# Analysis of Pore Structure and Thaw Settlement Characteristics of Frozen Silty Sand Based on Computer-Assisted Pulse Nuclear Magnetic Resonance

Authors: Maoyan Ma; Biao Zhang; Shuguang Peng
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Computer-assisted pulse nuclear magnetic resonance (NMR) can be used to get important parameters for pore structure characteristics of porous materials. In order to fully understand the effect of frozen soil thaw settlement, the mechanism of artificially frozen soil thaw settlement was examined from a microscopic perspective in conjunction with the frozen soil thaw settlement test. Additionally, to have a better understanding of how pore features change during the thaw settling process, the evolution of the pore size distribution in silty sand was studied. The findings demonstrate the porosity is obviously larger than the initial porosity after freeze-thaw, and the evolution of thaw settlement displacement is related to the change in porosity as thawing progresses, which grows exponentially with porosity. The fraction of medium and large pores (>0.1μm) in the soil increases significantly during the thawing process. Accordingly, there is a slight increase in the proportion of pores (<0.1 μm) during the thawing progress. The variation in the pore size distribution of silty sand is compatible with that in settlement displacement during the thawing process. Additionally, the thaw settling rate’s development law is consistent with that of the proportion of pores. The number of medium and large pores is critical in determining the rate of thaw settlement. In other words, the development law of thaw settlement rate is consistent with the development law of medium and large pore size distribution.


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## Body

## 1. Introduction

Due to its unique advantages in ground support and waterproofing, the artificial freezing ground method is the first choice for metro tunnel construction in water-rich soft strata [1]. However, since this technology has become more widely used, the influence of frost heave and thaw settlement on the surrounding environment has received increasing attention. Excessive or uneven frost heave and thaw settlement might cause damage to adjacent structures or roadways [2, 3]. Frost heave is generally caused by an increase in soil volume. When it proceeds to the thawing stage, the refrigeration system is closed, and the formation temperature gradually rises. Excess pore water created by thawing will result in a loss of strength and substantial deformation, that is, thaw settlement [4–6].The method for calculating the settlement of frozen soil during thawing was proposed by scholars represented by Tsytovich, which provided a basis for scholars to study the problem of thaw settlement [7]. Wu et al. [8] used a backpropagation (BP) neural network to predict frost heave and thaw settlement deformation of subgrade soil taken from the Qinghai-Tibet Plateau. Wang et al. [9] made a regression analysis of permafrost on the relationships between the rate of frost heaving, coefficient of thawing settlement, and various influencing factors and proposed the empirical formulas. As to the frozen soil thaw consolidation model, the one-dimensional thaw consolidation model proposed by Morgenstern et al. [10, 11] and Nixon and Morgenstern [12] are widely used, but the applicability of the model is limited to frozen soil with low ice content.Foriero and Ladanyi [13] established the one-dimensional large deformation thaw consolidation theory, but there is controversy on the determination of phase interface position change. Yao et al. [14, 15] established a three-dimensional large deformation thaw consolidation theory, and Qi et al. [16, 17] improved the model and established a new one-dimensional large deformation thawing consolidation model, which is applied in cold region engineering. Zhou et al. [18] established a one-dimensional thaw thermal consolidation model of frozen soil at high temperature considering the evolution of excess pore pressure and settlement. Freeze-thaw poses a great threat to soil structure and can damage it. When soil is exposed to the action of freeze-thaw, its strength decreases [19, 20]. In reality, the change in soil strength and deformation properties is caused by the influence of freeze-thaw on the soil’s microstructure [21, 22]. Therefore, it is necessary to study the evolution of microscopic pore properties of frozen soil during the thawing process to investigate the process of thaw settlement more thoroughly. The distribution of pore sizes in soil is the internal source of soil deformation [23, 24]. Computer technology is widely used in various fields [25–31]. The combination of computer information and network technology with soil mechanics has greatly promoted the development of geotechnical engineering. Computer-assisted pulse nuclear magnetic resonance (NMR) can be used to analyze the freeze-thaw properties of unfrozen water and the pore distribution in frozen soil during the phase transition process [32].In summary, there has been preliminary progress in the study of soil thaw settlement characteristics under freeze-thaw cycles, but there is a lack of research on the freeze-thaw characteristics of artificial frozen soil. Actually, the phenomena of frost heave and thaw settlement during the freeze-thaw process of artificial frozen soil are more visible than that of natural frozen soil due to the lower temperature and huge temperature gradient of artificial frozen soil [33]. Moreover, the macroscopic thaw settlement performance has not been explained yet by the change of pore structure in the soil during the thaw settlement before. The use of nuclear magnetic technology to explore the thaw settlement of frozen soil is a supplement to the existing research methods of thaw settlement. In this paper, the thaw settlement characteristics of artificial frozen silty sand were analyzed based on the thaw settlement test for the purpose of underground engineering construction under complex geological conditions and providing theoretical support for formulating more scientific design methods for artificial freezing engineering. The pore properties under the action of freeze-thaw in the thawing process were studied in conjunction with an NMR test. The mechanism of artificial frozen soil thaw settlement was studied at the microscopic level.


## 2. Experiments

### 2.1. Experiment Materials and Samples

The sand used in this study is silty sand, a frost heave-sensitive soil. The liquid limit is 18%, and the plastic limit is 15.33%. Table1 summarizes the particle composition of the sample.Table 1
Partical composition of the sample.
Partical size/mm<0.0750.075–0.250.25–0.50.5–1>1Content/%11.661.824.22.30.1The tests used remolded soil to avoid the mistake caused by undisturbed soil’s poor homogeneity. According to the national standard procedure for soil testing (GB/T 50123-2019), soil samples with an initial moisture content of 17.3 percent were prepared using self-made deionized distilled water and sealed for seven days to guarantee equal moisture distribution. The samples with a dry density of 1.6 g/cm3 were then compressed using a jack and saturated using the vacuum saturation method. To reduce the effect of ferromagnetic material on the uniformity of the main magnetic field, magnetic samples were made using a 20 mm × 45 mm PTFE ring cutter rather than the more typical stainless steel ring cutter. The size of a freeze-thaw sample is 5 cm × 10 cm cylindrical, and the samples were consolidated before the test using the load control method under an overlaying load of 2.7 kN steady pressure.


### 2.2. Experiment Methods and Schemes

The experiments consisted of macro and micro parts, namely a thaw settlement experiment and an NMR microstructural experiment. The macrosection involved studies of artificially frozen soil thaw settlement. To replicate the actual working conditions of artificial freezing, the test used unidirectional freezing and natural thawing under an open system. The test system includes a temperature control environment box, a sample tube, an upper cooling system, and an acquisition system for temperatures and vertical displacements. Two parallel trials had been scheduled. To begin, the temperature of the box, top and bottom plates, and the sample was cooled to 1°C and chilled for more than 6 hours. After adjusting the upper temperature to −10°C, the sample was frozen from the top with water replenishment from the bottom, and the temperature and displacement data gathering system was initiated for real-time monitoring. When the freezing process is complete, turn off the upper cooling system.MiniPQ-001 NMR microstructural analysis and imaging technology were used for the micro experiment. After inserting the sample into the cavity, the low-temperature system was begun. The sample was cooled to −10°C and then thawed to monitor the sample’s NMR signal throughout thawing. The NMR signals were obtained at temperatures of −10°C, −8°C, −6°C, −4°C, −2°C, 0°C, and 20°C.


## 2.1. Experiment Materials and Samples

The sand used in this study is silty sand, a frost heave-sensitive soil. The liquid limit is 18%, and the plastic limit is 15.33%. Table1 summarizes the particle composition of the sample.Table 1
Partical composition of the sample.
Partical size/mm<0.0750.075–0.250.25–0.50.5–1>1Content/%11.661.824.22.30.1The tests used remolded soil to avoid the mistake caused by undisturbed soil’s poor homogeneity. According to the national standard procedure for soil testing (GB/T 50123-2019), soil samples with an initial moisture content of 17.3 percent were prepared using self-made deionized distilled water and sealed for seven days to guarantee equal moisture distribution. The samples with a dry density of 1.6 g/cm3 were then compressed using a jack and saturated using the vacuum saturation method. To reduce the effect of ferromagnetic material on the uniformity of the main magnetic field, magnetic samples were made using a 20 mm × 45 mm PTFE ring cutter rather than the more typical stainless steel ring cutter. The size of a freeze-thaw sample is 5 cm × 10 cm cylindrical, and the samples were consolidated before the test using the load control method under an overlaying load of 2.7 kN steady pressure.


## 2.2. Experiment Methods and Schemes

The experiments consisted of macro and micro parts, namely a thaw settlement experiment and an NMR microstructural experiment. The macrosection involved studies of artificially frozen soil thaw settlement. To replicate the actual working conditions of artificial freezing, the test used unidirectional freezing and natural thawing under an open system. The test system includes a temperature control environment box, a sample tube, an upper cooling system, and an acquisition system for temperatures and vertical displacements. Two parallel trials had been scheduled. To begin, the temperature of the box, top and bottom plates, and the sample was cooled to 1°C and chilled for more than 6 hours. After adjusting the upper temperature to −10°C, the sample was frozen from the top with water replenishment from the bottom, and the temperature and displacement data gathering system was initiated for real-time monitoring. When the freezing process is complete, turn off the upper cooling system.MiniPQ-001 NMR microstructural analysis and imaging technology were used for the micro experiment. After inserting the sample into the cavity, the low-temperature system was begun. The sample was cooled to −10°C and then thawed to monitor the sample’s NMR signal throughout thawing. The NMR signals were obtained at temperatures of −10°C, −8°C, −6°C, −4°C, −2°C, 0°C, and 20°C.


## 3. Results and Discussion

### 3.1. Deformation Characteristics of Temperature and Displacement during the Freeze-Thaw Process

The frozen soil thaw settlement experiment may be used to determine the freeze-thaw characteristics of silty sand. Figure1 depicts the temperature variation curves and the displacement with time during freezing and thawing. The thaw settlement experiment findings clearly reveal that, under unidirectional freezing conditions, the evolution of temperature and displacement in the sample can be divided into three stages. At the first stage, known as the cooling stage, the sample temperature drops quickly from room temperature to the set constant temperature of 1°C, then remains constant for a period of time to ensure equal temperature distribution in the sample, and this time is not shown in Figure 1. The second stage is known as frost heave. At this stage, the sample temperature will reach the freezing point of −0.6°C, and the test sample will enter the freezing phase. The frost heave deformation rises continually as the temperature decreases. When the temperature gradually drops to −10°C, it is largely steady and persists for a period of time, and the frost heave displacement stays stable at this time. The last stage is the thaw settlement stage. Under the circumstance of an ambient temperature of 20°C, the temperature rises fast at this stage. In a short period of time, the temperature rises to a positive level. As a result, the sample undergoes thaw settlement. The thaw settlement displacement grows rapidly at first and eventually becomes steady. As a result, the history of displacement in the sample is consistent with the evolution of temperature. The temperature has an important role in soil deformation during the freeze-thaw cycle.Figure 1
Freeze-thaw process curves.


### 3.2. Analysis of Pore Distribution under Different Temperatures

Saturated porous materials may be measured for porosity and pore size distribution using a computer-assisted pulse low-field NMR instrument.T2 spectrum curves of the test sample during thawing progress can be obtained by RF pulse of the sample (Figure 2). In the nuclear magnetic resonance experiment, different relaxation times (T2) correspond to different occurrence states of water. T2 of adsorbed water, capillary water, and free water increases gradually and 2.5 ms is the dividing point between the capillary water and film water [34]. At low temperatures, the typical curves of the T2 spectrum still have a clear signal, indicating that there is still a certain quantity of pore water that does not freeze, as seen in Figure 2. The LF-NMR relaxation signal of film water is clearly greater than that of capillary water and free water at low temperatures because pore water in frozen saturated silty sand is mostly film water, whereas free water and the majority of capillary water have frozen. The peak of the T2 curve gradually shifts to the right of the figure during the thawing process, which indicates that the amount of free water and capillary water is increasing. After thawing, the amount of capillary water and free water increases significantly, which means that at low temperatures, freezing occurs mostly in free water and capillary water.Figure 2
T2 spectrum curves during thaw.The temperature has a significant impact on the porosity of the sample, as shown in Table2. When the temperature decreases, the measured porosity also decreases gradually. The porosity reduced from 18.4% to 0.8% when the temperature decreased from 20 to −10 degrees Celsius. The porosity of the sample rises with rising temperature as it thaws, and the porosity was 21.0% at 20°C after free-thaw. The porosity after freeze-thaw is obviously larger than the initial porosity, indicating that the microstructure of the silty sand is damaged after freeze-thaw, causing small pores to connect into large pores, and the pores, on the other hand, become larger after the frost heaving expansion caused by pore water freezing.Table 2
The porosity at different temperatures.
Temperature/°C20 (before freezing)−10−8−6−4−2020 (after thawing)Porosity/%18.40.80.91.11.31.41.821.0To understand the mechanism of thaw settlement, it is clear that understanding the change in porosity is insufficient. A study on the variation of pore size distribution during the process of thaw settlement must be carried out. There is a certain relationship between the volumetric distribution of pores andT2 spectrum of the test sample, which can be shown in the following equation [35]:(1)1T2=ρsvpore,where ρ is the surface relaxation rate; s and v are parameters of pores, which are the surface area and the volume, respectively.Equation (1) shows that the measured T2 by NMR can be converted to the pore size distribution of different diameters. The pore size distribution of test samples may thus be determined by measuring the T2 spectrum. If the pore volume of a certain diameter can be expressed by vi, then vi can be given as follows:(2)vi=Ai∑Ai⋅mρw,where Ai is the amplitude of the NMR signal; m is the total mass of water in the test sample; ρw is water density (1.0 g/cm3).The signal intensity of water in each pore and in the entire pore may be detected using nuclear magnetic resonance imaging. The fraction of a certain pore size in the total pores may be determined by the ratio between them. Figure3 depicts the varied pore size distribution of the test sample as a result of the freeze-thaw activity. The distribution pattern of the curve after freeze-thaw differs from that before freezing, indicating that the structure of the testing silty sand has been altered by the freeze-thaw. The peak of the curves consistently advances to the right of the figure during the thawing process, indicating that the fraction of medium and large pores increases significantly. For example, the proportion of 0.1 μm pore size at −10°C is 2.3%, and it rises to 31.5% after thawing.Figure 3
Pore size distribution curves under the action of freeze-thaw.


## 3.1. Deformation Characteristics of Temperature and Displacement during the Freeze-Thaw Process

The frozen soil thaw settlement experiment may be used to determine the freeze-thaw characteristics of silty sand. Figure1 depicts the temperature variation curves and the displacement with time during freezing and thawing. The thaw settlement experiment findings clearly reveal that, under unidirectional freezing conditions, the evolution of temperature and displacement in the sample can be divided into three stages. At the first stage, known as the cooling stage, the sample temperature drops quickly from room temperature to the set constant temperature of 1°C, then remains constant for a period of time to ensure equal temperature distribution in the sample, and this time is not shown in Figure 1. The second stage is known as frost heave. At this stage, the sample temperature will reach the freezing point of −0.6°C, and the test sample will enter the freezing phase. The frost heave deformation rises continually as the temperature decreases. When the temperature gradually drops to −10°C, it is largely steady and persists for a period of time, and the frost heave displacement stays stable at this time. The last stage is the thaw settlement stage. Under the circumstance of an ambient temperature of 20°C, the temperature rises fast at this stage. In a short period of time, the temperature rises to a positive level. As a result, the sample undergoes thaw settlement. The thaw settlement displacement grows rapidly at first and eventually becomes steady. As a result, the history of displacement in the sample is consistent with the evolution of temperature. The temperature has an important role in soil deformation during the freeze-thaw cycle.Figure 1
Freeze-thaw process curves.


## 3.2. Analysis of Pore Distribution under Different Temperatures

Saturated porous materials may be measured for porosity and pore size distribution using a computer-assisted pulse low-field NMR instrument.T2 spectrum curves of the test sample during thawing progress can be obtained by RF pulse of the sample (Figure 2). In the nuclear magnetic resonance experiment, different relaxation times (T2) correspond to different occurrence states of water. T2 of adsorbed water, capillary water, and free water increases gradually and 2.5 ms is the dividing point between the capillary water and film water [34]. At low temperatures, the typical curves of the T2 spectrum still have a clear signal, indicating that there is still a certain quantity of pore water that does not freeze, as seen in Figure 2. The LF-NMR relaxation signal of film water is clearly greater than that of capillary water and free water at low temperatures because pore water in frozen saturated silty sand is mostly film water, whereas free water and the majority of capillary water have frozen. The peak of the T2 curve gradually shifts to the right of the figure during the thawing process, which indicates that the amount of free water and capillary water is increasing. After thawing, the amount of capillary water and free water increases significantly, which means that at low temperatures, freezing occurs mostly in free water and capillary water.Figure 2
T2 spectrum curves during thaw.The temperature has a significant impact on the porosity of the sample, as shown in Table2. When the temperature decreases, the measured porosity also decreases gradually. The porosity reduced from 18.4% to 0.8% when the temperature decreased from 20 to −10 degrees Celsius. The porosity of the sample rises with rising temperature as it thaws, and the porosity was 21.0% at 20°C after free-thaw. The porosity after freeze-thaw is obviously larger than the initial porosity, indicating that the microstructure of the silty sand is damaged after freeze-thaw, causing small pores to connect into large pores, and the pores, on the other hand, become larger after the frost heaving expansion caused by pore water freezing.Table 2
The porosity at different temperatures.
Temperature/°C20 (before freezing)−10−8−6−4−2020 (after thawing)Porosity/%18.40.80.91.11.31.41.821.0To understand the mechanism of thaw settlement, it is clear that understanding the change in porosity is insufficient. A study on the variation of pore size distribution during the process of thaw settlement must be carried out. There is a certain relationship between the volumetric distribution of pores andT2 spectrum of the test sample, which can be shown in the following equation [35]:(1)1T2=ρsvpore,where ρ is the surface relaxation rate; s and v are parameters of pores, which are the surface area and the volume, respectively.Equation (1) shows that the measured T2 by NMR can be converted to the pore size distribution of different diameters. The pore size distribution of test samples may thus be determined by measuring the T2 spectrum. If the pore volume of a certain diameter can be expressed by vi, then vi can be given as follows:(2)vi=Ai∑Ai⋅mρw,where Ai is the amplitude of the NMR signal; m is the total mass of water in the test sample; ρw is water density (1.0 g/cm3).The signal intensity of water in each pore and in the entire pore may be detected using nuclear magnetic resonance imaging. The fraction of a certain pore size in the total pores may be determined by the ratio between them. Figure3 depicts the varied pore size distribution of the test sample as a result of the freeze-thaw activity. The distribution pattern of the curve after freeze-thaw differs from that before freezing, indicating that the structure of the testing silty sand has been altered by the freeze-thaw. The peak of the curves consistently advances to the right of the figure during the thawing process, indicating that the fraction of medium and large pores increases significantly. For example, the proportion of 0.1 μm pore size at −10°C is 2.3%, and it rises to 31.5% after thawing.Figure 3
Pore size distribution curves under the action of freeze-thaw.


## 4. Relationship between Thaw Settlement Characteristics and Pore Structure

### 4.1. Calculation of Thaw Settlement

The compression amount of frozen soil during thawing is greater than that of the same type of unfrozen soil [7]. The void ratio of soil changes during the thawing process, and the fluctuation of the void ratio during thawing impacts the amount of thaw settlement.When the soil is compressed uniformly without lateral expansion, the total stable settlement of soil can be expressed as follows:(3)s=h1+e0Δe,where s is the total settlement; h depicts the total soil thaw settlement; e0 is initial void ratio; Δe is the reduction in void ratio under uniform load.It can be seen from equation (3) that the total soil thaw settlement depends on the reduction in void ratio Δe, and Δe is related to the soil properties and external load and can be expressed as follows:(4)Δe=A+ap,where A is the variation of the void ratio independent of external pressure; ap represents the variation of the void ratio that is proportional to the external pressure p within the studied pressure range, and a is the compaction coefficient of the thawing soil.Substituting equation (4) into equation (3), the amount of one-dimensional thaw settlement can be expressed as follows:(5)s=A1+e0h+a1+e0ph.ConsiderA¯=A/1+e0; a¯=a/1+e0, then(6)s=A¯h+a¯ph,where A¯ is called thaw coefficient; a¯ is called relative compaction coefficient of the thawing soil.


### 4.2. Relationship between Thaw Settlement Displacement and Porosity

Both thawing displacement and porosity increase as the soil thaws, as seen in Figure4, with maximum values of 5.2 mm and 22.6%, respectively. Furthermore, at the intensive phase transition zone of −2°C-2°C, porosity and thawing displacement rise substantially. When the temperature increases more than 2°C, both porosity and displacement begin to stabilize. Obviously, the change in porosity affects the development law of thaw settlement displacement. The thaw settlement displacement development law is consistent with the porosity development law.Figure 4
Variation of displacement and porosity with time during thawing.In the thawing process, the settlement displacement grows exponentially with the porosity, as seen in Figure5. Because the volume of ice in pores decreases throughout the thawing process, the pore water level rises. That is, the value of NMR-measured porosity is increasing. Meanwhile, as ice-soil particles thaw, their structure progressively disintegrates, causing formation settlement due to their own weight. After the ice melts into water, it slowly drains through the pores, and the settlement displacement increases with the compression of pores. The settlement displacement stabilizes as the number of pores that can be closed decreases. At the same time, the porosity does not rise. As a result, the vertical deformation of the test sample is mostly due to ice-water phase change and recombination of soil particles under self-weight. After freeze-thaw, the compressibility of the silty sand increases because of structural weakening.Figure 5
Relationship between porosity and thawing settlement in thawing process.


### 4.3. Relationship between Thaw Settlement Rate and Pore Size Distribution

The relationship between thaw settlement rate and pore diameter distribution is seen in Figure6. As the temperature rises, so do the number of pores of various sizes. However, the magnitude of the increase varies with the pore size. The proportion of medium and large pores (>0.1 μm) increases rapidly, whereas the proportion of small pores (<0.1 μm) increases slightly, but both of them contribute to an increase in porosity after freeze-thaw. Each of them increases sharply in the −2°C-2°C intense phase transition zone before slowing down at temperatures above 2°C. The constant formation of ice crystals in pores throughout the freezing process has disrupted the link between the soil particles, causing them to be squeezed to create a new skeletal structure. Small pores are joined to generate big pores at the same time. The structure of the soil changes. At the same time, the absence of ice crystals during the thawing process cannot entirely rebuild the skeletal structure, which will eventually be weakened by freeze-thaw.Figure 6
Variation of pore size and thawing settlement rate in the thawing process.In the thawing process, the settlement rate grows exponentially with the proportion of pores, as seen in Figure7. The rate of thaw settlement increases as the temperature rises. When the proportion of pores increases, the development law of thaw settlement rate increases. When the temperature rises above freezing point, the rate of increase accelerates. The number of medium and large pores is the most important element in determining the rate of thaw settlement. The number of medium and large pores increases sharply in the intensive phase transition zone of −2°C-2°C, and a huge number of them are compressed. Thus, the thaw settlement rate increases significantly. The thaw settlement rate tends to be steady due to the dissipation of pore water pressure and the continual closing of pores.Figure 7
Relationship between pore size and thawing settlement rate in the thawing process.


### 4.4. Cause of Thaw Settlement

Studies have shown that the brittleness of soil will increase at low temperatures, and the humidity of the environment will lead to short-term or long-term damage to materials and structures, which is more pronounced after freeze-thaw cycles. Firstly, cyclic pressure caused by water during freezing and thawing can cause damage to materials, such as through erosion, microcracks, or thermodynamic mechanisms to weaken the performance of materials. Secondly, the damage caused may effectively increase the overall pore space and enhance permeability, resulting in increased water content. The increasing crack and void volume cause the overall decline of soil properties such as strength and stiffness. The soil becomes loose and contains ice crystals after freezing, which is not dense enough in the natural state, and thaw settlement occurs under the action of self-weight.When the soil is frozen, the soil experiences frost heaving. However, the volume expansion caused by the phase change of water which is 1/9 has little contribution to frost heave. The main reason for frost heave is that the water in other parts of the formation migrates to the frozen soil, and the increased part of water needs to occupy a certain space after freezing. At the same time, due to the migration of water and dispersed mineral particles, new and extremely complex cryogenic structures are formed. The formed ice causes the differentiation of soil in joints. The mineral particle aggregates and soil layers are squeezed by ice crystals, and the soil structure changes.When the temperature rises, the ice in the pores of the soil begins to thaw, the cohesion between the mineral particles controlled by the ice bonding decreases, and the cohesion of the soil decreases sharply after complete thawing. When the frozen soil thaws, the structure of soil in the open system with water supply changes dramatically, and its porosity increases significantly. Therefore, the compressibility of the soil after thaw is high, and the thaw settlement of the formation is obvious. The change of structure during the thawing of frozen soil not only affects the compressibility of soil, but also affects the permeability of the soil. The permeability coefficient of the soil after thaw is often many times larger than that of unfrozen soil with the same composition. The change of internal structure of soil after freezing and thawing leads to the decrease of foundation bearing capacity, which is characterized by the settlement of formation. The settlement of the foundation drives the longitudinal bending deformation of underground structures such as tunnel structures until the structure is damaged, which is an important reason for the occurrence of underground structure disasters by the ground freezing method.


## 4.1. Calculation of Thaw Settlement

The compression amount of frozen soil during thawing is greater than that of the same type of unfrozen soil [7]. The void ratio of soil changes during the thawing process, and the fluctuation of the void ratio during thawing impacts the amount of thaw settlement.When the soil is compressed uniformly without lateral expansion, the total stable settlement of soil can be expressed as follows:(3)s=h1+e0Δe,where s is the total settlement; h depicts the total soil thaw settlement; e0 is initial void ratio; Δe is the reduction in void ratio under uniform load.It can be seen from equation (3) that the total soil thaw settlement depends on the reduction in void ratio Δe, and Δe is related to the soil properties and external load and can be expressed as follows:(4)Δe=A+ap,where A is the variation of the void ratio independent of external pressure; ap represents the variation of the void ratio that is proportional to the external pressure p within the studied pressure range, and a is the compaction coefficient of the thawing soil.Substituting equation (4) into equation (3), the amount of one-dimensional thaw settlement can be expressed as follows:(5)s=A1+e0h+a1+e0ph.ConsiderA¯=A/1+e0; a¯=a/1+e0, then(6)s=A¯h+a¯ph,where A¯ is called thaw coefficient; a¯ is called relative compaction coefficient of the thawing soil.


## 4.2. Relationship between Thaw Settlement Displacement and Porosity

Both thawing displacement and porosity increase as the soil thaws, as seen in Figure4, with maximum values of 5.2 mm and 22.6%, respectively. Furthermore, at the intensive phase transition zone of −2°C-2°C, porosity and thawing displacement rise substantially. When the temperature increases more than 2°C, both porosity and displacement begin to stabilize. Obviously, the change in porosity affects the development law of thaw settlement displacement. The thaw settlement displacement development law is consistent with the porosity development law.Figure 4
Variation of displacement and porosity with time during thawing.In the thawing process, the settlement displacement grows exponentially with the porosity, as seen in Figure5. Because the volume of ice in pores decreases throughout the thawing process, the pore water level rises. That is, the value of NMR-measured porosity is increasing. Meanwhile, as ice-soil particles thaw, their structure progressively disintegrates, causing formation settlement due to their own weight. After the ice melts into water, it slowly drains through the pores, and the settlement displacement increases with the compression of pores. The settlement displacement stabilizes as the number of pores that can be closed decreases. At the same time, the porosity does not rise. As a result, the vertical deformation of the test sample is mostly due to ice-water phase change and recombination of soil particles under self-weight. After freeze-thaw, the compressibility of the silty sand increases because of structural weakening.Figure 5
Relationship between porosity and thawing settlement in thawing process.


## 4.3. Relationship between Thaw Settlement Rate and Pore Size Distribution

The relationship between thaw settlement rate and pore diameter distribution is seen in Figure6. As the temperature rises, so do the number of pores of various sizes. However, the magnitude of the increase varies with the pore size. The proportion of medium and large pores (>0.1 μm) increases rapidly, whereas the proportion of small pores (<0.1 μm) increases slightly, but both of them contribute to an increase in porosity after freeze-thaw. Each of them increases sharply in the −2°C-2°C intense phase transition zone before slowing down at temperatures above 2°C. The constant formation of ice crystals in pores throughout the freezing process has disrupted the link between the soil particles, causing them to be squeezed to create a new skeletal structure. Small pores are joined to generate big pores at the same time. The structure of the soil changes. At the same time, the absence of ice crystals during the thawing process cannot entirely rebuild the skeletal structure, which will eventually be weakened by freeze-thaw.Figure 6
Variation of pore size and thawing settlement rate in the thawing process.In the thawing process, the settlement rate grows exponentially with the proportion of pores, as seen in Figure7. The rate of thaw settlement increases as the temperature rises. When the proportion of pores increases, the development law of thaw settlement rate increases. When the temperature rises above freezing point, the rate of increase accelerates. The number of medium and large pores is the most important element in determining the rate of thaw settlement. The number of medium and large pores increases sharply in the intensive phase transition zone of −2°C-2°C, and a huge number of them are compressed. Thus, the thaw settlement rate increases significantly. The thaw settlement rate tends to be steady due to the dissipation of pore water pressure and the continual closing of pores.Figure 7
Relationship between pore size and thawing settlement rate in the thawing process.


## 4.4. Cause of Thaw Settlement

Studies have shown that the brittleness of soil will increase at low temperatures, and the humidity of the environment will lead to short-term or long-term damage to materials and structures, which is more pronounced after freeze-thaw cycles. Firstly, cyclic pressure caused by water during freezing and thawing can cause damage to materials, such as through erosion, microcracks, or thermodynamic mechanisms to weaken the performance of materials. Secondly, the damage caused may effectively increase the overall pore space and enhance permeability, resulting in increased water content. The increasing crack and void volume cause the overall decline of soil properties such as strength and stiffness. The soil becomes loose and contains ice crystals after freezing, which is not dense enough in the natural state, and thaw settlement occurs under the action of self-weight.When the soil is frozen, the soil experiences frost heaving. However, the volume expansion caused by the phase change of water which is 1/9 has little contribution to frost heave. The main reason for frost heave is that the water in other parts of the formation migrates to the frozen soil, and the increased part of water needs to occupy a certain space after freezing. At the same time, due to the migration of water and dispersed mineral particles, new and extremely complex cryogenic structures are formed. The formed ice causes the differentiation of soil in joints. The mineral particle aggregates and soil layers are squeezed by ice crystals, and the soil structure changes.When the temperature rises, the ice in the pores of the soil begins to thaw, the cohesion between the mineral particles controlled by the ice bonding decreases, and the cohesion of the soil decreases sharply after complete thawing. When the frozen soil thaws, the structure of soil in the open system with water supply changes dramatically, and its porosity increases significantly. Therefore, the compressibility of the soil after thaw is high, and the thaw settlement of the formation is obvious. The change of structure during the thawing of frozen soil not only affects the compressibility of soil, but also affects the permeability of the soil. The permeability coefficient of the soil after thaw is often many times larger than that of unfrozen soil with the same composition. The change of internal structure of soil after freezing and thawing leads to the decrease of foundation bearing capacity, which is characterized by the settlement of formation. The settlement of the foundation drives the longitudinal bending deformation of underground structures such as tunnel structures until the structure is damaged, which is an important reason for the occurrence of underground structure disasters by the ground freezing method.


## 5. Conclusions

The freeze-thaw curves of silty sand were determined using the artificial frozen soil thaw settlement experiment. When used in conjunction with the NMR test, the mechanism of thaw settlement can be examined from a microscopic perspective, taking pore structure evolution into account. The main conclusions are obtained as follows:(1)
The evolution of temperature and thaw settlement displacement in the sample under unidirectional freezing is classified into three stages: cooling, frost heaving, and thaw settlement. The thaw settlement displacement increases dramatically first and then stabilizes as the thawing progresses.(2)
Porosity reduces as temperature decreases but increases during the thawing process. After freeze-thaw, the porosity is greater than the initial porosity. From 20 to −10 degrees Celsius, the NMR porosity reduced from 18.37 to 0.8 percent. The porosity significantly increased during the thawing process, reaching 21.0 percent at 20°C. Porosity increases dramatically in the intensive phase transition zone between −2°C and 2°C. When the temperature exceeds two degrees Celsius, the porosity progressively achieves a stable state. The development of thaw settlement displacement is dependent on changes in porosity, and the displacement increases exponentially as porosity changes during the thawing process.(3)
The freeze-thaw progress has a substantial effect on the silty sand’s pore structure. After freeze-thaw, the proportion of medium and large pores (>0.1 m) grows rapidly, while the proportion of small pores (<0.1 m) decreases slightly. During the thawing progress, both of them increase rapidly in the temperature range of −2°C to 2°C and subsequently slow down. As a result, the thawing settlement rate’s development law is consistent with that of a proportion of pores. The amount of medium and large pores is a critical component in determining the rate of thaw settlement.(4)
The change of pore structure during the thawing of frozen soil increases the compressibility of soil. The change of internal structure of soil after freeze-thaw leads to the decrease of foundation bearing capacity. High compressibility of the soil after freeze-thaw results in thaw settlement of the formation, which is an important reason for the occurrence of underground structure disasters by ground freezing method.The research on thawing settlement can provide theoretical guidance for the construction of underground engineering using an artificial freezing method and reduce the negative impact of frost heaving and thawing settlement of soil caused by freezing on the environment. While the influence of soil seepage and thermal conductivity on pore characteristics was not considered in this study, the relationship between pore and hydrothermal parameters during freeze-thaw should be established in the follow-up study. In addition, in the laboratory test of the soil thaw process, the temperature control system of the test device is required to have high-performance temperature control ability. In the future, the temperature control performance of the test device needs to be improved to improve the level of the frozen soil test.



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*Source: 1249180-2022-05-13.xml*