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Laboratory investigation of the freezing point of saline soil
Cold Regions Science and Technology 67 (2011) 79–88
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Cold Regions Science and Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c o l d r e g i o n s
Laboratory investigation of the freezing point of saline soil Hui Bing ⁎, Wei Ma State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, CAS, Lanzhou Gansu 730000, China
a r t i c l e
i n f o
Article history: Received 21 September 2010 Accepted 19 February 2011 Keywords: Soil freezing Saline soil Freezing point Salt content Sodium chloride
a b s t r a c t This paper presents the results from an experimental laboratory investigation study on the freezing point of saline soil. The experiments were a part of a larger laboratory program whose objective is to understand how salt and water content as well as ion sort and type of soil affect the freezing point. Results show that the freezing point decreases with increasing salt content, and increases with increasing water content independent of the kind of soil. The freezing point is also controlled by the amount of soluble salt in the 2− + + 2+ soil water and is influenced by common anions and cations as follows: Cl− N CO2− , 3 N SO4 and K N Na N Ca respectively. Statistical results show a major fitting curve of freezing point with salt content that fits the exponential damping model except that the salt with chloride ion which agrees more with the linear model with a greater slop. At given water and salt contents, the freezing point of fine particle soils is lower than that of soils with a more coarse particle; however, the effect of the soil particle size on the freezing point decreases apparently with increasing water content. Crown Copyright © 2011 Published by Elsevier B.V. All rights reserved.
1. Introduction The study of the physical characteristics of frozen ground has revealed that soil water solutions have a significant influence on the freezing point of soil (Banin and Anderson, 1974). Under ordinary conditions, the freezing of pure normal water occurs at 0 °C and takes place at the ice–water interface until ice formation stops. The presence of solutes, high pressure, or dispersal in fine pores will lower the freezing point to temperatures below 0 °C (this effect is known as the freezing point depression). For a given soil, the freezing point is a function of its water content, salt content and imposed load. Kozlowski (2009a,b) used the differential scanning calorimetry technique to study the freezing point and found that the freezing point can be expressed as a power function of the water content and the plastic limit, with an asymptote at water content equal to the unfreezable water content. A soil's freezing point is important for engineering and construction applications including the design of frozen earthen walls for deep excavations, the structural underpinning of foundations, and the ability to establish temporary control over groundwater during construction projects (Pierce et al., 2005). The temperature at which a soil freezes affects both the depth of a frozen earth wall and the use of coolant. Research on freezing points is important for artificial ground freezing and for thermal modeling of natural conditions. In many experimental and numerical studies, the freezing point is used usually to determine whether the soil is freezing
⁎ Corresponding author. Tel.: +86 931 4967291; fax: +86 931 8271054. E-mail address: [email protected] (H. Bing).
or not. However, little has been published concerning the factors that affect the freezing point of saline soil. The main objective of this study is to understand how salt content, water content, ion sort as well as type of soil affect the freezing point of soils. The paper is organized as follows. We introduce the concepts related to the freezing point of wet soil and the methods used to measure the freezing point. Next, we explain the experimental conditions, the preparation of samples and methods used in our experimental study. The obtained results of freezing point with respect to water content, salt content, ion sort and kind of soil are analyzed. Finally, we present the conclusions drawn from the results of our experiments. 2. Freezing point of soil–water system and testing methods The formation of ice in the pores of soil involves the cooling of the soil–water system, as is illustrated in Fig. 1. As pure liquid water cools to the point of freezing, ice crystal nucleation and crystal growth begins to occur within a few molecules; this process is generally initiated a few degrees below the melting point of ice. In other words, some supercooling is needed to initiate the process of freezing (Kozlowski, 2009a); Under normal atmospheric pressure, pure water can be easily supercooled to as low as−25 °C and, with more difficulty, to as low as − 41 °C, depending to the droplet diameter (Fletcher, 1970). The pore water does not start to freeze until the temperature drops to the temperature of spontaneous nucleation Tsn. At this stage, the system is below the equilibrium freezing point and the supercooled water is in a metastable equilibrium state. The abrupt transformation of free water to ice causes water molecules to aggregate to soil particles. As the result of the release of latent heat,
0165-232X/$ – see front matter. Crown Copyright © 2011 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2011.02.008
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H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
Fig. 1. Cooling curve for the soil water system.
L, during ice formation, the temperature of the system rises again to the initial freezing temperature, Tf, at which point it stabilizes for a period (Andersland and Ladanyi, 2003). During the freezing of the soil–water system, the extraction of heat leads to successive freezing of the remaining unfrozen water. Even at temperatures well below the initial freezing point, some thermodynamically stable liquid water remains unfrozen, and undergoes successive phase changes as temperature is lowered. Thus, the process of soil–water freezing has four stages: (1) spontaneous nucleation, (2) an abrupt transition in temperature as ice formation begins, (3) an equilibrium period of constant temperature, and (4) a gradual temperature decrease. Free water in the soil pores will now be freezing at temperature Tf. All the free water and most of the bound water (the unfrozen water film on the soil particles) are frozen at the temperature of equilibrium, Te (about −70 °C). Within the fine-grained soils with high specific surface area, a significant amount of unfrozen water can exist at a higher temperature.
Kozlowski (2009a) defined the supercooling as the difference (ΔT) between the temperature of equilibrium freezing and the temperature of spontaneous nucleation, correlates to cooling rates, but is more directly related to the solution within the soil (Liu, 1986). The higher solute concentration, the greater the supercooling is. At Tsn, the release of latent heat of 332.9 J/g will slow the rate cooling until Te is reached as free water changes to ice. Thus there is a contradiction between temperature abrupt transition for latent heat release and the effect of outside cooling in the soil water system. The degree of counteraction determines how long the stable stage (at the freezing point) lasts. Thus, the Tf is reached only when the latent heat is sufficient to increase the system temperature to Tf. When a liquid is supercooled so deeply that the latent heat is not sufficient to raise its temperature to Tf, it is referred to as being hypercooled (Akyurt et al., 2002). Despite the seeming straightforward nature of the soil–water freezing process, some zone of water content with temperature curve proves that supercooling cannot be observed in a given sample (Kozlowski, 2009b). In our experiment some of the cooling curves of soil water have neither a point of inflection nor a stable stage. This occurred in soil samples with higher salt content and lower water content. Because the coexistence of ice and water in the soil pores is the most fundamental property of frozen soils, we consider that one reason is the mentioned above, the other is that the water plays unfrozen water in soil for a lower water content for salt crystallization, and under the condition of higher salt content and lower water content little or no free water exists to undergo the freezing in the soil–water system. The “classic” cooling curve method can be used to obtain the freezing point of the wet soil (Grechishchev et al., 2001); this is the basic method used in technique, such as the instruments for measuring freezing point. In addition to the cooling curve method to obtain the freezing point, Kozlowski (2004) used the method of numerical analysis of the differential scanning calorimetry (DSC) thermogram to determine the soil–water freezing point on warming. It is a new method and technique to obtain the soil–water freezing point in recent years. 3. Experimental conditions and the preparation of samples We used four different soil types in our experimental study: (1) silty clay along the Qinghai-Tibet Railway (QTR), (2) Lanzhou loess, (3) silty sand along QTR, and (4) Lanzhou sand. The grain size and the initial ion contents of the soils are presented in Tables 1 and 2.
Table 1 The grain composition of the tested soils. Tested soils
Silty clay along QTR Lanzhou loess Silty sand along QTR Lanzhou sand
Sand(%)
Silt(%)
Clay(%)
2–1 mm
1–0.5 mm
0.5–0.25 mm
0.25–0.1 mm
0.1–0.05 mm
0.05–0.02 mm
0.02–0.002 mm
b 0.002 mm
0.4
2.4 0.1 0.9 0.1
3.8 0.2 4.6 1.5
11.7 0.2 12.2 21.3
22.6 18.9 46.9 60.6
8.6 47.6 15.1 10.3
21.6 24.4 12.6 2.4
28.9 8.6 7.5 3.8
0.2
Table 2 The initial ions content of the tested soils. Tested soils
Ion content % Cation
Silty clay along QTR Lanzhou loess Silty sand along QTR Lanzhou sand
Total salt content %
Anion
Na+
K+
Ca2+
Mg2+
SO2− 4
Cl−
F−
NO− 3
0.021 0.144 0.004 0.006
0.004 0.006 0.003 0.004
0.046 0.078 0.053 0.059
0.015 0.019 0.011 0.008
0.029 0.459 0.004 0.016
0.014 0.159 0.006 0.006
0.002 0.003 0.001 0.001
0.009 0.008 0.008 0.012
0.140 0.876 0.090 0.102
H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
Each prepared soil sample was tamped with three layers into an iron cylinder with a diameter of 30 mm and a height of 50 mm that was closed on one end and lidded on the other end (Fig. 2). An opening in the center of the cylinder's lid allowed for the insertion of a thermocouple. The cylinder was placed in a coolant with a temperature of − 30 °C to create a homogenous sub-freezing temperature in the cell. The cylinder was airtight and completely immersed in the liquid for 5 h to allow the sample to freeze completely. The temperature of the sample was measured using a thermocouple (accuracy of ±0.01 °C) recorded every 10 s by a data logger (Datatake DT500), and stored on disk. The recorded temperatures were used to create cooling curves of temperature as a function of time, from which we obtained the freezing point of each sample.
Table 3 The experiment conditions. Tested soils
Salt types
Water content %
Silty clay along QTR Lanzhou loess Silty sand along QTR Lanzhou sand
NaCl, CaCl2
5, 10, 15, 20, 30, 40, 50 0, 0.2, 0.5, 1, 2, 3, 5
Salt content %
Na2SO4, NaCl, Na2CO3 Na2SO4, Na2CO3, K2SO4 5, 10, 15, 20, 30 Na2SO4, NaCl, Na2CO3
1
50mm
2 3 4
4. Experimental results and analysis 4.1. Influence of water and salt contents on the freezing point Fig. 3 through Fig. 6 show how the freezing point of the different soil samples varies with different water and salt contents. And Table 4 through Table 7 are the fitting curve parameters of the freezing point variation with salt content under the experimental condition to each soil. In general, the freezing point increases with increasing water content and decreases with increasing salt content for each of the four soils, regardless of the type of salt added. There is a significant difference of the freezing point for the samples with the higher salt content, but the curves is gentle and the difference reduction of freezing point appears as the water content increases. Thus the influence of salt content on the freezing point is greater than the influence of water content. The samples of silty sand along QTR show little change in the freezing point at higher water contents, especially those greater than 20% (Fig. 5), which indicates that to the soil with certain salt content, the freezing point is primarily controlled by salt content at high moisture levels. A similar pattern is shown by the Lanzhou sand sample (Fig. 6). These figures (Fig. 3 through 6) also indicate that the freezing point decreases in samples with the same water content to whatever type of salt added. In a soil–water system, the force of solution affected in the soil is changed for the adding of soluble solution. The solution affected not only the absorption by soil particle surfaces, but also the cementation from the sol and gel of the solution itself and the absorption, exchange, displacement, and the diffusion of ions. This increases the absorption
30mm 1- cover of the box 2- thermocouple 3- sample box 4- soil sample Fig. 2. Sample box for freezing point measurement.
During sample preparation, we dissolved a specific amount of salt in a specific amount of deionized water to enable us to investigate the behavior of each type of soil with known salt and water contents. The solution was then incorporated into a prepared 70 g dry soil (the original water content of each of the four soils was approximately 4%) to moisturize. Each soil sample was placed into a plastic bag and sealed for 6 h to ensure an even distribution of water and salt; this was especially important to the clay samples. The maximum water content for the sand samples is super-saturated and the maximum water content for the clay samples exceeds the liquid limit. The various salt combinations and the water and salt contents of the prepared samples are shown in Table 3. Altogether, a total of 455 different sample conditions were tested. w=5% w=10% w=15% fitted w=5% fitted w=10% fitted w= 30% fitted w=40%
w=20% w= 30% fitted w=15% fitted w =50%
S=0% S=0.2% S=0.5% fitted S=0% fitted S=0.2% fitted S=2% fitted S=3%
w=40% w =50% fitted w=20% CaCl2
NaCl
S=1% S=2% fitted S=0.5% fittedS=5% 0
-2
-2
-2
-2
-4
-4
-4
-4
-8
-10
-6
-8
-10
-12 20
30
40
water content/%
-8
50
10
20
30
-8
silty clay along QTR
silty clay along QTR
-12
-12 0
-6
-10
-10
-12 10
-6
silty clay along QTR
silty clay along QTR
0
freezing point/oC
0
freezing point/oC
0
-6
40
water content/%
50
S=3% S=5% fitted S=1% CaCl2
NaCl
0
freezing point/oC
freezing point/oC
81
0
1
2
3
4
5
salt content/%
Fig. 3. Variation of freezing temperature with water and salt contents to the silty clay along QTR.
0
1
2
3
salt content/%
4
5
82
H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
S=0% fitted S=0%
S=0.2% fitted S=0.2%
S=0.5% fitted S=0.5%
S=1% fitted S=1%
S=2% fitted S=2%
S=3% fitted S=3%
S=5% fitted S=5% Na2CO3
NaCl
Na2SO4 0
0
-2
-2
-4
-4
0
-4 -6 -8 -10
freezing point/oC
freezing point/oC
freezing point/oC
-2
-6 -8 -10
-12
Lanzhou loess
Lanzhou loess 10
20
30
40
50
-14 0
10
20
water content/% w=10% fitted w=10%
w=15% fitted w=15%
Na2SO4
0
30
40
50
0
w=20% fitted w=20%
w=30% fitted w=30%
NaCl
0
-10 -12
freezing point/oC
-4
freezing point/oC
-2
-4
-8
-6 -8 -10 -12
Na2CO3
-6 -8 -10
Lanzhou loess
Lanzhou loess -14
2
3
4
50
-12
Lanzhou loess -14
40
w=50% fitted w=50%
0
-2
-6
30
w=40% fitted w=40%
-4
1
20
water content/%
-2
0
10
water content/%
w=5% fitted w=5%
freezing point/oC
Lanzhou loess
-14
-14 0
-8
-10
-12
-12
-6
-14
5
0
1
2
salt content/%
3
4
5
0
1
2
salt content/%
3
4
5
salt content/%
Fig. 4. Variation of freezing temperature with water and salt contents to Lanzhou loess.
S=0% fitted S=0%
S=0.2% fitted S=0.2%
S=0.5% fitted S=0.5%
S=1% fitted S=1%
K2SO4
-1
-1
-1
-2
-2
-2
-3 -4 -5 -6
freezing point/oC
0
-3 -4 -5 -6 -7
10
15
20
25
30
35
-5 -6
silty sand along QTR -8
0
5
10
water content/%
15
20
25
30
35
0
w=10% fitted w=10%
Na2SO4
w=15% fitted w=15%
w=20% fitted w=20%
Na2CO3
0
-5 -6
freezing point/oC
-2
freezing point/oC
-1
-2
-4
-3 -4 -5 -6 -7
silty sand along QTR
-8 2
3
4
salt content/%
5
25
30
35
-3 -4 -5 -6 -7
silty sand along QTR
-8 1
20
K2SO4
0
-1
-3
15
w=30% fitted w=30%
-2
0
10
water content/%
-1
-7
5
water content/% w=5% fitted w=5%
0
-4
silty sand along QTR -8
5
-3
-7
silty sand along QTR -8 0
S=5% fitted S=5%
Na2CO 3 0
-7
freezing point/oC
S=3% fitted S=3%
0
freezing point/oC
freezing point/oC
Na2SO4
S=2% fitted S=2%
silty sand along QTR
-8 0
1
2
3
4
5
0
1
salt content/%
Fig. 5. Variation of freezing temperature with water and salt contents to the silty sand along QTR.
2
3
salt content/%
4
5
H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
S=0% fitted S=0%
S=0.2% fitted S=0.2%
S=0.5% fitted S=0.5%
S=1% fitted S=1%
Na2CO 3
-2
-2
-2
-4
-4
-4
-6 -8 -10
freezing point/oC
0
-6 -8 -10 -12
15
20
25
30
35
-14 0
5
10
water content/%
15
20
25
30
35
0
w=10% fitted w=10%
Na2SO4
w=15% fitted w=15%
w=20% fitted w=20%
NaCl
0
-4
-10 -12
freezing point/oC
-4
freezing point/oC
-4
-8
-6 -8 -10 -12
-14 3
4
25
30
35
-6 -8 -10 -12
-14 2
20
Na2CO3
0 -2
-6
15
w=30% fitted w=30%
-2
1
10
water content/%
-2
0
5
water content/%
w=5% fitted w=5% 0
-10
Lanzhou sand
-14 10
-8
Lanzhou sand
-14 5
-6
-12
Lanzhou sand 0
S=5% fitted S=5%
NaCl 0
-12
freezing point/oC
S=3% fitted S=3%
0
freezing point/oC
freezing point/oC
Na2SO4
S=2% fitted S=2%
83
-14
5
0
1
2
3
4
5
0
salt content/%
salt content/%
1
2
3
4
5
salt content/%
Fig. 6. Variation of freezing temperature with water and salt contents to Lanzhou sand.
ability of soil particles and decreases the soil–water potential for the adding of soluble solution. Consequently, a lower temperature is needed to freeze the free water freezing, and the freezing point will decrease even though the same water content is present. Moreover, at the same water content, the soil–water potential is greater for samples with higher salt content than that of samples with lower salt content, which is another reason for the freezing point to decrease with increasing salt content. Xu et al. (1987) showed that the curve of unfrozen water with temperature is very close to a soil with different water contents; this reflects the correlation between the water content and the freezing point. With higher water content the thickness of the water film on soil particles increases and the potential of capillary water or adhesive water decreases, leading to a depressed freezing point.
Table 4 Fitting value of parameters under every experiment condition to silty clay along QTR. Salt type
Water content w/%
Form of fitting curve Tf ~ S
A
B
R2
NaCl
5 10 15 20 30 40 50 5 10 15 20 30 40 50
Tf = A + BS
4.53 − 1.39 − 0.26 − 0.37 − 0.83 − 0.13 − 0.16 − 4.42 − 1.25 − 0.16 − 0.05 − 0.03 0.09 − 0.09
− 12.98 − 7.75 − 4.33 − 2.82 − 2.13 − 1.63 − 1.23 − 17.05 − 5.82 − 4.10 − 2.91 − 1.79 − 1.42 − 0.99
0.99 0.99 0.99 0.98 1.00 0.99 0.98 1.00 0.99 0.99 0.99 0.99 0.99 0.98
CaCl2
Tf = A + BS
4.2. Influence of different types of salt on the freezing point The influence of the different types of salt on the freezing point is shown in Fig. 7 though Fig. 10. Fig. 7 illustrates the influence of different salt types (NaCl and CaCl2) at varying concentrations on the freezing point of the silty clay along QTR. The influence of NaCl on the freezing point is stronger than that of CaCl2. It is also indicated from the study in the freezing point of Lanzhou loess that the influence of NaCl on the freezing point is strongest (Fig. 10), and the influence is as the same as that of the silty clay along QTR. As NaCl and CaCl2 have the same anion (Cl–), the influence of Na+ on the freezing point to silty clay along QTR must be greater than that of Ca2+. The difference in the influence of the two salts on the freezing point is small, and as the salt content increases (S ≥ 2%), the difference between the freezing point of the two salts is constant to the same salt content, indicating that the influence of NaCl and CaCl2 on the freezing point of silty clay along QTR tends toward stability as the salt content increases. Fig. 8 depicts the influence of different salt types (Na2SO4, NaCl and Na2CO3) on the freezing point of the Lanzhou loess. The difference in the effect of the salts on the freezing point is small when the salt content is low, but becomes stronger with increasing salt content. Comparing with the three salts, NaCl has the strongest effect on the freezing point, followed by Na2CO3, and then Na2SO4. As all three salts have the same 2− cation (Na+), the influence of Cl−is strongest, followed by CO2− 3 and SO4 . The freezing point of Lanzhou sand with the same three salts, and the influence trend is the same as that of Lanzhou loess (Fig. 10). Fig. 9 shows the influence of Na2SO4, Na2CO3, and K2SO4 on the freezing point of silty sand along QTR. The influence of the three salts on the freezing point is as near and makes no difference at low salt content (S ≤ 0.5%). As the salt content increases (S ≥ 1%), however, the different impacts of the three salts become more apparent, with the influence of the Na2CO3 being the strongest and that of the Na2SO4
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H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
Table 5 Fitting value of parameters under every experiment condition to Lanzhou loess. Salt type
Water content w/%
Form of fitting curve Tf ~ S
T0
A1
t
A
B
R2
Na2SO4
5 10 15 20 30 40 50 5 10 15 20 30 40 50 5 10 15 20 30 40 50
Tf = A1⋅ exp(− S/t) + T0
87.99 − 7.11 − 3.99 − 12.32 − 5.62 − 3.76 − 2.33 – – – – – – – − 25.15 − 6.48 − 5.00 − 5.00 − 4.94 − 16.85 –
84.46 5.71 2.75 11.37 5.02 4.61 1.74 – – – – – – – 22.00 4.38 3.78 4.38 3.97 15.38 –
19.95 1.64 2.08 25.12 17.17 13.22 6.56 – – – – – – – 3.70 1.24 1.32 1.85 2.49 19.98 –
– – – – – – – − 3.06 − 1.92 − 1.35 − 0.80 − 0.51 − 0.52 − 0.49 – – – – – – − 0.66
– – – – – – – − 12.88 − 6.71 − 4.34 − 3.28 − 2.31 − 1.62 − 1.36 – – – – – – − 0.65
0.99 0.97 0.95 0.98 0.99 0.99 0.79 0.98 0.99 0.99 1.00 1.00 1.00 0.99 0.95 0.97 0.92 0.97 0.98 0.98 0.92
NaCl
Na2CO3
Tf = A + BS
Tf = A1⋅ exp(− S/t) + T0
Tf = A + BS
Table 6 Fitting value of parameters under every experiment condition to the silty sand along QTR. Salt type
Water content w/%
Form of fitting curve Tf ~ S
T0
A1
t
A
B
R2
Na2SO4
5 10 15 20 30 5 10 15 20 30 5 10 15 20 30
Tf− A1⋅exp(− S/t) + T0
− 6.49 − 6.33 − 5.32 − 3.27 – − 8.68 − 6.27 − 3.67 − 3.56 − 3.56 − 4.07 − 2.96 − 2.69 − 2.35 − 2.05
6.18 6.18 5.00 3.26 – 8.42 6.23 3.66 3.73 3.60 3.71 2.57 2.61 2.43 2.00
2.69 6.13 7.62 7.34 – 1.26 2.21 1.53 1.58 2.36 1.01 1.40 1.56 1.62 1.85
– – – – 0.01 – – – – – – – – – –
– – – – − 0.33 – – – – – – – – – –
0.99 0.97 0.99 10.. 0.99 0.94 0.97 0.96 0.97 0.98 0.99 0.95 0.94 0.94 0.96
Na2CO3
K2SO4
Tf = A + BS Tf = A1⋅ exp(− S/t) + T0
Tf = A1⋅ exp(− S/t) + T0
being the weakest. Fig. 7 revealed that the influence of CO2− 3 on the freezing point of clay is stronger than that of SO2− 4 ; this same conclusion also can be applied to the silty sand along QTR. The influence of Na2SO4 and K2SO4 is stronger than that of Na2SO4, and as the two salts have the same di-anion (SO2− 4 ), the influence of Na2SO4
and K2SO4 on freezing point of the silty sand along QTR is attributed to the influence of cation: the influence of K+ on the freezing point of the silty sand along QTR is shown to be stronger than that of Na+. It is indicated in the statistical result in the table that the major fitting curve of freezing point with salt content agrees with the exponential
Table 7 Fitting value of parameters under every experiment condition to Lanzhou sand. Salt type
Water content w/%
Form of fitting curve Tf ~ S
T0
A1
t
A
B
R2
Na2SO4
5 10 15 20 30 5 10 15 20 30 5 10 15 20 30
Tf = A1⋅ exp(− S/t) + T0
1.25 − 9.23 4.54 − 2.31 6.59 – – – – – − 5.63 − 3.83 – − 3.39 − 3.61
− 1.83 9.23 − 4.76 2.14 − 6.59 – – – – – 5.66 4.08 – 3.48 3.68
− 1.98 9.62 − 12.50 2.51 − 2.63
– – – – – − 0.46 0.31 − 0.27 − 0.40 − 0.08 – – − 0.66 – –
– – – – – − 14.22 − 0.78 − 4.28 − 3.34 − 2.10 – – − 0.75 – –
0.99 0.97 0.99 0.79 0.97 1.00 1.00 1.00 1.00 1.00 0.93 0.94 0.84 0.94 0.96
NaCl
Na2CO3
Tf = A + BS
Tf = A1⋅ exp(− S/t) + T0 Tf–A + BS Tf = A + BS
0.94 1.00 1.37 2.11
NaCl
CaCl2
fitted NaCl
fitted CaCl2
0
0
-2
-2
-2
-4 S=0.2%
-6 -8 -10
-4 S=0.5%
-6 -8 -10
silty clay along QTR
-12 0
10
20
30
40
-4
10
20
water content/%
-8
30
40
50
0
-6 -8
-2
S=3%
-4 -6 -8 -10
-10
40
40
50
S=5%
-6 -8
-12 0
50
50
silty clay along QTR
-12 30
40
-4
silty clay along QTR
-12
30
-10
silty clay along QTR 20
20
water content/%
freezing point/oC
freezing point/oC
-4
10
10
0
-2
S=2%
0
silty clay along QTR
water content/% 0
-2
S=1%
-6
-12 0
50
85
-10
silty clay along QTR
-12
0
freezing point/oC
freezing point/oC
0
freezing point/oC
freezing point/oC
H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
10
20
water content/%
30
40
50
0
10
20
water content/%
30
water content/%
Fig. 7. Influence of different salt types on freezing temperature to the silty clay along QTR.
damping model except the freezing point influence by chloride ion. To summarize, the anion in this study with the strongest influence on the 2− 2− 2− − freezing point was Cl−, followed by CO2− 3 and SO4 (Cl N CO3 N SO4 ). The cation among the salts in the study with the strongest influence on freezing point was K+ followed by Na+ and Ca2+ (K+NNa+NCa2+).
Na2SO4
4.3. Influence of type of soil on freezing point Fig. 11 shows the variation in the freezing point at different water contents of the soil types added Na2SO4. For the same condition to the other salts of NaCl and Na2CO3 added in other soils, further details on
NaCl
fitted Na2SO4
Na2CO3
fitted NaCl
fitted Na2CO3
0
0
-2
-2
-4
-4
0
-4 -6
S=0.2%
-8 -10
-6 S=0.5%
-8 -10
Lanzhou loess
-14 0
10
20
Lanzhou loess
-14 30
40
50
-6 S=1%
-8 -10 -12
-12
-12
0
10
30
40
0
50
-4 -6 -8 S=2%
-10
freezing point/oC
0 -2
freezing point/oC
0 -2 -4 -6 -8 S=3%
-10 -12
-12
Lanzhou loess
-14 30
water content/%
40
50
30
40
50
-4 -6 -8
S=5%
-10 -12
Lanzhou loess -14 20
20
water content/%
0
10
10
water content/%
-2
0
Lanzhou loess
-14
20
water content/%
freezing point/oC
freezing point/oC
freezing point/oC
freezing point/oC
-2
10
20
Lanzhou loess
-14 30
40
50
water content/% Fig. 8. Influence of different salt types on freezing temperature to Lanzhou loess.
10
20
30
water content/%
40
50
H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
Na2SO4
Na2CO3
K2SO4
fitted Na2SO4
fitted Na2CO3
fitted K2SO4
0
0
-1
-1
-2
-2
-2
-3 S=0.2%
-4 -5 -6
-3 S=0.5%
-4 -5 -6
-3
-5 -6 -7
silty sand along QTR
silty sand along QTR
silty sand along QTR
-8
-8 0
5
10
15
20
25
30
-8 0
35
5
10
water content/%
15
20
25
30
35
0
-2
-2
-2
-3 -4 S=2%
-6 -7
freezing point/oC
0 -1
freezing point/oC
0 -1
-3 -4 S=3%
-5 -6
15
25
30
35
30
35
25
30
35
S=5%
-5 -6
silty sand along QTR 20
25
-4
silty sand along QTR -8
-8 10
20
-7
silty sand along QTR -8
15
-3
-7 5
10
water content/%
0
0
5
water content/%
-1
-5
S=1%
-4
-7
-7
freezing point/oC
freezing point/oC
0 -1
freezing point/oC
freezing point/oC
86
0
5
10
water content/%
15
20
25
30
0
35
5
10
water content/%
15
20
water content/%
Fig. 9. Influence of different salt types on freezing temperature to the silty sand along QTR.
molecules and salt particles and the thickness the water film around the soil particles, which leads to a lower freezing point. Adsorption decreases as the soil particles size increases, sand-sized particles have a much thinner water film around the soil particles and will freeze at a higher temperature. Thus, at the same water content and salt content, the freezing point of clay soils is lower than that of sand. The smaller the soil particles, the lower the freezing point. However, the
other salts are beyond the scope of this paper. At the same salt content, the freezing point of the Lanzhou loess is always lower than that of the silty sand along QTR and the Lanzhou sand, but as the water content increases, the difference of the freezing point among the three soils decreases. It is the reason that Lanzhou loess is a silty clay and its clay fraction has a greater specific area than that of the other particles. The greater the specific area, the larger the adsorption between water Na2SO4
NaCl
fitted Na2CO 3 0
-2
-2
-2
-4
-4
-4
-6
S=0.2%
-8 -10
-6
freezing point/oC
0
S=0.5%
-8 -10 -12
-12
5
10
-10
Lanzhou sand
15
20
25
30
-14 0
35
5
10
water content/%
15
20
25
30
35
0
0
0
-2
-2
S=2%
-8 -10 -12
-4
freezing point/oC
freezing point/oC
-4
S=3%
-6 -8 -10
15
20
water content/%
25
30
35
20
25
30
35
25
30
35
-4 S=5%
-6 -8 -10
Lanzhou sand
Lanzhou sand -14
-14 10
15
-12
-12 Lanzhou sand
-14 5
10
water content/%
0
-6
5
water content/%
-2
0
S=1%
-8
Lanzhou sand -14
0
-6
-12
Lanzhou sand -14
freezing point/oC
Na 2CO 3
fitted NaCl
0
freezing point/oC
freezing point/oC
fitted Na2SO4
0
5
10
15
20
25
30
35
0
water content/% Fig. 10. Influence of different salt types on freezing temperature to Lanzhou sand.
5
10
15
20
water content/%
H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
silty sand along QTR fitted silty sand along QTR
0
-2
-2
-2
-4 -6
S=0%
-8
freezing point/oC
0
-10
-4 -6
S=0.2%
-8
10
20
30
40
50
-6
0
10
-8
20
30
40
0
50
-2
-2
-2
S=1% -6 -8 -10
freezing point/oC
0
freezing point/oC
0
-4
-4 S=2% -6 -8
30
40
50
water content/%
40
50
40
50
-4 S=3% -6 -8
-12
-12 20
30
-10
-10
-12
20
water content/%
0
10
10
water content/%
water content/%
0
S=0.5%
-12
-12 0
-4
-10
-10
-12
freezing point/oC
Lanzhou sand fitted Lanzhou sand
0
freezing point/oC
freezing point/oC
Lanzhou loess fitted Lanzhou loess
87
0
10
20
30
40
50
water content/%
0
10
20
30
water content/%
0
freezing point/oC
-2 -4 -6
S=5%
-8 -10 -12 10
20
30
40
50
water content/% Fig. 11. Freezing point of Lanzhou loess, Lanzhou sand and silty sand along Qinghai-Tibet Railway added Na2SO4 (The conditions are the same to the tested soil added NaCl and Na2CO3, so further details on other salts are beyond the scope of this paper).
difference in the influence of the soil particle size on freezing point decreases with increasing water content.
5. Conclusions
variation form of freezing point influenced by other ions mostly fit the exponential damping model. 5. At the same water content and salt content, the freezing point of clay soil is lower than that of sandy soil and the smaller soil particles, the lower the freezing point. The effect of soil particle size on the freezing point decreases with increasing water content.
The investigating of the freezing point of saline soil with different water and salt contents, leads to the following conclusions: Acknowledgments 1. No matter what type of salt is added to the soil, the freezing point of the soil decreases as the salt content increases, and the freezing point increases with increasing water content. 2. In clay soils the difference of the freezing point increases as salt content increases, and the difference decreases when water content is higher. Sandy soil samples with at the same salt content have a nearly constant freezing point once the water content reaches a certain level. In all soils, the freezing point is most affected by the amount of soluble salt in the soil. 3. Common ions in saline soils have the following relative impacts: the influence of anions on the freezing point among the salts studied is + + 2+ 2− Cl− N CO2− . 3 N SO4 while the influence of cations is K N Na N Ca 4. The variation of freezing with salt content to the soil with chloride ion agrees well with the linear model with a greater slop, but the
Funding for this work was provided by the National Natural Sciences Foundation of China (no.40901039, no.40971046), the Foundation for Innovative Research Groups of the National Natural Sciences of China (no.40821001), the Western Project Program of the Chinese Academy of Sciences (no.KZCX2-XB2-10), and the West Light Doctoral Foundation of the Chinese Academy of Sciences (no.290928591). All support is gratefully acknowledged. References Akyurt, M., Zaki, G., Habeebullah, B., 2002. Freezing phenomena in ice–water systems. J. Energy Conv. Manage. 43, 1773–1789. Andersland, B.O., Ladanyi, B., 2003. Frozen Ground Engineering, second ed. ASCE Press and John Wiley & Sons, Reston, VA.
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Banin, A., Anderson, M.D., 1974. Effects of salt concentration changes during freezing on the unfrozen water content of porous material. Water Resour. Res. 10 (1), 124–128. Fletcher, N.H., 1970. The Chemical Physics of Ice. Cambridge Univ, Press, New York. Grechishchev, E.S., Instanes, A., Sheshin, B.J., Pavlov, V.A., Grechishcheva, V.O., 2001. Laboratory investigation of the freezing point of oil-polluted soils. Cold Reg. Sci. Technol. 32, 183–189. Kozlowski, T., 2004. Soil freezing point as obtained on melting. Cold Reg. Sci. Technol. 38, 93–101. Kozlowski, T., 2009a. Some factors affecting supercooling and the equilibrium freezing point in soil–water systems. Cold Reg. Sci. Technol. 59 (1), 25–33.
Kozlowski, T., 2009b. Some factors affecting supercooling and the equilibrium freezing point in soil–water system. Cold Reg. Sci. Technol. 59, 25–33. Liu, Zongchao, 1986. Freezing point of wet soil and its measurement. J. China Min. Technol. Chin. 3, 24–31. Pierce, M.E., Detournay, C., Lagger, H., 2005. “Numerical Modeling of Ground Freezing for Sub-surface Construction”, Alaska Rocks 2005, The 40th U.S. Symposium on Rock Mechanics (USRMS), June 25–29, 2005, Anchorage, AK. Xu, X., Oliphant, J.L., Tice, A.R., 1987. Factors affecting water migration in frozen soils, Cold Regions Research and Engineering Laboratory. CRREL Rep. 9, 16.
Contents lists available at ScienceDirect
Cold Regions Science and Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c o l d r e g i o n s
Laboratory investigation of the freezing point of saline soil Hui Bing ⁎, Wei Ma State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, CAS, Lanzhou Gansu 730000, China
a r t i c l e
i n f o
Article history: Received 21 September 2010 Accepted 19 February 2011 Keywords: Soil freezing Saline soil Freezing point Salt content Sodium chloride
a b s t r a c t This paper presents the results from an experimental laboratory investigation study on the freezing point of saline soil. The experiments were a part of a larger laboratory program whose objective is to understand how salt and water content as well as ion sort and type of soil affect the freezing point. Results show that the freezing point decreases with increasing salt content, and increases with increasing water content independent of the kind of soil. The freezing point is also controlled by the amount of soluble salt in the 2− + + 2+ soil water and is influenced by common anions and cations as follows: Cl− N CO2− , 3 N SO4 and K N Na N Ca respectively. Statistical results show a major fitting curve of freezing point with salt content that fits the exponential damping model except that the salt with chloride ion which agrees more with the linear model with a greater slop. At given water and salt contents, the freezing point of fine particle soils is lower than that of soils with a more coarse particle; however, the effect of the soil particle size on the freezing point decreases apparently with increasing water content. Crown Copyright © 2011 Published by Elsevier B.V. All rights reserved.
1. Introduction The study of the physical characteristics of frozen ground has revealed that soil water solutions have a significant influence on the freezing point of soil (Banin and Anderson, 1974). Under ordinary conditions, the freezing of pure normal water occurs at 0 °C and takes place at the ice–water interface until ice formation stops. The presence of solutes, high pressure, or dispersal in fine pores will lower the freezing point to temperatures below 0 °C (this effect is known as the freezing point depression). For a given soil, the freezing point is a function of its water content, salt content and imposed load. Kozlowski (2009a,b) used the differential scanning calorimetry technique to study the freezing point and found that the freezing point can be expressed as a power function of the water content and the plastic limit, with an asymptote at water content equal to the unfreezable water content. A soil's freezing point is important for engineering and construction applications including the design of frozen earthen walls for deep excavations, the structural underpinning of foundations, and the ability to establish temporary control over groundwater during construction projects (Pierce et al., 2005). The temperature at which a soil freezes affects both the depth of a frozen earth wall and the use of coolant. Research on freezing points is important for artificial ground freezing and for thermal modeling of natural conditions. In many experimental and numerical studies, the freezing point is used usually to determine whether the soil is freezing
⁎ Corresponding author. Tel.: +86 931 4967291; fax: +86 931 8271054. E-mail address: [email protected] (H. Bing).
or not. However, little has been published concerning the factors that affect the freezing point of saline soil. The main objective of this study is to understand how salt content, water content, ion sort as well as type of soil affect the freezing point of soils. The paper is organized as follows. We introduce the concepts related to the freezing point of wet soil and the methods used to measure the freezing point. Next, we explain the experimental conditions, the preparation of samples and methods used in our experimental study. The obtained results of freezing point with respect to water content, salt content, ion sort and kind of soil are analyzed. Finally, we present the conclusions drawn from the results of our experiments. 2. Freezing point of soil–water system and testing methods The formation of ice in the pores of soil involves the cooling of the soil–water system, as is illustrated in Fig. 1. As pure liquid water cools to the point of freezing, ice crystal nucleation and crystal growth begins to occur within a few molecules; this process is generally initiated a few degrees below the melting point of ice. In other words, some supercooling is needed to initiate the process of freezing (Kozlowski, 2009a); Under normal atmospheric pressure, pure water can be easily supercooled to as low as−25 °C and, with more difficulty, to as low as − 41 °C, depending to the droplet diameter (Fletcher, 1970). The pore water does not start to freeze until the temperature drops to the temperature of spontaneous nucleation Tsn. At this stage, the system is below the equilibrium freezing point and the supercooled water is in a metastable equilibrium state. The abrupt transformation of free water to ice causes water molecules to aggregate to soil particles. As the result of the release of latent heat,
0165-232X/$ – see front matter. Crown Copyright © 2011 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2011.02.008
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H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
Fig. 1. Cooling curve for the soil water system.
L, during ice formation, the temperature of the system rises again to the initial freezing temperature, Tf, at which point it stabilizes for a period (Andersland and Ladanyi, 2003). During the freezing of the soil–water system, the extraction of heat leads to successive freezing of the remaining unfrozen water. Even at temperatures well below the initial freezing point, some thermodynamically stable liquid water remains unfrozen, and undergoes successive phase changes as temperature is lowered. Thus, the process of soil–water freezing has four stages: (1) spontaneous nucleation, (2) an abrupt transition in temperature as ice formation begins, (3) an equilibrium period of constant temperature, and (4) a gradual temperature decrease. Free water in the soil pores will now be freezing at temperature Tf. All the free water and most of the bound water (the unfrozen water film on the soil particles) are frozen at the temperature of equilibrium, Te (about −70 °C). Within the fine-grained soils with high specific surface area, a significant amount of unfrozen water can exist at a higher temperature.
Kozlowski (2009a) defined the supercooling as the difference (ΔT) between the temperature of equilibrium freezing and the temperature of spontaneous nucleation, correlates to cooling rates, but is more directly related to the solution within the soil (Liu, 1986). The higher solute concentration, the greater the supercooling is. At Tsn, the release of latent heat of 332.9 J/g will slow the rate cooling until Te is reached as free water changes to ice. Thus there is a contradiction between temperature abrupt transition for latent heat release and the effect of outside cooling in the soil water system. The degree of counteraction determines how long the stable stage (at the freezing point) lasts. Thus, the Tf is reached only when the latent heat is sufficient to increase the system temperature to Tf. When a liquid is supercooled so deeply that the latent heat is not sufficient to raise its temperature to Tf, it is referred to as being hypercooled (Akyurt et al., 2002). Despite the seeming straightforward nature of the soil–water freezing process, some zone of water content with temperature curve proves that supercooling cannot be observed in a given sample (Kozlowski, 2009b). In our experiment some of the cooling curves of soil water have neither a point of inflection nor a stable stage. This occurred in soil samples with higher salt content and lower water content. Because the coexistence of ice and water in the soil pores is the most fundamental property of frozen soils, we consider that one reason is the mentioned above, the other is that the water plays unfrozen water in soil for a lower water content for salt crystallization, and under the condition of higher salt content and lower water content little or no free water exists to undergo the freezing in the soil–water system. The “classic” cooling curve method can be used to obtain the freezing point of the wet soil (Grechishchev et al., 2001); this is the basic method used in technique, such as the instruments for measuring freezing point. In addition to the cooling curve method to obtain the freezing point, Kozlowski (2004) used the method of numerical analysis of the differential scanning calorimetry (DSC) thermogram to determine the soil–water freezing point on warming. It is a new method and technique to obtain the soil–water freezing point in recent years. 3. Experimental conditions and the preparation of samples We used four different soil types in our experimental study: (1) silty clay along the Qinghai-Tibet Railway (QTR), (2) Lanzhou loess, (3) silty sand along QTR, and (4) Lanzhou sand. The grain size and the initial ion contents of the soils are presented in Tables 1 and 2.
Table 1 The grain composition of the tested soils. Tested soils
Silty clay along QTR Lanzhou loess Silty sand along QTR Lanzhou sand
Sand(%)
Silt(%)
Clay(%)
2–1 mm
1–0.5 mm
0.5–0.25 mm
0.25–0.1 mm
0.1–0.05 mm
0.05–0.02 mm
0.02–0.002 mm
b 0.002 mm
0.4
2.4 0.1 0.9 0.1
3.8 0.2 4.6 1.5
11.7 0.2 12.2 21.3
22.6 18.9 46.9 60.6
8.6 47.6 15.1 10.3
21.6 24.4 12.6 2.4
28.9 8.6 7.5 3.8
0.2
Table 2 The initial ions content of the tested soils. Tested soils
Ion content % Cation
Silty clay along QTR Lanzhou loess Silty sand along QTR Lanzhou sand
Total salt content %
Anion
Na+
K+
Ca2+
Mg2+
SO2− 4
Cl−
F−
NO− 3
0.021 0.144 0.004 0.006
0.004 0.006 0.003 0.004
0.046 0.078 0.053 0.059
0.015 0.019 0.011 0.008
0.029 0.459 0.004 0.016
0.014 0.159 0.006 0.006
0.002 0.003 0.001 0.001
0.009 0.008 0.008 0.012
0.140 0.876 0.090 0.102
H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
Each prepared soil sample was tamped with three layers into an iron cylinder with a diameter of 30 mm and a height of 50 mm that was closed on one end and lidded on the other end (Fig. 2). An opening in the center of the cylinder's lid allowed for the insertion of a thermocouple. The cylinder was placed in a coolant with a temperature of − 30 °C to create a homogenous sub-freezing temperature in the cell. The cylinder was airtight and completely immersed in the liquid for 5 h to allow the sample to freeze completely. The temperature of the sample was measured using a thermocouple (accuracy of ±0.01 °C) recorded every 10 s by a data logger (Datatake DT500), and stored on disk. The recorded temperatures were used to create cooling curves of temperature as a function of time, from which we obtained the freezing point of each sample.
Table 3 The experiment conditions. Tested soils
Salt types
Water content %
Silty clay along QTR Lanzhou loess Silty sand along QTR Lanzhou sand
NaCl, CaCl2
5, 10, 15, 20, 30, 40, 50 0, 0.2, 0.5, 1, 2, 3, 5
Salt content %
Na2SO4, NaCl, Na2CO3 Na2SO4, Na2CO3, K2SO4 5, 10, 15, 20, 30 Na2SO4, NaCl, Na2CO3
1
50mm
2 3 4
4. Experimental results and analysis 4.1. Influence of water and salt contents on the freezing point Fig. 3 through Fig. 6 show how the freezing point of the different soil samples varies with different water and salt contents. And Table 4 through Table 7 are the fitting curve parameters of the freezing point variation with salt content under the experimental condition to each soil. In general, the freezing point increases with increasing water content and decreases with increasing salt content for each of the four soils, regardless of the type of salt added. There is a significant difference of the freezing point for the samples with the higher salt content, but the curves is gentle and the difference reduction of freezing point appears as the water content increases. Thus the influence of salt content on the freezing point is greater than the influence of water content. The samples of silty sand along QTR show little change in the freezing point at higher water contents, especially those greater than 20% (Fig. 5), which indicates that to the soil with certain salt content, the freezing point is primarily controlled by salt content at high moisture levels. A similar pattern is shown by the Lanzhou sand sample (Fig. 6). These figures (Fig. 3 through 6) also indicate that the freezing point decreases in samples with the same water content to whatever type of salt added. In a soil–water system, the force of solution affected in the soil is changed for the adding of soluble solution. The solution affected not only the absorption by soil particle surfaces, but also the cementation from the sol and gel of the solution itself and the absorption, exchange, displacement, and the diffusion of ions. This increases the absorption
30mm 1- cover of the box 2- thermocouple 3- sample box 4- soil sample Fig. 2. Sample box for freezing point measurement.
During sample preparation, we dissolved a specific amount of salt in a specific amount of deionized water to enable us to investigate the behavior of each type of soil with known salt and water contents. The solution was then incorporated into a prepared 70 g dry soil (the original water content of each of the four soils was approximately 4%) to moisturize. Each soil sample was placed into a plastic bag and sealed for 6 h to ensure an even distribution of water and salt; this was especially important to the clay samples. The maximum water content for the sand samples is super-saturated and the maximum water content for the clay samples exceeds the liquid limit. The various salt combinations and the water and salt contents of the prepared samples are shown in Table 3. Altogether, a total of 455 different sample conditions were tested. w=5% w=10% w=15% fitted w=5% fitted w=10% fitted w= 30% fitted w=40%
w=20% w= 30% fitted w=15% fitted w =50%
S=0% S=0.2% S=0.5% fitted S=0% fitted S=0.2% fitted S=2% fitted S=3%
w=40% w =50% fitted w=20% CaCl2
NaCl
S=1% S=2% fitted S=0.5% fittedS=5% 0
-2
-2
-2
-2
-4
-4
-4
-4
-8
-10
-6
-8
-10
-12 20
30
40
water content/%
-8
50
10
20
30
-8
silty clay along QTR
silty clay along QTR
-12
-12 0
-6
-10
-10
-12 10
-6
silty clay along QTR
silty clay along QTR
0
freezing point/oC
0
freezing point/oC
0
-6
40
water content/%
50
S=3% S=5% fitted S=1% CaCl2
NaCl
0
freezing point/oC
freezing point/oC
81
0
1
2
3
4
5
salt content/%
Fig. 3. Variation of freezing temperature with water and salt contents to the silty clay along QTR.
0
1
2
3
salt content/%
4
5
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H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
S=0% fitted S=0%
S=0.2% fitted S=0.2%
S=0.5% fitted S=0.5%
S=1% fitted S=1%
S=2% fitted S=2%
S=3% fitted S=3%
S=5% fitted S=5% Na2CO3
NaCl
Na2SO4 0
0
-2
-2
-4
-4
0
-4 -6 -8 -10
freezing point/oC
freezing point/oC
freezing point/oC
-2
-6 -8 -10
-12
Lanzhou loess
Lanzhou loess 10
20
30
40
50
-14 0
10
20
water content/% w=10% fitted w=10%
w=15% fitted w=15%
Na2SO4
0
30
40
50
0
w=20% fitted w=20%
w=30% fitted w=30%
NaCl
0
-10 -12
freezing point/oC
-4
freezing point/oC
-2
-4
-8
-6 -8 -10 -12
Na2CO3
-6 -8 -10
Lanzhou loess
Lanzhou loess -14
2
3
4
50
-12
Lanzhou loess -14
40
w=50% fitted w=50%
0
-2
-6
30
w=40% fitted w=40%
-4
1
20
water content/%
-2
0
10
water content/%
w=5% fitted w=5%
freezing point/oC
Lanzhou loess
-14
-14 0
-8
-10
-12
-12
-6
-14
5
0
1
2
salt content/%
3
4
5
0
1
2
salt content/%
3
4
5
salt content/%
Fig. 4. Variation of freezing temperature with water and salt contents to Lanzhou loess.
S=0% fitted S=0%
S=0.2% fitted S=0.2%
S=0.5% fitted S=0.5%
S=1% fitted S=1%
K2SO4
-1
-1
-1
-2
-2
-2
-3 -4 -5 -6
freezing point/oC
0
-3 -4 -5 -6 -7
10
15
20
25
30
35
-5 -6
silty sand along QTR -8
0
5
10
water content/%
15
20
25
30
35
0
w=10% fitted w=10%
Na2SO4
w=15% fitted w=15%
w=20% fitted w=20%
Na2CO3
0
-5 -6
freezing point/oC
-2
freezing point/oC
-1
-2
-4
-3 -4 -5 -6 -7
silty sand along QTR
-8 2
3
4
salt content/%
5
25
30
35
-3 -4 -5 -6 -7
silty sand along QTR
-8 1
20
K2SO4
0
-1
-3
15
w=30% fitted w=30%
-2
0
10
water content/%
-1
-7
5
water content/% w=5% fitted w=5%
0
-4
silty sand along QTR -8
5
-3
-7
silty sand along QTR -8 0
S=5% fitted S=5%
Na2CO 3 0
-7
freezing point/oC
S=3% fitted S=3%
0
freezing point/oC
freezing point/oC
Na2SO4
S=2% fitted S=2%
silty sand along QTR
-8 0
1
2
3
4
5
0
1
salt content/%
Fig. 5. Variation of freezing temperature with water and salt contents to the silty sand along QTR.
2
3
salt content/%
4
5
H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
S=0% fitted S=0%
S=0.2% fitted S=0.2%
S=0.5% fitted S=0.5%
S=1% fitted S=1%
Na2CO 3
-2
-2
-2
-4
-4
-4
-6 -8 -10
freezing point/oC
0
-6 -8 -10 -12
15
20
25
30
35
-14 0
5
10
water content/%
15
20
25
30
35
0
w=10% fitted w=10%
Na2SO4
w=15% fitted w=15%
w=20% fitted w=20%
NaCl
0
-4
-10 -12
freezing point/oC
-4
freezing point/oC
-4
-8
-6 -8 -10 -12
-14 3
4
25
30
35
-6 -8 -10 -12
-14 2
20
Na2CO3
0 -2
-6
15
w=30% fitted w=30%
-2
1
10
water content/%
-2
0
5
water content/%
w=5% fitted w=5% 0
-10
Lanzhou sand
-14 10
-8
Lanzhou sand
-14 5
-6
-12
Lanzhou sand 0
S=5% fitted S=5%
NaCl 0
-12
freezing point/oC
S=3% fitted S=3%
0
freezing point/oC
freezing point/oC
Na2SO4
S=2% fitted S=2%
83
-14
5
0
1
2
3
4
5
0
salt content/%
salt content/%
1
2
3
4
5
salt content/%
Fig. 6. Variation of freezing temperature with water and salt contents to Lanzhou sand.
ability of soil particles and decreases the soil–water potential for the adding of soluble solution. Consequently, a lower temperature is needed to freeze the free water freezing, and the freezing point will decrease even though the same water content is present. Moreover, at the same water content, the soil–water potential is greater for samples with higher salt content than that of samples with lower salt content, which is another reason for the freezing point to decrease with increasing salt content. Xu et al. (1987) showed that the curve of unfrozen water with temperature is very close to a soil with different water contents; this reflects the correlation between the water content and the freezing point. With higher water content the thickness of the water film on soil particles increases and the potential of capillary water or adhesive water decreases, leading to a depressed freezing point.
Table 4 Fitting value of parameters under every experiment condition to silty clay along QTR. Salt type
Water content w/%
Form of fitting curve Tf ~ S
A
B
R2
NaCl
5 10 15 20 30 40 50 5 10 15 20 30 40 50
Tf = A + BS
4.53 − 1.39 − 0.26 − 0.37 − 0.83 − 0.13 − 0.16 − 4.42 − 1.25 − 0.16 − 0.05 − 0.03 0.09 − 0.09
− 12.98 − 7.75 − 4.33 − 2.82 − 2.13 − 1.63 − 1.23 − 17.05 − 5.82 − 4.10 − 2.91 − 1.79 − 1.42 − 0.99
0.99 0.99 0.99 0.98 1.00 0.99 0.98 1.00 0.99 0.99 0.99 0.99 0.99 0.98
CaCl2
Tf = A + BS
4.2. Influence of different types of salt on the freezing point The influence of the different types of salt on the freezing point is shown in Fig. 7 though Fig. 10. Fig. 7 illustrates the influence of different salt types (NaCl and CaCl2) at varying concentrations on the freezing point of the silty clay along QTR. The influence of NaCl on the freezing point is stronger than that of CaCl2. It is also indicated from the study in the freezing point of Lanzhou loess that the influence of NaCl on the freezing point is strongest (Fig. 10), and the influence is as the same as that of the silty clay along QTR. As NaCl and CaCl2 have the same anion (Cl–), the influence of Na+ on the freezing point to silty clay along QTR must be greater than that of Ca2+. The difference in the influence of the two salts on the freezing point is small, and as the salt content increases (S ≥ 2%), the difference between the freezing point of the two salts is constant to the same salt content, indicating that the influence of NaCl and CaCl2 on the freezing point of silty clay along QTR tends toward stability as the salt content increases. Fig. 8 depicts the influence of different salt types (Na2SO4, NaCl and Na2CO3) on the freezing point of the Lanzhou loess. The difference in the effect of the salts on the freezing point is small when the salt content is low, but becomes stronger with increasing salt content. Comparing with the three salts, NaCl has the strongest effect on the freezing point, followed by Na2CO3, and then Na2SO4. As all three salts have the same 2− cation (Na+), the influence of Cl−is strongest, followed by CO2− 3 and SO4 . The freezing point of Lanzhou sand with the same three salts, and the influence trend is the same as that of Lanzhou loess (Fig. 10). Fig. 9 shows the influence of Na2SO4, Na2CO3, and K2SO4 on the freezing point of silty sand along QTR. The influence of the three salts on the freezing point is as near and makes no difference at low salt content (S ≤ 0.5%). As the salt content increases (S ≥ 1%), however, the different impacts of the three salts become more apparent, with the influence of the Na2CO3 being the strongest and that of the Na2SO4
84
H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
Table 5 Fitting value of parameters under every experiment condition to Lanzhou loess. Salt type
Water content w/%
Form of fitting curve Tf ~ S
T0
A1
t
A
B
R2
Na2SO4
5 10 15 20 30 40 50 5 10 15 20 30 40 50 5 10 15 20 30 40 50
Tf = A1⋅ exp(− S/t) + T0
87.99 − 7.11 − 3.99 − 12.32 − 5.62 − 3.76 − 2.33 – – – – – – – − 25.15 − 6.48 − 5.00 − 5.00 − 4.94 − 16.85 –
84.46 5.71 2.75 11.37 5.02 4.61 1.74 – – – – – – – 22.00 4.38 3.78 4.38 3.97 15.38 –
19.95 1.64 2.08 25.12 17.17 13.22 6.56 – – – – – – – 3.70 1.24 1.32 1.85 2.49 19.98 –
– – – – – – – − 3.06 − 1.92 − 1.35 − 0.80 − 0.51 − 0.52 − 0.49 – – – – – – − 0.66
– – – – – – – − 12.88 − 6.71 − 4.34 − 3.28 − 2.31 − 1.62 − 1.36 – – – – – – − 0.65
0.99 0.97 0.95 0.98 0.99 0.99 0.79 0.98 0.99 0.99 1.00 1.00 1.00 0.99 0.95 0.97 0.92 0.97 0.98 0.98 0.92
NaCl
Na2CO3
Tf = A + BS
Tf = A1⋅ exp(− S/t) + T0
Tf = A + BS
Table 6 Fitting value of parameters under every experiment condition to the silty sand along QTR. Salt type
Water content w/%
Form of fitting curve Tf ~ S
T0
A1
t
A
B
R2
Na2SO4
5 10 15 20 30 5 10 15 20 30 5 10 15 20 30
Tf− A1⋅exp(− S/t) + T0
− 6.49 − 6.33 − 5.32 − 3.27 – − 8.68 − 6.27 − 3.67 − 3.56 − 3.56 − 4.07 − 2.96 − 2.69 − 2.35 − 2.05
6.18 6.18 5.00 3.26 – 8.42 6.23 3.66 3.73 3.60 3.71 2.57 2.61 2.43 2.00
2.69 6.13 7.62 7.34 – 1.26 2.21 1.53 1.58 2.36 1.01 1.40 1.56 1.62 1.85
– – – – 0.01 – – – – – – – – – –
– – – – − 0.33 – – – – – – – – – –
0.99 0.97 0.99 10.. 0.99 0.94 0.97 0.96 0.97 0.98 0.99 0.95 0.94 0.94 0.96
Na2CO3
K2SO4
Tf = A + BS Tf = A1⋅ exp(− S/t) + T0
Tf = A1⋅ exp(− S/t) + T0
being the weakest. Fig. 7 revealed that the influence of CO2− 3 on the freezing point of clay is stronger than that of SO2− 4 ; this same conclusion also can be applied to the silty sand along QTR. The influence of Na2SO4 and K2SO4 is stronger than that of Na2SO4, and as the two salts have the same di-anion (SO2− 4 ), the influence of Na2SO4
and K2SO4 on freezing point of the silty sand along QTR is attributed to the influence of cation: the influence of K+ on the freezing point of the silty sand along QTR is shown to be stronger than that of Na+. It is indicated in the statistical result in the table that the major fitting curve of freezing point with salt content agrees with the exponential
Table 7 Fitting value of parameters under every experiment condition to Lanzhou sand. Salt type
Water content w/%
Form of fitting curve Tf ~ S
T0
A1
t
A
B
R2
Na2SO4
5 10 15 20 30 5 10 15 20 30 5 10 15 20 30
Tf = A1⋅ exp(− S/t) + T0
1.25 − 9.23 4.54 − 2.31 6.59 – – – – – − 5.63 − 3.83 – − 3.39 − 3.61
− 1.83 9.23 − 4.76 2.14 − 6.59 – – – – – 5.66 4.08 – 3.48 3.68
− 1.98 9.62 − 12.50 2.51 − 2.63
– – – – – − 0.46 0.31 − 0.27 − 0.40 − 0.08 – – − 0.66 – –
– – – – – − 14.22 − 0.78 − 4.28 − 3.34 − 2.10 – – − 0.75 – –
0.99 0.97 0.99 0.79 0.97 1.00 1.00 1.00 1.00 1.00 0.93 0.94 0.84 0.94 0.96
NaCl
Na2CO3
Tf = A + BS
Tf = A1⋅ exp(− S/t) + T0 Tf–A + BS Tf = A + BS
0.94 1.00 1.37 2.11
NaCl
CaCl2
fitted NaCl
fitted CaCl2
0
0
-2
-2
-2
-4 S=0.2%
-6 -8 -10
-4 S=0.5%
-6 -8 -10
silty clay along QTR
-12 0
10
20
30
40
-4
10
20
water content/%
-8
30
40
50
0
-6 -8
-2
S=3%
-4 -6 -8 -10
-10
40
40
50
S=5%
-6 -8
-12 0
50
50
silty clay along QTR
-12 30
40
-4
silty clay along QTR
-12
30
-10
silty clay along QTR 20
20
water content/%
freezing point/oC
freezing point/oC
-4
10
10
0
-2
S=2%
0
silty clay along QTR
water content/% 0
-2
S=1%
-6
-12 0
50
85
-10
silty clay along QTR
-12
0
freezing point/oC
freezing point/oC
0
freezing point/oC
freezing point/oC
H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
10
20
water content/%
30
40
50
0
10
20
water content/%
30
water content/%
Fig. 7. Influence of different salt types on freezing temperature to the silty clay along QTR.
damping model except the freezing point influence by chloride ion. To summarize, the anion in this study with the strongest influence on the 2− 2− 2− − freezing point was Cl−, followed by CO2− 3 and SO4 (Cl N CO3 N SO4 ). The cation among the salts in the study with the strongest influence on freezing point was K+ followed by Na+ and Ca2+ (K+NNa+NCa2+).
Na2SO4
4.3. Influence of type of soil on freezing point Fig. 11 shows the variation in the freezing point at different water contents of the soil types added Na2SO4. For the same condition to the other salts of NaCl and Na2CO3 added in other soils, further details on
NaCl
fitted Na2SO4
Na2CO3
fitted NaCl
fitted Na2CO3
0
0
-2
-2
-4
-4
0
-4 -6
S=0.2%
-8 -10
-6 S=0.5%
-8 -10
Lanzhou loess
-14 0
10
20
Lanzhou loess
-14 30
40
50
-6 S=1%
-8 -10 -12
-12
-12
0
10
30
40
0
50
-4 -6 -8 S=2%
-10
freezing point/oC
0 -2
freezing point/oC
0 -2 -4 -6 -8 S=3%
-10 -12
-12
Lanzhou loess
-14 30
water content/%
40
50
30
40
50
-4 -6 -8
S=5%
-10 -12
Lanzhou loess -14 20
20
water content/%
0
10
10
water content/%
-2
0
Lanzhou loess
-14
20
water content/%
freezing point/oC
freezing point/oC
freezing point/oC
freezing point/oC
-2
10
20
Lanzhou loess
-14 30
40
50
water content/% Fig. 8. Influence of different salt types on freezing temperature to Lanzhou loess.
10
20
30
water content/%
40
50
H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
Na2SO4
Na2CO3
K2SO4
fitted Na2SO4
fitted Na2CO3
fitted K2SO4
0
0
-1
-1
-2
-2
-2
-3 S=0.2%
-4 -5 -6
-3 S=0.5%
-4 -5 -6
-3
-5 -6 -7
silty sand along QTR
silty sand along QTR
silty sand along QTR
-8
-8 0
5
10
15
20
25
30
-8 0
35
5
10
water content/%
15
20
25
30
35
0
-2
-2
-2
-3 -4 S=2%
-6 -7
freezing point/oC
0 -1
freezing point/oC
0 -1
-3 -4 S=3%
-5 -6
15
25
30
35
30
35
25
30
35
S=5%
-5 -6
silty sand along QTR 20
25
-4
silty sand along QTR -8
-8 10
20
-7
silty sand along QTR -8
15
-3
-7 5
10
water content/%
0
0
5
water content/%
-1
-5
S=1%
-4
-7
-7
freezing point/oC
freezing point/oC
0 -1
freezing point/oC
freezing point/oC
86
0
5
10
water content/%
15
20
25
30
0
35
5
10
water content/%
15
20
water content/%
Fig. 9. Influence of different salt types on freezing temperature to the silty sand along QTR.
molecules and salt particles and the thickness the water film around the soil particles, which leads to a lower freezing point. Adsorption decreases as the soil particles size increases, sand-sized particles have a much thinner water film around the soil particles and will freeze at a higher temperature. Thus, at the same water content and salt content, the freezing point of clay soils is lower than that of sand. The smaller the soil particles, the lower the freezing point. However, the
other salts are beyond the scope of this paper. At the same salt content, the freezing point of the Lanzhou loess is always lower than that of the silty sand along QTR and the Lanzhou sand, but as the water content increases, the difference of the freezing point among the three soils decreases. It is the reason that Lanzhou loess is a silty clay and its clay fraction has a greater specific area than that of the other particles. The greater the specific area, the larger the adsorption between water Na2SO4
NaCl
fitted Na2CO 3 0
-2
-2
-2
-4
-4
-4
-6
S=0.2%
-8 -10
-6
freezing point/oC
0
S=0.5%
-8 -10 -12
-12
5
10
-10
Lanzhou sand
15
20
25
30
-14 0
35
5
10
water content/%
15
20
25
30
35
0
0
0
-2
-2
S=2%
-8 -10 -12
-4
freezing point/oC
freezing point/oC
-4
S=3%
-6 -8 -10
15
20
water content/%
25
30
35
20
25
30
35
25
30
35
-4 S=5%
-6 -8 -10
Lanzhou sand
Lanzhou sand -14
-14 10
15
-12
-12 Lanzhou sand
-14 5
10
water content/%
0
-6
5
water content/%
-2
0
S=1%
-8
Lanzhou sand -14
0
-6
-12
Lanzhou sand -14
freezing point/oC
Na 2CO 3
fitted NaCl
0
freezing point/oC
freezing point/oC
fitted Na2SO4
0
5
10
15
20
25
30
35
0
water content/% Fig. 10. Influence of different salt types on freezing temperature to Lanzhou sand.
5
10
15
20
water content/%
H. Bing, W. Ma / Cold Regions Science and Technology 67 (2011) 79–88
silty sand along QTR fitted silty sand along QTR
0
-2
-2
-2
-4 -6
S=0%
-8
freezing point/oC
0
-10
-4 -6
S=0.2%
-8
10
20
30
40
50
-6
0
10
-8
20
30
40
0
50
-2
-2
-2
S=1% -6 -8 -10
freezing point/oC
0
freezing point/oC
0
-4
-4 S=2% -6 -8
30
40
50
water content/%
40
50
40
50
-4 S=3% -6 -8
-12
-12 20
30
-10
-10
-12
20
water content/%
0
10
10
water content/%
water content/%
0
S=0.5%
-12
-12 0
-4
-10
-10
-12
freezing point/oC
Lanzhou sand fitted Lanzhou sand
0
freezing point/oC
freezing point/oC
Lanzhou loess fitted Lanzhou loess
87
0
10
20
30
40
50
water content/%
0
10
20
30
water content/%
0
freezing point/oC
-2 -4 -6
S=5%
-8 -10 -12 10
20
30
40
50
water content/% Fig. 11. Freezing point of Lanzhou loess, Lanzhou sand and silty sand along Qinghai-Tibet Railway added Na2SO4 (The conditions are the same to the tested soil added NaCl and Na2CO3, so further details on other salts are beyond the scope of this paper).
difference in the influence of the soil particle size on freezing point decreases with increasing water content.
5. Conclusions
variation form of freezing point influenced by other ions mostly fit the exponential damping model. 5. At the same water content and salt content, the freezing point of clay soil is lower than that of sandy soil and the smaller soil particles, the lower the freezing point. The effect of soil particle size on the freezing point decreases with increasing water content.
The investigating of the freezing point of saline soil with different water and salt contents, leads to the following conclusions: Acknowledgments 1. No matter what type of salt is added to the soil, the freezing point of the soil decreases as the salt content increases, and the freezing point increases with increasing water content. 2. In clay soils the difference of the freezing point increases as salt content increases, and the difference decreases when water content is higher. Sandy soil samples with at the same salt content have a nearly constant freezing point once the water content reaches a certain level. In all soils, the freezing point is most affected by the amount of soluble salt in the soil. 3. Common ions in saline soils have the following relative impacts: the influence of anions on the freezing point among the salts studied is + + 2+ 2− Cl− N CO2− . 3 N SO4 while the influence of cations is K N Na N Ca 4. The variation of freezing with salt content to the soil with chloride ion agrees well with the linear model with a greater slop, but the
Funding for this work was provided by the National Natural Sciences Foundation of China (no.40901039, no.40971046), the Foundation for Innovative Research Groups of the National Natural Sciences of China (no.40821001), the Western Project Program of the Chinese Academy of Sciences (no.KZCX2-XB2-10), and the West Light Doctoral Foundation of the Chinese Academy of Sciences (no.290928591). All support is gratefully acknowledged. References Akyurt, M., Zaki, G., Habeebullah, B., 2002. Freezing phenomena in ice–water systems. J. Energy Conv. Manage. 43, 1773–1789. Andersland, B.O., Ladanyi, B., 2003. Frozen Ground Engineering, second ed. ASCE Press and John Wiley & Sons, Reston, VA.
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Banin, A., Anderson, M.D., 1974. Effects of salt concentration changes during freezing on the unfrozen water content of porous material. Water Resour. Res. 10 (1), 124–128. Fletcher, N.H., 1970. The Chemical Physics of Ice. Cambridge Univ, Press, New York. Grechishchev, E.S., Instanes, A., Sheshin, B.J., Pavlov, V.A., Grechishcheva, V.O., 2001. Laboratory investigation of the freezing point of oil-polluted soils. Cold Reg. Sci. Technol. 32, 183–189. Kozlowski, T., 2004. Soil freezing point as obtained on melting. Cold Reg. Sci. Technol. 38, 93–101. Kozlowski, T., 2009a. Some factors affecting supercooling and the equilibrium freezing point in soil–water systems. Cold Reg. Sci. Technol. 59 (1), 25–33.
Kozlowski, T., 2009b. Some factors affecting supercooling and the equilibrium freezing point in soil–water system. Cold Reg. Sci. Technol. 59, 25–33. Liu, Zongchao, 1986. Freezing point of wet soil and its measurement. J. China Min. Technol. Chin. 3, 24–31. Pierce, M.E., Detournay, C., Lagger, H., 2005. “Numerical Modeling of Ground Freezing for Sub-surface Construction”, Alaska Rocks 2005, The 40th U.S. Symposium on Rock Mechanics (USRMS), June 25–29, 2005, Anchorage, AK. Xu, X., Oliphant, J.L., Tice, A.R., 1987. Factors affecting water migration in frozen soils, Cold Regions Research and Engineering Laboratory. CRREL Rep. 9, 16.