Environmental Engineering Reference
In-Depth Information
where:
=
Table 10.6 Thermal Conductivity Values
λ
p
for Some
Rock-Forming Minerals
product of the thermal conductivity of a particular
mineral,
k
m
λ
p
(W/m/
◦
C)
Mineral
x
=
volumetric proportion of a particular mineral,
j
=
refers to the
j
th mineral, and
=
Amphibole
3.46
z
total number of minerals.
Calcite
3.59
Table 10.6 provides thermal conductivity values for most
common minerals. The thermal conductivity values were
compiled by Cote and Konrad (2005) from the database of
Horai (1971).
Further measurements of thermal conductivity on dry min-
erals,
λ
dry
, have been made by Cote and Konrad (2005). The
thermal conductivity of dry soils heavily relies on struc-
tural effects (e.g., cemented particles, angular particles, and
rounded particles) and the thermal conductivity ratio. For
example, a soil with a porosity of 40% could have a ther-
mal conductivity for natural quartz sand of 0.3 W/mK in the
dry state. For the same porosity, dry crushed quartzite has a
value of 0.65 W/mK and for naturally porous quartzite rock
the thermal conductivity could be 1.15 W/mK. The materi-
als have the same origin and porosity but different particle
arrangements. The lower the ratio of fluid thermal conduc-
tivity to particle thermal conductivity,
λ
f
/λ
p
, the higher will
be the effect of structural characteristics.
Cote and Konrad (2002) proposed the following equation
for two-phase porous materials (e.g., solid particles and a fluid
such as water in the pores) with any fluid filling the pores:
Chlorite
5.15
Dolomite
5.51
Feldspar
2.25
Mica
2.03
Olivine
4.57
Plagioclase
1.84
Plagioclase (labradorite)
1.53
Pyroxene
4.52
Quartz
7.69
Source
:Cote and Konrad (2005).
Round/subrounded
From Johansen [4]
HSU
Angular/subangular
Cemented/bound
1
(κ
2P
λ
p
−
λ
f
)(
1
−
n)
+
λ
f
λ
2P
=
(10.68)
0.1
1
+
(κ
2P
−
1
)(
1
−
n)
where:
κ
2P
=
an
empirical
factor
that
depends
on
structural
effects (two-phase thermal conductivity),
λ
p
=
thermal conductivity of the solid particles,
0.01
0.001
0.01
0.1
1
λ
f
=
thermal conductivity of the pore fluid such as water,
and
λ
f
/
λ
p
n
=
porosity.
Figure 10.21
Values for the structural effects factor,
κ
2
P
,for
various two phase porous materials.
The factor
κ
2P
, was empirically determined for a
number of soil types including porous rock and concrete.
Figure 10.21 shows the variation of
κ
2P
as a function of the
ratio,
λ
f
/λ
p
and particle types. The HSU and HSL lines
refer to the Hashin-Shtrikman (1962) theoretical bounds
for thermal conductivity of two-phase porous materials.
The relationship between
κ
2P
and the ratio,
λ
f
/λ
p
can be
expressed in the form
Table 10.7 Empirical
β
Factors for Materials with
Various Particle Types
1
1
λ
f
/λ
p
<
15
,
λ
f
/λ
p
<
15
,
Particle Type
Dry
Saturated
0
.
29
15
λ
f
λ
p
β
κ
2
P
=
(10.69)
Natural (rounded)
0.81
0.46
Crushed (angular)
0.54
0.46
where:
Cemented (bound)
0.34
0.46
β
=
factor related to particle type and depending on the
trigger value of
1
15
of the ratio of
λ
f
/λ
p
, (Table 10.7)
Source
:Cote and Konrad (2005).
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