Th l R i ti it f S il Thermal Resistivity of Soils and Engineered Materials

Thermal Resistivity it of Soils
and Engineered Materials
Gaylon S. Campbell, Ph. D.
Decagon Devices, Inc.
Pullman, WA
www.decagon.com

Phoenix Scout Mission to Mars
June 25, 2008 – Oct., 2008
TECP: Thermal and
electrical
properties p probe

TECP Purpose
•Measure thermal and electrical
properties of Martian regolith
•From those measurements, infer
liquid water content, ice content, and
pore size distribution

Some geotechnical applications
of soil thermal properties
• Buried power transmission cables
What is the thermal resistance between a buried
power line and the external environment?
• Ground source heat pump installations
For a given volume of soil, how much heat can be
stored? How fast can it be stored?
• Burial of high level radio-active active waste
How hot will it get? How will it affect moisture
patterns?

Thermal Properties of Soil
Impact Wind Power Generation

U. S. National Electrical
Code: Annex B (2005)
“Typical values of thermal resistivity: rho”
average soil (90 percent of USA) 90
Concrete 55
Damp soil 60
very dry soil 120

Outline
•Definitions
•Thermal properties of porous materials
•Measuring soil thermal properties
•Standards S d d for thermal properties
•Corrective measures

The thermal properties of
interest are
•Thermal conductivity (k )
Ratio of heat flux density to temperature
gradient: 0.1 to 3 W/(m·K)
•Thermal resistivity ( )
R ip l f th m l nd ti it :
Reciprocal of thermal conductivity :
33 to 1000 cm·C/W

Which is best, conductivity
or resistivity?
For soil, conductivity is almost always
preferable to resistivity:
•Better statistical properties
•More correct for averaging
•More linear with water content
•A more correct perception of
significance

More thermal properties
•Volumetric specific heat (C )
Heat required to raise the temperature of
unit volume by 1 K (or C):
1 to 3 MJ/(m 3 K)
•Thermal diffusivity (D )
Ratio of conductivity to specific heat;
Ratio of conductivity to specific heat;
measure of propagation rate of thermal
disturbances: 0.1 to 0.7 mm 2 /s

Modeling Soil Thermal
Properties
•Soil is a mixture of solid, liquid
(water) and gas (air and water vapor)
•The thermal properties of the soil
depend on the thermal properties of
the constituents, their volume
fractions, and how they are mixed

Soil Moisture Concepts and
Definitions
Air 25%
Water 25%
Solid 50%
• A “saturated” soil
has no air
• After saturation soils
typically quickly drain
to “field capacity”
• Further drying is
mainly due to plant
water uptake

Thermal properties of
“pure” soil constituents
k
W/(mK)
C
MJ/(m 3 K)
D
mm 2 /s
Soil Minerals 2.5 2.3 1.09
Granite 3 2.2 1.36
Quartz 8.8 2.1 4.19
Organic matter 0.25 2.5 0.10
Water 06 0.6 418 4.18 014 0.14
Ice 2.2 1.9 1.16
Air 0.025025 0.001001 20.83
From Campbell and Norman (1998)

Volumetric Specific Heat:
variation with water content
(MJ/m3 K )
Vo
l. Sp. Ht.
35 3.5
3
2.5
2
1.5
1
0.5
0
Sand
Clay
Organic
The specific heat of a mixture of
air, water and solids is the sum of
each volume fraction, multiplied by
its specific heat
0 0.1 0.2 0.3 0.4 0.5
Volumetric Water Content

Specific Heat Take-Home
• The volumetric specific heat of soil, rock
and concrete is about 2 (±1) MJ m -3 K -1
• Volumetric specific heat varies linearly
with water content
• Volumetric specific heat can often be
computed more accurately than measured –
you need volumetric water content t and bulk
density

Temperature dependence of
soil thermal conductivity
Thermal Co onductivity
- W/(m K)
1.8
1.6
1.4
12 1.2
1
0.8
06 0.6
0.4
0.2
0
50% solids
0 0.1 0.2 0.3 0.4 0.5
90 C
65 C
25 C
No Vap.
Water Content - m 3 /m 3

Liquid Return Flow: soil as a
heat pipe
1.8
Ther rmal Condu uctivity - W/(m K)
1.6
1.4
1.2
1
08 0.8
0.6
0.4
0.2
0
liq
90 C
vap
No vapor
0 0.1 0.2 0.3 0.4 0.5
Water Content - m 3 /m 3

Temperature Dependence of
Thermal Resistivity
C/W)
Thermal Res sistivity (cm
600
500
400
300
200
100
0
25 C
65 C
0 0.2 0.4 0.6
Water Content (m3/m3)
U. S. Electrical Code
90 C Average soil 90
Concrete 55
Damp soil 60
Very dry soil 120

Response to Thermal
Conductivity of Solids
Ther rmal Cond ductivity - W/(mC)
2.5
2
1.5
1
0.5
0
quartz sand
loam
organic
25 C
0 0.1 0.2 0.3 0.4 0.5
Water Content - m3/m3

Resistivity response to solids
properties
Th hermal Res sistivity (c cm C/W)
1000
900
800
700
600
500
400
300
200
100
0
loam
quartz
organic
0 0.1 0.2 0.3 0.4
Water Content (m3/m3)

Response to Compaction
2
The ermal Condu uctivity - W/( (m K)
1.8
1.6
1.4
1.2
1
0.8
0.6
04 0.4
0.2
0
Loam soil
25C
17% pores
50% pores
60% pores
0 01 0.1 02 0.2 03 0.3 04 0.4 05 0.5 06 0.6
Water Content - m 3 /m 3

Compaction effects on
thermal resistivity
stivity (cm
C/W)
The ermal Resi
600
400
200
0
60% pores
50% pores
17% pores
0 0.1 0.2 0.3 0.4 0.5
3 3
Water Content (m 3 /m 3 )

Take-home
• Thermal conductivity of porous material
depends on:
• Composition
• Temperature
• Density
• Water content
• Th i “ ld ” l f il th l
• There is no “golden” value for soil thermal
conductivity – you need to measure it

How to get values for
Thermal Properties
•Compute them from composition,
density, water content and
temperature (best for sp. Ht.)
•Measure them using the line heat
source (best for conductivity)

Line heat source methods
for thermal properties
•Place a line heat source in the sample
•Apply heat to the source and measure
its temperature over time
•From the slope of temperature vs.
logarithm of time determine k

Thermal conductivity: line
heat source method
ange (C )
Tem pe
ra ture C h
0.6
0.5
0.4
0.3
0.2
01 0.1
0
k = 0.5
k = 1.0
k = 2.0
0.1 1 10 100
Time (s)
k proportional to
1/slope

Making a reading on a
sample
• Insert the needle
• May need a pilot hole
• Turn on the controller
• Press Enter
• Wait 5 – 10 minutes –
controller heats needle,
measures temperature,
and computes k
• Read the result from
display

Example of k measurement
Temp perature Ris se (C)
0.4
0.3
0.2
0.1
0
y = 0.0906x + 0.0564
R 2 = 0.9998
=153 C cm/W
y = 0.0853x + 0.008
R 2 = 0.9996
=144 C cm/W
0 1 2 3 4
ln t or ln t/(t-t o
)
heating cooling heating, excluded cooling, excluded

Contact Resistance Errors
•Contact resistance errors occur any
time there is an air gap around a single
needle probe
•No simple correction is possible
•Long read times minimize these errors
•Worst W in dry materials
•Thermal grease sometimes helps

Standards for thermal
conductivity or resistivity
• ASTM D 5334-08 (2008) Standard test methods
for determination of thermal conductivity of soil
and soft rock by thermal needle probe procedure.
Vol. 04.08, 08 ASTM, 100 Barr-Harbor Dr., West
Conshocken, PA 19428-2059.
• IEEE STD 442-1981 IEEE guide for Thermal
Resistivity it Measurements . The Institute t of
Electrical and Electronics Engineers, Inc. 345 East
47 Street, New York, NY 10017
• Bristow, K. 2002 . Thermal Conductivity it . p1209-
1226. Methods of Soil Analysis. Part 4 Soil
Science Society of America, Inc. 677 South Segoe
Rd. Madison, WI 53711-1086
1086.

Comparison of standards
ASTM
IEEElab
SSSA
Probe length NS 100 mm NS
Probe diam. NS 2.4 mm “thin”
Record length NS 600 s 60 s
Recording Elect. hand Elect.
Analysis Rgr. 2 pt. Rgr
Heat/cool yes no yes

Important points
• Temperature drift during measurement can
cause serious errors in heating-only
analyses (as specified in older standards)
• Probes can’t be used in layered or
inhomogeneous media
• Probes must be in good contact with soil –
thermal grease can sometimes help. Long
read times help a lot

Thermal dryout curves
•The relationship between thermal
conductivity (or resistivity) and water
content for a soil or other porous
material
al
•Water content is an important
variable, but density, mineralogy and
temperature are also important.
Need to hold these constant.

Dryout Curves –
Measurement and Modeling
• Pack a sample
• Saturate with water
• Measure wet conductivity
• Weigh sample
• Oven dry
• Measure dry conductivity
• Compute water content
t
• Fit the model using wet and
dry conductivities

Dryout curves on Sand
uctivity (W /mK)
The ermal Cond
2.0
1.5
1.0
0.5
0.0
single sample 1
single sample 2
0 0.1 0.2 0.3 0.4 0.5
Volumetric Water Content (m 3 /m 3 )
Data from Dr. G. Todd Vanek

Dryout curves on Sand
uctivity (W /mK)
The ermal Cond
2.0
1.5
1.0
0.5
0.0
single sample 1
single sample 2
model singlesample
sample
0 0.1 0.2 0.3 0.4 0.5
Volumetric Water Content (m 3 /m 3 )
Data from Dr. G. Todd Vanek

Sand data on a resistivity
scale
Therm mal Resistivity
4
3
2
1
single sample 1
single sample 2
multisample
model single sample
model multisample
0
0 0.1 0.2 0.3 0.4 0.5
Volumetric Water Content

So – What’s needed for the
combined approach?
Wet conductivity and
water content
Dry conductivity
Volume fraction of solids
Clay content
Measure on saturated,
compacted sample
Measure on oven dried
sample
Compute from bulk
density of sample
Measure or estimate
from texture
See www.Decagon.com for application note

Measuring thermal
conductivity of concrete

Important points for
concrete
•The sample must have the same
density as the in situ material
•Grease the pin before inserting it
•Air gaps cause serious errors
•Sample can be used for saturated and
dry measurements

Measuring thermal conductivity
of cured concrete or rock
•Rotohammer
4 mm hole
•Thermal
grease in
bottom
•Insert
probe

Problem soils – what if I
need lower resistivity?
•Density: compact materials for low
resistivity
•Water content: low resistivity when wet
•Mineralogy: high quartz gives low
resistivity
Fl idi d Th l B kfill TM (FTB TM ) l
•Fluidized Thermal Backfill TM (FTB TM ): low
strength concrete, see www.geotherm.net

Conclusions
• “Measure to Know”
• Conductivity and capacity depend on
moisture, mineralogy, compaction and
temperature
• Specific Heat is 2 +/- MJ/m 3 K
• Measure conductivity with a heated needle
• Provide dryout curves with wet and dry k

For Additional Information
•www.decagon.com
•www.thermalresistivity.com
•www.geotherm.net