- Email: [email protected]
A new method for estimating salt expansion in saturated saline soils during cooling based on electrical conductivity
Cold Regions Science and Technology 170 (2020) 102943
Contents lists available at ScienceDirect
Cold Regions Science and Technology journal homepage: www.elsevier.com/locate/coldregions
A new method for estimating salt expansion in saturated saline soils during cooling based on electrical conductivity
T
Rui Tang, Guoqing Zhou , Jianzhou Wang, Guangsi Zhao, Zejin Lai, Fengyuan Jiu ⁎
State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining & Technology, Xuzhou 221008, China
ARTICLE INFO
ABSTRACT
Keywords: Salt expansion Electrical conductivity Saline soils Frost heave Freezing process
Salt expansion is known as a type of soil deformation induced by salt crystallization. In order to reveal the development of salt expansion or salt crystallization in saline soils during the freezing process, we propose a new model for estimating the variation of the pore solution concentration according to the strong dependence between electrical conductivity and concentration. Moreover, the proposed model can further calculate the crystallized salt content, salt expansion, and frost heave during the cooling process. Meanwhile, a series of experiments are conducted on the unfrozen water content, electrical conductivity, and deformation of saline soil with different salinity. The results show that the deformation of saline soil undergoes three stages and increases rapidly in the second stage. Meanwhile, the soil deformation can be well predicted by our model and has similar characteristics with the salt expansion calculated by our model during the cooling process. Salt expansion mainly occurs in the latter two stages for the saline soil with low salt content and throughout the process for the saline soil with high salt content. Meanwhile, the contribution of the ultimate salt expansion to the soil deformation increases significantly with the increase of the salt content, which conforms to the parabolic relationship. Thus, the prediction of crystallized salt by this model is conducive to monitoring salt expansion in the field and laboratory, and further to reveal the mechanism of salt expansion in saline soils.
1. Introduction The saline soil is widely distributed in the northwestern region of China (Xu et al., 1995), and such areas are often located in seasonally frozen soil and/or permafrost regions (Zhou et al., 2000). So the salt expansion and frost heave will occur simultaneously in cold regions, causing difficult and complicated to predict the deformation of saline soils (Padilla and Villeneuve, 1992; Zhao et al., 2013; Fang et al., 2018). Meanwhile, the soil deformation caused by salt expansion and/or frost heave (Ji et al., 2017) in cold regions causes significant threat to operational safety of major engineering such as roads, railways and pipelines (Li et al., 2009; Ma et al., 2017; Zhang et al., 2014; Nixon, 2011). Therefore, it is necessary and urgent to study the characteristics of salt expansion and frost heave of saline soils during the freezing process. Many scholars (Fang et al., 2018; Lai et al., 2016; Wu and Zhu, 2002; Zhang et al., 2016) believed that the saline soil deformation was mainly affected by salt type, salt content, water content, solute migration, temperature, and cooling rate. Recently, the estimated models for salt expansion were obtained based on the phase diagram of the solution in soils (Niu and Gao, 2015; Xu et al., 1995; Gao et al., 1996). ⁎
Fang et al. (2018) adopt theoretical analysis, microstructure observation, and salt expansion tests, and derived the calculation formula of salt expansion in soil. Meanwhile, Wan et al. (2017) concluded that the predicted model based on solution phase diagram cannot accurately estimate the salt expansion at natural conditions, so the relationship between the supersaturation ratio and temperature was derived from the perspective of thermodynamics, and the effect of different cooling rates on the supersaturation ratio was also considered. However, the above studies were mainly focused on measurement temperatures at an above-zero or small range of subzero. Moreover, salt expansion in the unfrozen state and the ultimate soil deformation in the frozen state were merely measured, but the variations of salt expansion and frost heave are not separately obtained during the freezing process. Due to the decrease in temperature and unfrozen water content, the solution concentration is higher than the solubility to generate salt crystals. The content of salt crystal can be estimated from known unfrozen water content and solution concentration in soils according to the conservation of salt mass, and then salt expansion can be calculated. However, the main challenge is difficulty determine the pore solution concentration in soil. Hayley et al. (2009) wonderful obtained solute redistribution induced by moisture migration based on the variation of
Corresponding author. E-mail addresses: [email protected] (R. Tang), [email protected] (G. Zhou).
https://doi.org/10.1016/j.coldregions.2019.102943 Received 3 June 2019; Received in revised form 3 November 2019; Accepted 7 November 2019 Available online 09 November 2019 0165-232X/ © 2019 Elsevier B.V. All rights reserved.
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
electrical conductivity in saline soils. Thus, the above method is extended to estimate the solution concentration induced by soil freezing. In this paper, a mathematical model is proposed to characterize the variation of pore solution concentration with electrical conductivity in soils during the cooling process. Subsequently, the frost heaving and salt expansion in saline soils are mathematically achieved. Meanwhile, the variations of unfrozen water content, electrical conductivity, and soil deformation with variable salinity (0.2%, 0.5%, 1.0%, and 3.5%) are investigated and the parameters of our model are obtained. Then, with the assistance of the proposed model, a quantitative evaluation of the soil deformations is conducted by drawing the comparison with experimental data. The results may be conducive to revealing salt expansion and provide a theoretical basis to monitor salt migration in cold regions.
concentration bears an association with solubility when in the unfrozen state. Therefore, the linear behaviour of Eq. (4) overestimates the electrical conductivity of pore solution. According to Weiss et al. (2013), the electrical conductivity of pore solution can be described by the following equations:
I 1+G I I=
=
Tr , w , c0 [1
+
(T
Tr )]
=F
Tr , w, c 0 [1
+
(T
Tr )] S n
(2)
T , s, cx
Tr , w, cx
=
T , s, cx
Tr , s, cx
Tr , s, cx
Tr , s, c0
= [1 +
(T
Tr )]
Ix 1 + G I0 n S I0 1 + G Ix
(7)
According to Eq. (7), the variation of the ionic strength in the pore solution during the cooling process can be given as follows:
2A + A2 G 2 + AG A2 G 2 + 4A 2 1 I0 T , s, cx A= S (T Tr ) 1 + G I0 Tr , s, c0 1 + Ix =
(3)
n
(8)
In Eq. (8), the ionic strength can be determined through the variations of soil electrical conductivity and unfrozen water content, and the pore solution concentration can be calculated by combining salt types and Eq. (5b) 2.3. Estimation of salt expansion and frost heaving For different types of salts, there are possibly multiple salt crystals arising from the salt crystallization process. Therefore, we assume that there is only one type of crystallized salt in the freezing process. Then, based on the analysis conducted in Section 2.2, the volumetric crystallized salt content can be obtained in the freezing process based on the conservation of mass.
uw initial
=
Tr , s, c 0
Nevertheless, soil electrical conductivity is subject to significant influence from temperature, water content and soil pore concentration (Li et al., 2012). Besides, the pore salinity concentration is changed as a result of including the reduction of unfrozen water content (the reducing of solvent) and the variation in the solubility of salt (change of the solute content) in freeing process. Moreover, the changes in unfrozen water content and the pore concentration both occur and affect each other. Considering the effect of salinity, some authors believed that the linear electrolyte with unfrozen water content due to ionic exclusion (Oldenborger and LeBlanc, 2018; Wu et al., 2017). Tr , w, c 0
(6)
In the unfrozen state, the solubility of salt declines as temperature decreases, thus leading to salt crystallization. Then, as a form of crystalline hydrate, the crystallized salt causes a decline in water content. Subsequently, the unfrozen water content is in decline gradually in the freezing state, the solutes are removed from the ice into the unfrozen water, and the potential crystalline hydrates may accelerate the reduction of the unfrozen water content. This makes the variation of pore solution concentration and the water content in soil inevitable throughout the freezing process. By combining Eqs. (3) and (6), the ratio of the soil electrical conductivity to the initial soil electrical conductivity can be obtained as follows:
where σTr, w, c0 indicates the electrical conductivity of the pore water with pore concentration c0 at the reference temperature Tr, and α denotes the slope compensation of the electrical conductivity versus temperature. Basically, α is approximated by 2.1% at Tr = 25 °C (Campbell et al., 1949). By combining Eqs. (1) and (2), the variation of soil electrical conductivity with temperature and water content can be obtained as follows: T , s, c0
Ix 1 + G I0 I0 1 + G Ix
2.2. Estimation of salt concentration in the pore solution
(1)
n
(5b)
where I0 and Ixare the ionic strengths of pore solution for the initial state and for the pore concentration cx in the cooling process, respectively.
where σT, s, c0 and σT, w, c0 represent the electrical conductivity of the soil and the electrical conductivity of the pore water with pore concentration c0 at the temperature T, respectively, S indicates the saturation, n is the saturation exponent, n = 2 (Oldenborger and Leblanc, 2018), and F refers to the dimensionless formation factor with regard to the pore connectivity. Meanwhile, the electrical conductivity of the pore water varies with temperature due to the changes in fluid viscosity. The linear model of the electrical conductivity versus temperature can be constructed in the following form (Campbell et al., 1949; Hayley et al., 2007): T , w , c0
=
Tr , w, c 0
Water content is considered as a significant factor for the soil electrical conductivity in many studies (Marie et al., 2016; Glover et al., 1997; Choo and Burns, 2014), and researchers generally used the following model based on Archie's law (Archie, 1942). T , w , c0 S
Zi2 ci i=1
Tr , w, cx
2.1. Theoretical basis
=F
N
where G is the electrical parameter, generally G = 0.4(mol/L)-0.5 for a typical pore solution (Weiss et al., 2013). I denotes the ionic strength of pore solution, which is determined by species with charge numbers Z and molar concentration c. Therefore, the variation in the electrical conductivity of pore solution can be written as follows:
2. Constructing mathematical model
T , s, c0
1 2
(5a)
(4)
where θuw and θinitial represent the volumetric unfrozen water content and initial volumetric water content, respectively. As argued by Konrad and Mccammon (1990), however, it is unlikely for solutes to be rejected completely from the pore ice, and ice crystals entrap solution into the ice in the form of “brine pockets” throughout freezing)(Luo et al., 2010). Moreover, the variation of pore solution
c
= (cr
r
cx
uw ) VMi Nj k H2O
(9)
where VMiNj⋅kH2O indicates the molar volume of the salt crystal MiNj· kH2O, (L/mol), i and j represent the numbers of cations M and anions N, and k represents the number of crystal water. Meanwhile, θr and cr are the volumetric water content and the solution concentration at the 2
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
reference temperature Tr，and cx is the solution concentration with the volumetric unfrozen water contentθuw. In the unfrozen state, the change in pore volume of the soil is only caused by salt expansion on account of the decline in the solubility of the salt and it includes two parts: Firstly, the increase in pore volume results from the salt crystallization. Secondly, the salt crystalline hydrate is possible to develop in the soil, and the crystal water is derived from pore water, thus causing a reduction in the water content. Therefore, the soil displacement in this state can be expressed as:
h unfrozen = hsalt expansion =
c
x
k
18(cr
cx r 1000
uw )
x
3. Testing apparatus and method 3.1. Testing apparatus Based on Eqs. (8) and (14), in order to determine frost heave and salt expansion of the soil, there was a necessity to obtain the variations of the unfrozen water content and the soil electrical conductivity with temperature. Meanwhile, the soil deformation test was also imperative monitored to verify the reliability of the prediction results. For soil resistivity testing, a two-phase electrode (Shan et al., 2015; Tang et al., 2018) and four-phase electrode (Chu et al., 2018) methods were often considered. However, the internal structure of the soil is possible to be affected by the four-phase electrode method, especially for small samples in the laboratory. Therefore, the two-phase electrode method was applied to measure soil resistivity in this research. The testing system was mainly composed of four modules: a temperature controlling system, a soil resistivity testing system, an unfrozen water content testing system, and a soil deformation monitoring system, as illustrated in Fig. 1. In Fig. 1, the temperature controlling system is comprised of two modules: (a) an incubator was employí to restrict sample temperature to the range from −30 °C to 40 °C with an accuracy of ± 0.05 °C; and (b) thermocouples (Fig. 2a) were applied to monitor soil temperature at varying intervals of 1 cm, 1.5 cm, 1.5 cm and 1 cm along the sample height with an error of ± 0.4% to ensure temperature uniformly. In the soil electrical resistivity testing system, the Datataker 85G (Fig. 2b) was taken for measurement of the soil resistivity, while the conductive copper paste was applied evenly on both ends of the sample surface and the electrode to mitigate contact resistance. Meanwhile, in order to ensure the stability of the test during the long period, the copper electrode and the copper wire were welded. In the unfrozen water content testing system, the moisture transducer (type: ECH2O EC-5) was applied to measure unfrozen water content with a temperature range from −40 °C to 60 °C and precision of 0.03 m3/m3, as shown in Fig. 2c. And a constant voltage DC power supply was made available to provide 3 V excitation power (Fig. 2d) for the moisture transducer. In the soil deformation monitoring system, one displacement sensor (type: ZS1100-DT40), with a range of 40 mm and an accuracy of ± 0.01 mm, was installed at the top end of the sample, as shown in Fig. 2e.
(10)
where Δxindicates the height of the soil sample. Eq. (10) indicates that soil deformation is divided into two aspects. The first one is the increasing displacement as a result of salt crystals, and the second one is the reduced displacement causing by the crystal water. In the frozen state, the segregated ice is unlikely to appear under the condition in absence of water supplement and temperature gradient, and then water migration can be ignored in sandy soils. Therefore, the frost heave deformation Δhfrozen non‐salinein‐situ for non-saline sand soils depends upon the volume change of the in-situ ice or unfrozen water (Xu et al., 2010). Thus, in situ h frozen non
saline
= 0.09(
uw )
r
(11)
x
However, the reduction of unfrozen water in the frozen saline soil is equivalent to the increase in ice and/or crystal water according to the conservation of mass. Based on the above analysis, in-situ frost heave Δhfrozenin−situ can be expressed as: in situ h frozen = 0.09
r
uw
k
18(cr
cx r 1000
uw )
x
(12)
Eq. (12) degenerates to Eq. (11) in the condition of k = 0. For frozen saline soils, the deformation of sandy soils is the sum of in-situ frost heave and salt expansion, and the salt expansion remains calculated by Eq. (10), thus, the soil displacement in this state can be defined as:
= 0.09
r
in situ + h h frozen = h frozen salt expansion 18(cr r cx uw ) 18(cr r cx uw ) k x+ c k 1000 1000
uw
x
(13)
In Eq. (13), the first item and the second item represent the in-situ frost heave and salt expansion, respectively, and the first item indicates that the in-situ frost heave will be reduced by the formation of crystalline hydrates. In order to unify the expressions of soil displacement in the unfrozen state and frozen state, the ultimate form of the soil displacement in the freezing process can be obtained by combining with Eqs. (10) and (13), as follows:
h = 0.09
+
c
r
x
uw
k
18(cr
k
18(cr
cx r 1000
cx r 1000 uw )
uw )
x
x (14)
where ξ is supposed to be one in the frozen state or equal to zero in the unfrozen state. In Eq. (14), the deformation ① is contributed to the decrease in water content due to the formation of crystalline hydrate, the deformation ② is attributed to the increasing volume of crystalline hydrate, and the in-situ frost heave ④ is caused by the increase in ice crystals, respectively. Meanwhile, the soil deformation ③, salt expansion, is determined by ① and ②, which satisfies the equation ③ = ① + ②.
Fig. 1. Schematic diagram of the test apparatus. 3
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
Fig. 3. The variation of volumetric unfrozen water content versus temperature for saline sand soils with different salt contents.
designed temperature, the soil electrical resistance R, the unfrozen water content, and the displacement indicator were recorded. Meanwhile, the soil electrical resistivity ρ was obtained by ρ = RS/ Δx, where S was the cross-section area of the sample. Afterwards, the temperature of the incubator was adjusted to the next designed temperature and recorded corresponding test results. Additionally, the designed temperatures respectively were: 25 °C, 10 °C~1 °C (at interval of 1 °C), 0 °C~-15 °C (at interval of −0.5 °C), and a total of 42.
Fig. 2. Testing equipments, (a) thermocouples; (b) a Datataker 85G; (c) a moisture transducer; (d) a constant voltage DC power supply; (e) a displacement sensor.
3.2. Testing method In this study, the used material was sand soils with the particle size distribution of 0.5–1.0 mm. In order to eliminate the interference of original salinity in the soil, the sandy soil was soaked and washed with the deionized water (electrical conductivity ≤0.25 μS/m) after being dried by a stove to obtain non-saline sand soils. The sodium sulfate with a purity of > 99.8% was used. The design for salt content was as follows. The low salt contents were 0.2%, 0.5%, and 1%, and the high salt content was 3.5%. Among them, on account of the natural soil contained a small amount of salinity (Wu et al., 2016), the salt content was set to 0.2% for simulation of natural soil. Meanwhile, the target solution was first prepared at 25 °C to ensure complete solute dissolution. The testing procedures were as follows:
4. Model validation and discussion 4.1. Unfrozen water content The variation of the volumetric unfrozen water content with temperature in saline soils during the freezing process is obtained under varying salt contents (0.2%, 0.5%, 1.0%, 1.5%, and 3.5%), as shown in Fig. 3. In Fig.3, the volumetric water content decreased with the decrease of temperature in saline soils with the salt content of 1% and 3.5% at above-zero temperature. Besides, the reduction of water content has positive feedback on the initial salt content. This is primarily attributed to a declining trend of the solubility of sodium sulfate with a decrease in temperature, meanwhile, the soil with high salinity gives rise to more crystalline hydrate in the form of Na2SO4·10H2O or/and Na2SO4·7H2O to absorb pore water during the freezing process. Then, the unfrozen water content decreases rapidly due to the formation of pore ice and more crystalline hydrates being in the temperature range from 0 °C ~ −3.5 °C. Subsequently, the volumetric unfrozen water content is ultimately maintained at about 5% and decreases slightly as the salt content increase. So we deduce that the ultimate unfrozen water content is basically not subject to the influence of the initial salt content. The cooling curves of saline soils with various salt contents are shown in Fig.4. The temperature fluctuation occurs in the region (I), which results from the heat released from phase transition between water and ice (Lai et al., 2016). Thus, the salt contents were 0.2%, 0.5%, 1% and 3.5%, with the freezing temperatures of soils being approximately −0.76 °C, −1.25 °C, −1.5 °C and −1.3 °C, respectively. The freezing temperature decreases first and then increases as the salt content increases due to the existence of two kinds of crystalline hydrates in the soil (Xiao et al., 2018). However, the cooling curve with 3.5% salt content shows two temperature fluctuation regions, where region (II) in the positive temperature segment is contributed to the
(1) The prepared non-saline sand soils were poured into three cylindrical moulds (a height of 5 cm and a diameter of 5.15 cm) to derive soil samples with a dry density of 1.57 g/cm3. Then, the soil sample was saturated by the solution (obtained by deionized water and a target salt content) using a vacuum device with a saturated water content of 24.54%. (2) The incubator was set to be the first designed temperature of 25 °C. Then 3 samples with moulds were placed in the incubator and labelled as samples #1, #2 and #3, respectively. Firstly, three temperature sensors were inserted into sample #1 at predetermined intervals along the height of the soil sample to monitor temperature changes in the soil during freezing, and the data measured by the middle-temperature sensor is used as the basis for drawing the cooling curve. The moisture transducer was then inserted into sample #2 through the cavity reserved in the upper copper plate. Finally, copper electrodes were added at the upper and lower ends of sample #3, with the displacement sensor fixed at the upper end of the sample. It is worth noting that a layer of uniform conductive copper paste was applied between the copper electrode and the soil, and a layer of uniform film was positioned between the upper-end electrode and the displacement sensor to reduce contact resistance. (3) When three temperature sensors in sample #1 were stabilized at the 4
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
Table 1 The calculation parameters required by the proposed model. Parameters
Value
cr
0.0598(salt content: 0.1496(salt content: 0.2993(salt content: 1.0474(salt content: 0.4 25 2.2 × 10−4 50
θr Tr VNa2SO4·10H2O Δx
Unit 0.2%) 0.5%) 1%) 3.5%)
mol/L
m3/m3 o C m3/mol mm
the soil electrical resistivity increases significantly compared to other salinity soils, which is attributed to the noticeable reduction of pore water content caused by the crystal water. Therefore, the electrical resistivity of soil with high salinity is affected by temperature and water. Subsequently, in the frozen state, the soil electrical resistivity increases significantly, which is determined by temperature, unfrozen water content, and pore solution concentration in most cases. To be specific, the reduction of conductive path by ice and temperature common contributes to a rapid increase in electrical resistivity (Tang et al., 2018), but the conductive particle (the solution concentration) has negative feedback with the soil electrical resistivity (Li et al., 2012).
Fig. 4. Cooling curves of saline sand soils with various salt contents.
heat released by salt crystallization, so the salt crystallization temperature is around 10.3 °C. Meanwhile, salt crystallization fails to trigger significant temperature fluctuations for saline soils with salt content between 0.2% and 1%. There are two major reasons to explain this phenomenon. Firstly, the latent heat released by salt crystallization is less compared to that released by ice-water phase change for saline soils with low salt content. Secondly, salt crystallization and ice-water phase transition occur simultaneously in the region (I) (Lai et al., 2016).
4.3. Salt expansion and frost heaving The sodium sulfate is taken as the research object, and we assume that the form of crystallized salt hydrate in the saline soils is limited to Na2SO4·10H2O during the cooling process. Besides, the calculation parameters required by the proposed model are listed in Table 1. According to the datum in Figs. 3, 5 and Eq. (8), the pore solution concentration in saline soils with varying salt contents in the cooling process can be determined, and then the volumetric crystallized salt content can be calculated by Eq. (9), as shown in Fig. 6. It can be seen from Fig. 6 that the variations of pore solution concentration and the volumetric crystallized salt content appear the opposite characteristic as the temperature decline. When the salt content reaches 0.2%, 0.5% and 1% (in Fig. 6a, b and c), the pore solution concentration remains approximately unchanged in the unfrozen state and therewith to a brief rise near the freezing temperature. Then, it falls sharply before a gradual decrease as the temperature declines after the freezing temperature. The above-mentioned characteristic of change in the pore solution concentration can be accounted for as follow: Broadly speaking, the water content remains unchanged in the unfrozen state,
4.2. Normalized electrical resistivity The normalized electrical resistivity, the ratio of the soil electrical resistivity to the initial soil electrical resistivity, is reciprocal to the normalized electrical conductivity. So the variation of the normalized electrical resistivity versus temperature under varying salt contents is shown in Fig. 5. The soil normalized electrical resistivity increases as temperature declines during the freezing process in Fig. 5, and the inflexion point as the freezing temperature (Wu et al., 2017) is close to the observed value shown in Fig. 3. In the unfrozen state, the soil normalized electrical resistivity increases slowly in consideration of the reduced migration velocity of conductive particles due to the decrease in temperature (Tang et al., 2018). However, for saline soil with high salinity (3.5%),
Fig. 5. The variation of normalized electrical resistivity versus temperature for saline sand soils with different salt contents. 5
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
Fig. 6. The variations of the pore salt concentration and the volumetric crystallized salt content in freezing process. (a) salt content of 0.2%, (b) salt content of 0.5%, (c) salt content of 1.0%, (d) salt content of 3.5%.
as result of which the concentration does not change significantly, despite a slight fluctuation in the pore solution concentration resulting from the error caused by using our method (accumulation of tests error). In the frozen state, the concentration increases instantaneously due to the decline in unfrozen water content. Subsequently, a substantial amount of salt crystals are generated (the black line in the Fig. 6), which causes the concentration to be decreased rapidly. Then, salt crystallization continues the trend of slow-paced precipitation, thus resulting in a continued decrease in the pore solution concentration. Nevertheless, the pore solution concentration showed a decreasing trend during the whole freezing process for saline soil with a 3.5% salt content (in Fig. 6d). The saline soil with high salinity gives rise to a greater amount of crystalline salt hydrates, leading to the reduction of soluble salts. Moreover, the reduction of water content is contributed to by the formation of crystalline hydrate throughout the process and ice in the frozen state. That is to say, both solvent and solute are in decline, which accounts for a platform stage on the variation of the pore solution concentration in the unfrozen state. Then, it is considered that the effect of reduced solute on concentration is more significant than that of the solvent, leading to a gradual decline in the concentration until the end. According to Eq. (14), the deformation characteristics of saline soils can be calculated and then compared with the measured results in the cooling process, as shown in Fig. 7. In Fig. 7, the measured soil deformation with different salt contents is broadly consistent with the value calculated by our model. However,
due to the development of crystallized salt, the sodium sulfate crystal firstly forms a metastable state of Na2SO4·7H2O, and then transforms the generation of Na2SO4·10H2O in a stable state with further absorption of water (Xiao et al., 2018), as a result of which there are two types of crystalline hydrates in soil during the freezing process. Therefore, the value calculated by our model shows a slight deviation from the measured value as considering only Na2SO4·10H2O in the soil. Meanwhile, the soil deformation can be divided into three stages, and the saline soils with low salt contents (0.2%, 0.5%, and 1%) demonstrate similar variation characteristics. In stage (I), there is no soil displacement deformation occurring due to the absence of salt crystallization in the soil from 25 °C to the freezing temperature shown as black lines in Fig. 6a, b, and c. Then in stage (II), the soil deformation increases rapidly on account of the increase in salt crystals (Fig. 6a, b, and c) and ice crystals from the freezing temperature to −3.5 °C. Subsequently, in stage (III) from −3.5 °C to −15 °C, the soil deformation slowly increases and then stabilizes gradually, which suggests that the salt crystals and the ice content are stable. This conforms to the variations of the crystallized salt as shown in Fig. 6 and the unfrozen water as illustrated in Fig. 5a. However, for soils with high salt content of 3.5%, the characteristic of soil deformation is different from that of soils with lower salt content. The soil deformation occurs through the cooling process, as shown in Fig. 7d. The soil deformation is roughly 0.55 mm in stage (I), which is attributed to salt solubility that gives rise to crystallized salt and accounts for 27.09% of the ultimate deformation. The variation of soil deformation is consistent with other soils with low salt contents in the 6
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
Fig. 7. The variation of saline sand soils displacement with different salt content during freezing process. (a) salt content of 0.2%, (b) salt content of 0.5%, (c) salt content of 1.0%, (d) salt content of 3.5%.
second and third stages. In Fig. 7, the in-situ frost heaving ④ and the deformation ② contribute to soil deformation, while the deformation ① exerts an inhibitory effect on the soil deformation. The deformation ① and the insitu frost heaving ④ decrease as the salt content increases, but the deformation ② is the opposite. Simultaneously, it can be seen that salt expansion ③ and total soil deformation undergo a similar variation process. When salt contents are 0.2%, 0.5%, 1% and 3.5%, the contribution of salt expansion ③ to the final soil deformation is approximately 2.933%, 7.019%, 13.072% and 38.245%, respectively. The relationship between the salt content and the contribution of the salt expansion is illustrated in Fig. 8, which satisfies Eq. (15) as follows:
=
0.00917cm2 + 0.14135cm
(15)
where η is the contribution of salt expansion to soil total displacement, and cm is the initial salt content (the mass ratio of salt to dry soil). As indicated intuitively by Eq. (15), the contribution of salt content to soil deformation is significantly improved as the increase of salt content, so salt expansion cannot be ignored. However, the contribution of in-situ frost heaving decreases with the increases of salt content due to more pore water being absorbed by more crystalline hydrates. The variations of the salt expansion ratio, the salt-frost heaving
Fig. 8. Relationship between the contribution of salt expansion to soil total displacement and the initial salt content.
7
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
Fig. 9. Deformation response of saline sand soils in freezing process (a) salt content of 0.2%, (b) salt content of 0.5%, (c) salt content of 1.0%, (d) salt content of 3.5%.
ratio, and the rate of soil deformation to temperature under varying salt contents are shown in Fig. 9, respectively. A substantial amount of pore water is absorbed during the formation process of crystalline hydrate, which causes the in-situ frost heave ratio to be reduced. Therefore, the salt-frost heaving ratio slightly improves from 3.064% to 4.06% when the salt content increases from 0.2% to 3.5% in Fig. 9. The rate of soil deformation to temperature varies significantly in stage (II), which first decreases and then increases with the decrease of temperature. This is due to the frost heaving and salt expansion occurring in stage (II) as shown in Fig.7. For soil with a high salinity of 3.5%, the rate of soil deformation to temperature shows a slowly decreased in stage (I), which consistent with the measured soil deformation shown in Fig. 7d. Meanwhile, we conclude daring that the salt-frost heaving ratio will increase based on ice lens growth with the assistance of water supplement for natural soils (Ji et al., 2018).
(2) For a higher salt content of 3.5%, the soil deformation occurs throughout the freezing process and its contribution in stage (I) to the ultimate deformation reaches up to 27.09%. Thus, for in-situ testing, there is a necessity to enhance the monitor of deformation occurring in both stages (II), and (I) for high salinity soils. (3) Salt expansion and frost heave can be calculated by our model, respectively, and the contribution of the salt expansion to the soil deformation is on the increase gradually with salt content, especially at the time when it reaches 38.245% for the salt content of 3.5%. Meanwhile, the contribution of the salt expansion and the initial salt content conform to the quadratic relation. Moreover, a mathematical description of the pore solution concentration by the proposed model can be applied to further study on the salt migration induced by the freezing or/and thawing process. (4) For saline soils with sodium sulfate, the ultimate unfrozen water content is insignificantly affected by the initial salt content and slightly decreases as the salt content increase. Meanwhile, the saltfrost heaving ratio insignificantly increases with salt content due to the reduced ice formation without water supply. Therefore, we will verify the applicability of our model under the condition of water supply for different soils in the future study.
5. Conclusions A new testing method or mathematical model was proposed to predict the frost heaving and salt expansion during the cooling process. Meanwhile, a series of experiments were performed on the variations of soil electrical conductivity, unfrozen water content, and deformation with temperature for freezing saline soils with varying salt contents. The main conclusions were drawn as follows:
Acknowledgement This research was support by the National Natural Science Foundation of China (grant no. 41772338, grant no. 41672343, grant no. 51104146, and grant no. 51204164) and 111 Project (grant no. B14021), Open Fund of State Key Laboratory of Frozen Soil Engineering (grant no. SKLFSE201704), and I am especially indebted to my best friend, “0.5”, for her encouragement and support!
(1) The excellent consistency between the predicted soil displacements obtained by the mathematical model and the measurement results validates our model for freezing saline soils. Meanwhile, the variation of saline soil deformation with temperature can be divided into three stages. In stage (I), the soil deformation is only affected by salt expansion deformation from 25 °C to the freezing temperature. Then, the soil deformation develops rapidly in stage (II) between the freezing temperature and − 3.5 °C, and then basically remains unchanged or shows a slight increase in stage (III).
Declaration of Competing Interest We declare that we have no financial and personal relationships 8
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
with other people or organizations that can inappropriately influence our work; there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.
quality of ice crystal during the freezing concentration for the brackish water. Desalination 260 (1), 231–238. Ma, Q.G., Lai, Y.M., Zhang, M.Y., et al., 2017. Model test study on the anti-saline effect of the crushed-rock embankment with impermeable geotextile in frozen saline soil regions. Cold Reg. Eng. 141, 86–96. Marie, N., Gilles, G., Philippe, L., et al., 2016. Electrical and thermal behavior of unsaturated soils: experimental results. J. Appl. Geophys. 128, 115–122. Niu, X.R., Gao, J.P., 2015. Expression for volume change of sulphate saline soil considering salt expansion and frost heave. Chin. J. Geotech. Eng. 37 (4), 755–760 (in Chinese). Nixon, J.F., 2011. Discrete ice lens theory for frost heave beneath pipelines. Can. Geotech. J. 29 (3), 487–497. Oldenborger, G.A., LeBlanc, A.M., 2018. Monitoring changes in unfrozen water content with electrical resistivity surveys in cold continuous permafrost. Geophys. J. Int. 215, 965–977. Padilla, F., Villeneuve, J.P., 1992. Modeling and experimental studies of frost heave including solute effects. Cold Reg. Sci. Technol. 20 (2), 183–194. Shan, W., Liu, Y., Hu, Z.G., et al., 2015. A model for the electrical resistivity of frozen soils and an experimental verification of the model. Cold Reg. Eng. 119, 75–83. Tang, L.Y., Wang, K., Jin, L., et al., 2018. A resistivity model for testing unfrozen water content of frozen soil. Cold Reg. Eng. 153, 55–63. Wan, X.S., You, Z.M., Wen, H.Y., et al., 2017. An experimental study of salt expansion in sodium saline soils under transient conditions. J. Arid Land 9 (6), 865–878. Weiss, J., Snyder, K., Bullard, J., et al., 2013. Using a saturation function to interpret the electrical properties of partially saturated concrete. J. Mater. Civ. Eng. 25 (8), 1097–1106. Wu, Q.B., Zhu, Y.L., 2002. Experimental studies on salt expansion for coarse grain soil under constant temperature. Cold Reg. Eng. 34 (2), 59–65. Wu, D.Y., Lai, Y.M., Ma, Q.G., et al., 2016. Model test study of water and salt migration and deformation characteristics in seasonally frozen soil. Rock Soil Mech., 32(2), 465–476 (in China). Wu, Y.X., Nakagawa, S., Kneafsey, T.J., et al., 2017. Electrical and seismic response of saline permafrost soil during freeze-Thaw transition. J. Appl. Geophys. 146, 16–26. Xiao, Z.A., Lai, Y.M., Zhang, M.Y., 2018. Study on the freezing temperature of saline soil. Acta Geotech. 13 (1), 195–205. Xu, X.Z., Wang, J.C., Zhang, L.X., et al., 1995. Mechanisms of Frost Heave and Salt Expansion of Soils. Science Press, Beijing. Xu, X.Z., Wang, J.C., Zhang, L.X., 2010. Frozen Soil Physics. Science Press, Beijing. Zhang, S., Sheng, D.C., Zhao, G.T., Niu, F.J., He, Z.Y., 2014. Analysis of frost heave mechanisms in a high-speed railway embankment. Can. Geotech. J. 53 (3), 520–529. Zhang, Y.H., Zhang, Y.F., Liu, K., Pan, L., 2016. Natural saline soil salt-frost heave cold end step continuous cooling and experimental study on water and salt migration. Sci. Technol. Eng. 31, 051. Zhao, X.W., Li, X., Liu, J.K., Zhang, Y., 2013. The effect of confining boundary on soil deformation in one dimensional frost heave tests and the theoretical volume correction. Sci. Cold Arid Regions 5, 587–590. Zhou, Y., Guo, D., Qiu, G., et al., 2000. Geocryology in China. Science Press, Beijing.
References Archie, G.E., 1942. The electrical resistivity log as an aid in determining some reservoir characteristics. Trans. Am. Inst. Min. Metall. Eng. 146, 54–61. Campbell, R.B., Bower, C.A., Richards, L.A., 1949. Change of electrical conductivity with temperature and the relation of osmotic pressure to electrical conductivity and ion concentration for soil extracts. Soil Sci. Soc. Am. J. 66–69. Choo, H., Burns, S.E., 2014. Review of Archie's equation through theoretical derivation and experimental study on uncoated and hematite coated soils. J. Appl. Geophys. 105, 225–234. Chu, Y., Liu, S.Y., Bate, B., et al., 2018. Evaluation on expansive performance of the expansive soil using electrical responses. J. Appl. Geophys. 148, 265–271. Fang, J.H., Li, X., Liu, J.K., et al., 2018. The crystallization and salt expansion characteristics of a silty clay. Cold Reg. Eng. 155, 63–73. Gao, J.P., Wu, J.H., Deng, Y.S., et al., 1996. A multi-factor study of salt expansion of sulphate salty soil. J. Glaciol. Geocryol. 18 (2), 170–177. Glover, P.W.J., Gomez, J.B., Meredith, P.G., et al., 1997. Damage of saturated rocks undergoing triaxial deformation using complex electrical conductivity measurements: experimental results. Phys. Chem. Earth 22 (1–2), 57–61. Hayley, K., Bentley, L.R., Gharibi, M., et al., 2007. Low temperature dependence of electrical resistivity: Implications for near surface geophysical monitoring. Geophys. Res. Lett. 34, L18402. Hayley, K., Bentley, L.R., Gharibi, M., 2009. Time-lapse electrical resistivity monitoring of salt-affected soil and groundwater. Water Resour. Res. 45 (W07425). Ji, Y.K., Zhou, G.Q., Zhao, X.D., et al., 2017. On the frost heaving-induced pressure response and its dropping power-law behaviors of freezing soils under various restraints. Cold Reg. Eng. 142, 25–33. Ji, Y.K., Zhou, G.Q., Zhou, Y., et al., 2018. A separate-ice based solution for frost heavinginduced pressure during coupled thermal-hydro-mechanical processes in freezing soils. Cold Reg. Eng. 147, 22–33. Konrad, J.M., Mccammon, A.W., 1990. Solute partitioning in freezing soils. Can. Geotech. J. 67, 726–736. Lai, Y.M., Wan, X.S., Zhang, M.Y., 2016. An experimental study on the influence of cooling rates on salt expansion in sodium sulfate soils. Cold Reg. Eng. 124, 67–76. Li, G., Yu, W., Ma, W., et al., 2009. Experimental study of characteristics of frost and salt heaves of saline highway foundation soils in seasonally frozen regions in Gansu Province. Rock Soil Mech. 38 (8), 2276–2280. Li, L., Zhou, Z.H., Zhang, H.Y., 2012. Experimental study on the electrical resistivity of saline soils. Environ. Eng. 30, 498–503 (In Chinese). Luo, C.S., Chen, W.W., Han, W.F., 2010. Experimental study on factors affecting the
9
Contents lists available at ScienceDirect
Cold Regions Science and Technology journal homepage: www.elsevier.com/locate/coldregions
A new method for estimating salt expansion in saturated saline soils during cooling based on electrical conductivity
T
Rui Tang, Guoqing Zhou , Jianzhou Wang, Guangsi Zhao, Zejin Lai, Fengyuan Jiu ⁎
State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining & Technology, Xuzhou 221008, China
ARTICLE INFO
ABSTRACT
Keywords: Salt expansion Electrical conductivity Saline soils Frost heave Freezing process
Salt expansion is known as a type of soil deformation induced by salt crystallization. In order to reveal the development of salt expansion or salt crystallization in saline soils during the freezing process, we propose a new model for estimating the variation of the pore solution concentration according to the strong dependence between electrical conductivity and concentration. Moreover, the proposed model can further calculate the crystallized salt content, salt expansion, and frost heave during the cooling process. Meanwhile, a series of experiments are conducted on the unfrozen water content, electrical conductivity, and deformation of saline soil with different salinity. The results show that the deformation of saline soil undergoes three stages and increases rapidly in the second stage. Meanwhile, the soil deformation can be well predicted by our model and has similar characteristics with the salt expansion calculated by our model during the cooling process. Salt expansion mainly occurs in the latter two stages for the saline soil with low salt content and throughout the process for the saline soil with high salt content. Meanwhile, the contribution of the ultimate salt expansion to the soil deformation increases significantly with the increase of the salt content, which conforms to the parabolic relationship. Thus, the prediction of crystallized salt by this model is conducive to monitoring salt expansion in the field and laboratory, and further to reveal the mechanism of salt expansion in saline soils.
1. Introduction The saline soil is widely distributed in the northwestern region of China (Xu et al., 1995), and such areas are often located in seasonally frozen soil and/or permafrost regions (Zhou et al., 2000). So the salt expansion and frost heave will occur simultaneously in cold regions, causing difficult and complicated to predict the deformation of saline soils (Padilla and Villeneuve, 1992; Zhao et al., 2013; Fang et al., 2018). Meanwhile, the soil deformation caused by salt expansion and/or frost heave (Ji et al., 2017) in cold regions causes significant threat to operational safety of major engineering such as roads, railways and pipelines (Li et al., 2009; Ma et al., 2017; Zhang et al., 2014; Nixon, 2011). Therefore, it is necessary and urgent to study the characteristics of salt expansion and frost heave of saline soils during the freezing process. Many scholars (Fang et al., 2018; Lai et al., 2016; Wu and Zhu, 2002; Zhang et al., 2016) believed that the saline soil deformation was mainly affected by salt type, salt content, water content, solute migration, temperature, and cooling rate. Recently, the estimated models for salt expansion were obtained based on the phase diagram of the solution in soils (Niu and Gao, 2015; Xu et al., 1995; Gao et al., 1996). ⁎
Fang et al. (2018) adopt theoretical analysis, microstructure observation, and salt expansion tests, and derived the calculation formula of salt expansion in soil. Meanwhile, Wan et al. (2017) concluded that the predicted model based on solution phase diagram cannot accurately estimate the salt expansion at natural conditions, so the relationship between the supersaturation ratio and temperature was derived from the perspective of thermodynamics, and the effect of different cooling rates on the supersaturation ratio was also considered. However, the above studies were mainly focused on measurement temperatures at an above-zero or small range of subzero. Moreover, salt expansion in the unfrozen state and the ultimate soil deformation in the frozen state were merely measured, but the variations of salt expansion and frost heave are not separately obtained during the freezing process. Due to the decrease in temperature and unfrozen water content, the solution concentration is higher than the solubility to generate salt crystals. The content of salt crystal can be estimated from known unfrozen water content and solution concentration in soils according to the conservation of salt mass, and then salt expansion can be calculated. However, the main challenge is difficulty determine the pore solution concentration in soil. Hayley et al. (2009) wonderful obtained solute redistribution induced by moisture migration based on the variation of
Corresponding author. E-mail addresses: [email protected] (R. Tang), [email protected] (G. Zhou).
https://doi.org/10.1016/j.coldregions.2019.102943 Received 3 June 2019; Received in revised form 3 November 2019; Accepted 7 November 2019 Available online 09 November 2019 0165-232X/ © 2019 Elsevier B.V. All rights reserved.
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
electrical conductivity in saline soils. Thus, the above method is extended to estimate the solution concentration induced by soil freezing. In this paper, a mathematical model is proposed to characterize the variation of pore solution concentration with electrical conductivity in soils during the cooling process. Subsequently, the frost heaving and salt expansion in saline soils are mathematically achieved. Meanwhile, the variations of unfrozen water content, electrical conductivity, and soil deformation with variable salinity (0.2%, 0.5%, 1.0%, and 3.5%) are investigated and the parameters of our model are obtained. Then, with the assistance of the proposed model, a quantitative evaluation of the soil deformations is conducted by drawing the comparison with experimental data. The results may be conducive to revealing salt expansion and provide a theoretical basis to monitor salt migration in cold regions.
concentration bears an association with solubility when in the unfrozen state. Therefore, the linear behaviour of Eq. (4) overestimates the electrical conductivity of pore solution. According to Weiss et al. (2013), the electrical conductivity of pore solution can be described by the following equations:
I 1+G I I=
=
Tr , w , c0 [1
+
(T
Tr )]
=F
Tr , w, c 0 [1
+
(T
Tr )] S n
(2)
T , s, cx
Tr , w, cx
=
T , s, cx
Tr , s, cx
Tr , s, cx
Tr , s, c0
= [1 +
(T
Tr )]
Ix 1 + G I0 n S I0 1 + G Ix
(7)
According to Eq. (7), the variation of the ionic strength in the pore solution during the cooling process can be given as follows:
2A + A2 G 2 + AG A2 G 2 + 4A 2 1 I0 T , s, cx A= S (T Tr ) 1 + G I0 Tr , s, c0 1 + Ix =
(3)
n
(8)
In Eq. (8), the ionic strength can be determined through the variations of soil electrical conductivity and unfrozen water content, and the pore solution concentration can be calculated by combining salt types and Eq. (5b) 2.3. Estimation of salt expansion and frost heaving For different types of salts, there are possibly multiple salt crystals arising from the salt crystallization process. Therefore, we assume that there is only one type of crystallized salt in the freezing process. Then, based on the analysis conducted in Section 2.2, the volumetric crystallized salt content can be obtained in the freezing process based on the conservation of mass.
uw initial
=
Tr , s, c 0
Nevertheless, soil electrical conductivity is subject to significant influence from temperature, water content and soil pore concentration (Li et al., 2012). Besides, the pore salinity concentration is changed as a result of including the reduction of unfrozen water content (the reducing of solvent) and the variation in the solubility of salt (change of the solute content) in freeing process. Moreover, the changes in unfrozen water content and the pore concentration both occur and affect each other. Considering the effect of salinity, some authors believed that the linear electrolyte with unfrozen water content due to ionic exclusion (Oldenborger and LeBlanc, 2018; Wu et al., 2017). Tr , w, c 0
(6)
In the unfrozen state, the solubility of salt declines as temperature decreases, thus leading to salt crystallization. Then, as a form of crystalline hydrate, the crystallized salt causes a decline in water content. Subsequently, the unfrozen water content is in decline gradually in the freezing state, the solutes are removed from the ice into the unfrozen water, and the potential crystalline hydrates may accelerate the reduction of the unfrozen water content. This makes the variation of pore solution concentration and the water content in soil inevitable throughout the freezing process. By combining Eqs. (3) and (6), the ratio of the soil electrical conductivity to the initial soil electrical conductivity can be obtained as follows:
where σTr, w, c0 indicates the electrical conductivity of the pore water with pore concentration c0 at the reference temperature Tr, and α denotes the slope compensation of the electrical conductivity versus temperature. Basically, α is approximated by 2.1% at Tr = 25 °C (Campbell et al., 1949). By combining Eqs. (1) and (2), the variation of soil electrical conductivity with temperature and water content can be obtained as follows: T , s, c0
Ix 1 + G I0 I0 1 + G Ix
2.2. Estimation of salt concentration in the pore solution
(1)
n
(5b)
where I0 and Ixare the ionic strengths of pore solution for the initial state and for the pore concentration cx in the cooling process, respectively.
where σT, s, c0 and σT, w, c0 represent the electrical conductivity of the soil and the electrical conductivity of the pore water with pore concentration c0 at the temperature T, respectively, S indicates the saturation, n is the saturation exponent, n = 2 (Oldenborger and Leblanc, 2018), and F refers to the dimensionless formation factor with regard to the pore connectivity. Meanwhile, the electrical conductivity of the pore water varies with temperature due to the changes in fluid viscosity. The linear model of the electrical conductivity versus temperature can be constructed in the following form (Campbell et al., 1949; Hayley et al., 2007): T , w , c0
=
Tr , w, c 0
Water content is considered as a significant factor for the soil electrical conductivity in many studies (Marie et al., 2016; Glover et al., 1997; Choo and Burns, 2014), and researchers generally used the following model based on Archie's law (Archie, 1942). T , w , c0 S
Zi2 ci i=1
Tr , w, cx
2.1. Theoretical basis
=F
N
where G is the electrical parameter, generally G = 0.4(mol/L)-0.5 for a typical pore solution (Weiss et al., 2013). I denotes the ionic strength of pore solution, which is determined by species with charge numbers Z and molar concentration c. Therefore, the variation in the electrical conductivity of pore solution can be written as follows:
2. Constructing mathematical model
T , s, c0
1 2
(5a)
(4)
where θuw and θinitial represent the volumetric unfrozen water content and initial volumetric water content, respectively. As argued by Konrad and Mccammon (1990), however, it is unlikely for solutes to be rejected completely from the pore ice, and ice crystals entrap solution into the ice in the form of “brine pockets” throughout freezing)(Luo et al., 2010). Moreover, the variation of pore solution
c
= (cr
r
cx
uw ) VMi Nj k H2O
(9)
where VMiNj⋅kH2O indicates the molar volume of the salt crystal MiNj· kH2O, (L/mol), i and j represent the numbers of cations M and anions N, and k represents the number of crystal water. Meanwhile, θr and cr are the volumetric water content and the solution concentration at the 2
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
reference temperature Tr，and cx is the solution concentration with the volumetric unfrozen water contentθuw. In the unfrozen state, the change in pore volume of the soil is only caused by salt expansion on account of the decline in the solubility of the salt and it includes two parts: Firstly, the increase in pore volume results from the salt crystallization. Secondly, the salt crystalline hydrate is possible to develop in the soil, and the crystal water is derived from pore water, thus causing a reduction in the water content. Therefore, the soil displacement in this state can be expressed as:
h unfrozen = hsalt expansion =
c
x
k
18(cr
cx r 1000
uw )
x
3. Testing apparatus and method 3.1. Testing apparatus Based on Eqs. (8) and (14), in order to determine frost heave and salt expansion of the soil, there was a necessity to obtain the variations of the unfrozen water content and the soil electrical conductivity with temperature. Meanwhile, the soil deformation test was also imperative monitored to verify the reliability of the prediction results. For soil resistivity testing, a two-phase electrode (Shan et al., 2015; Tang et al., 2018) and four-phase electrode (Chu et al., 2018) methods were often considered. However, the internal structure of the soil is possible to be affected by the four-phase electrode method, especially for small samples in the laboratory. Therefore, the two-phase electrode method was applied to measure soil resistivity in this research. The testing system was mainly composed of four modules: a temperature controlling system, a soil resistivity testing system, an unfrozen water content testing system, and a soil deformation monitoring system, as illustrated in Fig. 1. In Fig. 1, the temperature controlling system is comprised of two modules: (a) an incubator was employí to restrict sample temperature to the range from −30 °C to 40 °C with an accuracy of ± 0.05 °C; and (b) thermocouples (Fig. 2a) were applied to monitor soil temperature at varying intervals of 1 cm, 1.5 cm, 1.5 cm and 1 cm along the sample height with an error of ± 0.4% to ensure temperature uniformly. In the soil electrical resistivity testing system, the Datataker 85G (Fig. 2b) was taken for measurement of the soil resistivity, while the conductive copper paste was applied evenly on both ends of the sample surface and the electrode to mitigate contact resistance. Meanwhile, in order to ensure the stability of the test during the long period, the copper electrode and the copper wire were welded. In the unfrozen water content testing system, the moisture transducer (type: ECH2O EC-5) was applied to measure unfrozen water content with a temperature range from −40 °C to 60 °C and precision of 0.03 m3/m3, as shown in Fig. 2c. And a constant voltage DC power supply was made available to provide 3 V excitation power (Fig. 2d) for the moisture transducer. In the soil deformation monitoring system, one displacement sensor (type: ZS1100-DT40), with a range of 40 mm and an accuracy of ± 0.01 mm, was installed at the top end of the sample, as shown in Fig. 2e.
(10)
where Δxindicates the height of the soil sample. Eq. (10) indicates that soil deformation is divided into two aspects. The first one is the increasing displacement as a result of salt crystals, and the second one is the reduced displacement causing by the crystal water. In the frozen state, the segregated ice is unlikely to appear under the condition in absence of water supplement and temperature gradient, and then water migration can be ignored in sandy soils. Therefore, the frost heave deformation Δhfrozen non‐salinein‐situ for non-saline sand soils depends upon the volume change of the in-situ ice or unfrozen water (Xu et al., 2010). Thus, in situ h frozen non
saline
= 0.09(
uw )
r
(11)
x
However, the reduction of unfrozen water in the frozen saline soil is equivalent to the increase in ice and/or crystal water according to the conservation of mass. Based on the above analysis, in-situ frost heave Δhfrozenin−situ can be expressed as: in situ h frozen = 0.09
r
uw
k
18(cr
cx r 1000
uw )
x
(12)
Eq. (12) degenerates to Eq. (11) in the condition of k = 0. For frozen saline soils, the deformation of sandy soils is the sum of in-situ frost heave and salt expansion, and the salt expansion remains calculated by Eq. (10), thus, the soil displacement in this state can be defined as:
= 0.09
r
in situ + h h frozen = h frozen salt expansion 18(cr r cx uw ) 18(cr r cx uw ) k x+ c k 1000 1000
uw
x
(13)
In Eq. (13), the first item and the second item represent the in-situ frost heave and salt expansion, respectively, and the first item indicates that the in-situ frost heave will be reduced by the formation of crystalline hydrates. In order to unify the expressions of soil displacement in the unfrozen state and frozen state, the ultimate form of the soil displacement in the freezing process can be obtained by combining with Eqs. (10) and (13), as follows:
h = 0.09
+
c
r
x
uw
k
18(cr
k
18(cr
cx r 1000
cx r 1000 uw )
uw )
x
x (14)
where ξ is supposed to be one in the frozen state or equal to zero in the unfrozen state. In Eq. (14), the deformation ① is contributed to the decrease in water content due to the formation of crystalline hydrate, the deformation ② is attributed to the increasing volume of crystalline hydrate, and the in-situ frost heave ④ is caused by the increase in ice crystals, respectively. Meanwhile, the soil deformation ③, salt expansion, is determined by ① and ②, which satisfies the equation ③ = ① + ②.
Fig. 1. Schematic diagram of the test apparatus. 3
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
Fig. 3. The variation of volumetric unfrozen water content versus temperature for saline sand soils with different salt contents.
designed temperature, the soil electrical resistance R, the unfrozen water content, and the displacement indicator were recorded. Meanwhile, the soil electrical resistivity ρ was obtained by ρ = RS/ Δx, where S was the cross-section area of the sample. Afterwards, the temperature of the incubator was adjusted to the next designed temperature and recorded corresponding test results. Additionally, the designed temperatures respectively were: 25 °C, 10 °C~1 °C (at interval of 1 °C), 0 °C~-15 °C (at interval of −0.5 °C), and a total of 42.
Fig. 2. Testing equipments, (a) thermocouples; (b) a Datataker 85G; (c) a moisture transducer; (d) a constant voltage DC power supply; (e) a displacement sensor.
3.2. Testing method In this study, the used material was sand soils with the particle size distribution of 0.5–1.0 mm. In order to eliminate the interference of original salinity in the soil, the sandy soil was soaked and washed with the deionized water (electrical conductivity ≤0.25 μS/m) after being dried by a stove to obtain non-saline sand soils. The sodium sulfate with a purity of > 99.8% was used. The design for salt content was as follows. The low salt contents were 0.2%, 0.5%, and 1%, and the high salt content was 3.5%. Among them, on account of the natural soil contained a small amount of salinity (Wu et al., 2016), the salt content was set to 0.2% for simulation of natural soil. Meanwhile, the target solution was first prepared at 25 °C to ensure complete solute dissolution. The testing procedures were as follows:
4. Model validation and discussion 4.1. Unfrozen water content The variation of the volumetric unfrozen water content with temperature in saline soils during the freezing process is obtained under varying salt contents (0.2%, 0.5%, 1.0%, 1.5%, and 3.5%), as shown in Fig. 3. In Fig.3, the volumetric water content decreased with the decrease of temperature in saline soils with the salt content of 1% and 3.5% at above-zero temperature. Besides, the reduction of water content has positive feedback on the initial salt content. This is primarily attributed to a declining trend of the solubility of sodium sulfate with a decrease in temperature, meanwhile, the soil with high salinity gives rise to more crystalline hydrate in the form of Na2SO4·10H2O or/and Na2SO4·7H2O to absorb pore water during the freezing process. Then, the unfrozen water content decreases rapidly due to the formation of pore ice and more crystalline hydrates being in the temperature range from 0 °C ~ −3.5 °C. Subsequently, the volumetric unfrozen water content is ultimately maintained at about 5% and decreases slightly as the salt content increase. So we deduce that the ultimate unfrozen water content is basically not subject to the influence of the initial salt content. The cooling curves of saline soils with various salt contents are shown in Fig.4. The temperature fluctuation occurs in the region (I), which results from the heat released from phase transition between water and ice (Lai et al., 2016). Thus, the salt contents were 0.2%, 0.5%, 1% and 3.5%, with the freezing temperatures of soils being approximately −0.76 °C, −1.25 °C, −1.5 °C and −1.3 °C, respectively. The freezing temperature decreases first and then increases as the salt content increases due to the existence of two kinds of crystalline hydrates in the soil (Xiao et al., 2018). However, the cooling curve with 3.5% salt content shows two temperature fluctuation regions, where region (II) in the positive temperature segment is contributed to the
(1) The prepared non-saline sand soils were poured into three cylindrical moulds (a height of 5 cm and a diameter of 5.15 cm) to derive soil samples with a dry density of 1.57 g/cm3. Then, the soil sample was saturated by the solution (obtained by deionized water and a target salt content) using a vacuum device with a saturated water content of 24.54%. (2) The incubator was set to be the first designed temperature of 25 °C. Then 3 samples with moulds were placed in the incubator and labelled as samples #1, #2 and #3, respectively. Firstly, three temperature sensors were inserted into sample #1 at predetermined intervals along the height of the soil sample to monitor temperature changes in the soil during freezing, and the data measured by the middle-temperature sensor is used as the basis for drawing the cooling curve. The moisture transducer was then inserted into sample #2 through the cavity reserved in the upper copper plate. Finally, copper electrodes were added at the upper and lower ends of sample #3, with the displacement sensor fixed at the upper end of the sample. It is worth noting that a layer of uniform conductive copper paste was applied between the copper electrode and the soil, and a layer of uniform film was positioned between the upper-end electrode and the displacement sensor to reduce contact resistance. (3) When three temperature sensors in sample #1 were stabilized at the 4
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
Table 1 The calculation parameters required by the proposed model. Parameters
Value
cr
0.0598(salt content: 0.1496(salt content: 0.2993(salt content: 1.0474(salt content: 0.4 25 2.2 × 10−4 50
θr Tr VNa2SO4·10H2O Δx
Unit 0.2%) 0.5%) 1%) 3.5%)
mol/L
m3/m3 o C m3/mol mm
the soil electrical resistivity increases significantly compared to other salinity soils, which is attributed to the noticeable reduction of pore water content caused by the crystal water. Therefore, the electrical resistivity of soil with high salinity is affected by temperature and water. Subsequently, in the frozen state, the soil electrical resistivity increases significantly, which is determined by temperature, unfrozen water content, and pore solution concentration in most cases. To be specific, the reduction of conductive path by ice and temperature common contributes to a rapid increase in electrical resistivity (Tang et al., 2018), but the conductive particle (the solution concentration) has negative feedback with the soil electrical resistivity (Li et al., 2012).
Fig. 4. Cooling curves of saline sand soils with various salt contents.
heat released by salt crystallization, so the salt crystallization temperature is around 10.3 °C. Meanwhile, salt crystallization fails to trigger significant temperature fluctuations for saline soils with salt content between 0.2% and 1%. There are two major reasons to explain this phenomenon. Firstly, the latent heat released by salt crystallization is less compared to that released by ice-water phase change for saline soils with low salt content. Secondly, salt crystallization and ice-water phase transition occur simultaneously in the region (I) (Lai et al., 2016).
4.3. Salt expansion and frost heaving The sodium sulfate is taken as the research object, and we assume that the form of crystallized salt hydrate in the saline soils is limited to Na2SO4·10H2O during the cooling process. Besides, the calculation parameters required by the proposed model are listed in Table 1. According to the datum in Figs. 3, 5 and Eq. (8), the pore solution concentration in saline soils with varying salt contents in the cooling process can be determined, and then the volumetric crystallized salt content can be calculated by Eq. (9), as shown in Fig. 6. It can be seen from Fig. 6 that the variations of pore solution concentration and the volumetric crystallized salt content appear the opposite characteristic as the temperature decline. When the salt content reaches 0.2%, 0.5% and 1% (in Fig. 6a, b and c), the pore solution concentration remains approximately unchanged in the unfrozen state and therewith to a brief rise near the freezing temperature. Then, it falls sharply before a gradual decrease as the temperature declines after the freezing temperature. The above-mentioned characteristic of change in the pore solution concentration can be accounted for as follow: Broadly speaking, the water content remains unchanged in the unfrozen state,
4.2. Normalized electrical resistivity The normalized electrical resistivity, the ratio of the soil electrical resistivity to the initial soil electrical resistivity, is reciprocal to the normalized electrical conductivity. So the variation of the normalized electrical resistivity versus temperature under varying salt contents is shown in Fig. 5. The soil normalized electrical resistivity increases as temperature declines during the freezing process in Fig. 5, and the inflexion point as the freezing temperature (Wu et al., 2017) is close to the observed value shown in Fig. 3. In the unfrozen state, the soil normalized electrical resistivity increases slowly in consideration of the reduced migration velocity of conductive particles due to the decrease in temperature (Tang et al., 2018). However, for saline soil with high salinity (3.5%),
Fig. 5. The variation of normalized electrical resistivity versus temperature for saline sand soils with different salt contents. 5
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
Fig. 6. The variations of the pore salt concentration and the volumetric crystallized salt content in freezing process. (a) salt content of 0.2%, (b) salt content of 0.5%, (c) salt content of 1.0%, (d) salt content of 3.5%.
as result of which the concentration does not change significantly, despite a slight fluctuation in the pore solution concentration resulting from the error caused by using our method (accumulation of tests error). In the frozen state, the concentration increases instantaneously due to the decline in unfrozen water content. Subsequently, a substantial amount of salt crystals are generated (the black line in the Fig. 6), which causes the concentration to be decreased rapidly. Then, salt crystallization continues the trend of slow-paced precipitation, thus resulting in a continued decrease in the pore solution concentration. Nevertheless, the pore solution concentration showed a decreasing trend during the whole freezing process for saline soil with a 3.5% salt content (in Fig. 6d). The saline soil with high salinity gives rise to a greater amount of crystalline salt hydrates, leading to the reduction of soluble salts. Moreover, the reduction of water content is contributed to by the formation of crystalline hydrate throughout the process and ice in the frozen state. That is to say, both solvent and solute are in decline, which accounts for a platform stage on the variation of the pore solution concentration in the unfrozen state. Then, it is considered that the effect of reduced solute on concentration is more significant than that of the solvent, leading to a gradual decline in the concentration until the end. According to Eq. (14), the deformation characteristics of saline soils can be calculated and then compared with the measured results in the cooling process, as shown in Fig. 7. In Fig. 7, the measured soil deformation with different salt contents is broadly consistent with the value calculated by our model. However,
due to the development of crystallized salt, the sodium sulfate crystal firstly forms a metastable state of Na2SO4·7H2O, and then transforms the generation of Na2SO4·10H2O in a stable state with further absorption of water (Xiao et al., 2018), as a result of which there are two types of crystalline hydrates in soil during the freezing process. Therefore, the value calculated by our model shows a slight deviation from the measured value as considering only Na2SO4·10H2O in the soil. Meanwhile, the soil deformation can be divided into three stages, and the saline soils with low salt contents (0.2%, 0.5%, and 1%) demonstrate similar variation characteristics. In stage (I), there is no soil displacement deformation occurring due to the absence of salt crystallization in the soil from 25 °C to the freezing temperature shown as black lines in Fig. 6a, b, and c. Then in stage (II), the soil deformation increases rapidly on account of the increase in salt crystals (Fig. 6a, b, and c) and ice crystals from the freezing temperature to −3.5 °C. Subsequently, in stage (III) from −3.5 °C to −15 °C, the soil deformation slowly increases and then stabilizes gradually, which suggests that the salt crystals and the ice content are stable. This conforms to the variations of the crystallized salt as shown in Fig. 6 and the unfrozen water as illustrated in Fig. 5a. However, for soils with high salt content of 3.5%, the characteristic of soil deformation is different from that of soils with lower salt content. The soil deformation occurs through the cooling process, as shown in Fig. 7d. The soil deformation is roughly 0.55 mm in stage (I), which is attributed to salt solubility that gives rise to crystallized salt and accounts for 27.09% of the ultimate deformation. The variation of soil deformation is consistent with other soils with low salt contents in the 6
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
Fig. 7. The variation of saline sand soils displacement with different salt content during freezing process. (a) salt content of 0.2%, (b) salt content of 0.5%, (c) salt content of 1.0%, (d) salt content of 3.5%.
second and third stages. In Fig. 7, the in-situ frost heaving ④ and the deformation ② contribute to soil deformation, while the deformation ① exerts an inhibitory effect on the soil deformation. The deformation ① and the insitu frost heaving ④ decrease as the salt content increases, but the deformation ② is the opposite. Simultaneously, it can be seen that salt expansion ③ and total soil deformation undergo a similar variation process. When salt contents are 0.2%, 0.5%, 1% and 3.5%, the contribution of salt expansion ③ to the final soil deformation is approximately 2.933%, 7.019%, 13.072% and 38.245%, respectively. The relationship between the salt content and the contribution of the salt expansion is illustrated in Fig. 8, which satisfies Eq. (15) as follows:
=
0.00917cm2 + 0.14135cm
(15)
where η is the contribution of salt expansion to soil total displacement, and cm is the initial salt content (the mass ratio of salt to dry soil). As indicated intuitively by Eq. (15), the contribution of salt content to soil deformation is significantly improved as the increase of salt content, so salt expansion cannot be ignored. However, the contribution of in-situ frost heaving decreases with the increases of salt content due to more pore water being absorbed by more crystalline hydrates. The variations of the salt expansion ratio, the salt-frost heaving
Fig. 8. Relationship between the contribution of salt expansion to soil total displacement and the initial salt content.
7
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
Fig. 9. Deformation response of saline sand soils in freezing process (a) salt content of 0.2%, (b) salt content of 0.5%, (c) salt content of 1.0%, (d) salt content of 3.5%.
ratio, and the rate of soil deformation to temperature under varying salt contents are shown in Fig. 9, respectively. A substantial amount of pore water is absorbed during the formation process of crystalline hydrate, which causes the in-situ frost heave ratio to be reduced. Therefore, the salt-frost heaving ratio slightly improves from 3.064% to 4.06% when the salt content increases from 0.2% to 3.5% in Fig. 9. The rate of soil deformation to temperature varies significantly in stage (II), which first decreases and then increases with the decrease of temperature. This is due to the frost heaving and salt expansion occurring in stage (II) as shown in Fig.7. For soil with a high salinity of 3.5%, the rate of soil deformation to temperature shows a slowly decreased in stage (I), which consistent with the measured soil deformation shown in Fig. 7d. Meanwhile, we conclude daring that the salt-frost heaving ratio will increase based on ice lens growth with the assistance of water supplement for natural soils (Ji et al., 2018).
(2) For a higher salt content of 3.5%, the soil deformation occurs throughout the freezing process and its contribution in stage (I) to the ultimate deformation reaches up to 27.09%. Thus, for in-situ testing, there is a necessity to enhance the monitor of deformation occurring in both stages (II), and (I) for high salinity soils. (3) Salt expansion and frost heave can be calculated by our model, respectively, and the contribution of the salt expansion to the soil deformation is on the increase gradually with salt content, especially at the time when it reaches 38.245% for the salt content of 3.5%. Meanwhile, the contribution of the salt expansion and the initial salt content conform to the quadratic relation. Moreover, a mathematical description of the pore solution concentration by the proposed model can be applied to further study on the salt migration induced by the freezing or/and thawing process. (4) For saline soils with sodium sulfate, the ultimate unfrozen water content is insignificantly affected by the initial salt content and slightly decreases as the salt content increase. Meanwhile, the saltfrost heaving ratio insignificantly increases with salt content due to the reduced ice formation without water supply. Therefore, we will verify the applicability of our model under the condition of water supply for different soils in the future study.
5. Conclusions A new testing method or mathematical model was proposed to predict the frost heaving and salt expansion during the cooling process. Meanwhile, a series of experiments were performed on the variations of soil electrical conductivity, unfrozen water content, and deformation with temperature for freezing saline soils with varying salt contents. The main conclusions were drawn as follows:
Acknowledgement This research was support by the National Natural Science Foundation of China (grant no. 41772338, grant no. 41672343, grant no. 51104146, and grant no. 51204164) and 111 Project (grant no. B14021), Open Fund of State Key Laboratory of Frozen Soil Engineering (grant no. SKLFSE201704), and I am especially indebted to my best friend, “0.5”, for her encouragement and support!
(1) The excellent consistency between the predicted soil displacements obtained by the mathematical model and the measurement results validates our model for freezing saline soils. Meanwhile, the variation of saline soil deformation with temperature can be divided into three stages. In stage (I), the soil deformation is only affected by salt expansion deformation from 25 °C to the freezing temperature. Then, the soil deformation develops rapidly in stage (II) between the freezing temperature and − 3.5 °C, and then basically remains unchanged or shows a slight increase in stage (III).
Declaration of Competing Interest We declare that we have no financial and personal relationships 8
Cold Regions Science and Technology 170 (2020) 102943
R. Tang, et al.
with other people or organizations that can inappropriately influence our work; there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.
quality of ice crystal during the freezing concentration for the brackish water. Desalination 260 (1), 231–238. Ma, Q.G., Lai, Y.M., Zhang, M.Y., et al., 2017. Model test study on the anti-saline effect of the crushed-rock embankment with impermeable geotextile in frozen saline soil regions. Cold Reg. Eng. 141, 86–96. Marie, N., Gilles, G., Philippe, L., et al., 2016. Electrical and thermal behavior of unsaturated soils: experimental results. J. Appl. Geophys. 128, 115–122. Niu, X.R., Gao, J.P., 2015. Expression for volume change of sulphate saline soil considering salt expansion and frost heave. Chin. J. Geotech. Eng. 37 (4), 755–760 (in Chinese). Nixon, J.F., 2011. Discrete ice lens theory for frost heave beneath pipelines. Can. Geotech. J. 29 (3), 487–497. Oldenborger, G.A., LeBlanc, A.M., 2018. Monitoring changes in unfrozen water content with electrical resistivity surveys in cold continuous permafrost. Geophys. J. Int. 215, 965–977. Padilla, F., Villeneuve, J.P., 1992. Modeling and experimental studies of frost heave including solute effects. Cold Reg. Sci. Technol. 20 (2), 183–194. Shan, W., Liu, Y., Hu, Z.G., et al., 2015. A model for the electrical resistivity of frozen soils and an experimental verification of the model. Cold Reg. Eng. 119, 75–83. Tang, L.Y., Wang, K., Jin, L., et al., 2018. A resistivity model for testing unfrozen water content of frozen soil. Cold Reg. Eng. 153, 55–63. Wan, X.S., You, Z.M., Wen, H.Y., et al., 2017. An experimental study of salt expansion in sodium saline soils under transient conditions. J. Arid Land 9 (6), 865–878. Weiss, J., Snyder, K., Bullard, J., et al., 2013. Using a saturation function to interpret the electrical properties of partially saturated concrete. J. Mater. Civ. Eng. 25 (8), 1097–1106. Wu, Q.B., Zhu, Y.L., 2002. Experimental studies on salt expansion for coarse grain soil under constant temperature. Cold Reg. Eng. 34 (2), 59–65. Wu, D.Y., Lai, Y.M., Ma, Q.G., et al., 2016. Model test study of water and salt migration and deformation characteristics in seasonally frozen soil. Rock Soil Mech., 32(2), 465–476 (in China). Wu, Y.X., Nakagawa, S., Kneafsey, T.J., et al., 2017. Electrical and seismic response of saline permafrost soil during freeze-Thaw transition. J. Appl. Geophys. 146, 16–26. Xiao, Z.A., Lai, Y.M., Zhang, M.Y., 2018. Study on the freezing temperature of saline soil. Acta Geotech. 13 (1), 195–205. Xu, X.Z., Wang, J.C., Zhang, L.X., et al., 1995. Mechanisms of Frost Heave and Salt Expansion of Soils. Science Press, Beijing. Xu, X.Z., Wang, J.C., Zhang, L.X., 2010. Frozen Soil Physics. Science Press, Beijing. Zhang, S., Sheng, D.C., Zhao, G.T., Niu, F.J., He, Z.Y., 2014. Analysis of frost heave mechanisms in a high-speed railway embankment. Can. Geotech. J. 53 (3), 520–529. Zhang, Y.H., Zhang, Y.F., Liu, K., Pan, L., 2016. Natural saline soil salt-frost heave cold end step continuous cooling and experimental study on water and salt migration. Sci. Technol. Eng. 31, 051. Zhao, X.W., Li, X., Liu, J.K., Zhang, Y., 2013. The effect of confining boundary on soil deformation in one dimensional frost heave tests and the theoretical volume correction. Sci. Cold Arid Regions 5, 587–590. Zhou, Y., Guo, D., Qiu, G., et al., 2000. Geocryology in China. Science Press, Beijing.
References Archie, G.E., 1942. The electrical resistivity log as an aid in determining some reservoir characteristics. Trans. Am. Inst. Min. Metall. Eng. 146, 54–61. Campbell, R.B., Bower, C.A., Richards, L.A., 1949. Change of electrical conductivity with temperature and the relation of osmotic pressure to electrical conductivity and ion concentration for soil extracts. Soil Sci. Soc. Am. J. 66–69. Choo, H., Burns, S.E., 2014. Review of Archie's equation through theoretical derivation and experimental study on uncoated and hematite coated soils. J. Appl. Geophys. 105, 225–234. Chu, Y., Liu, S.Y., Bate, B., et al., 2018. Evaluation on expansive performance of the expansive soil using electrical responses. J. Appl. Geophys. 148, 265–271. Fang, J.H., Li, X., Liu, J.K., et al., 2018. The crystallization and salt expansion characteristics of a silty clay. Cold Reg. Eng. 155, 63–73. Gao, J.P., Wu, J.H., Deng, Y.S., et al., 1996. A multi-factor study of salt expansion of sulphate salty soil. J. Glaciol. Geocryol. 18 (2), 170–177. Glover, P.W.J., Gomez, J.B., Meredith, P.G., et al., 1997. Damage of saturated rocks undergoing triaxial deformation using complex electrical conductivity measurements: experimental results. Phys. Chem. Earth 22 (1–2), 57–61. Hayley, K., Bentley, L.R., Gharibi, M., et al., 2007. Low temperature dependence of electrical resistivity: Implications for near surface geophysical monitoring. Geophys. Res. Lett. 34, L18402. Hayley, K., Bentley, L.R., Gharibi, M., 2009. Time-lapse electrical resistivity monitoring of salt-affected soil and groundwater. Water Resour. Res. 45 (W07425). Ji, Y.K., Zhou, G.Q., Zhao, X.D., et al., 2017. On the frost heaving-induced pressure response and its dropping power-law behaviors of freezing soils under various restraints. Cold Reg. Eng. 142, 25–33. Ji, Y.K., Zhou, G.Q., Zhou, Y., et al., 2018. A separate-ice based solution for frost heavinginduced pressure during coupled thermal-hydro-mechanical processes in freezing soils. Cold Reg. Eng. 147, 22–33. Konrad, J.M., Mccammon, A.W., 1990. Solute partitioning in freezing soils. Can. Geotech. J. 67, 726–736. Lai, Y.M., Wan, X.S., Zhang, M.Y., 2016. An experimental study on the influence of cooling rates on salt expansion in sodium sulfate soils. Cold Reg. Eng. 124, 67–76. Li, G., Yu, W., Ma, W., et al., 2009. Experimental study of characteristics of frost and salt heaves of saline highway foundation soils in seasonally frozen regions in Gansu Province. Rock Soil Mech. 38 (8), 2276–2280. Li, L., Zhou, Z.H., Zhang, H.Y., 2012. Experimental study on the electrical resistivity of saline soils. Environ. Eng. 30, 498–503 (In Chinese). Luo, C.S., Chen, W.W., Han, W.F., 2010. Experimental study on factors affecting the
9