Proposal to Revise IEEE 442 Guide for Soil Thermal Resistivity Measurements

Gaylon S. Campbell, Ph.D.Decagon Devices, Inc.

Pullman, WA

PES-ICC Spring MeetingMay 17-20, Orlando, FLC20 Soil Thermal Stability

IEEE 442 History

First published: 1981Last reaffirmed: 2003Electronic publication 1998

The content is essentially as originally published

Applicable StandardsIEEE 442: Gude for Soil Thermal Resistivity Measurements (1981)

SSSA Methods of Soil Analysis: Thermal Conductivity (2002)

ASTM D 5334-08 Standard Test Method for Determination of Thermal Conductivity of Soil and Soft Rock by Thermal Needle Probe Procedure (2008)

Stated Purpose

Enable user to: Select useful commercial test equipmentManufacture equipment which is not readily available on the marketMake meaningful resistivity measurements with the equipment

Sections of the Guide

1. Scope2. Purpose3. References4. Factors influencing soil thermal resistivity5. Test equipment6. Test methods7. Analysis of test results

Sections in blue are those in need of revision

Sections needing revision

3. ReferencesUpdate to newest versions of standards

5. Test equipmentUpdate to give performance requirements

6. Test methodsMinor revisions for consistency

7. Analysis of test resultsUpdate to reflect current knowledge and practice

Recommended revision: Section 5.Test Equipment

Guide describes 30-40 year old technologyAppropriate technology is now commercially availableThe Guide should state performance requirements rather than dimensions and construction details (which can be given in an appendix)

ASTM D5334-08 describes relevant information

Thermal needle probe (linear heat source with temperature measuring element at center; sample design in an appendix)Constant current sourceTemperature readout unit or recorder (0.1 to 0.01 K resolution)Voltage-ohm-meter (0.01 volt and amp resolution)Timer (0.1 s resolution)

Recommended revision: Section 7. Analysis of test results

This section should be rewritten to Show a more correct analysis for a line heat source during heating and coolingSpecify regression, rather than arbitrary eye-fits to dataBetter specify the time periods over which data are validProvide more representative data for actual soils

Equations used to determine resistivity should be:

CorrectResistant to experimental errorAs easy to use as possible

The following slides show the assumptions for the currently used equation and give a basis for improvements

Complete equations for an infinite line heat source

( )

integrallexponentiaisEitimeheatingist

radiusheaterisrmWinputheatisq

ktCrEi

ttkCrEi

kqT

o

)/(

444

2

0

2

⎭⎬⎫

⎩⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛ −−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

−=Δ

π Cooling curve

Heating curve⎟⎟⎠

⎞⎜⎜⎝

⎛ −=Δ

tkCrEi

kqT

44

2

π

Reference:Carslaw, H. S. and J. C. Jaeger 1959 Conduction of Heat in Solids p. 258-262, Oxford

Looking just at the heating phase equation:

− − = −

= − − + − +

∞

∫Ei a u u du

a a aa

( ) ( / ) exp( )

ln / ...

1

42γ

⎟⎟⎠

⎞⎜⎜⎝

⎛ −=Δ

tkCrEi

kqT

44

2

π

Approximate equations for heating and cooling

qslope

Ctt

tqT

CtqT

⋅=

+⎟⎟⎠

⎞⎜⎜⎝

⎛−

≈Δ

+≈Δ

πρ

πρ

πρ

4

ln4

ln4

0

heating

cooling

y = 0.09x + 0.0564R2 = 0.9998

y = 0.0853x + 0.008R2 = 0.9996

0

0.1

0.2

0.3

0.4

0 1 2 3 4

ln t or ln t/(t-to)

Tem

pera

ture

Ris

e (C

)

heating cooling heating, excluded cooling, excluded

ρ =153 C cm/W

ρ =144 C cm/W

Important observations about probes

IEEE 442 probes are not infinite line heat sourcesBut, a semi-log plot of temperature response vs. time (ignoring early time data) produces a straight line even for these large probesThe slope of the semi-log plot is proportional to thermal resistivity,Unfortunately, the proportionality factor is not the one given by ILS theory But the correct proportionality factor for these probes can be obtained by calibration

Recommend:

Continued use of semi-log approximation, excluding early time dataUse cooling as well as heating data to minimize temperature drift errorsCalibration of probes in recognized resistivity standards to minimize effects of non-ideality and assure high quality resultsRegression analysis of data rather than eye-fits

Sample Temperature drift cause large errors with heating-only analysis

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.001 -0.0005 0 0.0005 0.001

Temperature Drift (C/s)

App

aren

t Con

duct

ivity

(W/m

C)

Log f it

Exp IntStabilized Water, 30 s heating

____ heating only

------- heat/cool

Large probes overestimate conductivity unless calibrated

Cond.W/(mK)

uncalibrated1.27 mmNeedle

uncalibrated2.4 mmNeedle

Water (stabilized) 0.6 0.579 ± 0.006 0.852 ± 0.005

glycerol 0.29 0.277 ± 0.007 0.427 ± 0.002

Guide Fig. 3: “Thermal Property Characteristics of Soils”

An improved version of Fig. 3 showing both soils and engineered materials

10

100

1000

10000

0 5 10 15 20 25 30

Water content % dry wt.

Ther

mal

Res

istiv

ity (C

cm

/W)

Palouse APalouse BVolkmarPeat mossQuartz sandCrushed stoneOttowa sand

IEEE should be updated for continued use in the industry

It contains valuable information specific to proper underground cable installationOnly two sections require extensive revision to be brought up to dateThe ASTM and SSSA standards, and the scientific literature contain sufficient basis for updating these sections without additional testing on the part of ICC