THERMAL RESISTIVITY OF SOILS

By Lawrence A. Salomone1 and William D. Kovacs,1 Members , ASCE

ABSTRACT: Information on the thermal properties of soils from different dis­ciplines of science and engineering is consolidated to identify low-cost, simple procedures for assessing the variation of the thermal resistivity of soils with changes in moisture content. Three procedures for determining the critical moisture content are presented. The critical moisture content is the moisture content at the knee of the fhermal-resistivity-versus-moisture-content curve. The optimum moisture content and plastic limit were found to be physical quan­tities indicative of the critical moisture content in soils. Also, the upper flex point of the soil-moisture-characteristics curve appears to establish the critical moisture content in soils.

INTRODUCTION

Despite recent advances in the use of soil as an insulating material and as a material to store and dissipate heat, heat transfer from earth contact surfaces (such as slab-on-grade floors, basement walls, and buried electric cables) has not been well understood. One difficulty in estimat­ing the heat transfer into the ground from these surfaces is the uncer­tainty involved in soil thermal properties, especially soil thermal resis­tivity (or its reciprocal, soil thermal conductivity). For example, over the normal range of soil moisture experienced in the field, the change in thermal conductivity can be tenfold or more (10). The thermal conduc­tivity can vary because of changes in soil type and density. In addition, progressive drying of the soil and subsequent decrease in thermal con­ductivity can occur due to thermal instability (9). Because of the problem in selecting values of soil thermal conductivity that are representative of field conditions, building thermal analysts involved in heat-flow mod­eling often use constant values of thermal conductivity obtained from handbooks. Likewise, cable engineers have had to be conservative in their selection of the value of soil thermal resistivity used to design buried electric cables because of the variation in soil thermal resistivity encoun­tered along transmission line routes.

To aid those faced with the problem of selecting appropriate values of soil thermal resistivity and the calculation of heat transfer in soils, Salomone (18) showed that thermal soil behavior can be correlated with soil limit states associated with moisture content, which, in turn, can be established by methods developed by geotechnical engineers and agron­omists. Additional work by Salomone, et al. (20,21) found that the crit­ical moisture content correlates with the optimum moisture content for fine-grained soils over a wide range of densities. However, as the den­sity of the fine-grained soil decreases to densities typical of unconsoli-

1 Research Geotechnical Engr., National Bureau of Standards, Geotechnical Engrg. Group, Washington, D.C. 20234.

Note.—Discussion open until August 1, 1984. Separate discussions should be submitted for the individual papers in this symposium. To extend the closing date one month, a written request must be filed with the ASCE Manager of Tech­nical and Professional Publications. The manuscript for this paper was submitted for review and possible publication on March 25, 1983. This paper is part of the Journal of Geotechnical Engineering, Vol. 110, No. 3, March, 1984. ©ASCE, ISSN 0733-9410/84/0003-0375/$01.00. Paper No. 18636.

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dated marine deposits (less than 1.6 Mg/m3), the correlation between critical moisture content and the plastic limit found by Salomone (18) is evident. The critical moisture content is the moisture content below which the thermal resistivity increases rapidly with further drying.

The correlation between the optimum moisture content and the plastic limit and the critical moisture content is important because the critical moisture content is of particular interest from a thermal instability view­point, as discussed in more detail later. Thermal instability occurs in moist soils because of significant moisture movement when the soil is subjected to thermal gradients due to the presence of a heat source (9). Therefore, a large increase in the thermal resistivity of the soil occurs when the moisture content of the soil falls below the critical moisture content (17) (dry side of optimum). Above the critical moisture content, the thermal resistivity is fairly constant (4) (wet side of optimum).

Selection of values of soil thermal resistivity for analysis of earth con­tact heat transfer problems requires knowledge of the critical moisture content. Extending the work of Salomone, et al. (20,21), this paper brings together knowledge from different disciplines of science and engineer­ing for the purpose of identifying the equipment, methods, and physical quantities that can be used to establish the critical moisture content. An approach for establishing the values of soil thermal resistivity for anal­ysis of earth contact heat transfer problems is also presented.

THERMAL RESISTIVITY OF SOIL

The thermal resistivity of a soil is influenced primarily by the following parameters: (1) Soil composition; (2) soil density; and (3) soil moisture content. The importance of these parameters is examined in detail else­where (e.g., Refs. 7, 15, and 23). However, a basic understanding of the

MOISTURE CONTENT IN PERCENT ' D«Y DENSITY IN M,/m>'

FIG. 1.—Effect of Soil Composition on FIG. 2.—Influence of Dry Density on Thermal Resistivity of Soils (22) Thermal Conductivity for AMRL Silty

Clay (21)

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significance of each of these parameters for granular and fine-grained soils can be obtained by examining Figs. 1-4.

Fig. 1 shows that fine-grained or cohesive soils and peaty soils exhibit higher thermal resistivities than granular soils at a given moisture con­tent. Therefore, fine-grained soils and peaty soils would not be expected to dissipate heat away from a heat source as rapidly as granular soils.

The influence of density on the thermal resistivity of a silty clay soil was studied by Salomone, et al. (21); the results can be seen in Fig. 2, where the variation of thermal conductivity (the reciprocal of thermal resistivity) with changes in density for constant values of moisture con­tent is presented. By reducing the total void volume and improving the contact between the soil grains through densification of the soil mass, a reduction in the thermal resistivity of the material can be achieved. Also, it is important to note that the influence of density on the thermal resistivity continues to decrease until a moisture content in the vicinity of the plastic limit of this soil (23.5%) is reached. At moisture contents close to the plastic limit, the effect of density is minimal.

The influence of soil moisture on the thermal resistivity can be studied by establishing the thermal resistivity versus moisture content relation­ship at a low compactive effort. An example of this for a silty clay soil is presented in Fig. 3. As moisture is added to the soil as a thin film around the soil particles or wedges at the contacts, a path for the flow of heat that bridges the air gaps between the soil particles is provided. By increasing the effective contact areas between particles, these films or wedges greatly reduce the thermal resistivity of the soil. As the mois­ture content increases further, the effective contact area no longer in­creases with increasing moisture content. Consequently, a significant decrease in thermal resistivity is not evident when additional moisture is added to fill the pore space. The moisture content at which the bridge mechanism breaks down, resulting in a disproportionate increase in the thermal resistivity with small reduction in moisture content, has been termed the critical moisture content by Radhakrishna, et al. (17). The crit-

230

210

| 190

t 170

i> 150

f. 130

I 110 I 90

I 7° I 50

" O 15 30 45 60

MOISTURE CONTENT IN PERCENT

FIG. 3.—Variation of Thermal Resistivity with Moisture Content for AMRL Silty Clay (19)

377

UNSTABLE REGION ' STABLE REGION

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40 I— LU

u 14J

K 3 0

=E 1—

as t— U3 O

£ =! 10 o t: K O

0

80 90 100 110 120 130

DRY DENSITY IN PCF

FIG. 4.—Influence of Dry Density on Critical Moisture Content for AMRL Silty Clay

ical moisture content defines the knee of the thermal-resistivity-versus-moisture-content curve (Fig. 3). As the moisture content increases past the critical moisture content, the thermal resistivity increases because the density decreases and more water is present with its higher resis­tivity. Fig. 4 shows that this critical moisture content depends on den­sity. As density decreases, the critical moisture content increases.

MEASURING THERMAL RESISTIVITIES OF SOILS

Several methods have been used to measure the thermal resistivity of soils, and details of these methods have been presented elsewhere (e.g., Ref. 16). For the reader's convenience, a short summary follows. Mitch­ell and Kao (16) provide an in-depth evaluation of the laboratory meth­ods for measurement of the thermal resistivity of soils. The methods can be divided into two categories: steady state and transient. Because of the relative simplicity and the short time required for measurement, a transient method is often selected for field investigations and laboratory testing programs. Moreover, the transient method is preferable to steady-state tests for determining the thermal resistivity of soils because mois­ture migration and subsequent change in thermal resistivity is likely to occur during the steady-state test. The transient method commonly used involves a thermal needle, the fundamental principle of which can be found in most heat conduction textbooks, such as Carslow and Jaeger (6).

The thermal needle or thermal probe has been developed to such a degree that field and laboratory measurements of thermal resistivity can be made routinely. The equipment used to make field and laboratory determinations of thermal resistivity includes: (1) Laboratory thermal probes; (2) field thermal probes; and (3) thermal property analyzer.

The thermal probes are commercially available and are generally man­ufactured to specifications to meet their special requirements. Informa­tion on field and laboratory thermal probes and a thermal property ana­lyzer developed by Ontario Hydro Research Laboratory for the Electric

AMRL SILTY CLAY Note: 1 Mg/m1 = 62.4 PCF

J I I L

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Power Research Institute (EPRI) can be found in Refs. 25 and 24, respectively.

The equipment can be used to measure a discrete thermal resistivity at a particular moisture content and density in situ or in the laboratory for a soil sample. Also, because in situ soil moisture and thus thermal resistivity continually changes, it is often required, for most applica­tions, to characterize fully the thermal behavior of the soil by developing the thermal-resistivity-versus-moisture-content curve.

Two methods have been used to determine the thermal-resistivity-versus-moisture-content curve. Method 1 involves stage drying a rela­tively undisturbed tube sample (e.g., Shelby tube sample) or a recon­stituted soil sample compacted to a dry density specified by the in situ dry density (natural) or to a dry density determined by some standard test, e.g., Standard Proctor test [ASTM D 698-78 (2)] or the modified Proctor test [ASTM D 1557-78 (2)]. Method 2 involves measuring the thermal resistivity of reconstituted soil samples at different moisture contents and densities and determining the thermal-resistivity-versus-moisture-content curves for a range of densities. Using the second method, moisture contents are more easily determined and controlled, but more effort is required. Adaptation of Methods 1 and 2 for use in the labo­ratory has been described by Steinmanis (25) and Salomone and Kovacs (19), respectively.

SOIL THERMAL INSTABILITY

The term soil thermal instability is the name for the condition observed for soils whose moisture content falls below the critical moisture content. A large increase in thermal resistivity with a small decrease in moisture content occurs when soil thermal instability occurs (Fig. 3). The term soil thermal stability is the name for the physical condition observed for soils whose moisture content is above the critical moisture. The thermal re­sistivity is fairly constant in this region (Fig. 3). From the laboratory re­search into the fundamental phenomena related to thermal instability performed by Radhakrishna, et al. (17), several basic conclusions con­cerning this condition have been drawn:

1. Thermal instability is caused by sustained moisture migration along a thermal gradient.

2. Such sustained moisture migration occurs for all soils below some critical moisture content below which vapor permeability increases to a point that vapor outflow exceeds liquid inflow, causing progressive drying.

3. The rate of drying for soils below the critical moisture content de­pends on the thermal gradient and soil properties. However, thermal instability will eventually manifest itself for any significant thermal gradient.

Hartley, et al. (9), working with a soil that had a critical moisture con­tent approaching 20%, showed that the occurrence of thermal instability depends on heat flux, time, and moisture content when the soil mois­ture content is less than the critical moisture content. On the other hand, Boggs, et al. (4), working with well-graded soils used as thermal backfills

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because critical moisture contents are low (less than 5%), found that thermal stability is maintained as long as the moisture content remains above the critical moisture content.

From the foregoing description, the "binary" concept defined by Boggs, et al. (4), appears to be valid, i.e., "a critical moisture exists above which the thermal resistivity is fairly constant and independent of heat flux (thermal stability) and below which the thermal resistivity increases rap­idly and is very dependent on heat flux (thermal instability)." The need for the following should be clear: (1) A physical quantity that defines the dividing line between "stability" and "instability;" and (2) investi­gating the influence of such factors as temperature, heat flux, and heat source geometry on this dividing line. A review of those physical pa­rameters that can be used to predict the onset of thermal instability follows.

Soil Suction.—Soil suction is a soil property that is indicative of the intensity with which a soil will attract water (14). In partially saturated soils, suction consists of the matrix suction (also called matrix potential, matric potential, or capillary potential) and the solute suction (some­times identified as solute potential or osmotic suction). The matrix suc­tion results from the capillarity and the particle surface adsorption in a soil. The solute suction depends on the concentration of soluble salts in the soil water. Herein the term soil suction refers primarily to the matrix suction. A graph showing moisture (or water) content on the X-axis and matrix suction on the Y-axis is called a soil-moisture-characteristics curve (11). A logarithmic scale for the matrix suction measured in centimeters of water is often used, with the symbol pF being used to refer to the logarithm to the base 10 of the matrix suction measured in centimeters of water.

The shape of the soil-moisture-characteristics curve depends on the distribution of pore sizes in the soil. Fig. 5, taken from Baver, et al. (3), presents soil-moisture-characteristics curves for soils with uniform grain size characteristics. Note the three regions of the soil-moisture-charac­teristics curve defined by the upper flex point, U, and the lower flex point, L. In practice, variation from these classical three-zone curves would be expected because of differences in grain size, grain distribution, and packing. A comparison of typical soil-moisture-characteristics curves for a sand, a silt, and a clay, that have been provided by Janssen and Demp-sey (11), are shown in Fig. 6. For the sand and silt, the upper and low­er flex points are observed. However, the variety of pore sizes typical

0 I 1 u—i 1 1 1 4—i— i 1—I LJ_L -4 -X -_ !— 0 10 20 30 40 SO 60 TO CO

PERCENT WATER BY V 0 1 M E

FI6. 5.—Soil-Molsture-Characteristios Curves Showing Upper and Lower Flex Points (Modified from Ref. 3)

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1 Nets:

a

cm 0.39 in.

0 5 10 IS 20 25 30

MOISTURE CONTENT

10'

c i

SU

CTI

ON

,

m»

HOSHEB A SILT

Note: fern = 0.39 in.

: \ : \

' b • i i

.

, , 10 15 20 25 30 35 40'

MOISTURE CONTENT

10 15 20 25 30 35

MOISTURE CONTENT

FIG. 6.~Soil-Moisture-Characteristfcs Curves: (a) Torpedo Sand; (b) Hosmer A Silt; (c) Bluford B Clay (Modified from Ref. 11)

of a clay soil results in a gradual and uniform decrease in matrix suction as the moisture content increases. The flex regions (particularly the up­per flex region) are not evident. The relevance of this information for determining the critical moisture content will now be discussed.

Jones and Kohnke (13) conducted laboratory tests to study the influ­ence of soil moisture tension on vapor movement of soil water. They

" \

_

1 1 1 1 KEV:

J pF at initial vapor movement

. ? pF at maximum vapor movement

\ K . {,— Crosby silt loam

^ ^ S ^ ^ ' l A

^ \ ^SS. -Fox l o a m ^ N . N .

| i i J — ^ 10 20 30 40

PERCENT MOISTURE BY VOLUME

50

FIG. 7.—Relationship between Moisture Tension and Water Vapor Movement (Modified from Ref. 13)

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found the following:

1. The movement of water vapor in the soils studied (sand, silt, and loam) increased rapidly with moisture tension up to the wilting point, and then decreased sharply. Note that the wilting point is defined as the soil-moisture condition at which the ease of release of water to the plant roots is just barely too small to counterbalance the transpiration losses.

2. The suction at which vapor movement was initiated and at which maximum movement occurred increased with a decrease in particle size.

In addition, Jones and Kohnke (13) measured the suction at which initial vapor movement and maximum vapor movement occurred for a Crosby silt loam and Fox loam. Plotting the points of initial vapor movement and maximum vapor movement on the soil-moisture-characteristics curves for these soils (Fig. 7) indicates that initial vapor movement and maxi­mum vapor movement occur approximately at the lower and upper flex points, respectively. Recalling that below some critical moisture content, vapor outflow exceeds liquid inflow and sustained moisture migration occurs, the critical moisture content should be the condition of moisture in the soil at which maximum vapor movement occurs or the upper flex point. This definition of critical moisture content suggests that the crit­ical moisture content referred to by Radhakrishna, et al. (17), is the ther­mal critical moisture content defined by Bouyoucos (5). Evaluating the effects of temperature on soils, Bouyoucos (5) found that the maximum thermal water movement depended upon a definite condition of mois­ture of any particular soil, and this condition was a specific constant or characteristic of the soil which he designated as the thermal critical mois­ture content. The thermal critical moisture content as defined by Bouy­oucos (5) is "that percentage of moisture in a soil which allows the great-

_ 200

0 0.10 0.20 0.30

VOLUMETRIC WATER CONTENT, IcmVcm' l

1

PG AND E CRUSHED LIMESTONE

Dry unit weight =

1.84 Mg/m'1115 pell

CRITICAL MOISTURE CONTENT

0 0.10 0.20 0.30

VOLUMETRIC HATER CONTENT, (cm'/cm11

FIG. 8.—PG and E Crushed Limestone Properties: (a) Soil-Moisture-Characteris­tics Curve; (b) Thermal Resistivity versus Volumetric Moisture Content (Modified from Ref. 1)

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TABLE 1.—Correlation of Critical Moisture Content and Upper Flex Point for Granular Soils

Soil description

(D PG&E crushed limestone Fire Valley thermal sand Round Robin sand

Monterey #0 sand

Moisture content at upper flex point, as a percentage

(2)

5.4 4.0 4.1 — 3.1

—

Sample dry density, in

megagrams per cubic

meter (3)

1.84 1.99 2.08 2.16 1.63 1.76

Critical moisture

content, as a percentage

(4)

5.5 3.5 — 3.5 — 3.4

est amount of water to move from a warm to a cold soil at any amplitude of temperature."

Using data from Abdel-Hadi and Mitchell (1) for a crushed limestone, Fig. 8 shows that the critical moisture content is the moisture content that determines the upper flex point on the soil-moisture-characteristics curve. Note that the upper flex point is defined as the point of inter­section of two lines approximating the soil-moisture-characteristics curve in the upper flex region. Additional data from Mitchell, et al. (15) for other granular soils also show this relationship between the upper flex point and critical moisture content. Using the soil-moisture-characteris­tics curves and the thermal-resistivity-versus-moisture-content curves presented by Mitchell, et al. (15), the moisture content at the upper flex point and the critical moisture content, respectively, were determined by the writers. Table 1 shows the correlation of critical moisture content and the upper flex point for granular soils. It would appear that the upper flex point on a soil-moisture-characteristics curve provides a good estimate of the critical moisture content for nonplastic granular soils. When the upper flex point is not apparent, as is the case for clay soils or if soil-moisture-characteristics curves are not available, the optimum moisture content and the plastic limit can be used as follows.

Optimum Moisture Content.—Index property and thermal resistivity test data for fine-grained soils presented by Salomone and Kovacs (19) show a correlation between the critical moisture content and optimum moisture content (Fig. 9). Further evidence of the correlation between the critical moisture content and the optimum moisture content is given in Fig. 10. Using data from Refs. 12 and 20, Fig. 10 shows that the re­lationship between critical moisture content and compactive effort for the AMRL silty clay, and the relationship between optimum moisture content and compactive effort for the other silty clay soils shown, are similar. Note that for soils with different plasticity characteristics, a dif­ferent family of curves is required; further research is needed to establish the critical moisture content versus compactive effort relationship for these soils.

To use the optimum moisture content to define the critical moisture content, it is important to understand the following:

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40

£ 30 S S

§

i §,. ^ 20 OS =3

s i x 3

I t 10 o

0

—1 1 1

SYMBOL SOIL

O D A

. - V

+ e m A

-

mm. siity clay

Niagara clay

Georgia clay

North way silt loam

Fairbanks silt loam

Fairbanks sllty clay loam

Healy clay

Ramsey sandy loam

Little Lons Till

Numeral Indicates number of data points

A>

/ / A

s

/ m

i i i

_j j j

/ si'

/ \ /

V / A

/ • 'T, X

'• -

i I I

5 10 15 20 25 30

CRITICAL MOISTURE CONTENT, PERCENT 35

FIG. 9.-(19)

-Correlation of Optimum Moisture Content with Critical Moisture Content

1. A dry density must be specified when defining the critical moisture content of a soil because the critical moisture content increases as den­sity decreases (Fig. 4).

2. The compactive effort(s) chosen to determine the optimum mois­ture content(s) will depend on the dry density for which the critical moisture content is being defined.

3. The compactive efforts chosen will be used to determine that por­tion of the "line of optimums" that is in the vicinity of the required dry

SOIL ° Texas Taylor Marl Heavy Clay & Vicksburg Sllty clay » Sllty Clay

o Texas Well-graded Clayey Sand o Clayey Sand

- AMP.L Sllty Clay (Critical moisture content)

LIQUID LIMIT

70 37

37 1 18

18 45

PLASTICITY INDEX

SO 14

14 3 2 22

H o t e l f t l b f / f t ' = 47.88 l/m>

2 3 4

COMPACTIVE EFFORT • IHbf/ft» x 10'

FiG. 10.—Effect of Compactive Effort on Optimum Moisture Content and Critical Moisture Content (Data from 12, 20)

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TABLE 2.—Approximate Critical Moisture Content for Various Soil Types

Soil description (1)

Granular Silts Clays Organic silts and

expansive clays

Approximate Standard Maximum Dry Unit Weight (ASTM D698-78)

Pounds per cubic feet

(2)

120 to 135 110 to 120 100 to 110

<100

Megagrams per cubic meter

(3)

1.92 to 2.16 1.76 to 1.92 1.60 to 1.76

<1.60

Approximate critical moisture

content,0 as a percentage

(4)

<12 12 to 16 16 to 22

>22

"Critical moisture content is defined for a dry density that is 100% of standard maximum density (ASTM D698-78). .

density. The "line of optimums" provides the relationship between crit­ical moisture content and dry density. Note that the "line of optimums" is a line drawn through the peak points of several compaction curves at different compactive efforts for the same soil. For example, Fig. 4 shows the line of optimums for the AMRL silty clay. The line of optimums was drawn from the compaction curves presented in Ref 21. Using Fig. 4, the critical moisture content at a variety of densities can be obtained.

Assuming optimum moisture content equals critical moisture content, Table 2 can be prepared using optimum moisture content and maximum dry density data collected by Woods and Litehiser (26) for 1,088 soil sam­ples. Using the standard maximum dry density (ASTM D 698-78) and Table 2, the critical moisture content can be estimated. Additional re­search can refine this table by narrowing the ranges of critical moisture content shown and correlating the soil descriptions with descriptions

TABLE 3.—Correlation of Critical Moisture Content and Plastic Limit for Other Fine-Grained Soils (from Ref. 21)

Soil description (1)

Lake Erie bottom sedi­ments (very soft clays)

Lake Erie bottom sedi­ments (soft clay)

Atlantic City marine sediments

Georgia Strait bottom sediments

Malaspina Strait bottom sediments

Unified soil classification

(2)

CH

CH

CH OH

OH

Critical moisture content,8

as a percentage (3)

30-40

25-30

30 66

74

Plastic limit, as a percentage

(4)

35-45

25-30

30 68

(45-90) 68

(45-90)

"Dry weight basis.

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defined by frequently used soil classification systems. Plastic Limit.—Because the plastic limit of low-density soils (i.e., less

than 1.6 Mg/m3) is only slightly above the optimum moisture content (26), the plastic limit may be used to determine the critical moisture con­tent of soils at low dry densities for fine-grained soils. Salomone, et al. (21) found that as the compactive effort for preparing samples of one soil type was decreased, a compactive effort of 1.42 x 105 J/m3, which is one-sixth of the standard Proctor effort, resulted in the critical mois­ture content, optimum moisture content, and plastic limit being ap­proximately equal. Data presented by Salomone, et al. (21) indicate that the critical moisture content of fine-grained soils can be defined by the plastic limit for such soils as marine sediments that have low natural dry densities. Table 3 taken from Salomone, et al. (21) shows the correlation between the plastic limit and the critical moisture content for marine sediments. Thus, for plastic low density soils the plastic limit is useful to estimate the critical moisture content.

APPLICATION

Selection of representative values of thermal resistivity is important for solving earth contact heat transfer problems. The approach for es­tablishing representative values of thermal resistivity involves:

1. Determining the critical moisture content at the in situ density us­ing the methods and physical quantities presented herein.

2. Determining the minimum moisture content expected under de­sign conditions by establishing the seasonal changes in soil moisture throughout the conduction region.

3. Comparison of the critical moisture content and the minimum moisture content expected under design conditions to determine if the minimum moisture content is greater than or less than the critical mois­ture content. If the minimum moisture content is greater than the critical moisture content, the soil can be considered stable, and selecting a con­stant value of thermal resistivity would be appropriate for the stable re­gion shown in Fig. 3. Laboratory thermal probe tests performed on sam­ples at moisture contents representative of the stable region can be used to establish this constant value of thermal resistivity. Note that the dry density of the samples tested should be at the dry density anticipated for a project. If the minimum moisture content is less than the critical moisture content, the soil can be considered unstable. In the unstable region shown in Fig. 3, moisture migration under thermal gradients is likely and large increases in thermal resistivity for small decreases in moisture content is likely. Consequently, the appropriate value of ther­mal resistivity would fall between the value of thermal resistivity estab­lished for the stable region and the thermal resistivity of the soil in the dry state. Laboratory thermal probe tests performed on air-dried sam­ples can be used to establish the thermal resistivity of the soil in the dry state. With the upper and lower bound for thermal resistivity estab­lished, the influence of this range in thermal resistivity on the solution to the earth contact heat transfer problem (e.g., heat loss in a building or cable ampacity of an underground electric transmission line) can be

E*W...

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evaluated. If the influence of this variation in thermal resistivity is too great, further analysis is required. One possible method of analysis in­volves incorporating the seasonal changes in soil moisture measured for step 2 into a computer program that uses the relationship between ther­mal resistivity and moisture content, and the changes in soil moisture, to provide statistically based estimates of soil thermal resistivity for a given time period. Details for the method can be found elsewhere (8).

CONCLUSIONS

Based on this study, the following conclusions are warranted:

1. A systematic approach that consolidates information from different disciplines of science and engineering has been presented to establish the variation in thermal resistivity of soils for earth contact heat transfer problems.

2. The critical moisture content and the minimum moisture content expected under design conditions are required when determining values of thermal resistivity for analyzing earth contact heat transfer problems.

3. The optimum moisture content and the plastic limit are physical quantities that can be used to estimate the critical moisture content for fine-grained soils. The critical moisture content correlates with the op­timum moisture content for soils over a wide range of densities and with the plastic limit for soils with dry densities less than 1.6 Mg/m3 (100 PCF).

4. The upper flex point of the soil-moisture-characteristics curve can be used to estimate the critical moisture content for nonplastic granular soils.

ACKNOWLEDGMENTS

James K. Mitchell critically reviewed this paper. His comments and suggestions are greatly appreciated.

APPENDIX.—REFERENCES

1. Abdel-Hadi, O. N., and Mitchell, J. K., "Coupled Heat and Water Flows Around Buried Cables," Journal of the Geotechnical Engineering Division, ASCE, Vol. 107, No. GT11, Nov., 1981, pp. 1461-1487.

2. ASTM Standards, Soil and Rock, Building Stones, Part 19, American Society for Testing and Materials, Philadelphia, Pa., 1982.

3. Baver, L. D., Gardner, W. H., and Gardner, W. R., Soil Physics, 4th ed., John Wiley and Sons, New York, N.Y.

4. Boggs, S. A., Chu, F. Y., and Radhakrishna, H. S., "Measurements for Un­derground Thermal Transmission Design," Underground Cable Thermal Back­fill, S. A. Boggs et al., eds., Pergamon Press, Inc., Toronto, Canada, 1982, pp. 134-146.

5. Bouyoucos, G. J., "Effect of Temperature on Some of the Most Important Physical Processes in Soils," Technical Bulletin No. 22, Michigan Agriculture College Experiment Station, July, 1915.

6. Carslow, H. S., and Jaeger, J. C, Conduction of Heat in Solids, 2nd ed., Oxford University Press, London, England, 1959.

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7. Fischer, J. A., Salomone, L. A., and Watson, I., "Influence of Soils on Extra High Voltage Offshore Transmission Lines," Marine Geotechnology, Vol. 1, No. 2, 1975, pp. 141-156.

8. Ford, G. L., and Steinmanis, J. E., "The Importance of Weather Dependent Processes on Underground Cable Design," Underground Cable Thermal Back­fill, S. A. Boggs, et a l , eds., Pergamon Press, Inc., Toronto, Canada, 1982, pp. 157-166.

9. Hartley, J. G., Black, W. Z., Bush, R. A., and Martin, M. A., "Measure­ments, Correlations and Limitations of Soil Thermal Stability," Underground Cable Thermal Backfill, S. A. Boggs et a l , eds., Pergamon Press, Inc., Toronto, Canada, 1982, pp. 121-133.

10. Hillel, D., Fundamentals of Soil Physics, Academic Press, New York, N.Y., 1980, p. 296.

11. Janssen, D., and Dempsey, B., "Soil-Moisture Properties of Subgrade Soils," Transportation Research Record 790, Shales and Swelling Soils, National Acad­emy of Sciences, Washington, D.C., 1981, pp. 61-66.

12. Johnson, A. W., and Sallberg, J. R., "Factors Influencing Compaction Test Results," Highway Reasearch Board Bulletin 319, National Academy of Sci­ences, Washington, D.C., 1962.

13. Jones, H. E., and Kohnke, H., "The Influence of Soil Moisture Tension on Vapor Movement of Soil Water," Proceedings of the Soil Science Society of Amer­ica, Vol. 16, No. 3, July, 1952, pp. 245-248.

14. McKeen, R. G., and Hamberg, D. J., "Characterization of Expansive Soils," Transportation Research Record 790, Shales and Swelling Soils, National Acad­emy of Sciences, Washington, D.C., 1981, pp. 73-78.

15. Mitchell, J. K., Abdel-Hadi, O. N., Chan, C. K., Kao, T. C , and McMillan, J. C , "Backfill Materials for Underground Power Cables: Phase II Backfill Treatments, Heat and Moisture Flow Analyses and Field Tests," Department of Civil Engineering, University of California, Berkeley, Calif., June, 1981.

16. Mitchell, J. K., and Kao, T. C , "Measurement of Soil Thermal Resistivity," Journal of the Geotechnical Engineering Division, ASCE, Vol. 104, No. GT10, Oct., 1978, pp. 1307-1320.

17. Radhakrishna, H. S., Chu, F. Y., and Boggs, S. A., "Thermal Instability and Its Prediction in Cable Backfill Soils," IEEE Transactions on Power Apparatus and Systems, Vol. PAS-99, No. 3, 1980, pp. 856-867.

18. Salomone, L. A., "Improving Geotechnical Investigations for Underground Transmission Lines," Underground Cable Thermal Backfill, S. A. Boggs et a l , eds., Pergamon Press, Inc., Toronto, Canada, 1982, pp. 57-71.

19. Salomone, L. A., and Kovacs, W. D., "The Use of Index Property Tests to Determine the Thermal Properties of Soils," ASTM Geotechnical Testing Jour­nal, Vol. 6, No. 4, Dec, 1983, pp. 173-180.

20. Salomone, L. A., Kovacs, W. E., and Kusuda, T., "Thermal Performance of Fine-Grained Soils," Journal of Geotechnical Engineering, ASCE, Vol. 110, No. 3, Mar., 1984, pp. 359-374.

21. Salomone, L. A., Kovacs, W. D., Wechsler, H., "Thermal Behavior of Fine-Grained Soils," Building Science Series BSS 149, National Bureau of Standards, Washington, D.C., 1982.

22. Salomone, L. A., Singh, H., and Fischer, J. A., "Geotechnical Considerations for Designing Underground Transmission Lines," presented at the 1979 Transmission and Distribution Conference and Exposition, held at Atlanta, Ga.

23. "Soil Thermal Characteristics in Relation to Underground Power Cables," Proceedings of the Summer General Meeting, American Institute of Electrical En­gineers, 1960.

24. "Soil Thermal Resistivity and Thermal Stability Measuring Instrument, Vol. 2: Manual for Operation and Use of the Thermal Property Analyzer and Sta­tistical Weather Analysis Program to Determine Thermal Design Parame­ters," EPR1 Final Report No. EL-2128, Ontario Hydro Research Laboratory for the Electric Power Research Institute, 1981.

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25. Steinmanis, J. E., 'Thermal Property Measurements Using a Thermal Probe," Underground Cable Thermal Backfill, S. A. Boggs, et al., eds., Pergamon Press, Inc., Toronto, Canada, 1982, pp. 72-85.

26. Woods, K. B., and Litehiser, R. R., "Soil Mechanics Applied to Highway Engineering in Ohio," Bulletin 99, Ohio State University Engineering Exper­iment Station, July, 1938.

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