Biosystems Engineering (2003) 86 (1), 97–102doi:10.1016/S1537-5110(03)00112-0

Available online at www.sciencedirect.com

SW}Soil and Water

Thermal Properties of Soils as affected by Density and Water Content

Nidal H. Abu-Hamdeh

Biosystems Engineering Department, Jordan University of Science and Technology, P.O. Box 3030, Irbid, Jordan; e-mail: nidal@just.edu.jo

(Received 2 April 2002; accepted in revised form 3 June 2003; published online 22 July 2003)

Thermal properties dictate the storage and movement of heat in soils and as such influence the temperatureand heat flux in soils as a function of time and depth. The ability to monitor soil heat capacity is an importanttool in managing the soil temperature regime to affect seed germination and crop growth. The effect of watercontent and bulk density on the specific heat, volumetric heat capacity, and thermal diffusivity of some sievedand repacked soils was investigated through laboratory studies. These laboratory experiments used thecalorimetric method to determine specific heat of soils. The soils used were classified as sand and clay. For thetype of soils studied, specific heat increased with increased moisture content. Also, volumetric heat capacityincreased with increased moisture content and soil density. Volumetric heat capacity ranged from 1�48 to3�54MJm�3 8C�1 for clay and from 1�09 to 3�04MJm�3 8C�1 for sand at moisture contents from 0 to 0�25(kg kg�1) and densities from 1200 to 1400 kgm�3. Specific heat ranged from 1�17 to 2�25 kJ kg�1 8C�1 for clayand from 0�83 to 1�67 kJ kg�1 8C�1 for sand at moisture contents from 0�02 to 0�25 (kg kg�1) and soil density of1300 kgm�3. The volumetric heat capacity and specific heat of soils observed in this study under varyingmoisture content and soil density were compared with independent estimates made using derived theoreticalrelations. The differences between the observed and predicted results were very small. Clay soil generally hadhigher specific heat and volumetric heat capacity than sandy soil for the same moisture content and soildensity. The results also show that thermal diffusivity vary with moisture content and soil texture. Sandy soilexhibited a thermal diffusivity peak at a definite moisture content range. Clay soil, however, did not exhibit asharp thermal diffusivity peak.# 2003 Silsoe Research Institute. All rights reserved

Published by Elsevier Ltd

1. Introduction

Soil thermal properties are required in many areas ofengineering, agronomy, and soil science. In recent years,considerable effort has gone into developing techniquesto determine these properties (Ochsner et al., 2001).Predicting the transport of water, heat, and solute in soilwould help manage soil and water resources in irrigatedagriculture. Thermal properties are necessary for mod-elling the transport of heat in soil. The propagation ofheat in a soil is governed by its thermal characteristics(De Vries, 1963). The heat capacity of a soil depends onseveral factors. These factors can be arranged into twobroad groups, those which are inherent to the soil itself,and those which can be managed or controlled to acertain extent. Those factors or properties that areinherent to the soil include the mineralogical composi-tion and the organic component of the soil (Wierenga

et al., 1969). Factors influencing soil heat capacity thatcan be managed externally include water content andsoil density (De Vries, 1952; Wierenga et al., 1969;Yadav & Saxena, 1973). Water content plays a majorrole in soil heat capacity but is the most difficult tomanage. Soil management affects heat capacity becausepractices that cause soil compaction will increasethe bulk density and decrease the porosity of a soil.This in turn will have a significant effect on heatcapacity.De Vries (1952, 1963) developed models that allow

estimation of thermal conductivity and volumetricheat capacity of soils from the volume fractions oftheir constituents and the shape of the soil particles.The dual-probe heat-pulse technique (Campbellet al., 1991; Bristow et al., 1993,1994; Kluitenberget al., 1993) has been used to measure soil thermalproperties.

ARTICLE IN PRESS

1537-5110/$30.00 97 # 2003 Silsoe Research Institute. All rights reserved

Published by Elsevier Ltd

For Jordanian soils, however, information on thermalproperties has been lacking. These data could be useful inconstructing models to predict the thermal regime of soils.Such information assumes greater importance withincreasing concerns and intentions in developing theagricultural industry in Jordan. Because the earlygrowth and development of a crop may be determinedto a large extent by microclimate, the practical signifi-cance of knowing the soil thermal capacity is mostimportant as it relates to the soil microclimate. In thisstudy, the first objective was to study the effect ofmoisture content on specific heat and thermal diffusivityand the effect of moisture content and bulk density onvolumetric heat capacity of two different soil types. Thesecond objective was to compare the predicted andobserved specific heat and volumetric heat capacity valuesunder varying water content, soil density and texture.

2. Prediction equations

Independent estimates of the soil heat capacity andspecific heat for comparison with the laboratorymeasurements were obtained using relations derivedbased on De Vries (1963) and Bristow (1998). Thefollowing is a summary of the procedure on which thederivation of these relations is based. Heat capacity H ofa soil is calculated as the sum of the heat capacities of itsdifferent constituents. Thus if ms, mw, ma and mo aremasses in kg of soil particles, soil water, soil air andorganic matter, respectively, then

H ¼ mscs þ mwcw þ maca þ moco ð1Þ

where: H is heat capacity of the soil in J 8C�1 and cs, cw,ca and co are the specific heats in J kg�1 8C�1 of dry soilparticles, soil water, soil air and organic matter,

respectively. A value for cs of 1�10 kJ kg�1 8C�1 wasused for clay and 0�90 kJ kg�1 8C�1 for sand (Bristow,1998). Usually, the contribution of air can be neglectedbecause of negligible mass of gaseous phase. Also, thecontribution of organic matter is ignored because theorganic matter contents of the soils under test are small,then H is given by

H ¼ mscs þ mwcw ð2Þ

Using Eqn (2), the specific heat c of a moist soil can begiven by the relation

ðms þ mwÞc ¼ mscs þ mwcw ð3Þ

Eqn (3), when divided by the total volume of the soilsample VT, yields

rc ¼ rdcs þ rdwcw ð4Þ

where: w¼mw/ms is the gravimetric moisture content inkg kg�1; r and rd are the wet bulk density and dry bulkdensity in kgm�3, respectively, and given by

r ¼ ðms þ mwÞ=VT ð5Þ

rd ¼ ms=VT ; ð6Þ

Since the volumetric heat capacity Cv of a moist soil isgiven by Cv ¼ rc, Eqn (4) can be rewritten in the form

Cv ¼ rdcs þ rdwcw ð7Þ

where: Cv is the volumetric heat capacity of moist soil inJm�3 8C�1; and rd cs is the volumetric heat capacity ofdry soil in Jm�3 8C�1.Since rd ¼ r / (1+w), Eqn (4) can also be rewritten in

the following fc ¼ ðcs þ wcwÞ=ð1þ wÞorm to give thespecific heat c of a moist soil:

c ¼ rdðcs þ wcwÞ=r

ARTICLE IN PRESS

Notation

c specific heat of moist soil, J kg�1 8C�1

ca specific heat of soil air, J kg�1 8C�1

co specific heat of soil organic matter,J kg�1 8C�1

cs specific heat of dry soil particles, J kg�1 8C�1

cw specific heat of soil water, J kg�1 8C�1

Cv volumetric heat capacity of moist soil(Jm�3 8C�1)

H heat capacity of the soil, J 8C�1

ma mass of soil air, kgmo mass of soil organic matter, kgms mass of dry soil particles, kgmw mass of soil water, kgr radius of the cylinder, m

S slope of a line between the log of thetemperature ratio (Tc�T)/(Tc�To) and heat-ing time t

t heating time, minTo room temperature, 8CTc water bath temperature, 8CT thermocouple temperature, 8CVT total volume of the soil sample, m3

r wet bulk density, kgm�3

rd dry bulk density, kgm�3

w moisture content on weight basis, (kg kg�1)k thermal diffusivity, m2 s�1

Y constant

N.H. ABU-HAMDEH98

or

c ¼ ðcs þ wcwÞ=ð1þ wÞ ð8Þ

3. Materials and methods

Measurements of heat capacity were made on twosoils: sand (90% sand, 5% silt, and 5% clay) with a soilorganic matter content of 0�95% and clay (20% sand,22% silt, and 58% clay) with a soil organic mattercontent of 1�13%. Soils were air-dried and screenedthrough a 2-mm sieve. For the determination of specificheat and volumetric heat capacity of soil in drycondition and at different moisture contents andcompaction, the calorimetric method was followed withsome modifications (Taylor & Jackson, 1965). The soilsample was heated in a double-walled steam chamber.The sample could thus be heated without coming incontact with steam. A small cylindrical capsule ofcopper of diameter 10mm and length 35mm wasprepared. Its one end was closed and at the other end,there was a removable cap. The thickness of the wall ofthe capsule was approximately 1mm. A copper-con-stantan thermocouple was used for recording tempera-tures. The heat capacity of the calorimeter, includingthermometer, stirrer, and capsule was 104�14 J 8C�1.For the study of variation of specific heat and

volumetric heat capacity with moisture content, the soilwith certain moisture content was packed in a cylind-rical copper container. The capsule was then pushed intothe soil till it was just filled up. By this technique, smallsoil samples at any desired density could be convenientlyobtained. Specific heat of the soil was determined inusual way by method of mixture. The experiment wasrepeated with soils at different moisture contents andpacked into the container to same density. To investi-gate the effect of density, the soil of known weight at agiven moisture content was packed to different knownvolumes marked on the container. Various levels ofmoisture contents and bulk density used for the twosoils are indicated in Figs 1–4. The experiment wasreplicated four times for each treatment. A statisticalanalysis was performed to test the null hypothesis that‘replicate’ had no effect on the results obtained. Meanswere separated by the LSD procedure at alpha level a of5% to compare means between replicates for eachtreatment. The analysis indicated that the replicate effectwas not significant. Thus, the results were combinedover the four replicates for each treatment in this study.Independent estimates of specific heat and volumetricheat capacity under varying water content, soil density,and soil texture were also made using the proceduredescribed in details in Section 2.

ARTICLE IN PRESS

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0 0.05 0.1 0.15 0.2 0.25 0.3

Spec

ific

hea

t c, k

J/kg

Moisture content w, kg/kg

Fig. 1. Observed ( ) and predicted ( ) specific heat asa function of moisture content for a clay soil at a bulk density of

1300 kg m�3

1

1.5

2

2.5

3

3.5

4

0 0.05 0.1 0.15 0.2 0.25 Vol

umet

ric

heat

cap

acity

Cv,

MJ/

m3

°C

Moisture content w, kg/kg

Fig. 3. Observed (}}) and predicted (- - - -) volumetric heatcapacity as a function of moisture content for a clay soil at thebulk densities: & and &, 1200 kg m�3; m and n, 1300 kg m�3;

* and *, 1400 kg m�3

0.8

1

1.2

1.4

1.6

1.8

0 0.05 0.1 0.15 0.2 0.25 0.3

Spec

ific

hea

t c, k

J/kg

Moisture content w, kg/kg

Fig. 2. Observed ( ) and predicted ( ) specific heat asa function of moisture content for a sandy soil at a bulk density

of 1300 kg m�3

THERMAL PROPERTIES OF SOILS 99

Thermal diffusivity of the two soils at differentmoisture contents was determined by the method ofParikh et al. (1979). Soil samples were encased in thin-walled brass cylinders 180mm long and 20mm indiameter. From one end of the cylinder a copper-constantan thermocouple was inserted in the centre ofthe sample. Before it was packed, the soil sample wasbrought to a desired moisture content by adding aknown amount of distilled water and then mixingthoroughly. The sample was allowed to equilibrateovernight with the room temperature To. The cylinderwas then immersed in a constant temperature Tc waterbath, and the thermocouple temperature T was recordedas a function of time. Thermal diffusivity was deter-mined from the equation (Ghuman & Lal, 1985)

S ¼ Yk=ð2�303r2Þ ð9Þ

that form a part of the solution of the differentialequation for unsteady-state heat conduction in acylinder. In Eqn (9), S is the slope of a line betweenthe log of (Tc�T)/(Tc�To) and heating time t (7–9minin this study), k is the thermal diffusivity in m2 s�1, r isthe radius of the cylinder (10mm), and Y is a constant.The value of Y was found to be 2�382 using glass beadswith a value for k of 1�3� 10�7m2 s�1 (Weast, 1983).

4. Results and discussion

Specific heat of two sieved and repacked Jordaniansoils as a function of water content is shown in Figs 1

and 2. The two figures show both observed andpredicted specific heat of the clay and sandy soils as afunction of water content at a given bulk density. Atvarious water contents and at a given bulk density,specific heat increased with increasing soil water contentfor both soils. It is observed that the specific heat of both

the soils, exhibit a nearly linear relationship up to 15%moisture content. For higher values of moisture content,specific heat increased less rapidly in case of sandy andmore rapidly in case of clay soil. Moreover, thecurvatures of the curves are oppositely directed. Ingeneral, the clay soil had higher specific heat than thesandy soil. Similar results were reported by Yadav andSaxena (1973) and Ghuman and Lal (1985). Rapidincrease in the specific heat of clay soil with increasingmoisture content is probably due to adsorption of waterforming thick hulls around charged clay particles, whichgreatly enhanced its effective specific heat comparedwith sandy soil. It is expected that this type of relationbetween specific heat and water content holds up tosaturation point beyond which specific heat of soil tendsto approach the specific heat of water quite rapidly.Comparisons of the specific heat values observed by thecapsule method with the values determined using thetheoretical relations derived in the Theory section areshown in Figs 1 and 2. The differences between theobserved and predicted results were small.Variation of volumetric heat capacity of two sieved

and repacked Jordanian soils as a function of moisturecontent and bulk density is shown in Figs 3 and 4. Thetwo figures show both the observed and predictedvolumetric heat capacity of the clay and sandy soils as afunction of moisture content and bulk density. Theresults show that at various moisture contents and at agiven bulk density, volumetric heat capacity increasedwith increasing soil moisture content for both soils.Figure 4 shows that Cv varies linearly with moisturecontent for sandy soil which is in conformity with thepredictions of Eqn (7). The linearity was equally goodfor clay soil (Fig. 3). The slopes of the curves for the twosoils shown in Figs 3 and 4 are practically the same.Volumetric heat capacity increased with increasing bulkdensity for the two soils as a result of particle contactenhancement as porosity is decreased, and because ofgreater mass of solids per unit volume. For the clay soil,volumetric heat capacity did not increase uniformly withincreasing bulk density at various water contents(Fig. 3). Initially, volumetric heat capacity increasedrapidly with an increase in bulk density for clay soil.However, further increases in bulk density increased thevolumetric heat capacity only slightly. Such a phenom-enon was absent in the sand soil. It appears that increasein bulk density of sand beyond 1300 kgm�3 did improvecontact between the relatively larger sand particles, andproduced relatively more homogenous soil samples.Comparisons of the volumetric heat capacity values

observed by the capsule method with the valuesdetermined using theoretical relations derived in Section2 are shown in Figs 3 and 4. The results show that Cv

predicted using Eqn (7) agreed closely for both soils with

ARTICLE IN PRESS

1

1.5

2

2.5

3

3.5

0 0.05 0.1 0.15 0.2 0.25 Vol

umet

ric

heat

cap

acity

Cv,

MJ/

m3

°C

Moisture content w, kg/kg

Fig. 4. Observed (}}) and predicted (- - - -) volumetric heatcapacity as a function of moisture content for a sandy soil at thebulk densities: & and &, 1200 kg m�3; m and n, 1300 kg m�3;

* and *, 1400 kg m�3

N.H. ABU-HAMDEH100

Cv measured by the calorimeter method. The differencesbetween the observed and predicted volumetric heatcapacity values were small, and were constant over thefull moisture content range used in this study. Theresults, therefore, clearly reveal that the calorimetermethod yielded Cv values very close to those generatedfrom Eqn (7) for both soils. In general, the clay soil hadhigher volumetric heat capacity than the sandy soil. Asshown in Table 1, similar results were reported by otherresearchers (Bristow, 1998; Ghuman & Lal, 1985; Yadav& Saxena, 1973).Thermal diffusivity of the two soils as a function of

moisture is shown in Fig. 5. Sandy soil had higherthermal diffusivity than clay soil. By definition, thermaldiffusivity is the ratio of thermal conductivity andvolumetric heat capacity. Abu-Hamdeh and Reeder(2000) reported that beyond a certain bulk density,higher values of moisture content increased thermalconductivity less rapidly in the case of clay and morerapidly in the case of sand. Increasing water content insand perhaps completed water films around the largersand particles than silt and clay, thus increasing thecontact area between sand particles, which caused thethermal conductivity to increase rapidly. In addition, thedifferences in mineralogy and sand, silt, and clayfractions could be the primary reasons that sandy soilsoften have a higher thermal conductivity and diffusivitythan clay soils. The sandy soils often contain morequartz. Also, Figs 3 and 4 show that higher values ofmoisture content caused almost the same amount ofconstant increase in volumetric heat capacity for bothsoils. As a result, sandy soil had higher thermaldiffusivity than clay soil. The differences in thermaldiffusivity of both soils were smaller at air-dry wetnessthan at higher moisture contents. In general, thermaldiffusivity for sandy soil was small at low moisture andincreased with moisture content to a maximum valueand then decreased as moisture content continues toincrease towards saturation (Fig. 5). This trend was notfollowed by the clay soil. The diffusivity peak in sandysoil might be caused by the relative changes in thermal

conductivity and volumetric heat capacity of soil.Before the peak value of thermal diffusivity, it seemsan increase in thermal conductivity with an increase inmoisture content was relatively greater than in volu-metric heat capacity. However, after the peak, therelative increase in thermal conductivity of soil maybewas lower than the constant increase in volumetric heatcapacity. As a result, thermal diffusivity decreased afterthe peak value. In clay soil, however, it appears thatthere was only increase in thermal conductivity andvolumetric heat capacity. And, therefore, thermaldiffusivity did not exhibit peak at the moisture contentsstudied.Regression equations between volumetric heat capa-

city and thermal diffusivity, and the soil separates werededuced utilising data given in Figs 3–5. Though severalequations were tried, the following equations gave thebest estimates:

Cv ¼ �0�224� 0�00561N þ 0�753rd þ 5�81w ð10Þ

k ¼ �14�8þ 0�209N þ 4�79w ð11Þ

where: Cv and k are the volumetric heat capacityin Jm�3 8C�1 and thermal diffusivity in m2 s�1,

ARTICLE IN PRESS

0

2

4

6

8

0 0.1 0.2 0.3 0.4 0.5

The

rmal

dif

fusi

vity

κ, ×

10-

7 m

2 /s

Moisture content w, kg/kg

Fig. 5. Thermal diffusivity as a function of moisture content forclay (- - - - - -) and sandy (}}) soils

Table 1Comparison of thermal properties obtained in this study with values obtained by other researchers

Source Specific heat kJ kg�1 8C�1 Volumetric heat capacity, MJ m�3 8C�1

Sand Clay Sand Clay

This study 0�83–1�67 1�17–2�25 1�09–3�04 1�48–3�54Ghuman and Lal (1985) 0�91 1�35 1�52 1�44Yadav and Saxena (1973) 0�82–1�61 1�13–1�98 1�14–3�14 1�56–3�51Bristow (1998) } } 1�10–3�00 }

Dashes indicate that property was not investigated.

THERMAL PROPERTIES OF SOILS 101

respectively; N is the sum of sand and clay inpercentages; rd is the dry bulk density in kgm�3; andw is the gravimetric moisture content in kg kg�1, andwhere the coefficients of regression R2 were 0�99 and0�88, respectively. Some statistical analysis results forEqns (10) and (11) are shown in Table 2. Thoughempirical in nature, these equations could be useful inestimating thermal properties of soils if their composi-tion is known.

5. Conclusions

The effect of water content and bulk density on thespecific heat, volumetric heat capacity, and thermaldiffusivity of some sieved and repacked soils wasinvestigated through laboratory studies. For the typeof soils studied, specific heat increased with increasedmoisture content. Also, volumetric heat capacity in-creased with increased moisture content and soil density.The differences between the observed and predictedresults of the volumetric heat capacity and specific heatwere very small. Clay soil generally had higher specificheat and volumetric heat capacity than sandy soil for thesame water content and soil density. The results alsoshow that thermal diffusivity varies with moisturecontent and soil texture. Sandy soil exhibited a thermaldiffusivity peak at a definite moisture content range.Clay soil, however, did not exhibit a sharp thermaldiffusivity peak. Moisture content values and bulkdensities were chosen to represent actual values thatcan be found in natural soils. Additional studies are nowneeded to test the effect of the above parameters onthermal conductivity of undisturbed soils.

References

Abu-Hamdeh, N H; Reeder R C (2000). Soil thermalconductivity: effects of density, moisture, salt concentration,and organic matter. Soil Science Society of America Journal,64, 1285–1290

Bristow K L (1998). Measurement of thermal properties andwater content of unsaturated sandy soil using dual-probeheat-pulse probes. Agricultural and Forest Meteorology, 89,

75–84Bristow K L; Campbell G S; Calissendorff C (1993). Test of aheat-pulse probe for measuring changes in soil watercontent. Soil Science Society of America Journal, 57, 930–934

Bristow K L; White R D; Kluitenberg G J (1994). Comparisonof single and dual-probes for measuring soil thermalproperties with transient heating. Australian Journal of SoilResearch, 32, 447–464

Campbell G S; Callissendorff C; Williams J H (1991). Probe formeasuring soil specific heat using a heat pulse method. SoilScience Society of America Journal, 55, 291–293

De Vries D A (1952). The Thermal Conductivity of Soil.Meded. Landbouwhogesch, Wageningen, p 52

De Vries D A (1963). Thermal properties of soils. In: Physics ofPlant Environment (Van Wijk W R, ed), pp 210–235. North-Holland, Amsterdam

Ghuman B S; Lal R (1985). Thermal conductivity, thermaldiffusivity, and thermal capacity of some Nigerian soils. SoilScience, 139, 74–80

Kluitenberg G J; Ham M; Bristow K L (1993). Error analysis ofthe heat-pulse method for measuring the volumetric heatcapacity of soil. Soil Science Society of America Journal, 57,1444–1451

Ochsner T E; Horton R; Ren T (2001). A new perspective onsoil thermal properties. Soil Science Society of AmericaJournal, 65, 1641–1647

Parikh R J; Havens J A; Scott H D (1979). Thermal diffusivityand conductivity of moist porous media. Soil ScienceSociety of America Journal, 43, 1050–1052

Taylor S A; Jackson R D (1965). Heat capacity and specificheat. In: Methods of Soil Analysis, Part 1, Vol. 9,Agronomy, (Black C A, ed), pp. 345–348. American Societyof Agronomy, Madison, Wisconsin, USA

Weast R C (1983). Handbook of Chemistry and Physics. CRCPress, Boca Raton, FA

Wierenga P J; Nielsen D R; Hagan R M (1969). Thermalproperties of soil based upon field and laboratory measure-ments. Soil Science Society of America Proceedings, 33,

354–360Yadav M R; Saxena G S (1973). Effect of compaction andmoisture content on specific heat and thermal capacity ofsoils. Journal Indian Society of Soil Science, 21, 129–132

ARTICLE IN PRESS

Table 2Some statistical analysis results for Eqns (10) and (11)

Source Sums ofsquares

error (SS)

Mean sumsof squares

error (MS)

F P-value

Eqn (10) 8�52 2�84 847�20 0�001Eqn (11) 66�87 33�44 36�85 0�001

N.H. ABU-HAMDEH102