremostcommoninareasofperennialpermafrostandaregenerallythelargerofthetwotypes.

Open-system pingos are mainly associated with discontinuouspermafrost zones, where taliks and mobile ground water arecommon, typically forming on slopes where they obtain theirwaterviaartesianflow.

Palsas resemble small pingos, although unlike their largercounterparts,theyarenotlimitedtothepermafrostenvironmentand their genesis is different (Gurney, 2001). Aptly named(palsaisaFinnishmodificationoftheNorthernSamiwordbalsa,meaning “a hummock rising out of a bogwith a core of ice”),palsas typically occur in peat bogs and other wetlands as low,oval-shapedmoundsthatrarelyexceed300feet(100m)inlengthor risemuch higher than about 30 feet (10m) (fig. 11). Theyconsistofacoreofalternatinglayersofsegregatediceandpeatorfinesedimentthat,insulatedbyacoveringofvegetation,oftenremainsperenniallyfrozen,growingalittlethickereachwinterasmoreiceisadded.

Whereas the core ice of pingos is derived from water under

Figure10(left).LargepingosnearTuktoyaktukintheMackenzieDeltainCanada’sNorthwestTerritories. Theone intheforeground is IbyukPingo, Canada’s highest at 161 feet (49m) and the second-highest intheworld.Itisstillgrowingatarateofaboutthree-quartersofaninch(2cm)ayearandisestimatedtobeatleast1,000yearsold.PhotobyEmmaPike.

Figure 11 (right). An aerial view of a group of well-developedpalsasinnorthernSweden.PhotobyDentrenaten.wikipedia.

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hydrostaticorhydraulicpressure,palsasareformedbycryosuctioninmore-or-lessthesamewayasthehummocksthatappearonourroadseveryspring.Besidestheabundantwatersupply,theirapparentaffinityforboggygroundisduetobarespotswherethewindhasremovedmostorallof thesnowcover,allowingfrosttopenetratedeeperintothesubsurfacethaninthesurroundingareas. Onceapalsahasbeguntoform,itscontinuedgrowthisfavoredbyitsincreasingsurfaceelevation,whichthewindismorelikelytokeepclearofsnow.Moreover,asthepalsariseshigherabovethewatertable, itscoveringofwetlandvegetationstartstodryout,whichmakesitamoreeffectualinsulatorofthefrozencore.Anincreaseinsurfacealbedo,broughtaboutbyachangeinvegetationfrompeatmossestolighter-coloredplantspeciessuchas Cladonia (reindeer or cup lichens) may also influence palsaformation.

Heaveisalsotheunderlyingcauseoffrostcreep,thedownslopemovementofsoilinresponsetocyclicexpansionandcontractioninducedbyfreeze-thawaction.Incombinationwithsolifluctionorgelifluction(itsfrozen-groundequivalent),frostcreepoperatesongradientsaslowas1°butismosteffectiveon5°-20°slopes.Landforms are genetically similar and are usually classifiedmorphologically. Features include lobes, benches, sheets, andstreams.

ReferencesBeskow, G., 1935, Soil freezing and frost heaving with special

application to roads and railroads: Technological Institute,Northwestern University, Swedish Geological Society, C,no. 375, Year Book no. 3 (translated by J.O. Osterberg).[Reprinted in Black, P.B. andHardenburg,M.J., eds., 1991,Historical perspectives in frost heave research: U.S. ArmyCorpsofEngineers,ColdRegionsResearchandEngineeringLaboratorySpecialReport91-23,169p.

Dash,J.G.,1989,Thermomolecularpressureinsurfacemelting–motivationforfrostheave:Science,v.246,no.4937,p.1591-1593,doi.10.1126/science.246.4937.1591.

Dash,J.G.,Rempel,A.W.,andWettlaufer,J.S.,2006,Thephysicsof premelted ice and its geophysical consequences:ReviewsofModernPhysics,v.78,p.695-791,doi.10.1103/RevModPhys.78.695.

Gurney,S.D.,2001,Aspectsof thegenesis,geomorphologyandterminologyofpalsas–perennialcryogenicmounds,ProgressinPhysicalGeography,v.25,no.2,p.249-260.

Henry, K.S.,Danyluk, L.A., andAnderson, T.A., 2004, Field testsof frost jackingof unexplodedordnance, in Proceedings ofthe Army Science Conference, 24th, Orlando, Fla., 2005.http://64.78.11.86/uxofiles/enclosures/Frost-movement-paper.pdf,(retrieved24June2011).

Jensen,R.E.,Nodate,ClimateofNorthDakota:NationalWeatherService,NorthDakotaStateUniversity,Fargo,NorthDakota.http://www.npwrc.usgs.gov/resource/habitat/climate/index.htm,(Version2April1998,retrieved24June,2011).

Kessler,M.A.,andWerner,B.T.,2003,Self-organizationofsortedpatterned ground: Science, v. 299, no. 5605, p. 380-383.http://www.jstor.org/stable/3833385, (retrieved 15 July,2011).

McFadden, T.T., and Bennett, F.L., 1991, Construction in coldregions:NewYork,Wiley,615p.

Mokwa, R., 2004, Transportation Engineering in Cold Regions- State of the Practice Review, in Proceedings of the 12thCold Regions Engineering Specialty Conference, Edmonton,Alberta,2004.

North Dakota State Climate Office, 2011, Archived deep soiltemperatures at select NDAWN stations, http://www.ndsu.edu/ndsco/soil/index.html,(retrieved24June2011).

Peterson, R.A., and Krantz, W.B., 2003, A mechanism fordifferential frost heave and its implications for patternedgroundformation:Journalofglaciology,v.49,p.69-80.

Peterson, R.A., and Krantz,W.B., 2008, Differential frost heavemodel for patterned ground formation – corroborationwith observations along a North American arctic transect:Journal of Geophysical Research, v. 113, G03S04, doi10.1029/2007JG000559.

Péwé,T.L.,andPaige,R.A.,1963,Frostheavingofpileswithanexample from Fairbanks, Alaska: U.S. Geological SurveyBulletin1111-1,p.333-407.

Rempel,A.W.,2010,Frostheave:JournalofGlaciology,v.56,no.200,p.1122-1128.

Taber,S.,1929,Frostheaving:JournalofGeology,v.37,p.428-461.

---1930,Themechanicsoffrostheaving:JournalofGeology,v.38,p.303-317.

Washburn, A.L., 1980, Geocryology – a survey of periglacialprocessesandenvironments:NewYork,Wiley,406p.

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