ESTIMATING THE DEPTH OF PAVEMENT FROST AND THAW PENETRATIONS
ESTIMATING THE DEPTH OF PAVEMENT FROSTAND THAW PENETRATIONSG. H. Argue and B. B. Denyes, Construction Engineering and Architectural Branch,Canadian Air Transportation Administration, OttawaThe design of foundations and pavements is affected by the depth to whichfrost penetrates during the winter or, in the case of permafrost areas, thedepth reached by summer thaw. This report contains information on thedepth of these penetrations as recorded at a number of Canadian airports.Correlations are developed between site air freezing index and the maximum depth of frost penetration beneath both asphalt and portland cementconcrete pavements kept clear of snow during the winter. The standarderror of these correlations is approximately 16 and 12 in. (41 and 30 cm)respectively. The maximum frost penetration that might be expected inundisturbed snow-covered areas is related also to site air freezing index.Similarity, for permafrost areas, relationships are developed between· thawpenetration and site thawing index. More accurate estimates of frostpenetration may be calculated if detailed soils information is available.Air freezing indices normally available for a site must be corrected to apavement surface freezing index when making these calculations. Themeasurements recorded in the frost depth study indicate that the ratio ofpavement surface/ air freezing index decreases as site air freezing indexdecreases. THE design of many structures is influenced by ground frost conditions. The depth ofseasonal frost penetration dictates thickness requirements for frost-protected pavements and is also an important factor to be considered when deciding on burial depthsfor building foundations and facilities such as water and sewer lines. Similarly, inpermafrost regions, the depth of the active layer has a major influence on pavementthickness requirements and on the depth of pile embedment for building foundations.Both types of ground frost conditions are encountered in Canada. In the southernpart of the country the ground is normally unfrozen, and subfreezing temperaturespenetrate the surface layers only during the winter months. In Arctic regions theground is permanently frozen, with surface thaw occurring in the summer. The depthof these seasonal frost and thaw penetrations varies extensively throughout the countrydue to a wide range of climatic factors and soil conditions.From 1964 to 1971, seasonal frost and thaw penetrations were recorded at a numberof Canadian airports by the Construction Engineering and Architectural Branch of theiv1uii::nry u1 .i rarnspurt. The information resuiting from this survey is usefut in estimating the ma.ximum depth of frost and thaw penetrations at sites where actual measurements are not available.THE FROST AND THAW DEPTH SURVEYFrost Depth IndicatorThe depths of frost and thaw penetrations were recorded at airports instrumentedwith frost depth indicators of the type devised by Gandahl (1). This instrument, withslight modifications incorporated by the Ministry of Transport, is shown in Figure 1.Publication of this paper sponsored by Committee on Frost Action .18
19The instrument consists of a transparent acrylic plastic tube inside a heavier plasticcasing. The tube and casing are inserted into a vertically bored hole to a depth exceeding the expected frost or thaw penetration. The inner acrylic tube contains a 0.05 percent solution of xylene cyanol. Normally a blue color, this solution turns colorlessupon freezing. The depth of frost penetration is measured by simply extracting theinner acrylic tube from its casing and recording the depth of colorless solution. Inthe case of thaw, the depth of blue solution is measured.Unlike thermocouple installations, which record actual soil temperatures, the frostdepth indicator identifies only frozen and unfrozen zones. The frost depth indicator hascertain advantages compared to thermocouples, provided that the only point of interestis the location of the ground frost line. The device is inexpensive, and a large numberof installations for a comprehensive survey can be made without the necessity of complex recording devices at each site. Moreover, the simplicity of the instrument is suchthat it can be readily understood and used by inexperienced personnel. Instrumentmalfunctions can usually be easily identified.In general, the Gandahl frost depth indicator performed satisfactorily during the frostsurvey program. Occasional difficulties arose when the indicator was frozen in andextraction of the instrument was either damaging or impossible.Sites InstrumentedIn 1964 frost depth indicators were installed at 30 airports in Canada. An additional25 airports were instrumented in 1967, and some of the previous installations were thendeleted from the program. The location of the instrumented airports is shown in Figure 2 .i n relation to the approximate boundaries of the continuous and discontinuouspermafrost zones in Canada. Forty-two of these airports are situated in the southernpart of the country, which experiences seasonal frost, and the depth of frost penetrationduring the winter was recorded at these sites. The eight airports located in the discontinuous permafrost zone have mean annual temperatures below 32 F (0 C), but thefrost depth indicators recorded a seasonal frost penetration at these airports ratherthan permafrost. Thaw penetrations during the summer were recorded at five sitesfounded on permafrost (Cambridge Bay, Churchill, Frobisher, Inuvik, and Resolute).Two or three frost depth indicators were usually installed at each airport. One indicator was located in a paved area surfaced with either asphaltic concrete or portlandcement concrete kept relatively free of snow during the winter. Another indicator waslocated in an unpaved area with typical organic cover where snow was allowed to accumulate undisturbed.Frost and Thaw Penetration RecordsFrost and thaw penetration depths were recorded at weekly intervals throughout theseason of interest by maintenance personnel or meteorological observers stationed ateach airport. Table 1 gives the average maximum depth of frost penetration measuredat each airport under pavement surfaces only. Table 2 gives the average maximumdepth of thaw penetration recorded at permafrost sites. Site freezing or thawing indices are also given in these tables.The freezing index is a measure of the severity of subfreezing temperatures experienced at a site, and it is the most influential climatic factor in predicting the depthof frost penetration. The freezing index is recorded in degree-days and is computed byaccumulating from day to day during the freezing season the differences between 32 F(0 C), and the mean daily temperature. The freezing index begins to accumulate in thefall when the mean daily temperature falls below 32 F (O C) and it reaches a maximumin the spring prior to thaw. The thawing index, which is of use in predicting the depthof summer thaw in permafrost regions, is similar to the freezing index except that itmeasures the above-freezing temperatures experienced during the summer.For each set of frost or thaw penetration records, the corresponding freezing orthawing indices were computed from air temperatures recorded approximately 4 ft(1.2 m) above ground level by the Meteorological Branch of the Ministry of Transport.Show depth data were obtained during the winter months for those indicators located
Figure 1. Gandahl·type frost depthindicator (DOT pattern).Set cop to be lush with povement 11.1rlo e7//.&W'///,EE.015 21115 2 mm Ar1c h or plotttilllt! clomp ro hold oncho plalet9mmP.V.C TubingE11terior ofcosin to be Qreoud fl) diecourOQ8soil odfreezmg and frosfClear, rigid, acrylic plosl1c11heavinglubing,16mm 0.013 m m. l. D.Surgicallale:i:lubing, llm m. 0 . Dl7 . 9 m.m. I 0{under tension)Annularspace between lalex and acrylic plasticlubing filled wllh o eolulion of Xylene Cyanol(0 CS 0/0 by we1g .t)NofJ1,Figure 2. Airports instrumented in frost depth survey .,/IA.,/I/I//CANADA000 so' drubberplugTip of cosing 1o be heatsolvenl ctmenlsealedanddippedin
21Table 1. Average frost penetrations, 1964-1971 .Average Frost Penetration(in . )Seasonal Frost SitesBagotville, Que.Calgary, Alta.Chatham, N.B .Cold Lake, Alta.Edmonton, Alta.Fort Nelson, B.C.Fort St. John, B.C.Fredericton, N.B.Gander, Nfld.Glmli, Man.Grande Prairie, Alta.Halifax, N.S.Hay River, N.W.T.Lakehead, Ont.Lethbridge, Alta.London, Ont.Moncton, N.B.Montreal, Que.Moose Jaw, Sask.Namao, Alta.Ottawa, Ont.Prince Albe rt, Sask.NumberofYearsObse rvedAverageFreezingIndex (Fdegree - days)45.l32,8402, 0671,6923, 5493, 3014, 8522,6031,5731,0923, 4383,5459415,6412,8331,5119881,3661, 7302, 8203,0971,6624,3284,1391, 7572,2903,4881,4016113,3722,2701, 7801,2098751,0024,6201, 0223,1274,0223,5963, 7627,55967l3 I344243I3343343Prince George, B.C.Quebec, Que.Regina, Sask.St. John, N.B .St. John's, Nfld.Saskatoon, Sask.Sept-Iles, Que.Smithers, B.C.Summerside, P .E.I.Sydney, N.S.Te rrace, B.C.The Pas, Man.To ronto, Ont.Val d'Or, Que .Whitehorse, N.W.T.Winnipeg, Man.4374422344I33734Yellowknife, N.W.T 645180622869706049366011936641277384169Table 2. Average thaw penetrations, 1965-1971.Ave rage Thaw Pene trations (In. )Permafrost SitesCambridge Bay, N.W .T .Frobisher, N.W.T.Inuvik, N.W.T.Resolute, N.W.T .NumberofYearsObservedAverageThawingIndex (Fdegree-days)324521,0871,2922, 0532, urbedNaturalSurface's5778895326
22in areas with undisturbed snow cover. At the time of installation, bore holes weredrilled for soil-sampling purposes. The thicknesses of distinct soil layers were measured and samples were taken for mechanical analysis and determination of moisturecontent. No density measurements were made.MAXIMUM PENETRATIONS RELATED TO CLIMATIC INDICESFrost Penetration in Snow - Cleared PavementsThe depth of frost penetration depends on both climatic factors and soil conditions.However, rough estimates of maximum frost penetration, which are sufficient for somepurposes, can be predicted with a knowledge of the air freezing index only. From thedata collected at Canadian airports, Figures 3 and 4 show the relationship betweenthese variables for snow-cleared pavements surfaced with asphaltic concrete and portland cement concrete respectively. H the maximum frost penetration in inches isdenoted by X and the maximum air freezing index by F (F degree - days), the regressionrelationships are approximatelyPavement SurfaceAsphaltConcreteEquationx x -24 2.0-10 1.9Standard ErrorVF\IF15.8 in. (40.1 cm)12.2 in. (31.0 cm)The negative values at low freezing indices indicate that the air freezing index mustreach certain minimum values before frost penetration is experienced. This effectoccurs because average pavement surface temperatures are slightly higher than thecorresponding air temperatures measured approximately 4 ft (1.2 m) above the groundsurface and the freezing index at the pavement surface will lag behind the air freezingindex. Due to the black color of asphalt, slight differences also occur in the averagetemperature of asphalt and portland cement concrete surfaces, which leads to a lesserdepth of frost penetration in asphalt pavements than in portland cement concrete pavements for the same air freezing index.In Figures 3 and 4, a distinction is made between observations in pavements havingco.hesive subgrades and those having predominantly granular subgrades. Normally,with other factors equal, one would expect deeper penetrations in granular subgrades,but this trend is not noticeable in Figures 3 and 4. Most likely, the influence of subgrade type is not noticeable in Figures 3 and 4 because dense pavement layers are generally thicker on cohesive subgrades than on granular subgrades and because the substantial thicknesses of airport pavements in general tend to attenuate the effects ofsubgrade type .Frost Penetration in Undisturbed Snow-Covered AreasFigure 5 shows the maximum frost penetrations observed in undisturbed snowcovered areas plotted against the maximum air freezing index. Because of differencesin the depth of snow cover, these observations are much more variable than those forsnow - cleared pavementi;; , However, for design purposes, an upper limit representingthe maximum frost penetration that might be expected can be established from Figure 5.The equation, X 1. 7 VF, describes this upper boundary. The maximum expectedpenetration occurs when little or no snow cover is present during the freezing season.A comparison of Figure 5 with Figures 3 and 4 shows that the average depth of frostpenetration in undisturbed snow-covererJ areas amounts to approximately one-half thepe11et ration that occurs unde1· snow-cleared paved areas.The insulating effects of snow cover are shown in Figure 6, where the ratio X/ YFis plotted against average depth of snow cover. The points are dispersed because theinsulation effect depends not only on the average depth of snow but also on the time ofseason it is in place and on the snow density. A trend, however, is quite noticeable inFigure 6. Beginning at approximately 1.2, for no snow cover, the proportionality constant between depth of frost penetration and square root of lhe freezing index decreaseswith increasing depth of cover to a value of about 0.4 for 2 ft (61 cm) of snow.
23Figure 3. Maximum frost penetrations in asphalt-surfaced pavements.SNOW CLEARED ASPHALT;;;"':I:0z130x.-24 SURFACES120 15 .8 IN .STANDARD ERROR OF ESTIMATEl40. I CM)110 100z900.o a:80w70"'"-60.2/FNUMBER OF OBSERVATIONS 93SUBGRADES 'PRED MINATELYSILTPR 00MINATELYSAND ANO GRAVE LtANO CLAYIV 050IL Oa:IL/ o:I:200. .vv .//vv"wv ""./v 10)56330Z1.'ze'V22 9k' 17-;./ICMI/.,,, "'-v0v. 15I 1210'VV0I-0,.,.v -to . . v . . . .1-z.-ISUBGRAOESI ,.1 07651u,,,/0001 c - 1?.000{ 16671(DEGREE50006000127781133331DAYS)Figure 4. Maximum frost penetrations in PCC-surfaced pavements.ICMI!56 OSNOW CLEAR ED P C C .(i)'l.!0:I:uzz0 a:0r2012,2 IN ,STANDARD ERROR OF ESTIMATEI 31 .0 CM IzAND CL AYSUBGRADESPREDOMINATELYSILTo SUBGRADESPREDOMINATELYSAND ANO GRAVEL 70500.a:.0:I:l-40,. . v30v vi'- ./2290I/,./17 8I 52/.I 27I 0276./20/100. V /o.UJ0279//80IV ) )0/. . . . ./9060/v .100"'"-/0 /1UJ0IINUMBER OF OBSERVATIONS 50110)(. ' . . . o/vSURFACES)( -IO l.9ffw51"25/001000(oc - DAYS)15561AIRFREEZINGI NOEXF200030004000(1111)116671122221(DEGREE DAYS)50001277816000(33331
24Figure 5. Maximum frost penetrations in undisturbed snow-covered areas.ICM)!58 o;;;w!Ox :I:uzSNOW COVERED SURFACESUNDISTURBED-15 1.1./FSTANDARD ERROR OF ESTIMATE./-19. 2 IN 1 8.&CM)110)(AP PAC ilC U ATEz090 80"' wzwQ. 0."'"- O20.-·114.-"/zt,,. l179 ,,.,., . '.--"10./" 00t C- DAYS)-pAIR.2000(1111)1000(556)FREEZING76 Iv 102L--· i.o:127to'.-IU - /J:0 Ji- , ,.--379 so!O a.X 1,7LIM l lJ'/100wUPP R.,,.,./.,,. .·.--v-- . .). .·-.;, .- --::. . . . . ."". .v. ." ---: . ". . . . .bUU):so:./NUMBER OF OBSERVATIONS : I2''"600013333)DAYS)Eigure 6. Ratio of X/JF versus average snow cover.1.8UNDISTURBEDSNOW COVERED SURFACESNUMBER OF OBSERVATIONS1.6. 1.2o.e0.60.4o.z131. . . . .- . .' . . . . . . . . . . . . . . - . . . . . . -·: ·-.- r:-- . . . ·- - - . . . . . . . . .,I"'-.1.0 '- -.i .·.: .o :Ilor- t-- !-;-- ,.;-, . 411SNOWCOVER(I NCH ES)IB(46)20(51)(56)24(61)lCMJ
25Thaw Penetration in PermafrostThe data obtained from the study on the maximum depth of summer thaw in bothasphalt and gravel-surfaced pavements founded on permafrost are limited by the fewsites instrumented. The observations recorded for gravel surfaces are plotted in Figure 7 against maximum thawing index on a square-root scale. Figure 7 provides avery approximate indication only of the maximum thaw penetration that might be expected; more measurements are needed to adequately define the relationship.Figure 8 shows some measurements of maximum thaw depths recorded in undis turbed natural ground areas. Most of these measurements were obtained during apreviously conducted program in which maximum thaw depths at a number of northernpermafrost sites were established by soundings. Although the thaw depths are quitevariable because of variations in soil condition and depth of organic cover, an upperboundary can be established from Figure 8. If the site thawing index is denoted by I,the maximum active layer depth in inches that might be expected at the site is in theorder of 1.85 W.CALCULATION OF FROST PENETRATION IN PAVEMENTSModified Berggren EquationThe theoretical calculation of frost penetration depths is commonly based on themodified Berggren equation i, ). The equation may be written in the followingform for layered soil systems such as pavements ( 2):(sAFn -- 224 AwhereAFnthe partial pavement surface freezing index required to freeze the nth layer(F degree-days);thickness of the nth layer (ft);latent heat of fusion of the nth layer (Btu/ft3);correction coefficient based on site soil and climatic factors;thermal resistance of the i th layer AX1/ K1 ; andthermal conductivity of th.e i th layer (Btu/ft/hour/deg F).As Figure 9 shows, the total pavement surface freezing index required to freeze nlayers in the pavement structure is determined by summing the partial freezing indices,AFn, required to freeze each layer.Soil Thermal PropertiesFor use in the modified Berggren equation, the coefficient of thermal conductivityK, latent heat of fusion L, and correction coefficient A may be estimated from Figure 10.The thermal conductivity values given in Figure 10 were established by Kersten (8).Latent heat of fusion depends on the amount of water in the soil and may be calculatedas 1.434 Yd Wn, where ')Id is the dry density of the soil in pounds per cubic foot and Wnis the moisture content in percent. As given by Aldrich (5), the correction coefficient. . is a function of the mean annual temperature experienced at a site, the average freezing temperature, and the soil moisture content. In Figui·e 10, which gives approximatevalues for . ., the variables of mean annual temperature and average freezing temperature have been replaced by the site air freezing index by using empirical correlationsbetween these statistics.Freezing Index Surface/Air Correction FactorsAn additional factor entering frost depth calculations is the relationship betweenpavement surface freezing index and air freezing index. Calculations with the modified
26Figure 7. Maximum thaw penetrations in gravel-surfaced runways on DOFRUNWAYSOBSERVATIONS 16z;::: (a::. IvBO/)(0.r .70y2Tt.,, 90. /I/v.v6050la /30II//40I 02/H., /20,,10.203.,/, .2 /01001000THAWINGIINDEX30002000(5561('6)( 1111)0 111(DEGREE DAYS)Figure 8. Maximum thaw penetrations in undisturbed permafrost areas.(CMIJ !II140BYDEPTH OF THAW DETERMINEDu;"'::c . zSOUNDINGS IN1201961a)3 01962NUMBER OF OBSERVATIONS03053v-110,/100)(0z0!;ia::.RECORDED 8Y GANOAHL INDICATOR90, ,voo.70"'60.40.0JO::c.ll.0. ·/20,,.-"10,,.-"/0( C - DAYS) ·017,,IZ1I/10I/20001000(5561THAWING 0I/27'-l)'/,/0UPPER LIMIT1. 85./I/ ::cx /zll. . . . .v . -·. .APPROXIMATEINDEXI 1111 JI(DEGREE 1
27Figure 9. Layered soil system.FA AIA FREEZING INDEX::: 4' t 1-2 111)-3 .:IAF2f PAVDO'. H1liHIJ:"A.CC r1ua ING !NOD :L AYERf,:R 1.!.ll:t/J(II .;;-;. Y(tf ·2·":;:i .4- ; ; ; : :.--- -- ·:.!·:·:.!::;'"': ·i/l'\:·11l::-, tr.F,N'"'[ :::. :LAYER"' ,. .,'3 "11Rz 11XzlK2--A3 6X3/K3 .::. - ::-:.Figure 10. Soil parameters versus moisture content.
ESTIMATING THE DEPTH OF PAVEMENT FROST AND THAW PENETRATIONS G. H. Argue and B. B. Denyes, Construction Engineering and Architectural Branch,
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