Observations of ground temperature and heat flow at Ottawa, Canada

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Journal of Geophysical Research, 64, 9, pp. 1293-1298, 1959-11-01

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Observations of ground temperature and heat flow at Ottawa, Canada

Pearce, D. C.; Gold, L. W.

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N ~ T I O N A L

RESEARCH

COUNCIL

CANADA DIVISION O F BUILDING R E S E A R C H

-

OBSERVATIONS OF GROUND TEMPERATURE AND

HEAT FLOW AT OTTAWA, CANADA

BY

D. C. PEARCE AND L. W. GOLD

R E P R I N T E D F R O M

JOURNAL O F GEOPHYSICAL RESEARCH VOL. 64, NO. 9. SEPTEMBER 1959. P . 1 2 9 3 -1298

R E S E A R C H PAPER NO. 86 O F THE DIVISION O F BUILDING R E S E A R C H NOVEMBER 1959 P R I C E 1 0 C E N T S -

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NRC 5304

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Observations of Ground Temperature and Heat Flow

a t Ottawa, Canada

D. C. PEARCE

AND

L. W. GOLD

Division of Building Research National Research Council, Ottawa, Canada

Absl~nct-Observations were made at a sitc in Ottanra, Canada, on thc 1,hcrmal rrgime of t.he ground and thc hcat flow 10 cnl below thc ground surf:lce. Close agreement was fount1 I](:-

tween the thcrrnal diffusivities calculated from the depth dependence of the temper:~ture amplitude and the depth depcntlence of the phase anglc. I t mas also found that tlic annual component of the rate of heat flaw was out of phase with the annual component of the gro11nc1 te~nperature by 45.8 degrees. These observ:ltions showed that for the Ottawa site the annual ~vavc of ground tcmpcrature and tlie annual component of the rate of heat flow arc consistent

with tlic simple theory of periodic heat floiv in a one-dimcnsional, semi-infinite, homogeneous medimn. I n accordance with this theory, thermal constallts for the soil a t the tcsl site nrerc calculated from the observations

Introduction-Since its inception, many of the problems encountered by t h e Division of Building Research of the National Research Council have rcquired for their solution a knowl- edge of the thermal regime of t h e ground. Con- sequently, this has bcen a subject of estensive study. Sevcral reports describing previous work have been published [Crawford ancl Legget, 1957; Peurce, 1958; Gold, 19581. Late in 1956, t h e instrumentation of the test arca on the Mon- treal Road property a t Ottawa was considerably cxpancled. This paper deals with observations inaclc a t this site on ground temperature a n d hcat flow during thc period from January I , 1957 t o January 1, 1958.

Z~~st~.z~mentation-The area under investiga- tion was situated in an open grass-covered field. T h e soil in this region is a Lecla clay which ex- tends t o t h e bedrock a t a depth of about thirty feet. The instrumentation was designed to meas- ure both soil temperatures a n d t h e heat flow through tlie soil.

F o r temperature measurements, sealed ther- inonlcter units were fabricated, each containing a glass-encloscd bead-type thermister and a copper constantan thermocouple. T h e thermom- eter elclnents mere sealed in y4-inch o.d. alumi- n u m tubing. T e n such units were installed a t depths of 5, 10, 15, 20, 30, 40, 50, GO, 75, a n d 90 cm belo~v thc srouncl surfncc. T h e units were installed horizontally from t h e vertical wall of

a. trench. Each tllermorileter was located about

3 feet from t h e trench mnll. After installation of the thermometers, tlle trench was backfilled

with thc original inatcrial ancl tampcd.

T h e elcctrical leads were brouglit to t h e ground surface through a wax-filled conduit and were then carried t o an adjacent scrvicc tunnel about 150 feet from the test area by a n elevated surface conduit. Temperatures were recorclcd with Leeds a n d Northrup recording cquipmcnt located in t h e tunnel.

T h e heat flow mas mensured with heat mrtcrs of the Gier a n d Dunkle t y p e which had becn calibratecl in a hot-platc apparatus. F o r the observations in the spring of 1957, two adjacent heat meters a t a depth of about 5 c m were employed. The heat flow was detcrininecl from t h c output of t h e two meters. T h e installation was modified somewhat in the early autumn of 1957. Thereafter, four heat meters were usecl in two separate units of two meters in series a t t h e 10-cm depth. This gave a n average hcat flow over a larger area of ground than did the original installation. T h e lends f o r t h e hcat metcrs were carried t o t h e service tunncl through t h c elevated conduit, a n d the outputs of the heat meters were recorded with automatic equip- ment.

Shortly .after installation, faults clcveloped in thc thrnnister circuits. Thc source of the cliffi- culty was discovered to be tlic devclop~ncnt of

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L

1

,

I I I I

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC

DATE

FIG. I-Annual colnponent of the rate of heat flow and of the ground temperature at the 10 cm level accumulated lieat flow the rate of heat flow a t

tlie 10-cm depth is i ( t ) = -0.738 cos w t

+

0.240 sin wt cal/cm'lir. The annual component of tlie rate of heat flow and tlie annual component of the ground temperature are plotted in Figure 1. The observed accumulatecl heat flow ancl its annual component are given in Figure 2. To obtain tl~erlllal constants for tlie soil, these observations were compared witli the theory of heat flow in a homogeneous semi-infinite medium. The tlieoretical temperature distribution is glven by the equation

where

where I< is the thermal conductivity of the medium.

Figures 3 and 1 are plots of the amplitucle and the phase of the observed annual-temperature- wave a t various depths. For the selected coor- dinates, tlie curves shoulcl be linear if tlie tem- persture obeys simple conduction theory. I t can be seen tliat tlie observations are consistent with this theory, escept near the ground surface. Both curves give essentially the same value for the thermal diffusivity, 11 cmZ/hr. Estrapolation of the linear curves to zero clepth yields the values 13.1°C and 2.007 respectively for the constalits .-I ancl 6.

From equations (I) and (2) i t is seen tliat a t any depth the annual co~nponcnt of the rate of heat flow sliould be 45" out of pluse witli the annual component of the ground temperature. Pronl the observations i t was found that the calculatecl annual coinponents were out of phase by 45.8' a t the 10-cm level-very close to the U(c, t) is the temperature a t depth c and time t

theoretically espected value. This suggests that

AO is the mean temperature of the medium

the annual component of the heat flow can be

w is the angular frequency of the temperature

described by simple conduction theory; that is, variation

the process can be characterized by a unique,

i l l sin (wt

+

6) is the surface temperature

real value of the thermal conductivity of the variation

soil mhich can bc calculated from the observa-

CY is tlie thermal diffusivity of the nlecliunl.

tions. This was done and tlie resulting value of -

The theoretical rate of heat flo~v a t depth 1: K was found to be equal to 8.45 (cal)/(cm lir "C).

ant1 time t is given by the equation Using this value for li: and CY = 11 (cm2)/(hr)

- gives for the volumetric heat capacity of the

@ ( x , t ) =

&

Kill

exp (-1:

4:)

soil a value of 0.77 (cal)/(cm3 "C). This is

CY , not unreasonable for the soil a t the test site,

tz) _{which has a dry density of about 1.40 gm/cm3 a t}

a

+

6

+

- - 1: a water content of 30 to 40 per cent by dry

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1296 PEARCE AND GOLD J 3 r _-1000 3 U U a -1400

JAN F E E M A R A P R M A Y J U N E JULY A U G SEPT OCT NOV DEC DATE I I I I I I I I I I I -

-

335.1 COS WT -1025.2 S I N WT * lo80 SIN ( ~ ~ + 6 + 0 . 8 0 - 1 0 ~ ~ )

-

- O B S E R V E D A C C U M U L A T E D H E A T FLOW

FIG. 2-The observed accumulated heat flow and its annual component

The values of the thermal properties of the temperature and the rate of heat flow and t h e soil for the test area, computed from the annual observed dependence on depth of the amplitude component of the rate of heat flow, and the of the annual component of the ground tempera- observations of the ground temperature are ture was consistent with theory, it was assumed given in Table 2. that unique thermal constants existed for the Discussion-This analysis has demonstrated soil. I n the Ottawa area, however, the upper that the annual temperature variation in the part of the soil is always frozen for a part of t h e soil a t the Ottawa test site is remarkably con- year, and, since the thermal constants of frozen sistcnt with the theory of hcat flow in a one- and unfrozen soil are quite different [Kersten, tlirnensional, honiogcneous, semi-infinite medium. 19521, it is possible that the thermal behavior Furthermore, the conlputed value of the ther- of the upper soil layers cannot be described ma1 diffusivity is vcry close to the values ob- satisfactorily by these average values. This could tained for clay soils in the Ottawa area in other account for the deviation in the observed ground years [Pea~ce, 19581. This indicates that in the temperatures near the surface, which were neg- Ottawa area the thermal diffusivity of the soil lected in the calculations. Nevertheless, it is as determined from annual tcmperature varia- concluded that the simple conduction model does tions does not vary appreciably from year to yield a satisfactory description of the thermal year. behavior of the soil a t the test site for depths

Only near the air-soil interface do significant greater than about 30 cm.

deviations from this theory occur. The observa- Other studies by the Division of Building tions suggest that the thermal conductivity in- Research have deinonstrated difficulties in the creases near the ground surface. This interpreta- use of heat meters. Problems with contact re- tion should, however, be employed with caution. sistance are particularly troublesome. Conse- Because tlie observed phase relationsliips be- quently, the observed heat flows are estimated tween the annual components of the ground to be accurate only t o about -+I0 per cent.

TABLE 2-Thermal properties of soil

Thermal dilrusivity

I

Volumetric heat capacity

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GROUND TEMPERATURE A N D I1li:Arl? PI,O W 1297

FIG. 3-Amplitude of the annual ground tempcm- ture changc as a function of depth Freezing and thawing of the soil and heat transfer by vapor and water movement occur below the 10-cm level. Since the values for the thermal properties which were calculated from the annual components of the ground temperature and the rate of heat flow are reasonable for the soil in question, it would appear that the influence of such effects on the annual component is not very great at the Ottawa site. Some justification for this conclusion was observed for the winter period during which the maximum difference of about 400 cal/cm2 be- tween the observed accumulated heat flow and the computed annual component, as shown in Figure 1, was in fact about equal to the estimated heat associated with the freezing of the soil water. The following method was used to estimate the ice content per unit volume of the frozen soil. First, an estimate based on the work of Love11 [I9571 was made of the amount of water still unfrozen at the time of observation. This amount was then subtracted from the measured total water content per unit volume to yield the ice content.

The recorded results in this paper indicate that a calculation of the depth of the 32" isotherm might be used to estimate the depth of frost penetration. Once, in the spring of 1958, the actual depth of freezing was determined by probing. This depth was almost a foot less than the measured depth of the 32" isotherm. This may inean only that the soil freezes at a temperature below 32"F, a riot unexpected result,

DLPTH (CMI

FIG. 4-Phase of the annual ground temperature as a function oi depth

but it illustrates that caution is nccessnry when trying to predict the depth of tlle freezing plane with simple theories.

The fact that the thermal diffusivity which was obtained from this analysis is in agreement with the results of previous studies, including those of areas with and without snow cover, indicates that a snow cover has verv little influence on the thermal properties of the soil. Thus the effect of snow cover can be treated purely as a surface boundary condition. This assump- tion allows the prediction of certain general thermal relationships at the soil-air interface. This analysis indicates that approsilnate thermal properties of the ground, and an estimate of the annual component of the rate of heat flow from the ground, can be determined from a measurement of ground temperature and the volumetric heat capacity of the soil. We believe that approximate values which are obtained in this way may have numerous practical appli- cations.

Aclznowleclgmcnts-The authors ~ v i s l ~ to ac- lcnowledge tlle able assistance of R. llrmour and R. Jaekel in the instrumentation and the analysis of the results. They also wish to express their appreciation to members of the Division of Build- ing Research for their contribution through discussion. This is a contribution from the Division of Building Research of the National Research Council of Canada and is published with the approval of the Director of the Division.

C R I ~ F O R D , C. B., AND R.

F.

~ C C I C T , Ground tem-

~)ernl,u~c invcstig:dions in Cnri:~tlo, Eng. J. Mon- treal, 40, 263-269, 290, 1957.

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1298 PEARCE A N D GOLD

Corn, L. I\.'., Influence of snow cover on heat flow U . S . Eiigl~luay Resenrcl~ Board, Bull. 188, 79-95,

from the ground-some observations nlnde in 1957.

the Ottawa area, Extrail des Comples R e n d . 1 ~ ~ et PEARCE, D . C., Ground temperature studies at

Rapports, Assoc. I,z.Lern. II?ldrol. Sci.. U G G I , S:lskatoon and Ottnmtl, E z l ~ a i l des Conaptes

Toronto 1957, Gentbrugge, I V , 13-21, 1958. ir'ei~tlr~s el IZapporls, Assoc. It7,le,-n. Hyclrol. Sci.,

I ~ E R S T E S , M . S., Thern1:ll propel.ties of soils, 11% U G G I , Toronto 1957, Gentbrugge, I V , 279-290,

Frost Action in Soils, n Symposium, U . S. Z3igl~- 1958.

~ u a y R e s e a ~ c h Board, Spec. R e p l . :?, 161-166, 1952.

LOVELL, C . IFT., Ten~pernturc effects in phase 00111- (Manuscript, received March 12, 1959; revised