Research on the Temperature Field and Frost Heaving Law of Massive Freezing Engineering in Coastal Strata

School of Civil and Architecture Engineering, East China University of Technology, Nanchang 330013, China Nanjing Coal Mine Design & Research Institute, Nanjing 211800, China School of Civil Engineering, Fujian University of Technology, Fuzhou 350118, China Fuzhou Metro Co. Ltd., Fuzhou 350004, China Irrigation Management Office of Water Conservancy Project in Kuitun River Basin of Yili Kazak Autonomous Prefecture, Kuitun 833200, China


Introduction
Natural frozen soil is mainly formed by the freezing of water in soil due to the low temperature of the natural environment. Artificial freezing is the use of artificial refrigeration to make the soil around the freezing pipe freeze. en underground engineering construction is carried out under the protection of the freezing curtain. e artificial freezing method is an effective underground construction method that is widely used in mine construction and municipal engineering. Frozen soil is an extremely temperature-sensitive soil medium with rheological properties. Due to the uneven distribution of moisture, soil can produce uneven frost heaving deformation, accompanied by the generation of a frost heaving force. Frost heaving can potentially cause many engineering problems, including road cracking, foundation damage, building tilt, freezing pipe fractures, tunnel collapse, and pipeline fractures. In natural permafrost areas, frost damage control is relatively passive, such as salt injection to treat subgrade frost damage. Artificial freezing is designed artificially, and its freezing range, temperature, and time are controllable. erefore, compared with natural frozen soil, artificial freezing can better control the influence of frost heaving and thawing settlement on the original environment and structures by controlling the freezing volume, rapid freezing, setting pressure relief holes, thawing settlement compensation grouting, and other measures.
Previous scholars have done a large amount of research on the theory of frozen soil frost heaving and the law of freezing and thawing, and they have achieved many results [1][2][3][4][5]. Wang et al. [6][7][8][9] studied the frost heaving characteristics and frost heaving force through frozen soil tests. Yue et al. [10] studied the variation laws of frozen soil temperature and frost heaving pressure. He et al. [11] put forward the coupling equations of water, heat, and force in the process of soil freezing. Xia et al. [12] and Wang et al. [13] analyzed the mechanical properties of frozen wall and studied the uneven frost heaving. Many achievements have been made regarding the theoretical derivation, field measurement, and numerical simulation of freezing temperature field [14][15][16]. Chen et al. [17][18][19] studied the law of the temperature field of frozen soil and its influencing factors based on a freezing project. Long et al. [20] carried out a model test and obtained the development law of the temperature. Zhang et al. [21] established a three-dimensional temperature field model and proposed a new frost heaving model. Li et al. [22] studied the optimal excavation time of soil and the variations of the saltwater temperature, soil temperature, surface performance, and tunnel deformation. Hu et al. [23][24][25][26] established a frozen soil finite element model to analyze the development law of the frozen temperature field.
In this study, based on massive freezing engineering in coastal strata, thermal physical tests and frost heaving tests were carried out to obtain the soil thermal physical parameters and the frost heaving law. Moreover, 3D numerical simulation was carried out to further explore the changes of the freezing temperature field and frost heaving law of the long connecting passage under the on-site freezing conditions. is study is expected to provide a reference for the design and construction of freezing projects.

Overview of Freezing Engineering and Soil
Thermal Physical Parameters 2.1. Project Overview. In this study, a super long subway connecting passage was taken as the engineering background. e center distance of the connecting passage was 42.68 m, and the main body of the passage was located in silty soil and muddy sand. ere were hot springs in the strata, resulting in a high ground temperature about 40°C. e connecting passage was reinforced by horizontal freezing and constructed with the mining method. e cross section of connecting passage and the freezing curtain is shown in Figure 1. e excavation and the construction of the super long connecting passage took a long time, which led to the long freezing time for the freezing project. e connecting passage passed through a subway tunnel with a clear distance of about 7 m. erefore, in the construction process of connecting passage, the accuracy of the frost heaving control was required to be high. If large frost heaving deformation were to occur, the building would be inclined and cracked, the road or underground pipeline would be damaged, and the safety of the existing tunnel would be endangered, which would in turn cause a serious negative social impact.

Soil ermal Physical Parameters.
e main thermal physical parameters of each soil layer were obtained through experiments. e experimental results are shown in Table 1.

Multifunctional Frost Heaving Testing Machine.
e tests were carried out using a WDC-100 multifunctional frost heaving testing machine, which was composed of a loading system, a temperature control system, a moisture compensation system, and a measurement system. is machine could control the applied force, cold temperature, and ambient temperature. e test machine and the sample chamber are shown in Figures 2 and 3.
A cylindrical soil sample with dimensions φ50 × 100 mm is used, and the soil sample was placed in the sample chamber, as shown in Figure 3. ere was a set of devices at the top and bottom of the soil sample. A refrigerant circulating pipe and a temperature sensor were arranged inside the device. e cold source was formed by circulating the refrigerant, and the temperature sensor monitored the temperature. A row of evenly distributed temperature measuring holes was set at the soil sample position of the sample cylinder. e distances between the temperature measuring holes and the bottom of the sample were 0.50 cm, 1.75 cm, 3.00 cm, 4.25 cm, 5.50 cm, and 6.75 cm. e temperature acquisition probes extended into the soil through the reserved temperature measuring hole to measure the relationship between the temperature inside the soil and the distance from the cold source.

Tests and Results
Analysis. Single factor controlled frost heaving tests were carried out with the upper load being 0.6 MPa and the moisture content of the soil sample being 26%. e freezing temperatures adopted five levels of −5°C, −10°C, −15°C, −20°C, and −25°C, and the freezing time was 12 h. When considering the influence of the freeze-thaw cycles on the soil, the freezing temperature was −15°C, and the thawing temperature was 15°C. e designed freeze-thaw cycle was 24 h (12 h freezing and 12 h thawing) and the number of freeze-thaw cycles was six.

Temperature Field.
e distribution of the soil temperature field for different cold source temperatures is shown in Figure 4, and the distribution of the soil temperature field for the freeze-thaw cycles is shown in Figure 5. (1) e entire cooling process could be roughly divided into three stages: the active freezing stage, the attenuation cooling stage, and the stability stage. (2) In the initial stage of freezing, the temperature of the soil was high and the temperature of the freezing tube was very low. ere was a large temperature difference between the freezing tube and the soil. e temperature gradient was large and the cooling rate of the soil was very fast. e active freezing stage was a stage in which the soil temperature dropped rapidly. (3) With the decrease of the soil temperature, the temperature gradient between the freezing pipe and the soil decreased and the temperature rate of the soil decreased more. e water in the soil began to freeze and release latent heat, and the soil entered attenuation cooling stage.
(4) As the freezing time went by, the soil temperature continued to decrease. e temperature difference between the freezing pipe and the soil gradually decreased and the heat exchange generally tended to balance. e soil temperature dropped slowly and finally tended to be stable. (5) e tendencies of the temperature changes at different measuring points were roughly the same. e closer the location was to the cold source, the faster the soil cooling rate was and the lower the stable temperature was. When the temperature of the cold source was −5°C, the final stable temperature of the farthest measuring point (6.75 cm away from the    Advances in Materials Science and Engineering cold source) was 0.75°C and the final stable temperature of the measuring points nearest to the cold source (0.5 cm away from the cold source) was −3°C.
(6) e lower the cold source temperature was, the faster the soil temperature change rate was and the lower the final stable temperature was. When the temperatures of the cold source were −5°C, −10°C, −15°C, and −20°C, the final stable temperatures of the farthest measuring point (6.75 cm away from the cold source) were 0.75°C, −3°C, −4°C, and −7.5°C, respectively. e temperature differences between the stable temperatures and the corresponding cold sources were 5.75°C, 7°C, 9°C, and 12.5°C, respectively. e lower the cold source temperature was, the greater the temperature difference was. is showed that the range of frozen soil expansion did not increase linearly with the decrease of the freezing temperature, and there was a limit radius of frozen soil expansion. When the radius was reached, the frozen soil did not expand outward.
In the temporary frozen soil areas, with the seasons and day and night temperature changes, natural frozen soils will produce changes in freeze-thaw cycles. In the process of artificial freezing, due to power failures, freezing pipe fractures, salt water leakages, and other reasons, the freezing process will be interrupted, and the frozen soil will thaw. With measures taken to restore the freezing, the thawed frozen soil will start to freeze again, and the freezing and   thawing processes will also occur. In this experiment, the experimental conditions were closed and undrained, and the amount of soil and water in the test tube did not change. Under freeze-thaw cycles conditions, the soil temperature field changed periodically.

Frost Heaving Rate.
When the temperature was −15°C, the relationship between the frost heaving rate and time is shown in Figure 6.
It can be seen from Figure 6 that, during the beginning of freezing, the frost heaving rate was reduced and became a negative value; that is, the phenomenon of "freeze shrinkage" occurred. is phenomenon was caused by the negative pore water pressure in the soil during the beginning of freezing, which reduced the volume of the soil. When the volume reduction caused by the negative pore water pressure was greater than the increase caused by water freezing, the total volume of soil decreased. After the freezing shrinkage reached the critical point, the frost heaving began to occur in the soil. e frost heaving continued to increase and finally tended to be stable. e test results of the soil frost heaving rate for different freezing temperatures are shown in Table 2. e values in Table 2 are the frost heave rates at the stable stage of freezing, that is, the maximum frost heaving rates.
e experimental data were plotted on a scatter plot, and it was judged that the frost heaving rate and the freezing temperature were approximately linearly related according to the image. erefore, linear fitting was performed to obtain the correlation coefficient R Square � 0.98605, which showed a good fitting effect. e results of the fitting test are shown in Figure 7.
Combining Table 2 and Figure 7, it can be seen that, within the range of the test conditions, the frost heaving rate of the soil became larger as the freezing temperature decreases, which was roughly linear.

Frost Heaving Force.
When the temperature was −15°C, the relationship between the frost heaving force and time was as shown in Figure 8.
According to Figure 8, the frost heaving force of the soil gradually increased with the freezing time and finally tended   to be flat. Due to the limitation of experimental instruments, only the compressive stress could be detected. at is, the frost heaving force could be monitored at the stage of frost heaving rate increasing. e frost heaving force in the freezing shrinkage stage could not be monitored, and its value was 0 by default. e test results of the soil frost heaving force for different freezing temperatures are shown in Table 3. e values in Table 3 are the frost heave forces at the stable stage of freezing, that is, the maximum frost heaving forces.
e experimental data were plotted on a scatter plot, and it was judged that the frost heaving force and the freezing temperature were approximately linearly related according to the image. erefore, a linear fitting was performed to obtain the correlation coefficient R Square � 0.97396, which showed a good fitting effect. e results of the fitting test are shown in Figure 9.
Combining Table 3 and Figure 9, it can be seen that, within the range of the test conditions, the frost heaving force of the soil increased with the decrease of the freezing temperature, which was roughly linear. In the experiment, the maximum frost heaving rate and the maximum frost heaving force of each layer of soil samples at −10°C were as shown in Table 4.

Model Parameters.
A three-dimensional numerical model was established to simulate the variation law of the formation temperature field and the frost heaving caused by the actual freezing condition. Taking the vertical plane passing through the longitudinal axis of the connecting passage as the symmetry plane, the 1/2 finite element model was established. e material thermal physical parameters of each part are shown in Table 5.

Model
Building. e finite element model was established according to the actual situation of the freezing project. e model of the tunnel and the freezing pipes is shown in Figure 10, and the finite element model after meshing is shown in Figure 11.

Numerical Simulation Analysis of Temperature Field.
A transient thermal calculation was carried out for the development of the soil temperature field in the active freezing period. e distribution cloud charts of the soil temperature field were selected when the freezing times were 15 d, 30 d, 45 d, and 60 d, with 15 d as the interval, as shown in Figure 12.
When freezing, the temperature of the soil around the freezing pipes began to drop rapidly, and the frozen soil cylinder was gradually formed around the freezing pipes. With the increase of the freezing time, the frozen soil cylinder developed outward along the radial direction of the

ermal-Mechanical Coupling Simulation and Analysis.
To explore the coupling evolution law of the freezing temperature field and soil displacement field, the thermalmechanical coupling solution was carried out. e distribution of the soil displacement field under the thermal load is shown in Figure 13.
e frost heaving of the soil around the freezing pipes was caused by freezing, and because of the uneven distribution of the freezing pipes, the overall frost heaving was not uniform. When freezing for 15 days, the larger frost heaving areas were scattered. When freezing for 30 days, the freezing curtain gradually intersected. e frost heaving areas also showed a homogenization phenomenon and gradually gathered and merged. When freezing for 60 days, the frost heaving areas at the top were connected as a whole, showing a phenomenon of the middle parts being large and the two sides being small. en as the freezing continued, the frost heaving areas were further homogenized and gradually spread from the middle area to both sides, finally becoming steady.
According to the calculation results, the maximum frost heaving of the strata occurred above the middle of the connecting passage. To further analyze the distribution law of the frost heaving at this position, the displacement duration curve of the maximum displacement area was drawn for analysis, as shown in Figure 14. e whole frost heaving process could be roughly divided into two stages. e first was the frost heaving generation stage, during which the frost heaving began to slowly increase. e second stage was the frost heaving development stage, during which the frost heaving began to increase rapidly and reached the maximum value of 193.03 mm in 65 days.

Freezing Temperature Field Measurement.
To accurately understand the development law of the freezing curtain in the long connecting passage, temperature measuring points were arranged in the surrounding strata to obtain the temperature field data of the freezing curtain. e layout of the freezing holes and the temperature measuring holes on the left side of the connecting passage are shown in Figure 15. e temperature measuring points were arranged at 5 m, 12 m, and 19 m of the hole depth to monitor the development of the temperature field at different depth sections. e temperature measuring points were numbered Ti−j, the labels i � 1-8 were used according to the different temperature measuring holes, and the labels j � 1-3 were used according to different positions of 5 m, 12 m, and 19 m along with the hole depth. e temperature measuring hole T5 was located at the edge of the excavation area, and T7 was located      Advances in Materials Science and Engineering at the edge of the nonexcavation area. e temperature and time relationship curves of the measuring points at different depths are shown in Figures 16 and 17. e temperature trends for T5 and T7 temperature measuring holes were basically the same, and the entire freezing process could be divided into the active freezing stage, the attenuation cooling stage, and the stability stage. In the active freezing stage, the formation temperature decreased rapidly, lasting for about 40 days. In the attenuation cooling stage, the temperature of the formation was close to 0°C, and the moisture in the soil began to solidify into ice. Due to the effect of the latent heat of the phase change, the temperature slowed down. In the stability stage, the formation temperature dropped to a negative temperature, and the latent heat of the phase change was completed. e soil temperature continues to slow down and finally tended to be stable. e temperature at the T4-3 measuring point was calculated with finite element software and compared with the measured temperature, as shown in Figure 18.
In the early stage of active freezing, there was a certain difference between the simulated temperature and the measured temperature. e temperature drop curve of the finite element simulation was smoother, but the change of the measured temperature drop curve was more violent. During the late stage of the active freezing period and the maintenance freezing period, the simulated temperature and The active freezing stage Advances in Materials Science and Engineering the measured temperature almost coincided. erefore, the numerical simulation described above could accurately reflect the variation of the soil temperature field.

Frost Heaving Measurement.
Forty-one monitoring points were arranged on the ground surface within the freezing influence range of the connecting passage to study the frost heaving law of the freezing project. e layout of the monitoring points is shown in Figure 19. e measuring points DZ5-1−DZ5-7 were located in the middle of the connecting passage, where the frost heaving was more severe. e measuring points DZ5-1−DZ5-4 were selected as the research object to analyze the distribution law of frost heaving during the freezing period. e distances between DZ5-1−DZ5-7 were 3 m, 5 m, and 7 m, respectively. e measured surface deformation values are shown in Figure 20, and the surface frost heaving duration distribution is shown in Figure 21.
e process of surface uplift caused by frost heaving could be divided into a rapid growth stage and a steady growth stage. e rapid growth stage corresponded to the early and late stages of the active freeze period. e stable growth stage corresponded to the maintenance freeze period, during which the soil temperature was basically stable and the frost heaving was also in a relatively stable state. e numerical model was used to further study the frost heaving law of frozen soil, and the accuracy of the numerical model was evaluated by comparing the model with the field measured data. e numerical calculation was carried out with the corresponding model position of the DZ5-4 measuring point, and the comparative analysis was carried out with the measured value, as shown in Figure 22.
It can be seen from Figure 22 that there was a small deviation in the middle part, and the initial stage and the final stage were relatively consistent. Generally speaking, the final calculation results of the numerical simulation were consistent with the measured data. erefore, the above numerical simulation could accurately reflect the law of soil frost heaving caused by freezing.

Conclusions
e temperature field and the frost heaving characteristics are the keys to the study of the freezing method. e temperature field is the most direct inducement for the formation and development of freezing curtain, and frost heaving can cause structural deformation and damage. In this study, the thermal physical parameters and the frost heaving parameters of soil were obtained through the soil thermal physical tests and frozen soil frost heaving tests. A three-dimensional finite element model was established to simulate the temperature field and frost heaving changes of soil under on-site working conditions, and the model was further compared with the field measured values.
(1) ermal physical tests and frost heaving tests for frozen soil were carried out to study the temperature field, frost heaving rate, and frost heaving force of soil during frost heaving. (2) e entire cooling process could be roughly divided into three stages: the active freezing stage, the attenuation cooling stage, and the stability stage. e range of frozen soil expansion did not increase linearly with the decrease of the freezing temperature, and there was a limit radius for the frozen soil expansion. When the radius was reached, frozen soil did not expand outward. For the freeze-thaw cycle, the soil temperature changed periodically. (3) When the freezing temperatures were −5°C, −10°C, −15°C, and −20°C, the frost heaving rates of soil were 0.53%, 0.95%, 1.28%, and 1.41%, and the frost heaving forces of the soil were 0.37 MPa, 0.46 MPa, 0.59 MPa, and 0.74 MPa, respectively. In the range of test conditions, the frost heaving rate and the frost heaving force of the soil increased with the decrease of the freezing temperature, and the relationship was roughly linear with the temperature. (4) e development of the formation temperature field could be divided into three periods. In the early stage of active freezing, the formation temperature decreased rapidly. In the late stage of active freezing, the temperature dropped slowly. In the maintenance freezing period, the temperature tended to be stable. (5) In the finite element model, the calculated temperature value corresponding to the T4-3 measuring point was compared with the measured temperature, and the calculated frost heaving value corresponding to the DZ5-4 measuring point was compared with the measured value, which verified the fact that the numerical calculation could reflect the temperature field change and the frost heaving law of the formation accurately.
Data Availability e figures and tables data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that they have no conflicts of interest.