Thermal Conductivity of Lateritic Clays: Temperature Effects

International Journal of Heat and Mass Transfer 138 (2019) 562–570
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer
journal homepage: www.elsevier.com/locate/ijhmt
Effect of temperature on thermal conductivity of lateritic clays over a
wide temperature range
Yunshan Xu a, De’an Sun a,b,⇑, Zhaotian Zeng b,⇑, Haibo Lv b
a
b
Department of Civil Engineering, Shanghai University, Shanghai 200444, China
Guangxi Key Laboratory of New Energy and Building Energy Saving, Guilin University of Technology, Guilin 541004, China
a r t i c l e
i n f o
Article history:
Received 17 September 2018
Received in revised form 14 March 2019
Accepted 16 April 2019
Keywords:
Lateritic clay
Thermal conductivity
Temperature effect
Aggregate structure
Model prediction
a b s t r a c t
The temperature dependence of the relationship between thermal conductivity and saturation of lateritic
clays is more complex than that of other soils. This paper reports sample-scale measurements of thermal
conductivity of two lateritic clays with aggregates and dual-porosity at different saturations and temperatures. Test results indicate that the thermal conductivity increases with increasing temperature. The
effects of the latent heat transfer (LHT) of vapor on the thermal conductivity were more pronounced
at intermediate saturations and temperatures above 60 °C. The thermal conductivity resulting from the
LHT of vapor has obvious peak value with saturation, and its peak value and corresponding saturation
are related to the clay content. The difference in the thermal conductivity from the LHT of vapor between
two clays at a given temperature is due to the effect of the microstructure. The mercury intrusion
porosimetry (MIP) tests were also performed to observe the pore-size distribution (PSD) of two lateritic
clays, which can explain the difference in the temperature effect on thermal conductivity. The interparticle contact heat transfer (IPCHT) model provides good agreement with test data at temperatures
ranging from 5 to 90 °C for two lateritic clays. The soil-water retention curves play an important role
in predicting the thermal conductivity by the IPCHT model, which can be further improved by better consideration of the microstructure and phase configuration.
Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction
Soil’s thermal conductivity (k) is an essential thermophysical
parameter in characterizing the heat transfer or thermal diffusivity
property of soils. During the past few decades much attention and
research effort have been focused on the soil thermal property in
the fields of geothermal, agricultural and civil engineering. Soil is
a complex porous medium consisting of solid particles, water,
and gas phase, and thus there are many factors affecting k. Previous
studies have shown that k is affected by soil texture, mineralogical
compositions, bulk density, particle-size distribution, salt content
and saturation (S), etc. [1]. The studies mentioned above mainly
focused on the ambient temperatures ranging from 0 to 30 °C,
although satisfactory experimental results and some well-known
predictive models have been obtained. Little work was devoted
to the study on the property of soil heat transfer at high temperatures (60–90 °C). Thorough knowledge of soil thermal properties at
⇑ Corresponding authors at: 99 Shangda Road, Shanghai 200444, China (D. Sun).
12 Jiangan Road, Guilin, Guangxi Province 541004, China (Z. Zeng).
E-mail addresses: [email protected] (D. Sun), [email protected]
(Z. Zeng).
https://doi.org/10.1016/j.ijheatmasstransfer.2019.04.077
0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
high temperatures is particularly required in several important
processes, such as thermal treatment of contaminated soils [2],
high-temperature thermal storage of soils [3] and long- or shortterm interactions between soil and ground-contact engineering
facilities such as the high-level radioactive waste repositories [4]
and buried high-voltage power cables [5].
Over past few decades, few works have been conducted on the
thermal conductivity measurements and predictive models at
high temperatures. Philip and de Vries [6] observed that at intermediate water contents, water vapor flux is enhanced because of
the effects of thermal gradients on the water vapor diffusion. Lu
and Ren [7] confirmed that k increased dramatically with temperature in moist soil for loam samples, reaching values two to four
times the 22 °C value when the temperature was 81 °C. Similar
observations were also made by Hiraiwa and Kasubuchi [8] and
Liu et al. [9] who investigated the temperature effect of k. Their
results showed that the temperature effect on k is more pronounced at intermediate water contents, whereas k varies
insignificantly with water content and temperature at low water
contents. More recently, Smits et al. [10] measured k at temperatures varying from 30 to 70 °C for silica sand samples. They suggested that the thermal conductivity and diffusivity increased
Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570
noticeably at temperatures above 50 °C due to the enhanced
latent heat transfer (LHT). As for the study of k predictive models,
de Vries [11] proposed a model that accounts for the enhanced
heat transfer by vapor distillation in soils at high temperatures,
but this model involves many parameters and is more dependent
on the calculated value of the critical water content. Also, a new
predictive model, based on a modified de Vries approach, was
developed by Campbell et al. [12]. This model was, however,
designed to correlate with experimental data, and it cannot be
strictly applied to different soils. It is of note that a simple
inter-particle contact heat transfer (IPCHT) model for predicting
k at different temperatures (0–90 °C) has been proposed by Tarnawski et al. [13] and Leong et al. [14]. Based on the selfconsistent approximation model, the model considered synthetically the modified interparticle contact heat transfer and LHT of
vapor. However, it has not been thoroughly verified by more
accurately measured data for a wide variety of soils. It is generally recognized that k increases with temperatures due to the
enhanced LHT. At elevated temperature, water evaporation and
the associated LHT become an increasingly important or even
dominant, contributing to an increase of heat transfer in the soil
air compared to the moderate temperatures. Both the processes,
the conduction and LHT, take place under the same temperature
gradient [15]. Thorough knowledge of the LHT of vapor at different temperatures is vital to understand these phenomena, and
therefore corresponding work on this issue should be further
studied.
Natural soils are mainly characterized by soil structure and texture. For many of the multi-pore structured media, a unique permittivity response is exhibited on the relationship between
volumetric water content (h) and dielectric permittivity [16]. Similar observations about thermal properties were also made by Zeng
et al. [17] who investigated the relationship between volumetric
water content and thermal conductivity for four lateritic clays. In
China, lateritic clay spreads in tropical and subtropical zones with
an approximate area of 2,000,000 km2, and a number of works has
been devoted to investigating the engineering property during the
past few decades [18–20]. However, little work was devoted to the
study on the thermal property of lateritic clay. Particularly, several
engineering problems or environmental issues, such as the utilization of shallow geothermal energy, urban heat island effect and
prevention of heat hazard in underground space, have not been
effectively solved because of limited knowledge on the temperature dependence of thermal property of lateritic clay. Moreover,
to the best of our knowledge, the lateritic clays are very unique
soils in the microstructures and mineralogical compositions, which
have a significant impact on engineering property and may have an
influence on the temperature dependence of thermal property.
Therefore, there is a great need for study on the temperature
dependence of thermal property of lateritic clay and its LHT of
vapor.
This paper presents a study on the k -S relationship of two
lateritic clays from Guanxi, China over a wide range of temperatures (5–90 °C) and tries to provide some more insight into the
microscopic mechanism of the LHT of vapor affecting the k-S relationship. The thermal probe method was used to measure k. To this
end, the application of the IPCHT model for predicting the k-S relationship was evaluated and thus its reliability was verified. Furthermore, probing the soil microstructures and soil-water
retention behaviour can aid understanding the temperature effect
on the LHT of vapor. In this study, the mercury intrusion porosimetry (MIP) tests were conducted to measure the micro-porosity
structures, together with the measured soil-water retention curves
(SWRCs), which were applied to reveal the temperature effect on
the thermal property of lateritic clays.
563
2. Materials and method
2.1. Soil samples
The lateritic clays used in this study were taken near the ground
surface from Guilin and Liuzhou areas in Guangxi Autonomous
region, China. The sampling sites are shown in Fig. 1. Prior to the
commencement of laboratory tests on the soil samples, they were
air-dried, passed through a required sieve (a 2-mm sieve for k measurement) and thoroughly mixed. Table 1 listed the sampling
depth and major physical property indexes including liquid and
plastic limits and grain fractions of two soils. The mineralogical
compositions and their relative contents, determined using the
X-ray diffraction (XRD) and chemistry analysis tests simultaneously, are listed in Table 2.
The Lateritic clays were formed by the weathering and laterization of carbonate rocks under humid tropical climates, followed by
eluviation or slope. The clay minerals, iron and manganese oxide
minerals and gibbsite are the indicative minerals for three pedogenesis geochemical processes respectively: (i) enrichment of silicon
and aluminum and depletion of calcium and magnesium, (ii)
enrichment of iron and manganese, and (iii) enrichment of aluminum and depletion of silicon. It can be seen from Table 1 that
the Guilin lateritic clay contains 11.44% gibbsite, whereas the Liuzhou lateritic clay contains no gibbsite. This indicated that the
degree of laterization of Guilin lateritic clay is higher than that of
Liuzhou lateritic clay, which may have an influence on the physical
property indexes, as shown in Table 1.
2.2. Measurement of thermal conductivity
Laboratory testing was performed to measure the values of k
over a wide range of temperature (5–90 °C). The measurement of
k was conducted using a commercially available non-steady-state
thermal needle probe (KD2 Pro, Decagon Devices Inc., Pullman,
WA), which is equipped with three types of thermal probes (i.e.,
KS-1, TR-1 and SH-1) for different test samples. Its operating principle is based on the hot wire method and the thermal conductivity
can be obtained by heating the samples and monitoring tempera-
Fig. 1. Sampling locations of two lateritic clays.
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Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570
Table 1
Physical property indexes of soil samples studied.
Soil
Depth (m)
Specific gravity
Liquid limit (%)
Plastic limit (%)
Sand (%)
Silt (%)
Clay (%)
Guilin lateritic clay
Liuzhou lateritic clay
2–4
0–3
2.74
2.73
77.8
58.0
42.1
24.6
14.30
11.71
32.20
40.70
53.50
47.59
Table 2
Mineralogical compositions of soil samples studied.
Soil
Kaolinite (%)
Gibbsite (%)
Illite (%)
Geothite (%)
Quartz (%)
Guilin lateritic clay
Liuzhou lateritic clay
56.59
19.71
11.44
—
—
23.1
15.61
7.45
12.45
44.0
ture variation during the linear heat transfer [1]. The resolution of
KD2 Pro is 0.001 W/(mK) for measurements of thermal conductivity. SH-1 type thermal probe is widely used for measuring thermal
conductivity of soils with an accuracy of better than 5% in the
range of 0.02 to 2 W/(mK), and was adopted in this study. SH-1
probe consists of dual needles with 30 mm length and 1.28 mm
diameter, which are spaced 6 mm apart. In testing process, a current firstly passes through the heater in one of the needles for a
set time (30 s) and the change in temperature is measured using
a thermocouple in the other needle, and then the cooling period
of 30 s lasted following the heating period. Through monitoring
the heat dissipation of linear heat resource in specimens, the thermal conductivity of specimens was calculated and displayed on the
controller’s screen.
The test procedure for measuring the value of k is as follows: (i)
a given amount of air-dried soil was put into a plastic bag; (ii) the
required amount of distilled water was sprinkled on the soil to
reach a specified gravimetric water content; (iii) the wet soil was
kept in closed plastic bags for 72 h to allow uniform distribution
of moisture throughout the soil mass; (iv) the wet soil was packed
into the steel ring (90-mm in height, 75-mm inside diameter, 3mm in wall thickness) and then was compacted to desired bulk
density of 1.1 g/cm3 for both lateritic clay by the static compaction
method; and (v) the soil samples were tightly wrapped with plastic
film and placed in a box with a constant temperature (controlled to
±0.1 °C), which was set from 5 to 90 °C for 48 h before the thermal
conductivity measurement.
Before the tests, SH-1 sensor was calibrated using the Delrin
block. The thermal probe was inserted into the compacted soil col-
Steel ring
Support
Fig. 2. Diagram for measuring thermal conductivity.
Measurements of soil-water retention curves (SWRCs) were
conducted for explaining the thermal properties and for being used
in the prediction model of thermal conductivity. The compacted
specimens of the lateritic clay were prepared with the same bulk
density as the soil specimens for measuring k by the static compaction in a stainless-steel specimen ring (61.8-mm inside diameter and 20-mm height). For lateritic clay, a laboratory testing
program consisting of several different methods for suction control
or measurement was designed to measure the SWRCs over a wide
suction range. The pressure plate method (PPM) was used to control the matric suction ranging from 0 to 1.5 MPa. The tests were
performed by increasing the matric suction from 0 to 1.5 MPa by
several steps at zero net stress. When the water content and the
vertical deformation of the specimen reached equilibrium, the next
suction level was applied. The filter paper method (FPM) was used
to measure the matric suction ranging from 0.5 to 40 MPa. For
details of the relative test devices and measurement procedures
of PPM and FPM, see Sun et al. [20].
The prediction model of k is useful for understanding the
dependence of k on the water content (w), temperature (T) and soil
physical property. Some prediction models of k based on physical
theory have been proposed to describe the k-w relationship
accounting for soil physical property [11–13]. Among various kinds
of k predictive models, the inter-particle contact heat transfer
(IPCHT) model [14] was adopted for its convenience since the
model does not include any geometrical fitting parameter, and
the effective thermal conductivity of soils (keff) was calculated as:
Transmission cable
Soil sample
2.3. Measurement of soil-water retention curve
2.4. Application of IPCHT model
Constant temperature box
Thermal probe
umn and then k was measured, as shown in Fig. 2. After that, the
water content and bulk density were determined by measuring
the specimen volume and the specimen weights before and after
drying the samples in an oven at 105 °C for 24 h. The results of
repeated tests for measuring the thermal conductivity under
respective the same condition are listed in Table 3. It can be seen
from Table 3 that the standard deviation (SD) of the measured values is within 1%. To further improve the measurement accuracy,
the obtained values of repeated measurements on thermal conductivity were averaged as the final value.
KD2
Pro
keff
"
#1
3
1 X
hi
¼
3 i¼1 2keff þ ki
ð1Þ
where ki and hi are the thermal conductivity and volumetric fraction
of phase i, respectively.
The volumetric fractions of solid (h1), water (h2) and air (h3) are
defined and calculated as:
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Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570
Table 3
Repeated tests for measuring thermal conductivity of Guilin lateritic clay under the same condition.
Dry density (g/cm3)
Saturation (%)
Temperature (°C)
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
4.0
4.0
4.0
4.0
4.0
4.0
44.9
44.9
44.9
44.9
44.9
44.9
83.9
83.9
83.9
83.9
83.9
83.9
5
25
40
60
80
90
5
25
40
60
80
90
5
25
40
60
80
90
Thermal conductivity (Wm1K1)
No.1
No.2
No.3
No.4
No.5
Mean
0.199
0.237
0.249
0.301
0.402
0.462
0.607
0.686
0.825
1.071
1.304
1.548
0.904
1.026
1.040
1.166
1.289
1.359
0.197
0.234
0.245
0.298
0.392
0.474
0.605
0.691
0.828
1.063
1.307
1.542
0.900
1.028
1.042
1.179
1.299
1.364
0.205
0.229
0.246
0.314
0.393
0.475
0.603
0.686
0.827
1.069
1.306
1.542
0.909
1.029
1.043
1.183
1.306
1.376
0.207
0.228
0.241
0.309
0.405
0.464
0.609
0.689
0.827
1.064
1.303
1.551
0.912
1.029
1.045
1.177
1.304
1.372
0.204
0.227
0.243
0.316
0.401
0.479
0.604
0.689
0.827
1.068
1.295
1.555
0.909
1.032
1.04
1.183
1.290
1.380
0.202
0.231
0.245
0.308
0.399
0.471
0.606
0.688
0.827
1.067
1.303
1.548
0.907
1.029
1.043
1.178
1.298
1.370
h1 ¼
Vs
qd
¼
V v þ V s qw Gs
ð2Þ
h2 ¼
Vw
SðGs qd =qw Þ
¼
Gs
Vv þ Vs
ð3Þ
Va
¼ 1 ðh1 þ h2 Þ
h3 ¼
Vv þ Vs
ð4Þ
where Vs, Vw and Vv are the volumes of solid, water and voids in
soils, respectively. qd is the dry density of soil specimens, qw is
the density of water, and Gs is the specific gravity.
Thermal conductivity of soil solid (k1) is given by
k1 ¼ aks
ð5Þ
where a is a dimensionless heat transfer correction factor of soils,
representing reduction of heat flow due to an imperfect contact
between soil particles, i.e., thermal contact resistance (TCR) and
can be expressed as a function of saturation (S):
a ¼ Keðasat adry Þ
ð6Þ
Ke ¼ 0:7logS þ 1
ð7Þ
where Ke is the Kersten coefficient, asat and adry are the heat transfer correction factors of saturated and dry soils respectively, and are
calculated as:
adry ¼
1
ðb=ks þ ð1 bÞ=kda Þks
ð8Þ
asat ¼
1
ðb=ks þ ð1 bÞ=k2 Þks
ð9Þ
where kda and k2 is the thermal conductivities of dry air and water
respectively, b is an effective solid fraction at the contact points of
soil particles, and can be expressed as a function of soil porosity (u):
b ¼ 1 0:12833u þ 0:06461u2 þ 0:06491u3
ð10Þ
S is defined and calculated as:
S¼
Vw
wGs
¼
V v Gs qw =qd 1
ð11Þ
ks is the average thermal conductivity of the solid particles, and
ks ¼ khqq koml q
1h
Standard deviation (%)
ð12Þ
0.4
0.4
0.3
0.8
0.6
0.7
0.2
0.2
0.1
0.3
0.5
0.6
0.5
0.2
0.2
0.7
0.8
0.9
where kq is the thermal conductivity of quartz, koml is the thermal
conductivity of other minerals in soils and hq is the volumetric fraction of quartz.
Thermal conductivity of water (k2) is given by:
k2 ¼ 0:569 þ 1:884 103 T 0:772 106 T 2
ð13Þ
where T is temperature in Celsius.
Thermal conductivity of air (k3) is given by:
k3 ¼ kda þ hkvs
ð14Þ
where h is the relative humidity of soil air and kvs is the thermal
conductivity of saturated water vapor.
When applying the IPCHT model to the prediction, the values of
kq and koml were respectively assumed 8.8 W/(mK) and 2.0 W/
(mK) for all the soils, which were used by de Vries [11]. The value
of h was estimated from the measured SWRCs.
3. Measured results of thermal conductivity and discussion
3.1. Effect of temperature on relation between thermal conductivity
and saturation
Fig. 3 presents the change in thermal conductivity (k) of two
lateritic clays for each temperature (T) with saturation (S) from
the KD2 pro measurements. It can be seen from Fig. 3 that for a
given saturation (4–84%), measured k increases with increasing
temperature. The increase in k with temperature is mainly seen
at intermediate saturations and temperatures above 60 °C. At sample temperatures below 60 °C, the effect of temperature on the k-S
relationship is small. When saturation is very high or low, the
effect of temperature on the k-S relationship is relatively smaller.
These results agree with Smits et al. [10] who suggested that the
increase in k may be due to the additional heat transfer in the form
of latent heat due to evaporation and condensation between the
‘‘liquid islands”. This process is so-called latent heat transfer
(LHT) of vapor, which requires enough liquid water to form the liquid islands and void space in soils through which vapor can move.
This can explain that temperature has little effect on k when the
sample is very dry or wet. Also, this can explain why temperature
effect on k is related to the saturation.
It can be seen from Fig. 3 that except for some cases with high
temperature and saturation, k increases with increasing saturation
and tends to be constant when the saturation is near 100%. k starts
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Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570
2.0
(a)
λ (W/m·K)
SFC
SPWP
1.6
T decreasing
1.2
0.8
Temperature(ºC)
5
25
40
60
80
90
0.4
0.0
0
20
40
60
80
100
S (%)
2.5
(b)
SFC
SPWP
2.0
λ (W/m·K)
T decreasing
1.5
1.0
Temperature(ºC)
5
25
40
60
80
90
0.5
0.0
0
20
40
60
80
100
S (%)
Fig. 3. Change in thermal conductivity (mean ± standard deviation, n = 5) for each
temperature with saturation for lateritic clays: (a) Guilin lateritic clay; (b) Liuzhou
lateritic clay. The critical water contents were calculated using the empirical
function of Rawls et al. [23] (short-dashed lines).
to decrease from the saturation of about 54% at temperatures of 80
and 90 °C. This is because, the thermal conductivity of water in
soils is much higher than that of air in the voids of unsaturated
lateritic clays, leading to an increase in k as water replaces the
air when the water content increases. At low saturation, water first
coats the soil particles. When the particles are fully coated with
water and a further increased water fills the voids in soil, resulting
in a rapid increase in k. Finally, when all the voids are nearly full of
water, further increasing the water content no longer increases the
heat flow between the soil particles, and k does not appreciably
increase. Hiraiwa and Kasubuchi [8] also observed that at volumetric water content (h) between 0.3 and 0.4 m3/m3 (from 0.33 m3/m3
to 0.42 m3/m3 in this study), k decreased with h at temperatures
above 65 °C (above 60 °C in this study). A possible explanation is
that the water in soils modifies the extent or quality of the LHT
of vapor in soils and thus the effective heat flow paths. As reported
by Blonquist et al. [21], the pore system in aggregated soils was
separated into two types: intra-aggregate pores within an aggregate, and relatively larger inter-aggregate pores between aggregates. Accordingly, they suggested that at high saturation, a
further increase in water content filled the inter-aggregate pores,
resulting in an abrupt decrease in void space required for the
LHT of vapor. As mentioned above, k increases with the LHT of
vapor, which requires enough void space in soils. Therefore, at
temperature above 60 °C k decreases severely when the saturation
is beyond a given value (i.e., from 55% to 70%).
Comparing Fig. 3(a) and (b) shows that for the same temperature and saturation, the thermal conductivity of Liuzhou lateritic
clay is higher than that of Guilin lateritic clay. In general, the soil
thermal conductivity depends on the mineralogical composition
(especially for quartz), particle composition, water content, dry
density and temperature. For the same water content, dry density
and temperature, the mineralogical composition is an important
factor that affects its thermal conductivity. As shown in Table 2,
Liuzhou lateritic clay contains 40% quartz, while Guilin lateritic
clay contains only 12.45% quartz. As the thermal conductivity of
quartz (7.7 W/mK) is much higher than that of other minerals
(2.0 W/mK), the proportion of quartz may significantly affect the
thermal conductivity. Tang et al. [4] and Xu et al. [22] suggested
that the bentonite with higher quartz content has the greater value
of thermal conductivity. This can explain why Liuzhou lateritic clay
has higher thermal conductivity than Guilin lateritic clay.
Hiraiwa and Kasubuchi [8] observed that the change in k with
water content was related to the critical water content corresponding to the permanent wilting point (PWP) and field capacity (FC). In
Fig. 3, there exhibit some obvious inflection points in the k-S
curves. Rawls et al. [23] suggested that the critical water content
associated with the particle-size distribution, which can be calculated through the linear regression formulas. The critical water
contents (SPWP and SFC) of two lateritic clays were estimated by
the empirical function of Rawls et al. [23], which are also shown
in Fig. 3. It can be seen from Fig. 3 that the change in k-S for each
temperature can be divided into some characteristic intervals of
saturations by calculated results of the critical water contents
(Guilin lateritic clay: SPWP = 49.1%, SFC = 70.7%; Liuzhou lateritic
clay: SPWP = 27.4%, SFC = 56.1%). This indicates that the heat conduction is also related to the form and distribution of water in soils.
Conceptually, we outline five important physical stages of the
lateritic clays with aggregate structure: (i) the soil is completely
dry; (ii) in the moisture range from full dryness to the PWP, water
in soil is hold tightly in the intra-aggregate pores and the formation of water micro-wedges between the contact points of the soil
grains occurs (connects the primary particles effectively); (iii) for
the moisture near FC (FC), the intra-aggregate pores are fully
filled with water, while the inter-aggregate pores are nearly filled
with air; (iv) the intra-aggregate pores are water saturated and
the inter-aggregate pores are partly filled with water under gravity; (v) both intra and inter-aggregate pores are water saturated
and there is no air in soils. Fig. 4 presents the detailed physical
states during the saturation process for aggregated soil, and these
physical states can be applied to provide some more insight in
understanding the temperature effect on the k-S relationship of
lateritic clays.
3.2. Effect of temperature on the LHT of vapor
The thermal conductivity resulting from the LHT of vapor (kLHT)
characterizes the contribution of LHT on the heat transfer in soils
and can be separated from k by several methods in the literature.
Cass et al. [24] considered that the temperature dependence of k
was mainly attributed to kLHT, and suggested a separation method.
Although, kLHT can be obtained by the separation method, its accuracy is not enough when investigating the temperature dependence of k. Hiraiwa and Kasubuchi [8] suggested that k can be
separated into the thermal conductivity due to conduction (kC)
and the LHT of vapor (kLHT). This separation method is based on
the assumptions that the temperature dependence of kC is much
smaller than that of kLHT, and at a low temperature the kLHT is negligibly small. Recently, the method of Hiraiwa and Kasubuchi [8]
has been verified, and it is reliable in analyzing the temperature
effect on the thermal conductivity [9]. Therefore, in this paper, a
similar method of separation was adopted, i.e., kLHT is obtained
from k by subtracting the thermal conductivity near 5 °C (kT=5°C)
(kLHT = k-kT=5°C).
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Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570
Fig. 4. Five physical stages during saturation process for aggregated soils.
1.5
(a)
λLHT (W/m·K)
1.2
0.9
Temperature(ºC)
25
Peak value decreasing
40
60
80
90
T decreasing
0.6
0.3
0.0
0
20
40
60
80
100
S (%)
2.4
(b)
λLHT (W/m·K)
2.0
Temperature(ºC)
25
40
60
80
90
Peak value decreasing
1.6
1.2
T decreasing
0.8
0.4
as shown in Table 2. This is because the gaps between particles or
soil aggregates can be filled with the relatively small clay particles
effectively. The higher the clay content, the less the gaps between
particles, resulting in a decrease in kLHT. On the other hand, it has
been suggested that the water adsorption capacity of clayed soils
is positively related to the specific surface area (SSA) of soils
[25]. Here, the SSAs of Guilin and Liuzhou lateritic clays are 78
and 40 respectively in m2/g, determined by the ethylene glycol
monomethyl ether (EGME) adsorption method. Our results agree
with Lv et al. [25] who suggested that the SSA of clayed soils
increased with the clay content, resulting in an increase in water
adsorption capacity. Therefore, for Guilin lateritic clay, it requires
more water content to form the ‘‘liquid island”, which affects the
LHT of vapor greatly. As mentioned above, the LHT of vapor
requires enough material condition (vapor) and transmission space
(pores in soils). Hence, this is capable of explaining why the temperature effect on kLHT is smaller at high or low saturations than
that at intermediate saturations.
The temperature dependence of kLHT-S relationship of soils is
related to several factors such as soil type and soil microstructure,
etc. For the same type of soil, the soil microstructure is an important factor that affects its kLHT-S relationship, and can be simply
represented by the pore-size distribution (PSD), which can be
determined by the mercury intrusion porosimetry (MIP) tests.
Fig. 6 shows the PSDs of compacted Guilin and Liuzhou lateritic
clays from the MIP tests. The specimen preparation for the MIP
tests is the freeze-dried method and the MIP apparatus used in this
0.0
20
40
60
80
100
S (%)
Fig. 5. Change in thermal conductivity resulting from the latent heat transfer of
vapor for each temperature with saturation: (a) Guilin lateritic clay; and (b) Liuzhou
lateritic clay.
The k-S relationships at different temperatures were shown in
Fig. 5. During the saturation process, kLHT increases with increasing
temperature and temperature effect on kLHT becomes significant
when temperature is above 60 °C. This is consistent with temperature dependence of k (see Fig. 3). For a given temperature, kLHT first
increases rapidly as saturation increases, and then it reaches a peak
value. Finally, kLHT decreases as saturation increases to near 100%.
The peak value of kLHT at 90 °C is three to four times that at 5 °C.
Moreover, the peak kLHT and its saturation are related to the clay
content. That is, the peak kLHT decreases with increasing clay content, whereas its saturation increases with increasing clay content,
Differential pore volume (mL/g)
0
0.8
0.7
Intra-aggregate pores
Guilin lateritic clay
Liuzhou lateritic clay
0.6
0.5
0.4
Inter-aggregate pores
0.3
0.2
0.1
0.0 -3
10
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
Pore diameter (μm)
Fig. 6. Pore-size distribution of lateritic clays measured by MIP tests (dry
density = 1.1 g/cm3).
Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570
study was the Micromeritics AutoPore IV with a maximum intrusion pressure of 413.7 MPa. In Fig. 6, compacted Guilin and Liuzhou
lateritic clays all shows a bimodal PSD, that means there are two
peaks in their PSDs. According to Lloret and Villar [26] and Xu
et al. [27], the pore system is simply separated into two types:
intra-aggregate pores (at pore size r < 0.15 lm) within aggregates,
and relatively larger inter-aggregate pores (at r > 0.15 lm)
between aggregates. The amount of relatively larger interaggregate pores in Liuzhou lateritic clay is larger than that in Guilin
lateritic clay. This implies that for Liuzhou lateritic clay, the number of gaps between particles or aggregates is greater, leading to a
favorable transmission space for the enhanced LHT of vapor,
whereas the volume fraction of intra-aggregate pores become
reversed. Therefore, this can explain that for a given temperature
the kLHT-S curve of Liuzhou lateritic clay is higher than that of Guilin lateritic clay (see Fig. 5).
The results of d(kLHT)/dT (kLHT differentiated with T) was also
calculated for analyzing the temperature dependence of kLHT, as
shown in Fig. 7. It can be seen from Fig. 7 that d(kLHT)/dT increases
with increasing temperature for the same saturation. This is
because, the higher the temperature, the more significant the
LHT of vapor. On the other hand, pores in the lateritic clays with
the double porosity system are tortuous, resulting in a non-linear
temperature dependence of kLHT and k. For the same temperature,
d(kLHT)/dT increases firstly and then deceases with saturation. This
indicates that the temperature effect on kLHT is also related to the
saturation. At temperatures between 60 °C and 90 °C, d(kLHT)/dT
of Liuzhou lateritic clay is nearly two times that of Guilin lateritic
clay at intermediate saturations. This implies that the latent heat
transfer of vapor for Liuzhou lateritic clay is more sensitive to temperature than that for Guilin lateritic clay. This can be explained by
the difference in the soil-water retention curves of two lateritic
clays, which will be discussed later.
3.3. Soil-water retention tests
Fig. 8 shows the measured water retention behavior: the
changes in saturation with suction of specimens with the dry density of 1.1 g/cm3 by using two methods (i.e., the PPM, and the FPM).
In Fig. 8, it can be seen that the soil-water retention curves
(SWRCs) exhibit different shapes for Guilin and Liuzhou lateritic
clays, especially in the suction range from 102 to 104 kPa. The
air-entry value of Guilin lateritic clay is different from that of Liuzhou lateritic clay. The air entry value of Guilin lateritic clay is about
30 kPa while the air entry value of Liuzhou lateritic clay is about
130 kPa, as shown in Fig. 8. This can be attributed mainly to the differences in the PSDs for soils used in the tests (see Fig. 7). Sun et al.
LHT
d(λ )/dT (W/m·K·ºC)
0.03
0.02
Temperature(ºC)
Liuzhou Guilin
60
60
80
80
90
90
0.01
T decreasing
0.00
0
20
40
60
80
100
S (%)
Fig. 7. Change in d(kLHT)/dT of two lateritic clays for each temperature with
saturation.
100
Air entry value
80
Saturation (%)
568
60
40
20
0
0
10
Guilin lateritic clay
Liuzhou lateritic clay
10
1
10
2
10
3
10
4
10
5
Suction (kPa)
Fig. 8. Soil-water retention curves of Guilin and Liuzhou lateritic clays.
[20] made an experimental study on the SWRCs and microstructures of compacted Guilin lateritic clay. They suggested that the
SWRCs were related to the features of the PSDs and can be predicted by them. Furthermore, it can also be seen from Fig. 8 that
the SWRCs of Guilin and Liuzhou lateritic clays differed significantly at intermediate saturations, which is consistent with the
mentioned changes in d(kLHT)/dT with saturation. This can be
explained by the difference in soil-water retention curves for two
lateritic clays, and the difference causes variations in the evaporation and diffusion of water in soils. As shown in Fig. 8, the same
amount of water added to Guilin lateritic clay will result in a
greater decrease in the suction than that in Liuzhou lateritic clay
at intermediate saturations. That is, water in soil changes more
rapidly for Liuzhou lateritic clay, which causes rapid change in
the relative humidity of air in soil, providing a favorable material
condition for the LHT of vapor. Therefore, the LHT of vapor for Liuzhou lateritic clay is more sensitive to temperature than that for
Guilin lateritic clay (see Fig. 7). Also, this is capable of explaining
that saturations corresponding to peak kLHT of Liuzhou lateritic clay
is smaller than that of Guilin lateritic clay (see Fig. 5).
4. Comparison of measured and predicted thermal
conductivities
Measured and predicted thermal conductivities of two lateritic
clays are shown in Fig. 9(a) and (b). The predicted one is calculated
by the IPCHT model. Verifications of the IPCHT model for unsaturated soils have been performed using measured thermal conductivities of sand and silty clay from Liu et al. [9], as shown in Fig. 9(c)
and (d). ±5% lines from the isoline of measured and predicted values are plotted in Fig. 9. It can be seen from Fig. 9(a)–(c) that at
temperatures ranging from 5 to 90 °C, the predicted k of finegrained soils (Guilin and Liuzhou lateritic clays, and silty clay)
compares well with the measured k.
However, for coarse-grained soil (sand), there is an obvious
deviation between measured and predicted k, as shown in Fig. 9
(d). The predicted k is smaller than the measured k of coarsegrained soil. A possible explanation about lower accuracy of predicted results for sand is the uncertainty of soil-water retentions,
which would result in considerable deviation in the determination
of k (see Eq. (14)). As reported by Liu et al. [9], the soil-water retention curve of sand was estimated by the RETC code, which is a very
crude.
As reported by Tang and Cui [28], for given water contents the
relative humidity h decreased with increasing temperature. In this
study, the soil-water retention curves of lateritic clays were only
conducted at room temperature (20 °C), without considering the
569
Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570
Predicted λ (W/m·K)
2.0
Temperature(ºC)
5
25
40
60
80
90
1.6
Table 4
Summary of RMSE of IPCHT model.
+5%
-5%
Guilin lateritic clay
Liuzhou lateritic clay
Silty clay
Sand
1.2
0.8
Dry density: 1.1g/cm
Saturation: 4%~84%
0.4
(a)
0
0.8
1.2
1.6
Temperature(ºC)
5
25
40
60
80
90
2.5
2.0
+5%
-5%
1.5
1.0
3
Dry density: 1.1g/cm
Saturation: 10%~78%
0.5
(b)
0
0.5
1.0
1.5
2.0
2.5
3.0
Measured λ (W/m·K)
2.5
Temperature(ºC)
5
20
40
58
78
88
2.0
+5%
-5%
1.5
1.0
Liu et al. (2011)
3
Dry density: 1.24g/cm
Saturation: 11%~99%
0.5
(c)
0.0
0
0.5
1.0
1.5
2.0
2.5
Measured λ (W/m·K)
4.5
+5%
Temperature(ºC)
5
20
40
58
78
88
3.6
-5%
2.7
1.8
Liu et al. (2011)
3
Dry density: 1.47g/cm
Saturation: 1%~75% (d)
0.9
0.0
0
0.9
0 °C < T < 30 °C
30 °C T 90 °C
0 < T 90 °C
12
18
25
41
31
30
19
29
26
21
21
33
tions, which mainly depend on the microstructure and
mineralogical compositions, play an important role when the
IPCHT model is applied to predict the temperature dependence of
thermal conductivity.
For each type of soil, the fitness of the IPCHT model to measured
data was evaluated by the root mean square error (RMSE):
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u n u1 X kexp kpre2
RMSE ¼ t
n 1
kexp
0.0
Predicted λ (W/m·K)
2.0
Measured λ (W/m·K)
3.0
Predicted λ (W/m·K)
0.4
RMSE (%)
3
0.0
Predicted λ (W/m·K)
Soil
1.8
2.7
3.6
ð15Þ
where n is the number of observations, kexp and kpre are measured
and predicted thermal conductivities. A summary of the RMSE error
analyses is listed in Table 4.
The RMSE provides useful information regarding the error
extent. According to the RMSE in Table 4, at temperature between
0 and 90 °C, the IPCHT model can predict k within 30% RMSE for all
types of soils, except for sand with 33% RMSE. However, the RMSEs
of two lateritic clays from 30 to 90 °C are twice from 0 to 30 °C.
This means that the applicability of the IPCHT model is limited
for lateritic clays when the temperature is higher than 30 °C. This
is mainly because the evaporation and the associated latent heat
transfer become an increasingly complicated at elevated temperature due to the microstructure and phase configuration effects.
Blonquist et al. [21] suggested that the microstructure and
phase configuration play an important role in determining the
dielectric response for their aggregated porous media. The heat
conduction and dielectric response in soils are practically similar.
Although the soil-water retentions were taken into account in
the IPCHT model, it reflected partly the microstructure of soils.
Accordingly, Blonquist et al. [21] proposed the extended dual
three-layer composite sphere model to take into account water
distribution and the processes of water filling in intra-aggregate
and inter-aggregate pores. This model includes four-phase composite and used sigmodal functions as a weight function, which
can describe aggregate structure effects on dielectric permittivity
since there is an addition of a layer dividing water phase into
intra-aggregate and inter-aggregate pores parts. Therefore, it is
believed that the performance of the IPCHT model could be further
improved by better consideration of the microstructure and phase
configuration. More accurately measured data for a wide variety of
aggregated soils are needed for further improvements of the IPCHT
model.
4.5
Measured λ (W/m·K)
Fig. 9. Measured and predicted thermal conductivity for each temperature: (a)
Guilin lateritic clay; (b) Liuzhou lateritic clay; (c) Silty clay; and (d) Sand.
effect of temperature when applying the IPCHT model. Therefore,
at temperatures above 20 °C, most predictions are slightly below
the measured values, as shown in Fig. 9(a) and (b). From the comparison of four soils, it can be deduced that the soil-water reten-
5. Conclusions
The relationship between thermal conductivity (k) and saturation (S) for two lateritic clays at different temperatures was experimentally investigated. The effects of clay content, aggregate
structure and mineralogical compositions on the temperature
dependence of the k-S relationship were discussed, together with
the predictions by the IPCHT model. The following conclusions
can be obtained from this study:
570
Y. Xu et al. / International Journal of Heat and Mass Transfer 138 (2019) 562–570
(1) For lateritic clays, k increases with temperature due to the
enhanced LHT of vapor. At temperatures ranging from 5 to
60 °C, k increases with S. At temperatures above 60 °C, k
decreases with increasing saturation when S is beyond about
54%.
(2) The soil heat conduction is related to the form and distribution of water in soil. The thermal conductivity resulting from
the LHT of vapor has obvious peak value with saturation, and
its peak value and corresponding saturation are related to
the clay content. The peak value decreases with increasing
clay content, whereas its saturation increases with increasing clay content.
(3) The differences in PSDs and soil-water retentions of compacted lateritic clays demonstrated clearly that the more
the water content and void space for LHT, the more obvious
the temperature effect on the thermal conductivity.
(4) The IPCHT model can provide good agreement with experimental data at different temperatures ranging from 5 to
90 °C. The accurate acquisition of the soil-water retentions
can improve the agreement. Further work may aim toward
the effects of the microstructure and phase configuration
on the k prediction models.
Acknowledgements
This research was supported by National Natural Science Foundation of China (Grant No. 51568014, 41502284) and opening fund
from Guangxi Key Laboratory of New Energy and Building Energy
Saving (Guilin University of Technology) (Grant No. 17-J-22-1).
Conflict of interest
The authors declare that there is no conflict of interest.
Appendix A. Supplementary material
Supplementary data to this article can be found online at
https://doi.org/10.1016/j.ijheatmasstransfer.2019.04.077.
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