Soil Thermal Resistivity Measured Simply and Accurately

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  • IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS, VOL. PAS-89, NO. 2, FEBRUARY 1970

    for the closure distance after 10 load breaks, the effect would be forthe 60-in/s line to have a slope less than one half of that shown. Inother words, this new line would not be as steep as the 30-in/s lineshown in the figure. The results would be to consistently obtain highinstantaneous voltage on closure and to produce excessive arcingtimes. Thus serious contamination of arc-quenching material canyield very poor fault-closure performance after load-break life.Materials are available which do not contaminate as readily as thatshown.

    In regard to the load-break test circuit shown in Fig. 16, the authorstates that it is essentially the same as that in the proposed IEEE-NEMA standard. Fig. 19 demonstrates the difference in these twocircuits. The voltage diagrams show the half-cycle of the voltagewave in which the current is extinguished. A 70-percent power factoris assumed, and the series impedance is 10 percent of the total and ismostly reactive.

    After the connector current goes to zero, the currents in theparallel R and L load impedances are equal and opposite. They decaygradually, and the voltage across this part of the circuit decays asshown. The voltage across the open connector is the difference be-tween this voltage and the source. The values of these two voltagedrops are the same for each circuit, and they are merely inter-changed with respect to ground.Assuming that the elbow is connected to the source side of the

    connector, the heavy black line shows the voltage of the elbow toground. This is the most important factor since failure occurs whenthe elbow flashes over to ground. Fig. 19 clearly demonstrates whythe "standard" circuit is the more severe. At the instant of currentzero, the elbow voltage is less than 10 percent for the circuit inthe paper and 70 percent for the "standard" circuit.

    In summary, the author's paper can be considered a fine contribu-tion to the understanding of this relatively new device. It must benoted however that the remarks pertain to one specific device andnot to all available load-break connectors.

    Norman M. Sacks: The author wishes to express his appreciationfor the interest shown by Mr. Ruete in his paper.Mr. Ruete's comments are well taken, and they underscore points

    made in the paper. As he points out, the data in Figs. 14 and 18 lendthemselves to a calculation of the velocity required for contaminatedparts as a result of load-break life. The paper shows that the termina-tor tested will give satisfactory fault-closure performance after 10load breaks using the velocity of 60 in/s. Subsequent to the publica-tion of the paper we have found that improved arcing materials candecrease the contamination that results from load switching. Thesematerials allow speeds lower than 60 in/s for successful fault closures.Mr. Ruete is correct in his conclusion that the position of the paral-

    lel impedance in load-break circuits is an important element inswitching. As stated in the paper, the parallel impedance was locatedas a testing convenience before the IEEE-NEMA standard circuitbecame firm. Subsequent tests used the parallel impedance betweenthe test samples and the ground. It is agreed that this would increasethe likelihood of flashover to ground.

    Manuscript received October 7, 1969.

    Soil Thermal Resistivity MeasuredSimply and Accurately

    JOHN STOLPE, MEMBER, IEEE

    Abstract-There is a growing need for each utility to gain athorough knowledge of the soil thermal resistivity throughout itssystem. The volume of heavily loaded multiduct runs of power cablespromises to increase rapidly in the years ahead. We can no longerafford to plan for cable loadings based purely on an assumed soilthermal resistivity. Rather, we must compile information thataccurately describes the thermal resistivity of soils commonlyfound within specific geographic areas; then very realistic values ofsoil thermal resistivity can be used in the planning of new under-ground systems in these areas.This paper describes the design and utilization of apparatus that

    has demonstrated convenience and reliability in the analysis ofthermal properties of soils and soil-like materials. The scope ofestablished test procedures is related. Test results and variouscorrelations that have been found from preliminary testing arereviewed and illustrated.

    Paper 69 C 1-PWR, recommended and approved by the InsulatedConductors Committee of the IEEE Power Group for presentationat the IEEE Underground Distribution Conference, Anaheim,Calif., May 12-16, 1969. Manuscript submitted December 2, 1968;made available for printing October 7, 1969.The author is with the Southern California Edison Company,

    Los'Angeles, Calif. 90053.

    INTRODUCTIONANYONE involved in the design of underground power

    transmission and distribution systems knows that in orderto accurately predetermine the ampacity of such systems, onemust know, along with other data, the thermal resistivity of thesoil surrounding the system. There are several techniquesreported in the literature [1]-[4] for determining the thermalresistivity (rho) of soils, and they have been used with varyingdegrees of accuracy, convenience, and success.A new technique, with some advantages, has been developed

    to measure the thermal resistivity of soils. The apparatus iscalled a rhometer, and is basically a laboratory device. Samplesof soil are taken from the field and recompacted to any desireddensity when they are tested for rho. The soil can be tested atthe field density and over a range of moisture content; then thesoil density can be changed and the soil rho remeasured todetermine the effect of getting more compaction. This flexibilityof being able to measure rho under conditions of varying knownsoil density and varying moisture content has obvious advan-tages when making preliminary investigations in the design oflarge underground power systems. Since the rhometer can also

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  • IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS, FEBRUARY 1970

    induce variable heat fluxes on a soil, it may become possible todevelop a correlation of heat flow through a soil and some equi-librium moisture content that can be held within the soil matrix.The foregoing idea is indeed a subject for future work.As holds true for all methods of measuring the rho of soil in the

    field, the rhometer can only measure the soil rho at a point, ormany points, along a proposed underground trench. Frequencyof sampling along the route in order to locate thermal troublespots is a subject in itself and is covered in the literature [5],[6]. Once the samples have been taken, each specific soil typeencountered can be placed in the rhometer at precisely the samedensity and moisture content as in the field, and the respectivesoil rhos may be accurately determined.

    It is felt that there will be no loss of accuracy by taking samplesfrom the field and remolding them to the same density andmoisture conditions as they experienced when taken from thefield. Tests have not actually been performed to establish thisbelief, but it is generally recognized that most granular soilscomposed of silt and sand do not lose their physical charac-teristics upon being remolded to the same density and moisturecontent as an undisturbed sample [7 ]. The types of soils that maycause errors when they are remolded are "sensitive" clays, but itis doubtful that even as much as 10-percent error can be intro-duced in the measurement rho of sensitive clays.

    It has been stated that the correct laboratory determinationof soil rho must be made on undisturbed soil samples, andreference was made to tests on fragmented, or mechanicallycrushed, soils [8]. Undisturbed samples were taken of soil withaverage maximum particle diameters of about 10 mm andthe undisturbed soil rho was determined. Then the samplewas crushed between rollers to a maximum particle size of about2 mm, and the soil rho was again measured. These two rhovalues were then compared, and as would be expected, thevalues were quite different because, indeed, the soils were dif-ferent.The rhometer technique applies Fourier's law of heat con-

    duction in a steady-state laboratory apparatus; therefore, rho isdetermined from its basic scientific definition [9]. Measuringrho of a given soil, as diagramed in Fig. 1, involves placing thesoil between two concentric cylinders and allowing heat to flowradially from the inside surface to the outside surface. Therho of the soil between concentric cylinders is found by in-tegrating Fourier's law of heat conduction in cylindrical geom-etry to get

    2ir(L) (Td- TD) (1)Q ln (D/d)

    wherep thermal resistivity, WC cm/WL axial length of cylinder, cmTd- TD temperature drop between d and D, CQ total heat flowing from d to D, wattsD diameter of outer cylindrical surfaced diameter of inner cylindrical surface.There are no simplifying assumptions in the application of

    (1), and the relation always holds under conditions of steady-state radial heat flow.

    Since the rhometer method is an application of steady-stateheat flow, heat can be applied continuously for weeks in dura-tion without affecting the rho measurement. This permits thesoil specimen to gradually dry out, making possible comparison

    Fig. 1. Radial heat flow through hollow cylinder.

    of the drying rates of several soils. If it is desired to determine theeffect of compaction on the thermal resistivity of a given soil,the soil can be placed at any desired density and its rho can bemeasured as it slowly dries out.

    This method also allows soil to be tested under varying heatfluxes of realistic magnitudes, giving an indication of the heatthat can be conducted by a soil without causing excessive dryingin a field application.These soil thermal properties are being acquired for "typical"

    soils found in various populated regions throughout southernCalifornia. The object of such a large investigation is to be ableto establish "typical" values of rho for the soils found in thevarious regions. It is felt that the practice of assuming a stan-dard rho of 900C cm/W for the entire service territory of autility could be sacrificing a great deal of economy, and in somecases it could lead to overheated cable systems. Therefore, arather large program is being conducted in order to gain knowl-edge of typical soil conditions at the normal burial depth ofelectric power systems. It is not anticipated that every soiltype in each populated area of southern California can bedetected; however, enough samples can be taken so that theactual soil rho can be intelligently estimated instead of merelyguessed.

    SOIL SAMPLING METHODSSamples of soil are taken from various field locations and

    tested for moisture content and thermal resistivity in thelaboratory. Whenever possible, samples are taken from aboutfour feet below grade so that the ambient soil temperature canalso be measured. This is usually accomplished by coordinatingsoil sampling in an area with underground construction, andtaking the soil sample just after the trench is opened.The only test performed in the field is the determination of the

    in-place density of the soil. Two methods can be used, both ofwhich yield good results. One that can be used in all cases isthe sand cone method (ASTM D1556-64). It involves carefullydigging a small hole and then refilling the hole with a knownvolume of specially calibrated sand. The other, the thin-walledtube method (ASTM D1587-63T), simply involves driving atube into the ground and determining the weight and volume ofthe soil sample removed. This method is much faster than thesand cone method, but it cannot be used with acceptable accuracyin very hard or gravel-type soils.

    All samples are returned to the laboratory, tested for fieldmoisture content and subjected to grain size analysis (ASTMC136-63). This permits each soil to be classified as a clay, silt,or sand; and samples are stored until they can be tested for rho.

    In an extensive soil investigation that is an attempt to cor-relate many variables, it is best if testing is done under thecontrolled conditions found only in a laboratory. This is why noattempts were made to measure rho in the field. Even if rhowere measured in the field, to get complete meaning from the

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  • STOLPE: SOIL THERMAL RESISTIVITY MEASUREMENT

    results a sample would have to be taken at the test depth inorder to know the soil moisture content and degree of soilcompaction. Thus, it is nearly as fast, and more accurate, totake one large soil sample from the field and perform the thermaltests in a laboratory.

    CONSTRUCTION DETAILSBefore the methods of testing soils for thermal resistivity are

    discussed, the details of construction of the rhometer will beexplained. Several materials have been chosen for use in therhometer and each has a specific physical and/or thermalpurpose. Fig. 2 shows the apparatus and the details of its con-struction; the description of each component follows.

    1) Power Resistor: This serves as the heat source; it is a 2000-ohm 50-watt resistor connected to a 115-volt ac regulated powersupply. It has a temperature coefficient of resistance of onlyabout 75 ppm/C and it is noninductive. Thus, the watts dis-sipated can be determined simply by measuring the currentflowing through the essentially constant resistance.

    2) Copper Pipe: The outside diameter of the copper was chosenas large as possible in order to provide a large surface area forheat to pass into the soil, but it had to be small enough, withrespect to the concrete cylinder, so that a measurable tem-perature drop would result between the inside and outsidesurfaces of the soil sample. These opposing criteria arise becauseit is necessary that the rhometer give accurate rho valueswhen operating under a low heat flux of 10 W/ft2 at thesoil/heat source interface; for handling purposes, the overalldiameter of the soil had to be restricted to about 8 inches sothat the volume of soil being tested could be handled easily. Thematerial used for the copper tube is extra-heavy-wall copperpipe. The large thickness will equalize any temperature varia-tions, thus producing an isothermal surface at the soil inter-face. Actual measurements have shown that the copper has lessthan 0.0250 C variation in temperature over its surface.

    3) Concrete Cylinder: Two requirements of the concrete pipe aresufficient strength to withstand the internal soil pressure fromcompaction, and porosity, so that moisture can be driven out ofthe soil, through the concrete, and finally to the surrounding air.This piece is mass produced as an extension neck for a waterhandhole.

    4) Insulating Disks: The primary function of the disks is toinsure radial heat flow through the soil. The thermal resistanceof the foam disks, made of material with p = 30000 C - cm/W,is much greater than the thermal resistance of the soil. Becausethe heat will flow along the path of lowest thermal resistance, theheat therefore flows radially to the concrete. The disk on thebot...

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