Experimental Study on Freezing Mode to Reduce Frost Heave

Abstract

Frost heave is an important factor affecting the safety and practicability of buildings in cold regions or artificial freezing engineering. In order to reduce frost heave, frost-susceptible silty clay was used in a one-dimensional frost heave testing system in three different freezing modes. The results show that, compared with the continuous freezing mode, frost heave in the intermittent freezing mode and the continuous-intermittent freezing mode is reduced by 14.4% and 43.6%, respectively. These results clearly demonstrate that frost heave can be restrained in the continuous-intermittent freezing mode more effectively than in the other two freezing modes. The periodic step growth on the frost heave curves in the continuous-intermittent freezing mode is the main reason for this, as explained by the frost heave theory in this paper. To acquire appropriate settings on the cold end temperature, frost heave tests were carried out at different amplitudes and periods of temperature change in the continuous-intermittent freezing mode. The frost heave decreases with the increase of the amplitude of temperature change and period of temperature change. The power function growth, periodic step growth and periodic polyline growth are shown on the frost heave curves at different periods of temperature change of 2, 4, and 8 h, respectively. Due to the good inhibition effect of frost heave, periodic step growth will be a better way to reduce frost heave, which is of great significance to the life cycle safety of buildings.

1. Introduction

Frost heave refers to the phenomenon in which the moisture in the soil freezes into ice and forms an ice lens, which causes the soil volume to expand during the process of soil freezing [1]. Excessive frost heave causes uneven deformation of the ground surface, damage to the foundation of upper structures, and damage to gas, electricity, communication, water supply and drain pipelines, causing great economic losses and safety risks [2]. From 1950–1970, many buildings and roads in Ulaanbaatar were badly damaged, and some were even destroyed as a result of frost heaving [3]. When frost action takes place under a pavement structure, distress in the form of distortions and swelling occurs. Distresses in the pavement can lead to a reduction in service life and poor ride quality for road users [4].

The artificial freezing method is a special construction technology that uses artificial refrigeration technology to freeze the water in the stratum, turning the natural rock and soil into frozen soil to increase the strength and stability to carry out underground engineering under the protection of a frozen wall [5]. The large-scale development of underground space and the utilization of deep energy by human beings will inevitably lead to a large number of underground projects, most of which are in water-bearing, weak, broken, low-strength, and low-stability geotechnical strata. The artificial freezing method is a reliable and mature technology; therefore, artificial freezing is the most common and effective construction method to use in particularly complex stratum and environmental conditions.

With the wide application of the artificial freezing method, frost heave has become a problem that must be faced in artificial ground freezing engineering. For a specific project, geological conditions and climatic temperature are predetermined, and the only controllable factor of the artificial freezing method is the freezing temperature. For frost heave to be reduced in the freezing process, the adjustment of the freezing temperature is the key factor, which is actually a choice of freezing mode.

Scholars have done lots of research on frost heave [6,7,8,9,10,11]. Since the 1960s, scholars had put upward a large number of frost heave theories [12,13,14,15,16,17,18,19,20,21] and mathematical models [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36], revealing the mechanism of frost heave and predicting the frost heave caused by soil freezing. The rapid development of frost heave theory and mathematical models have laid a solid foundation for the research of frost heave. Zhou [37] first proposed the idea of changing the freezing temperature to reduce frost heave and used a mathematical model to calculate and simulate soil frost heave in the condition of changing freezing temperature. Zhou [38] calculated frost heave by means of numerical simulation in the intermittent freezing mode, acquired the same conclusions as above, and explained the test results by frost heave theory. Relevant scholars [39,40] had further studied the effect of the intermittent freezing mode on frost heave. However, there is a lack of experimental data on frost heave in the intermittent freezing mode, and there are no relevant research results on the specific effects of amplitudes and periods of freezing temperature change on frost heave in the continuous-intermittent freezing mode.

In this paper, frost heave-susceptible silty clay was used to perform frost heave tests in a one-dimensional frost heave testing system developed by the State Key Laboratory for Geomechanics and Deep Underground Engineering. The freezing mode is divided into the continuous freezing mode, the intermittent freezing mode, and the continuous-intermittent freezing mode by controlling the exact moment at which the cold end temperature begins to change. The effects of the three different freezing modes on frost heave were analyzed and compared. After that, the effects of amplitudes and periods of temperature change on frost heave were studied in the continuous-intermittent freezing mode, which provided data support and theoretical basis for the inhibition of frost heave in the construction process of artificial freezing engineering.

2. Apparatus and Materials

2.1. Apparatus

As shown in Figure 1, the one-dimensional frost heave testing system consists of a thermostatic chamber, a plexiglass container, a measuring and data acquisition system, and a water supply system.

Figure 2a shows the thermostatic chamber, which consists of two constant temperature circulation devices and a constant temperature cabinet. The output temperature range of the constant temperature circulation device is −50–+90 °C, and the temperature fluctuation is ±0.05 °C, which can meet the temperature boundary conditions required for the frost heave tests. A constant ambient temperature is provided inside the constant temperature cabinet. There is an observation window on the side of the chamber, which is convenient for observing the soil samples and the working condition of the refrigeration system.

The wall thickness of the plexiglass container is 10 mm, and the inner dimension is 100 mm × 100 mm × 150 mm. Temperature measurements were taken by using sixteen resistance temperature detectors (RTDs) embedded in the soil samples (Figure 1 and Figure 2b). These RTDs were spaced at intervals of 1 cm, with the lowest RTD located on the surface of the warm end. The RTDs have a reported accuracy of ±0.05 °C. The transmittance of the plexiglass is 95%, and the state of the soil sample during the test can be observed. The plexiglass container is shown in Figure 2b.

The measuring and data acquisition system consists of three parts: (1) the displacement sensor YHD-50 was used to measure the frost heave with a range of 50 mm and an accuracy of 0.01 mm. YHD-50 is a differential resistance displacement sensor, which can convert displacement into an electrical signal; (2) the resistance temperature detectors (RTDs) MF5E-2.202F were used to measure the temperature in freezing soils with an accuracy of ±0.1%; and (3) the data acquisition system consists of data acquisition devices such as computers and the DataTaker (Figure 2c).

To eliminate the influence of gravity on the process of water replenishment, the siphon principle was applied to design the Mariotte bottle of the water supply system. The diameter and length of the Mariotte bottle are 30 mm and 600 mm, respectively.

2.2. Materials

Frost heave-susceptible silty clay was used for the frost heave tests. Silty clay, because of the extremely small size of its particles, or gradation, permits and encourages the flow of water by capillary action through its pores. Consequently, silty clay soils are considered amongst the most frost-susceptible. The results of soil grain analysis and the soil properties are shown in

Table 1. Analysis of soil grain.

Particle Size/mm.	>0.05	0.05~0.01	0.01~0.005	<0.005
Percentage/%	5.5	44.5	17	33

and

Table 2. Geotechnical testing results, where W_p is the plastic limit; W_L is the liquid limit; d_s is the specific gravity; and I_p is the plastic index.

Material	Wp(%)	WL(%)	ds	Ip
Silty clay	14.2	27.0	2.72	12.8

, respectively. Salt analysis showed that the soil sample had low small salt content, and the influence of salt on the soil freezing process could be ignored. The soil samples were remolded after drying and crushing. Particle distribution is shown in Figure 3.

2.3. Methods

2.3.1. Frost Heave Tests in the Three Different Freezing Modes

In order to study the effects of the three different freezing modes on frost heave, tests were carried out in continuous freezing mode, intermittent freezing mode and continuous-intermittent freezing mode respectively.

Table 3. Testing scheme.

Testing Number	Freezing Mode	Testing Description
A1	Continuous freezing mode	With water supply Without vertical loads
B1	Intermittent freezing mode
C1	Continuous-intermittent freezing mode

shows the testing scheme. The variation of the cold end temperature is shown in Figure 4.

Before each freezing test, soil samples were precooled so that the temperature of the samples was stable at about +12 °C to ensure that the initial temperature of the samples was consistent. After pre-cooling, the warm end temperature remained at +12 °C, and the cold end temperature was adjusted to adapt to different freezing modes. In continuous freezing mode, the cold end temperature remained at −22 °C until the end of the frost tests. The freezing temperature in artificial freezing engineering is usually set to −18–−26 °C. This is why we use −22 °C as the cold end temperature. In intermittent freezing mode, the cold end temperature was set to alternate between −18 °C and −26 °C every 4 h. In continuous-intermittent freezing mode, the cold end temperature remained at −22 °C at the beginning of the tests, and then the cold end temperature was set to alternate between −18 °C and −26 °C every 4 h after the freezing front remained constant in the soil samples. In this paper, the cold end temperature remained at −22 °C for about 935 min. Figure 4 shows the cold end temperature in different freezing modes.

2.3.2. Frost Heave Tests in the Continuous-Intermittent Freezing Mode

In order to study the effects of the amplitudes and periods of temperature change on frost heave, tests were carried out in the continuous-intermittent freezing mode. The testing scheme is shown in

Table 4. Testing scheme.

Testing Number	Warm End Temperature/°C	Cold End Temperature/°C	Amplitude of Temperature Change/°C	Period of Temperature Change/h
D1	+12	−22	±4	2
D2	+12	−22	±4	4
D3	+12	−22	±4	8
D4	+12	−22	±2	4

.

In order to keep the initial temperature of the soil samples consistent, the samples were precooled so that the temperature of the samples was stable at about +12 °C before conducting the frost heave tests. After the pre-cooling stage, the warm end temperature remained at +12 °C, and the cold end temperature remained at −22 °C at the beginning of the tests and then changed according to the testing scheme after the freezing depth of the soil samples was stable.

3. Results and Discussion

3.1. Effects of the Three Different Freezing Modes

As shown in Figure 5, the frost heave curves show a periodic step growth in both the intermittent freezing mode and the continuous-intermittent freezing mode. In each step growth period, the frost heave curves can be divided into growth period and nongrowth period. For example, in the continuous-intermittent freezing mode, the period from 1720 to 2200 min was a typical step growth period. Frost heave increased from 4.07 mm to 4.57 mm in the growth period from 1720 to 1940 min and stabilized from 4.57 mm to 4.60 mm in the nongrowth period from 1940 to 2200 min. The fluctuation of the freezing front was caused by the intermittently changed cold end temperature, which was the main reason why a nongrowth period exists in both the intermittent freezing mode and the continuous-intermittent freezing mode.

Figure 6 shows the freezing front and frost heave curves in the continuous-intermittent freezing mode. The freezing front curve shows a periodic zigzag. In each period of zigzag, the freezing front curve can be divided into an upward period and a downward period. It can be seen from Figure 6 that the upward period and the downward period on the freezing front curve correspond to the growth period and the nongrowth period on the frost heave curve, respectively. For example, during the period from 1720 to 1940 min, the freezing front moved upward from 9.771 cm to 10.386 cm away from the cold end, whereas it moved downward from 10.386 cm to 9.718 cm during the period from 1940 to 2200 min.

The schematic diagram of freezing soil is shown in Figure 7. The soil sample is divided into the frozen zone, frozen fringe, and unfrozen zone by the final ice lens and the freezing front. The relevant research results [12,13] showed that water migration in the frozen zone was negligible compared to that in the frozen fringe and the unfrozen zone. Therefore, the water migration in the frozen zone would not be considered in the following discussion. The frozen zone could be considered a passive zone, as water migration in the frozen zone was negligible. However, the unfrozen zone could be considered an active zone, as significant water migration occurred in this zone. The water migration in the active zone could be regarded as Darcy flow under equivalent water pressure [41]. The equivalent water pressure could be obtained by applying the Clausius–Clapeyron equation at the bottom of the final ice lens, as shown in Equation (1) [28,41,42,43]. Unfrozen water content and negative temperature always maintained a dynamic equilibrium and could be expressed by Formula (2) [44]. The moisture conductivity in the frozen fringe decreased exponentially with the decrease of unfrozen water content, as shown in Formula (3) [45]. We have

$$P=\frac{v_{\mathrm{S}}}{v_{\mathrm{L}}}{P}_{\mathrm{ob}}+\frac{LT}{T_0{v}_{\mathrm{L}}},$$

(1)

where $P$ is the equivalent water pressure in the active zone, $v_{\mathrm{S}}$ and $v_{\mathrm{L}}$ are specific volumes of solid and liquid phases, respectively, $P_{\mathrm{ob}}$ is the overburden pressure, $L$ is latent heat, $T$ is temperature, and $T_0=273.15$ $\mathrm{K}$. We also have

$${\theta }_{\mathrm{u}}=A{(T_0-T)}^B,$$

(2)

where ${\theta }_{\mathrm{u}}$ is the unfrozen water content, A and B are both testing parameters (Nixon, 1975, 1991): $A>0$ and $-1<B<0$. We also have

$$K_{\mathrm{f}}=K_{\mathrm{u}}{(\frac{{\theta }_{\mathrm{u}}}{n})}^{\gamma },$$

(3)

where $K_{\mathrm{f}}$ is the moisture conductivity in the frozen fringe, $K_{\mathrm{u}}$ is the moisture conductivity of the saturated soil, $n$ is the soil porosity, and $\gamma$ is a testing parameter (Cao, 2007), and $7<\gamma <9$.

The parameter $T$ at the bottom of the final ice lens raised with the increase of the cold end temperature (Hu, 2015; Zhou,2018). It is known from Equation (1) that the equivalent water pressure $P$ at the bottom of the final ice lens decreases as the parameter $T$ increases. The unfrozen water content ${\theta }_{\mathrm{u}}$ increases with the increase of temperature in the frozen fringe as $-1<B<0$ in Equation (2). The moisture conductivity $K_{\mathrm{f}}$ in the frozen fringe increases slowly with the increase of the unfrozen water content in the frozen fringe as $7<\gamma <9$ in Equation (3). In summary, the rising temperature of the cold end leads to a decrease of suction force at the bottom of the final ice lens, which finally causes a decrease in frost heave and a nongrowth period on the frost heave curve. Therefore, the downward period on the freezing front curve corresponds to the nongrowth period on the frost heave curve in the continuous-intermittent freezing mode.

As shown in Figure 5, the frost heave in test A1, B1, and C1 is 11.62 mm, 9.95 mm, and 6.55 mm, respectively. Compared with the frost heave in the continuous freezing mode, the frost heave in the intermittent freezing mode and the continuous-intermittent freezing mode was reduced by 14.4% and 43.6%, respectively. These results clearly demonstrated that the continuous-intermittent freezing mode could be more efficient than the intermittent freezing mode. The main reason for the above testing results is that the temperature gradient in the specimens in the continuous-intermittent freezing mode is more conducive to restraining the frost heave. Figure 8 shows the temperature gradient curves at different positions in the specimens. As shown in Figure 8, both in the intermittent and the continuous-intermittent freezing mode, the temperature gradient at 9 cm and 13 cm changed periodically with elapsed time. The temperature gradient in the continuous-intermittent freezing mode is less than it is in the intermittent freezing mode. For example, the average temperature gradient at 9 cm away from the cold end is 1.804 °C/cm and 2.153 °C/cm in the continuous-intermittent mode and the intermittent freezing mode, respectively; the average temperature gradient at 13 cm from the cold end is 2.276 °C/cm and 2.906 °C/cm, respectively. It can be seen from the Konrad segregation ice theory [46,47] that the relationship between the water absorption rate at the bottom of the final ice lens and the temperature gradient in the active zone in soil samples is shown in Equation (4). In the continuous-intermittent freezing mode, the temperature gradient in soil samples was less than it in the intermittent freezing mode, which results in a small water absorption rate and frost heaving rate. Thus, it is reasonable for a smaller frost heave to occur in the continuous-intermittent freezing mode than it in the intermittent freezing mode. Meanwhile, the above conclusion can be observed in Figure 5; i.e., there is a smaller slope on the frost heave curves during the growth period in the continuous-intermittent freezing mode than that in the intermittent freezing mode. We have

$$V=SP·gradT,$$

(4)

where $V$ is the water absorption rate, $gradT$ is the temperature gradient in the active zone, and $SP$ is the segregation potential.

3.2. Effects of the Amplitudes and Periods of Temperature Change on Frost Heave in the Continuous-Intermittent Freezing Mode

3.2.1. Effects of the Amplitudes of Temperature Change on Frost Heave

As shown in Figure 9, frost heave curves in different amplitudes of temperature change were obtained. The frost heave curves in different amplitudes of temperature change show a similar shape of periodic step growth in test D2 and D4. The frost heave curves consist of several periodic cycles, each of which can be divided into growth period and nongrowth period. The duration of each cycle is approximately 480 min. The lower temperature was kept for 4 h, and the higher temperature followed for the next 4 h. It is shown in Figure 9 that the second periodic cycle in the frost heave curve is from 600 min to 1080 min. Frost heave in test D2 and D4 increased from 1.83 mm and 0.95 mm to 2.36 mm and 1.33 mm, respectively, in the growth period from 600 to 840 min and stabilized in the nongrowth period from 840 to 1080 min. Due to the failure of the displacement sensor, the frost heave of test D2 slightly decreased from 2300 min to 2500 min. However, it seems that the slight decreases has no obvious impact on the test conclusion. The frost heave in test A1, D4, and D2 is 4.40 mm, 3.38 mm, and 2.55 mm, respectively. Compared with the frost heave in test A1, the frost heave in test D4 and D2 is reduced by 23.2% and 42.0%, respectively. The results show that frost heave decreases with the increase of amplitudes of temperature change.

Figure 10 shows the average temperature gradient in the unfrozen zone in specimens in test D4 and D2, in which the amplitude of temperature change is ±2 °C and ±4 °C, respectively. As shown in Figure 10, the curves of the average temperature gradient in the unfrozen zone show periodic cycles, each of which can be divided into linear increase period and decrease period. We can conclude that the average temperature gradient in test D2 is less than it in test D4, as shown in Figure 10. The relationship between the water absorption rate at the bottom of the final ice lens and the temperature gradient in the unfrozen zone is shown in Equation (4) as mentioned in the Konrad segregation ice theory [46,47]. In summary, the smaller average temperature gradient in test D2 results in a small water absorption rate and frost heave rate. Therefore, it is reasonable that the frost heave in test D2 is smaller than that in test D4.

It is shown in Figure 11 that the second periodic cycle for the freezing front is from 480 min to 960 min. The freezing front curves show a periodic zigzag. In each period of zigzag, the freezing front curve can be divided into an upward period and a downward period. During the period of 480–720 min, the freezing front in test D4 and D2 moved upward from 10.05 cm and 9.75 cm to 10.34 cm and 10.42 cm away from the cold end, respectively. During the downward period from 720 to 960 min, the freezing front in test D4 and D2 moved downward from 10.34 cm and 10.42 cm to 10.08 cm and 9.70 cm away from the cold end, respectively. The fluctuation of the freezing front increased with the increase of the amplitude of temperature change. For example, during the period from 480 to 960 min, the freezing front in test D4 moved upward and downward by 0.29 cm and 0.26 cm. However, the freezing front in test D2 moved upward and downward by 0.67 cm and 0.72 cm, respectively.

3.2.2. Effects of the Periods of Temperature Change on Frost Heave

The freezing front curves at different periods of temperature change are shown in Figure 12. The amplitude of temperature change is ±4 °C in test D1, D2, and D3, whereas the periods of temperature change are 2, 4, and 8 h, respectively. As shown in Figure 12, the freezing front curves show a periodic zigzag. From 960 to 1920 min, there were four periodic cycles on the freezing front curve in test D1, and the freezing front moved 0.29 cm on average in each cycle. Meanwhile, two periodic cycles occurred on the freezing front curve in test D2 in the same duration, which moved upward and downward by 0.68 and 0.74 cm, respectively. In test D3, there was only one periodic cycle, the freezing front moved upward and downward by 1.15 cm and 1.2 cm. The average freezing velocity is 0.0023 mm/min, 0.0028 mm/min and 0.0024 mm/min in test D1, D2, and D3, respectively. It is the main reason why the average moving distance of the freezing front in test D1, D2, and D3 basically conforms to the law of 1:2:4.

The frost heave curves at different periods of temperature change in test D1, D2, and D3 are shown in Figure 13. It can be seen from Figure 13 that the evolution of the frost heave curves in test D1, D2, and D3 are different as the periods of temperature change are 2 h, 4 h, and 8 h on the cold end, respectively. The periodic cycle and nongrowth period do not appear on the frost heave curve in test D1, whereas the frost heave increases continuously. The frost heave curve shows a periodic step growth in test D2, which can be divided into growth period and nongrowth period. A periodic polyline growth appears on the frost heave curve in test D3; the frost heave decreases when the cold end temperature increases by 4 °C and lasts for 8 h.

The frost heave increased during the period from 1080 to 1560 min and then decreased nearly 0.19 mm from 1560 to 2040 min. The segregation temperature increased with the increase of the cold end temperature [41,48]. The final ice lens in soil samples began to melt with the increase of the segregation temperature. This melting was the main reason why the frost heave in test D3 reduces during the period from 1560 to 2040 min.

The frost heave in tests A1, D1, D2, and D3 is 4.40, 2.82, 2.55, and 1.81 mm, respectively, in the same duration. Compared with test A1, the frost heave is reduced by 35.9%, 42.0%, and 58.9% in test D1, D2, and D3, in which the period of temperature change on the cold end is 2, 4, and 8 h, respectively. The frost heave decreased with the increase of the period of temperature change. The schematic diagrams of frost heave curves at different periods of temperature change are shown in Figure 14. In order to avoid the melting of the final ice lens, the periodic polyline growth should not appear on frost heave curves. For actual freezing engineering, this will affect the strength of the frozen wall in soils. As shown in Figure 14, the periodic step growth will be the best way to reduce frost heave in the continuous-intermittent freezing mode.

4. Conclusions

In order to reduce frost heave, frost-susceptible silty clay was used in a one-dimensional frost heave testing system in three different freezing modes. The effects of the three different freezing modes on frost heave were analyzed and compared, and the following conclusions were developed.

Compared with the continuous freezing mode, the frost heave curves show a periodic step growth in both the intermittent freezing mode and the continuous-intermittent freezing mode. The periodic variation of the cold end temperature causes the periodic zigzag on the freezing front curves. The frost heave reduces and eventually approaches zero after the freezing front moves downward, which is the main reason for the appearance of the nongrowth period on the frost heave curves.

The frost heave in the intermittent freezing mode and the continuous-intermittent freezing mode is reduced by 14.4% and 43.6%, respectively, compared with the continuous freezing mode. These results clearly demonstrate that the continuous-intermittent freezing mode can be more efficient than the intermittent freezing mode. In the continuous-intermittent freezing mode, the temperature gradient in soil samples is less than it is in the intermittent freezing mode, which results in a small water absorption rate and frost heaving rate.

Compared with the continuous freezing mode, frost heave at an amplitude of temperature change of ±2 °C and ± 4 °C decreases by 23.2% and 42.0%, respectively. These results show that frost heave decreases with the increase of the amplitude of temperature change.

The frost heave is reduced by 35.9%, 42.0%, and 58.9% at the period of temperature change of 2, 4, and 8 h, respectively, compared with the frost heave in the continuous freezing mode. The frost heave decreases with the increase of the period of temperature change. The power function growth, periodic step growth, and periodic polyline growth are shown on the frost heave curves at different periods of temperature change of 2, 4, and 8 h, respectively. In order to avoid the melting of the final ice lens, the periodic polyline growth should not appear on frost heave curves. For actual freezing engineering, this will affect the strength of the frozen wall in soils. The periodic step growth will be a better way to reduce frost heave in the continuous-intermittent freezing mode.