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Accepted Manuscript
Experimental study of hydro-thermal characteristics and frost heave behavior
of a saturated silt within a closed freezing system
Xiyin Zhang, Mingyi Zhang, Wansheng Pei, Jianguo Lu
PII:
DOI:
Reference:
S1359-4311(17)32470-5
https://doi.org/10.1016/j.applthermaleng.2017.10.116
ATE 11314
To appear in:
Applied Thermal Engineering
Received Date:
Revised Date:
Accepted Date:
13 April 2017
28 September 2017
19 October 2017
Please cite this article as: X. Zhang, M. Zhang, W. Pei, J. Lu, Experimental study of hydro-thermal characteristics
and frost heave behavior of a saturated silt within a closed freezing system, Applied Thermal Engineering (2017),
doi: https://doi.org/10.1016/j.applthermaleng.2017.10.116
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Experimental study of hydro-thermal characteristics and frost heave behavior of
a saturated silt within a closed freezing system
Xiyin Zhanga,b Mingyi Zhanga? Wansheng Peia Jianguo Lua
a. State Key Laboratory of Frozen Soil Engineering, Northwest Institute of Eco-Environment and
Resources, Chinese Academy of Sciences, Lanzhou 730000, China
b. School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
Abstract: Frost heave behavior during soil freezing process is an important issue of
concern in cold regions, which is influenced by the hydro-thermal characteristics
including the freezing point and water migration. The frost heave is caused by the
freeze of water from different sources, i.e. pristine water, migrated water or both;
however, it is difficult to identify the contributions of the different water sources to
the frost heave, especially for a closed freezing system. Therefore, the calculation
method to evaluate the frost heave induced by different water sources still need to be
developed. Definitely, freezing experiments under controlled laboratory conditions
can help to give a detailed description of the soil freezing process. Therefore, a
large-scale one-directional freezing experiment within a closed system was carried out
to investigate the hydro-thermal characteristics and frost heave behavior of a saturated
silt. The research results show the effect of the hydro-thermal behavior on the frost
heave of the silt within a closed freezing system, and a calculation method was
presented to evaluate the frost heaves from pristine water and migrated water,
respectively.
Key words: hydro-thermal characteristics, frost heave behavior, one-directional
freezing experiment, saturated silt, closed freezing system
?
Corresponding author. myzhang@lzb.ac.cn (Mingyi Zhang)
0 Introduction
The frost heave of soils in cold regions destabilizes the local infrastructure, cracks
canals, breaks buried pipelines, and causes other engineering problems [1-3]. There
are three necessary conditions for frost heave to occur [4]: frost susceptible soil,
availability of water, and the temperature, or more specifically, thermal conditions that
will cause the freezing front to move slow enough to allow water to migrate.
Therefore, for frost-susceptible soil, the hydro-thermal characteristics including the
freezing point and water migration are vital for determining the frost heave amount.
Some of hydro-thermal characteristics during soil freezing process have been
investigated by previous researchers. Bouycous [5] found that an equilibrium between
ice and unfrozen water exists in soils on the condition that the soil temperature is
below the freezing point. It has been confirmed that the unfrozen water content is
closely related to negative temperature, and strongly influences heat and mass
transports of freezing soil [6]. Therefore, it is essential for hydro-thermal
characteristics of freezing soil to determine the unfrozen water content. Williams [7]
measured the unfrozen water content of several soils by calorimeter, and presented a
calculation method to determine the unfrozen water content at negative temperatures.
Lots of experimental studies showed that the unfrozen water can be simply taken as a
function of negative temperature, and in most cases, the relation is expressed as a
simple power equation [8-10]. Besides the water-ice phase change, it has been found
that unfrozen water was redistributed because of water migration in freezing soils
[11-13], which means that the change of the unfrozen water content of soil is not only
related to negative temperature, but also water migration during soil freezing process.
When a fine-grained moist soil is subjected to a freezing process, the water migrates
mainly from the unfrozen zone of the soil towards the freezing front [14]. However,
the presence of ice lens can greatly reduce water migration in frozen zone [15]. A
large number of experimental results have confirmed that the permeability decreases
rapidly as soon as pore ice forms [16-18]. So there are reasons to believe that the
water migration is negligible in frozen zone compared to unfrozen zone during soil
freezing process. These research results for hydro-thermal characteristics of freezing
soils provide a basis to study the frost heave behavior of soils in cold regions.
Frost heave behavior during soil freezing process is another important issue of
concern in cold regions. It has been confirmed that the frost heave was not only
caused by the freeze of pristine water but also by migrated water [19], and the water
migration contributed the main part of the frost heave, especially for the soil with a
sufficient water supply. Consequently, the freezing soils with a sufficient water supply
(open-freezing system) are of particular concern in theoretical and experimental
studies [20-23]. However, some previous researches have focused on the water
migration and frost heave in one-dimension without water supply [24, 25]. In some
cases, a closed- freezing system can be often more accurate to simulate the freezing
behavior of soil than an open-freezing system [26, 27]. For the soil in a
closed-freezing system, the water content increases in the freezing front (i.e. the
frozen-unfrozen interface), while decreases in the unfrozen zone [28]. The
contribution of pristine water and migrated water to the frost heave is different and
hard to be calculated. It has been clear that water migration towards the freezing front
plays important role in contributing to the frost heave within a closed system. And yet,
research has hardly identified the source of frozen water from pristine water, migrated
water, or both, and the calculation method to evaluate the frost heave induced by
different water sources still need to be improved. Freezing experiments of soils under
controlled laboratory conditions in a closed system can help to further describe the
soil freezing process.
In this study, a frost heave test in the laboratory was carried out under controlled
conditions to investigate freezing characteristics of a saturated silt within a closed
freezing system. The hydro-thermal characteristics and frost heave behavior of the silt,
a frost-susceptible soil, were analyzed under one-directional freezing condition. A
large-scale soil sample was used in this study to reduce dimension effects, and to
conveniently embed the temperature and volumetric water content sensors. The
temperature and volumetric unfrozen water content in different locations, and the total
deformation of the soil sample were measured during the whole freezing process.
1 Theory
It is well-known that the frost heave of a soil within a closed freezing system
consists of two parts: one is from the freeze of pristine water, and the other is from the
freeze of migrated water. However, there is continuous migrating of the water during
the whole freezing process, so it is difficult to identify the frost heave from the
contributions of the different water sources (pristine water and migrated water).
Therefore, there are difficulties in calculating the frost heave induced by freeze of
different water sources, respectively. In order to make it possible to perform the
calculation, a type of soil with direct solid-to-solid contacts between soil particles,
which was designated as the ?SS soils? [29], is selected in this study to simplify the
problem. The pore geometry of the ?SS soils? was assumed to be fixed, and the
decrease of water content causes no shrinkage of the soil volume in the unfrozen zone.
Therefore, the frost heave of the ?SS soils? under one-directional freezing condition
with a closed system can be determined by the soil porosity, the expansion parameter of
water-ice phase change, the pristine and migrated water content, the unfrozen water
content and the height of the soil layer [30].
The frost heave will occur once the ice transformed by the pristine water fills
whole pore in soil. Therefore, the frost heave induced by the freeze of the pristine
water can be defined as the pristine frost heave, expressed as,
m
?
?
? ?
??
?hpristine?t ? ? ?? ? ? ? 1? ? if ? ?ui ?t ? ? ni ? ? if hi
(1)
i ?1
Where ? is the expansion parameter of water-ice phase change, equals to the ratio of
water density to ice density, ?w/?i, ?f is the volumetric unfrozen water content at soil
freezing point, defined as the freezing volumetric water content, ?u is the volumetric
unfrozen water content of the soil, n is the porosity of the soil, hi is the height of the
soil layer, i is the number of soil layer, and ? is a adjusting parameter, expressed as:
i
i
i
i
?
?1??? ( ? ? 1)(? f ? ?u ) ? (n ? ? f ) ? 0
???
i
i
i
i
?
?0??? ( ? ? 1)(? f ? ?u ) ? (n ? ? f ) ? 0
(2)
In this study, the silt has a saturated volumetric water content initially, and the
volumetric water content reduces due to the water migration where the temperature is
still above the soil freezing point. Because the water migration in frozen zone can be
ignored [16-18], therefore, it can be assumed that all the migrated water towards to
freezing front has been frozen into segregated ice and contributed to the frost heave.
Therefore, the frost heave induced by the freeze of the migrated water can be defined
as the migrated frost heave, expressed as:
m
?
?
?hmigrated ?t ? ? ? ? ?si ? ?si ?t ? hi
(3)
i ?1
Where ?s is the initial volumetric water content of the soil layer, ?s (t) is the
volumetric water content of the soil layer above soil freezing point at time t.
Based on Eqs. (1-3), the total frost heave of the soil sample under one-directional
freezing condition within a closed system can be calculated by the following formula:
m
? ?
?
? ?
?? ?
??
?htotal ?t ? ? ? ? ? ? ? 1? ? if ? ?ui ?t ? ? ni ? ? if ? ? ?si ? ?si ?t ? hi
(4)
i ?1
2 Experiments
2.1 Experimental apparatus
The freezing test in this study was carried out in a freezing-thawing apparatus,
which was schematically shown in Fig. 1. It consists of a test chamber, a temperature
controlling system and a data acquisition system.
Fig. 1 Schematic diagram of the freezing-thawing apparatus: 1- Test chamber with insulation
layer; 2- Top cold plate; 3- Bottom cold plate; 4- Cooling baths; 5-Cooling fans;
6-Temperature sensor; 7-Volumetric water content sensor; 8- Displacement sensor; 9-Data
logger; 10-Computer; 11-Soil specimen
The test chamber was insulated by the rigid polyurethane foam panel with a
thickness of 15cm. The inner dimension of the test chamber was 100 cm �0 cm
�0 cm, and thus the large space could effectively reduce the size effect compared
with the traditional devices with small size. The test chamber wall was lubricated using
petroleum jelly to reduce the friction developed between the soil and the test chamber
wall when the frost heave occurs. The temperature controlling system was composed
of top and bottom cold plates, two cooling baths, pipes for cooling liquid circulation,
and cooling fans. The data acquisition system was composed of temperature sensors
(thermistor sensor, precision: �05 癈), volumetric water content sensors (dielectric
permittivity soil moisture sensor, precision: �03 m3/m3) and displacement sensors
(linear displacement sensor, precision: �01 mm). All sensors were connected to a
data logger which was connected to a computer. Then, the data could be automatically
collected during the testing process.
2.2 Experimental materials and methods
The freezing experiment was carried out with a silt, and its grain-size distribution
was shown in Fig. 2. The plastic and the liquid limits of the silt were 17.89% and 27.01%,
respectively. To minimize the influence of salts, the silt were washed and then saturated
with distilled deionized water.
Fig. 2. Grain-size distribution of the silt
The saturated silt was packed in the test chamber with a dimension of
100cm�0cm�cm (Fig. 1). Nine temperature sensors (T1-T9) and six volumetric
water content sensors (W2-W4, W6-W8) were embedded in the center of the soil
sample along its height, and three displacement sensors were stalled on the top surface
of the soil sample, as shown in Fig. 1.
Firstly, the packed soil was kept at 2 癈 until a heat-water balance in the soil was
achieved, and the consolidation process was performed to ensure that the redundant
water in the soil can flow out under gravity to reach a high consolidation degree. The
average dry density of the soil sample is about ?d=1.65 g/cm3. Then, the top cold plate
was gradually reduced from 2 癈 to -16 癈 and the bottom cold plate was kept at a
constant of 2 癈 in the whole freezing process. The changes of the measured
temperatures at the top and bottom of the soil sample were shown in Fig. 3.
Fig. 3 Temperatures changing with time at the top and bottom of the soil sample
3 Results and analysis
3.1 Hydro-thermal characteristics
Figs. 4 and 5 show the changes of temperature and volumetric unfrozen water
content with time at different heights within the soil sample, respectively. Initially, with
the temperature decrease (Fig. 4), the volumetric unfrozen water content reduces
slowly when the temperature is higher than 0 癈 (Fig. 5). This indicates that the
decrease of volumetric water content is induced by the water migration in this stage.
Then the volumetric unfrozen water content decreases rapidly once the temperature is
lower than a certain value (below 0 癈). Finally, the volumetric unfrozen water
content becomes steady when the temperature is significantly lower than 0 癈. The
changes of temperature and volumetric water content (Figs 4 and 5) confirms that the
volumetric unfrozen water content of the soil is not only related to negative
temperature, but also the water migration during soil freezing process.
Fig. 4 Temperatures changing with time at different heights within the soil sample
Fig. 5 Volumetric unfrozen water content changing with time at different heights
within the soil sample
The temperature distribution at different freezing time (i.e. 5 h, 20 h, 50 h, 80 h, 120
h, 200 h, and 400 h) are shown in Fig 6. It is found that the temperature gradients are
different in the frozen and unfrozen zones along the height of the soil sample after the
soil starts to freeze downwards. It is verified that because the thermal conductivity
increases as the ice content increases with the decrease of temperature [31], the
temperature gradient in frozen zone should be smaller than that in unfrozen zone in
order to satisfy the principle of continuity of heat flow if there is no internal heat
generation in soils [32]. However, the temperature gradient in the frozen zone is larger
than that in unfrozen zone in this experiment, as shown Fig. 6. This is related to the
temperature boundary conditions (Fig.3) and the soil thermal characteristics; however,
the influence of the additional heat is also significant, i.e. the heat carried by the
migrated water from the unfrozen zone and the latent heat released by water-ice phase
change in the freezing front. The added heat at the freezing front increases the
temperature gradient in the frozen zone to maintain continuity of the heat flow within
the freezing soil sample [32].
Because the silt in this study freezes without external water supply, the strong
absorbability of the soil particle to bond water make it difficult to migrate when the
initial pore water decreased to a certain value. Therefore, the added heat, i.e. the heat
carried by the migrated water from the unfrozen zone and the latent heat released by
water-ice phase change in the freezing front, decreases with freezing time.
Furthermore, the temperature boundary conditions also tends to a steady state (Fig. 3).
That?s why the difference of temperature gradient between frozen and unfrozen zone
gradually decreased with freezing time, and eventually the temperature gradients of
frozen and unfrozen zone gradually decreased with freezing time (Fig. 6).
Fig. 6 Temperature distributions at different times within the soil sample
3.2 Freezing point and freezing front
The relationships between the volumetric unfrozen water contents and the
temperatures at the different heights of the soil sample are shown in Figs 7(a)-(f). It is
known that the pore water is frozen firstly in the largest pores of soils, and
subsequently frozen in smaller pores with the decreased temperatures during freezing
process [33]. The temperature, especially the freezing point, is a key factor in
determining the volumetric unfrozen water content in freezing soils. The freezing
point in the soil-water system is regarded as the temperature T f, at which the
equilibrium of the soil-water system is broken and the liquid water starts to freeze
[34]. The soil freezing point (SFP) is influenced by many factors, e.g. soil particle size,
mineral composition, initial water content, soil temperature, external pressure and so
on. For one-directional freezing condition, the unfrozen water migrates upwards from
the unfrozen zone to the freezing front. Therefore, the volumetric unfrozen water
content of the soil has reduced significantly before the temperature drops to the soil
freezing point (Fig. 7a-f). The changes of volumetric unfrozen water content with
temperature can obviously be divided into two stages by the SFP (Fig. 7a-f): the water
migration stage above the SFP and the water freeze stage below the SFP. Therefore,
the soil freezing point is the critical point to divide the two stages. Because the
decreasing rates of volumetric unfrozen water content are different in migration and
freeze stages, a new method to determine the soil freezing point (SFP) is presented,
namely, the intersection point of the two linear relationship lines between volumetric
unfrozen water content and temperature for the two stages near the critical
temperature point is defined as the SFP (Fig. 7).
Fig. 7 Relationship between volumetric unfrozen water content and temperature:
?s is the initial volumetric unfrozen water content, ?f is the volumetric unfrozen
water content at SFP, defined as the freezing volumetric water content
The SFPs of the silt in this study obtained at different locations are listed in Table
1. It shows that the SFP decreases with the freezing volumetric water content ?f. The
relationship between freezing volumetric water content and SFP is linear, as shown in
Fig. 8. Based on the relationship, it is deduced that the soil freezing point is equal to
0 癈 (freezing point of the free water) when the volumetric water content reaches to
about 37.9%, which is close to the saturated volumetric water content of the silt in this
study.
Table 1 Volumetric water content and freezing point at different locations of the
soil sample
Fig 8 Relationship between the soil freezing point (SFP) and the freezing
volumetric water content
Based on the change of temperature with time (Fig 4) and the soil freezing points
(SFPs) in Table 1, the locations of the interface between the frozen and unfrozen
zones, taken as the freezing front [35], are shown in Fig. 9. From the Fig. 9, it is found
that the freezing front starts to move downwards from the top of the soil sample after
about 6 hours because of the top temperature change, and then to the height of 6.5 cm
at the end of freezing process. The freezing front is taken as the interface between the
frozen and unfrozen zones, which is a key factor to in determining the frost heave of
soils during freezing process.
Fig. 9 Change of freezing front with time
3.3 Frost heave behavior
The total mass water contents at different heights before and after freezing are as
shown in Fig. 10. From Fig 10, it can found that the water contents after freezing are
close to those before freezing over around 35 cm; however below the height, the mass
water contents after freezing are higher than those before freezing. Those are from the
fact that the advance rate of the freezing front decreases with freezing time (Fig. 9).
The pore water has enough time to migrate to the freezing front when the freezing
front is below the 35 cm height (or after around 124 h); therefore, more water is
involved in the 8-35 cm height, and the water content decreases below 8 cm height
due to the water migration.
Fig. 10 Distributions of mass water contents with height before and after freezing
Before freezing, a consolidation process under gravity is performed to ensure the
direct solid-to-solid contacts between soil particles, so that the pore geometry of the
silt in this study can be assumed to be fixed. Therefore, the calculation method for the
?SS soils? (Eqs. (1-4)) can be used to predict the frost heave of the silt in this study.
Based on Eqs. (1-4), the pristine frost heave, migrated frost heave, and total frost
heave of the soil sample were calculated respectively.
In the experiment, the total deformation is measured by the three displacement
sensors stalled on the top surface of the soil sample (Fig. 1), and the average value of
the measured deformations is taken as the measured value of the total frost heave. All
the measured and calculated values of the frost heave are shown in Fig. 11. From the
figure, it can be found that the calculated total frost heave is in good agreement with
the measured one. This suggests that Eq. (4) can effectively calculate the total frost
heave of the soil sample under the one-directional freezing process with the closed
system, and it also gives us confidence that the calculated pristine frost heave,
migrated frost heave, and total frost heave are also acceptable.
Fig. 11 Freezing process and frost heaves of the soil sample
At the beginning time (about 0~6 h), the top temperature of the silt is decreasing,
but above the SFP, and the measured and calculated frost heaves are close to 0 cm at
this stage. In the following time (about 6~50 h), the calculated pristine water frost
heave increases slowly, while the calculated migrated frost heave increases rapidly
and makes a dominant contribution to the total frost heave. This is from the fact: the
ice from the pristine water fills the pores firstly, and then contributes to the frost heave;
however the migrated water will directly make a frost heave due to ice segregation at
the freezing front. After a freezing period of 50~200 h, the frozen zone expands
quickly with the advance of the freezing front (Figs. 9 and 11), and the pristine frost
heave increases quickly in this stage. After 200 h, it is found that the pristine frost
heave in total frost heave gradually tends to steady. However, the migrated frost heave
contributes a large part of total frost heave in the whole freezing process. These
results indicate that the migrated water is a major factor in determining the frost heave
of the saturated silt although there is no external water supply during the freezing
process; however, the pristine frost heave cannot also be ignored in evaluating the
total frost heave of the saturated soil.
4 Conclusions
The hydro-thermal characteristics and the frost heave behavior of a saturated silt
in the closed freezing system were experimentally investigated. From the
experimental results and analysis, some conclusions are drawn:
(1) There exist a significant difference of temperature gradient between the unfrozen
and frozen zone in the freezing soil. The difference is not only from the influences
of temperature boundary conditions and the thermal characteristics of the soil
sample, but also from the effect of the heat carried by the migrated water from the
unfrozen zone and the latent heat released by water-ice phase change in the front.
(2) The one-directional freezing behavior of the saturated silt within the closed
freezing system involves the freeze and migration of pore water. Based on the
different changing rates of volumetric unfrozen water with temperature in the
migration and freeze stages, the soil freezing point (SFP) is determined.
(3) The frost heave of the saturated silt in the one-directional freezing process is
related to many factors, e.g. soil properties, water content, soil sample size,
environmental conditions, etc. For the saturated silt in the closed freezing system,
the frost heaves from pristine water and migrated water were evaluated
respectively, and it is found that the frost heave from pristine water is an important
part for the total frost heave; however the migrated water is the dominant source
of frost heave even if there is no water supply.
Acknowledgments
This research was supported by the National Natural Science Foundation of China
(Grant No. 41471063), the 100-Talent Program of the Chinese Academy of Sciences
(Granted to Dr. Mingyi Zhang), the Program of the State Key Laboratory of Frozen Soil
Engineering (Grant No. SKLFSE-ZT-23), the Key Research Program of Frontier
Sciences of the Chinese Academy of Sciences (QYZDY-SSW-DQC015), and the STS
Program of the Chinese Academy of Sciences (Grant No. HHS-TSS-STS-1502). On
behalf of all authors, the corresponding author states that there is no conflict of interest.
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[32] J.M. Konrad, Influence of freezing mode on frost heave characteristics, Cold
Regions Science and Technology, 15 (1988) 161-175.
[33] E.N. Ashworth, F.B. Abeles, Freezing Behavior of Water in Small Pores and the
Possible Role in the Freezing of Plant Tissues, Plant Physiology, 76 (1984)
201-204.
[34] T. Kozlowski, Some factors affecting supercooling and the equilibrium freezing
point in soil?water systems, Cold Regions Science and Technology, 59 (2009)
25-33.
[35] R.D. Miller, Freezing and heaving of saturated and unsaturated soils, in: 51st
Annual Meeting of the Highway Research Board, Washington District of Columbia,
United States, 1972, pp. 1-11.
Figure Captions
Fig. 1 Schematic diagram of the freezing-thawing apparatus: 1- Test chamber with insulation
layer; 2- Top cold plate; 3- Bottom cold plate; 4- Cooling baths; 5-Cooling fans;
6-Temperature sensor; 7-Volumetric water content sensor; 8- Displacement sensor;
9-Data logger; 10-Computer; 11-Soil specimen
Fig. 2. Grain size distribution of the silt
Fig. 3 Temperatures changing with time at the top and bottom of the soil sample
Fig. 4 Temperatures changing with time at different heights within the soil sample
Fig. 5 Volumetric unfrozen water content changing with time at different heights within the
soil sample
Fig. 6 Temperature distribution at different times within the soil sample
Fig. 7 Relationship between volumetric unfrozen water content and temperature: ?s is the
initial volumetric unfrozen water content, ?f is the volumetric unfrozen water content at
freezing point, defined as the freezing volumetric water content
Fig. 8 Relationship between the soil freezing point (SFP) and the freezing volumetric water
content
Fig. 9 Change of freezing front with time
Fig. 10 Distributions of mass water contents with height before and after freezing
Fig. 11 Freezing process and frost heaves of the soil sample
Table Captions
Table 1 Volumetric water content and freezing point at different locations of the soil sample
Fig. 1 Schematic diagram of the freezing-thawing apparatus: 1- Test chamber with insulation
layer; 2- Top cold plate; 3- Bottom cold plate; 4- Cooling baths; 5-Cooling fans;
6-Temperature sensor; 7-Volumetric water content sensor; 8- Displacement sensor; 9-Data
logger; 10-Computer; 11-Soil specimen
Cumulative mass percentage less than a certain size /%
100
90
80
70
60
50
40
30
20
10
0
1000
100
10
Grain size /?m
1
0.1
Fig. 2 Grain-size distribution of the silt
Temperature(?)
0
Temperature at the top (T1)
Temperature at the bottom (T9)
-5
-10
-15
0
100
200
300
Time(h)
400
500
Fig. 3 Temperatures changing with time at the top and bottom of the soil sample
5
Temperature(?)
0
T8
T7
-5
T6
T5
-10
T4
T3
T2
-15
0
100
200
300
400
500
Time(h)
Fig. 4 Temperatures changing with time at different heights within the soil sample
Volumetric unfrozen water content(%)
40
35
30
25
20
W4
W6
W8
W7
15
10
W3
W2
5
0
0
100
200
300
400
500
Time(h)
Fig. 5 Volumetric unfrozen water content changing with time at different heights within the
soil sample
90
Frost heave
Height of the soil sample (cm)
80
70
60
50
40
30
Time
5h
20h
50h
80h
120h
200h
400h
Initial height
20
10
0
-20
-15
-10
-5
0
5
10
Temperature (癈)
Fig. 6 Temperature distribution at different times within the soil sample
40
40
30
Volumetric water content (%)
Volumetric water content (%)
?s
?f
25
20
15
10
5
-16
?s
35
35
-14
-12
-10
-8
-6
-4
Temperature(癈)
-2
0
2
?f
30
25
20
15
10
5
-16
4
-14
-12
(a) T2-W2
-10
-8
-6
-4
Temperature (癈)
-2
0
2
4
(b) T3-W3
40
40
?f
Volumetric water content (%)
Volumetric water content (%)
35
?s
35
30
25
20
15
10
5
-16
-14
-12
-10
-8
-6
-4
-2
Temperature (癈)
(c) T4-W4
0
2
4
?s
?f
30
25
20
15
10
5
-16
-14
-12
-10
-8
-6
-4
-2
Temperature (癈)
(d) T6-W6
0
2
4
40
40
35
?s
30
Volumetric water content (%)
Volumetric water content (%)
35
?f
25
20
15
10
5
-16
-14
-12
-10
-8
-6
-4
-2
Temperature (癈)
0
2
?s
?f
30
25
20
15
10
4
5
-16
-14
(e) T7-W7
-12
-10
-8
-6
-4
Temperature (癈)
-2
0
2
4
(f) T8-W8
Fig. 7 Relationship between volumetric unfrozen water content and temperature: ?s is the
initial volumetric unfrozen water content, ?f is the volumetric unfrozen water content at SFP,
defined as the freezing volumetric water content
Soil freezing point(? )
-0.03
-0.04
-0.05
y=0.0076x-0.288
R2=0.92
-0.06
-0.07
28
29
30
31
32
33
34
35
Freezing water content(%)
Fig 8 Relationship between the soil freezing point (SFP) and the freezing volumetric water
content
Height of the soil sample(cm)
80
70
Freezing front
60
50
40
6h
Frozen zone
30
20
Unrozen zone
10
0
0
100
200
Time(h)
300
400
Fig. 9 Change of freezing front with time
90
Frost heave
Height of the soil sample(cm)
80
70
60
50
40
Before freezing
After freezing
30
20
10
0
10
15
20
25
30
Mass water content (%)
35
Fig. 10 Distributions of mass water contents with height before and after freezing
Measured total frost heave
Calculated total frost heave
Calculated migrated frost heave
Calculated pristine frost heave
3.0
2.5
2.0
1.5
1.0
0.5
0.0
80
70
Freezing front
60
50
40
30
20
10
0
100
200
Time(h)
300
400
Fig. 11 Freezing process and frost heaves of the soil sample
0
Height of the soil sample(cm)
Frost heave(cm)
3.5
Table 1 Volumetric water content and freezing point at different locations of the
soil sample
Sensor number
Initial water content
?0 /%
Freezing water content
?f/%
Soil freezing
point/癈
T2-W2
T3-W3
T4-W4
T6-W6
T7-W7
T8-W8
33.2
35.2
35.8
34.0
32.0
34.8
30.8
33.7
33.9
31.6
28.7
31.7
-0.05
-0.03
-0.03
-0.04
-0.07
-0.05
Highlights:
Large-scale freezing test was conducted to study hydro-thermal characteristics
The temperature, unfrozen water content and the relation between them were analyzed
A new approach to determine the soil freezing point was presented
The advance of the freezing front during freezing were analyzed
The frost heaves from pristine water and migrated water of the silt were analyzed
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