Ground Temperature Monitoring and Simulation of Temperature Field Changes in Block-Stone Material Replacement Foundation for the Shiwei–Labudalin Highway

Abstract

The current thermal balance of permafrost in northeastern China has been upset by human engineering construction disturbances and global warming. This has resulted in a rise in ground temperature and a fall in the permafrost table, which has a major impact on the stability, longevity, and operational safety of highway subgrades. To solve the issues above, the ground temperature monitoring data at K60+230 of the Shiwei–Labudalin highway were analyzed, and the numerical simulation of the temperature field change over 15 years was carried out for the ordinary subgrade as well as for sections of block-stone material subgrade with 1 m of straight-filled and different thicknesses of replacement fill (1 m, 2 m, 3 m, 4 m) by applying Comsol Multiphysis software. The results show that the temperature field of the subgrade exhibits significant asymmetry. There are variations in the rate of decline at different sites during the course of the 15 years when compared to where the permafrost table was located at the start of the study. Still, the rate of decline of the permafrost table is decreasing yearly. The straight-filled 1 m block-stone subgrade has a permafrost table 0.77 m higher in the bottom portion of its top surface than the ordinary subgrade. The replacement 1 m, 2 m, 3 m, and 4 m block-stone subgrade has a permafrost table in the lower portion of the top surface that is 1.05 m, 2.12 m, 3.32 m, and 4.75 m higher than the ordinary subgrade. The replacement block-stone subgrades, as opposed to ordinary subgrades, can strengthen the foundation, raise the permafrost table, and effectively reduce the impact of the upper boundary temperature on the lower permafrost. They can also increase the stability of permafrost subgrades. Of them, the block-stone filling with a thickness of 4 m and a particle size of 6–8 cm had the best impact.

1. Introduction

Permafrost is extremely susceptible to temperature fluctuations outside. Changes in the permafrost table are directly impacted by human activity and highway construction, disrupting the heat balance of warm permafrost. Field investigations and monitoring are crucial techniques for researching the impacts of the temperature field on permafrost subgrades. Analyzing the distribution and change rule of the temperature field inside the subgrade is a prerequisite for studying the thermal stability of the subgrade, and it is also the key to the comprehensive design and management of subgrade diseases. Therefore, a large number of scholars have conducted relevant research work.

Mu et al. [1] found that highway diseases in permafrost areas are closely related to the change in permafrost ground temperature through field investigation and monitoring. Xu et al. [2] analyzed the ground temperature monitoring data of different types of subgrade structures in the high-temperature permafrost zone and found that ordinary subgrades could not maintain the thermal stability of the permafrost under them for many years. Cheng et al. [3] analyzed the effects of engineering geological factors, subgrade structural factors, and natural environmental factors on the thermal stability of permafrost subgrade based on the thermodynamic properties of permafrost. He et al. [4] analyzed the distribution law of the temperature field of the typical subgrade section in the Naqu–Yangbajing section of the permafrost zone and determined that the subgrade monitoring section as a whole does not exist due to freezing and the expansion of uneven deformation triggered by the instability of the subgrade safety hazards. Merzlikin et al. [5] calculated the temperature distribution of a combined model of a frozen subgrade in winter in the Northern Hemisphere. Li et al. [6] conducted continuous monitoring of subgrades of two selected highway sections in the warm permafrost zone along the Qinghai–Tibet Highway for a period of three years, and the field monitoring data showed that the settlement of the subgrades was mainly caused by the thawing of the permafrost. According to the above literature, the current monitoring of the temperature field of subgrades in permafrost regions in China mainly focuses on the high-altitude permafrost region of the Qinghai–Tibet Plateau, and there are relatively few studies on the monitoring of the temperature field and highway diseases in the high-latitude permafrost region of northeastern China. By monitoring the regional climate and the temperature field of the roadbed where the Murola Highway is located, we can fill the gap in the study of the temperature field of the permafrost subgrade in the high-latitude permafrost region of northeastern China and provide basic information for the construction of road projects in this region. Numerical simulation research on the object of study is essential because, despite recent advancements in research on subgrade disease in permafrost regions, the problem remains unsolved due to the variety and complexity of various objective conditions in various road sections. Based on this research, it can be tailored to the local conditions to formulate more effective prevention and control measures for highway disease.

Jiang et al. [7] numerically simulated the temperature field of the permafrost subgrade using different boundary conditions to obtain the effect of different pavement types on the temperature field of the subgrade. Ordinary hot rods use the difference between the atmospheric temperature and the temperature of the workmass in the device to drive a phase change in the workmass to draw heat from the permafrost [8]. Pan et al. [9] concluded that the use of hot bars to protect permafrost and enhance the thermal stability of the subgrade is successful and effective in subgrade engineering by comparatively analyzing the changes in temperature field distribution of the subgrade for different climatic conditions. Block-stone subgrades mainly use natural convection to cool the permafrost subgrades, i.e., cold air convection is used to cool down the subgrades in the cold season and hot air is blocked in the warm season [10], thus cooling the permafrost foundations and enhancing the stability of the subgrades [11]. Ma et al. [12] analyzed the change in ground temperature under the joint action of block-stone and subgrade fill in permafrost areas with different ground temperatures and obtained that the block-stone subgrade plays a positive role in cooling the lower soil. For the long-term thermal stability of subgrades, a large number of scholars have also conducted relevant studies through numerical simulations, which have promoted the application and development of cooling measures in the permafrost zone. Liu et al. [13] carried out a two-dimensional finite element analysis of subgrades with different depths of insulation in a permafrost area in Tibet, where the lower permafrost was protected by changing the size and location of the insulation. Yang et al. [14], through the establishment of a finite element analysis model on different subgrades and melt depth change rules, obtained the composite subgrade cooling effect is optimal. Li et al. [15] obtained that the separated ventilation pipe subgrade has a better cooling effect by establishing a numerical model, which can ensure the long-term thermal stability of the subgrade and its lower permafrost. Pei et al. [16] simulated the ground temperature, principal strain, deformation, and factor of safety for four typical seasons during the operation of the embankment, and the results showed that the crushed rock interlayer was effective in cooling the slope embankment and its foundation. As the development and storage conditions of permafrost in Northeast China are more complicated, the above management measures are not fully applicable [17], so it is necessary to propose control measures suitable for the permafrost areas in Northeast China.

In the context of global warming and permafrost degradation, research around the cooling effect of block-stone subgrades in actual engineering and the long-term thermal stability of block-stone subgrades using numerical simulation has attracted extensive attention from scholars in recent years [18,19], but the related research in northeast China is relatively small and still in the development stage [20]. In this paper, the K60+230 section of the Shiwei–Labudalin highway is taken as the research object. By analyzing the monitoring section’s temperature field distribution and variation law, a heat transfer model of the permafrost subgrade is established, considering the phase transformation of ice water and the natural convection heat transfer of air in the block-stone layer. The temperature field of the subgrade for 15 years is simulated by COMSOL Multiphysics 6.0. By comparing the simulation results with the monitoring data, the variation law of the temperature field of the permafrost subgrade and the influence law of the block-stone subgrade on the lower soil temperature are analyzed, which provides a scientific basis for the design, maintenance, and reinforcement of highway subgrade in cold regions.

2. Study Area

The Shiwei–Labudalin highway is the transit section of the G331 highway in Erguna City. Its construction grade is a secondary highway, and work on it began in June 2013 and was finished and opened to traffic in October 2016. The research location is situated in the northern region of Nei Mongol, Erguna City, as shown in Figure 1. This area has a temperate monsoon climate and a mid-temperate continental steppe climate, with a short and fast warming spring, a warm and rainy summer, a short and fast cooling autumn, and a cold and long winter. The variations in the study area’s monthly average temperature and precipitation over 2020–2023 are depicted in Figure 2, based on data from the Erguna meteorological station. The region’s average annual temperature is roughly −0.45 °C, with a modest increase in recent years. The lowest temperature is −39.2 °C in January, and the highest temperature is 37.1 °C in July. The precipitation total for the year is 363.4 mm, with the majority falling between June and September. This represents around 79% of the annual precipitation. The research area’s surface water is abundant with rivers that twist and turn, creating many oxbow lakes. The river valleys have a lot of wetland development and are often open and level. Most places with permafrost are verdant landscapes, terraces, river floodplains, and mountain valleys with shaded slopes. Permafrost is in a hydrothermally unstable state, deteriorates, and experiences high ground temperatures.

3. Methods

The monitoring of the temperature field of the Shiwei–Labudalin highway adopts methods such as on-site investigation and the deployment of temperature sensors. By deploying sensors to monitor the temperature of the soil body of the roadbed and combining it with the changes in atmospheric precipitation and temperature, the basic data can be obtained to analyze the degradation of the permafrost and its influence on the stability of the roadbed. Based on the ground temperature data, the initial conditions and boundary conditions are provided for the subsequent numerical simulation, and the finite element model is used to simulate the temperature field of the Shiwei–Labudalin highway. The methods and data used in the study are mainly as follows:

3.1. Soil Temperature Sensors

Temperature monitoring using a high-precision thermistor, temperature measurement range: −50~50 °C, accuracy of ±0.02 °C, dissipation constant: not less than 0.5 mv/°C; time constant: not more than 5 s.

3.2. Meteorological Data

Meteorological data were obtained from the China Meteorological Data Network (http://data.cma.cn) accessed on 20 March 2024. Precipitation and temperature data were collected from 2020 to 2023 at the Erguna meteorological station.

3.3. Numerical Simulation

A numerical simulation of an ordinary roadbed was carried out using Comsol Multiphysics software to establish a computational model for the temperature field of an unsteady phase change roadbed, considering the effect of climate warming on the temperature field. The numerical simulation of the block roadbed is coupled with three physical fields of the Brinkman equation, fluid heat transfer, and coefficient-type partial differential equation in Comsol Multiphysics software.

4. Analysis of Ground Temperature Monitoring Data

4.1. Layout of Monitoring Point

The K59–K61 sections experienced varying degrees of subgrade settlement following the road’s opening to traffic. To monitor the distribution of temperature field conditions and changes within the subgrade, the station was constructed in June 2019, with high-precision thermistors used for temperature monitoring and five temperature measurement holes set up in each section, as shown in Figure 3 below. Five temperature measurement holes are located in the medial divider: the right toe of the slope, the left toe of the slope, the right natural hole, and the left natural hole. The depth of the measurement holes is 15 m. A measurement temperature hole is positioned at a distance of 0.5 meters to each in the range of 0 to 13 meters and at a distance of 1 meter to each in the range of 13 to 15 meters.

4.2. Overall Change in Ground Temperature

Based on the monitoring data of the subgrade section at K60+230 of the Shiwei–Labudalin highway from January 2020 to December 2023, the contour plots of soil temperature changes at different locations of the subgrade were plotted using Surfer 15 software, as shown in Figure 4.

The contours in the contour plots are denser at the surface, indicating that the degree of soil temperature variation with air temperature increases with proximity to the surface. In general, in any season, the contour lines at the surface are denser, and as depth increases, they progressively become sparser. The temperature of the shallow soil layer that makes up the highway subgrade is more sensitive to changes in the atmosphere, and it varies more and exhibits clear seasonal patterns. In the summer, the air temperature rises gradually, and the subgrade’s shallow soil temperature likewise exhibits a quick increase in trend. However, as the soil’s depth progressively increases, the rate of soil temperature rise also gradually decreases and eventually tends to stabilize. In winter, the air temperature gradually drops, and the subgrade’s shallow soil layer also experiences a sharp drop in temperature. As soil depth increases, the rate at which the lower subgrade’s soil cools down gradually slows down and eventually tends to stabilize. Because it does not experience freeze–thaw cycles and is kept in a relatively steady negative temperature condition, the soil deeper in the subgrade responds to variations in ambient temperature less strongly.

From 2020 to 2023, the active layer thickness under the medial divider increased by 0.5 m from 7.5 m to 8 m; the active layer thickness under the right toe of the slope increased by 0.5 m from 4.5 m to 5 m; the active layer thickness under the right natural hole increased by 2 m from 2 m to 4 m; and the active layer thickness under the left toe of the slope increased by 0.5 m from 2 m to 2.5 m. The thickness of the active layer under the left natural hole did not increase significantly. The melting depth at each location is significantly greater than the freezing depth, indicating that the lower permafrost at each place is unstable and that the lower soil collects more heat than it dissipates.

Taking the medial divider as an example, the soil of the subgrade started freezing from the top surface first in November 2020, i.e., from the surface layer of the soil freezing from the top downwards, the external atmospheric temperature decreased, and the temperature of the soil in the lower part of the subgrade also decreased. At the same time, the freezing fronts inside the soil continued to develop downward and reached the maximum freezing depth of about 4 m in April 2021. There was a roughly five-month freeze. In 2021, when the temperature of the top surface of the embankment was persistently higher than 0 °C in May, the soil layer inside the embankment began to melt. From June to August, in the shallow soil of the embankment, the temperature of the soil at a depth of 0~2 m increased rapidly. Compared with the deep soil temperature significant changes, the temperature of the deeper soil recovered relatively slowly, and the medial divider reached a maximum melt depth of about 8 m in October 2023.

In 2020, the soil at 0.5 m depth at the medial divider reached the highest temperature of 23.29 °C in late July and the lowest temperature of −17 °C in February. The date of the lowest and highest temperatures attained by the lower soil exhibited a progressive delay as the depth increased, indicating the existence of a hysteresis phenomenon in the temperature change in the soil at the lower section of the subgrade with the depth. At a depth of 4.5 m, the highest temperature of the soil was 3.99 °C; the date when the soil temperature reaches the highest value is delayed by nearly 4 months compared with the depth of 0.5 m. The lowest temperature of the soil is −0.13 °C; the date when the soil temperature reaches the lowest value is delayed for nearly 3 months compared with the depth of 0.5 m. It can be concluded that the hysteresis effect of the temperature of the soil in the lower part of the subgrade is smaller than that of the warm season in the cold season. The heat transfer is more rapid during the cooling process of the soil under the subgrade.

To see the thickness of the active layer at different locations more clearly, the origin software was applied to draw the envelope diagram, as shown in Figure 5. The 0 amplitude depth of the four positions is different. The depth of 0 amplitudes at the medial divider and the right toe of the slope is about 4 m, and the depth of 0 amplitudes at the left natural hole and the left toe of the slope is about 2 m. It can be concluded that the heat absorption of the road surface has a large impact on the medial divider, resulting in a significant perturbation of the permafrost in the lower portion of this location, which is specifically reflected in the increase in the depth of the 0 amplitude in the lower part of the location. Under the influence of the heat absorption of the road surface, the maximum temperature of the surface at the medial divider can be up to 26.37 °C, and the maximum temperature is significantly higher than in other locations. The minimum temperature of the surface in the medial divider is −20.37 °C, and the minimum temperature is smaller than the minimum temperature of other locations. The large difference in ground temperatures at the left and right toe of the slope, i.e., the large lateral difference in subgrade temperatures, is due to the sunny–shady slope effect, which also leads to significant disturbance of the permafrost in the lower part of the right toe of the slope.

4.3. Heat Flux Near the Permafrost Table

Temperature field changes in the permafrost regions are mainly affected by surface radiation and earth heat flow. External energy enters the interior of the subgrade through the active layer, affecting the development of the permafrost table within the subgrade. In the study of temperature field changes and the distribution of subgrades in cold regions, the heat flow changes in permafrost are often estimated by calculating heat fluxes near the permafrost table [21].

According to the principle of heat conduction, the heat flux into the depth range in the one-dimensional vertical direction can be approximately described as:

$$\mathrm{Q}=\sum _{\mathrm{i}=1}^{12}{\mathrm{q}}_{\mathrm{i}}$$

(1)

$${\mathrm{q}}_{\mathrm{i}}=\mathsf{\lambda }{\displaystyle \frac{\mathsf{\partial }\mathrm{T}}{\mathsf{\partial }\mathrm{H}}}{\mathrm{T}}_{\mathrm{I}}\approx \mathsf{\lambda }{\displaystyle \frac{{\mathrm{T}}_1-{\mathrm{T}}_2}{\mathsf{\Delta }\mathrm{H}}}{\mathrm{T}}_{\mathrm{i}}$$

(2)

where Q is the heat flux into the set depth range in one year; ${\mathrm{q}}_{\mathrm{i}}$ is the heat flux in month i; λ is the thermal conductivity of the soil, which is taken as 1.19 W∙m⁻¹∙K⁻¹ for melting and 1.43 W∙m⁻¹∙K⁻¹ for freezing [22]; Ti is the length of time in month i; ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ are the ground temperatures at the depth near the permafrost table in the medial divider and the right natural hole, respectively; H is the depth of permafrost; ΔH is the calculated depth range of the heat flux, taken as 0.5 m.

Figure 6 shows the heat flux of the soil beneath the medial divider and the right natural hole, calculated according to the ground temperature monitoring data from 2020 to 2023. It can be observed that there is essentially no difference in the trend of heat flux change between the medial divider and the right natural hole. Both of the lower soils’ heat fluxes exhibit cyclical patterns. The heat-absorbing period is relatively shorter, and the trend of the change is more intense. The heat-exporting period is relatively longer, and the trend of the change is milder.

During the monitoring period, the medial divider and the right natural hole at this depth were heat-absorbing. For instance, in 2023, the right natural hole had a total heat flow of 131.85 W/m², while the medial divider had a total heat flux of 171.07 W/m². The permafrost in the bottom portion of the medial divider is more unstable than that in the right natural hole, as indicated by the greater vertical heat absorption rate in the medial divider compared to the right natural hole. The primary cause is that, at the same depth below the ground surface, the medial divider is more susceptible to the effects of engineering disturbance and external ambient temperature.

5. Numerical Simulation of Temperature Field of Permafrost Subgrade

The temperature distribution within the subgrade can be immediately reflected by on-site ground temperature monitoring. However, on-site monitoring can only be carried out in a limited range of time and space in most cases, which is not only unable to accurately describe the internal conditions of the subgrade and the lower part of the foundation but also unable to carry out a long-term prediction of the use of the subgrade. Therefore, it is essential to perform a more thorough simulation of the temperature field. To further study the temperature field change characteristics of the subgrade of the Shi-La highway, a finite element numerical model was established to analyze the temperature field change in the subgrade within 15 years.

5.1. Model Description

5.1.1. Geometric Model

This model uses the Shi-La highway’s K60+230 subgrade section as an example. To accurately simulate the actual situation of the subgrade and simplify the calculation process of the model, the dimensions of the model are determined according to the actual situation of the project, and the model is treated as a two-dimensional model for analysis.

The specific performance is as follows: 3 m is the set height of the embankment, 10 m is the set width of the top of the embankment, and 1:1.5 is the set slope of the embankment side slope. The calculation range is from the top of the embankment to the bottom of the foundation, taking a total depth of 18 m and a width of 40 m. The thickness of the upper 3 m is the embankment fill. The middle 10 m of thickness is silty clay. The distance from the ground below 10 m is the moderately weathered andesite, and the thickness of the moderately weathered andesite is 5 m. The model specifics are shown in Figure 7.

5.1.2. Mathematical Model

The subgrade is simplified as a planar structure, and for the two-dimensional hydrothermal coupling problem of the subgrade, according to Fourier’s law and considering the latent heat of the phase transition as a heat source, obtain the temperature field control equation under the phase transition [23].

$$\mathsf{\rho }{\mathrm{C}}_{\left(\mathsf{\theta }\right)}={\displaystyle \frac{\mathsf{\partial }\mathrm{T}}{\mathsf{\partial }\mathrm{t}}}={\mathsf{\lambda }}_{\left(\mathsf{\theta }\right)}{\nabla }^2\mathrm{T}+\mathrm{L}{\mathsf{\rho }}_{\mathrm{I}}{\displaystyle \frac{\mathsf{\partial }{\mathsf{\theta }}_{\mathrm{I}}}{\mathsf{\partial }\mathrm{t}}}$$

(3)

where ρ is the density of the soil; C is the volumetric heat capacity; λ is the thermal conductivity of the soil; $\nabla$ is the differential operator, representing the differentiation of the space; L is the latent heat of the phase transition of ice and water (355 j/g); ${\mathsf{\rho }}_{\mathrm{I}}$ is the volumetric weight of ice; ${\mathsf{\theta }}_{\mathrm{I}}$ is the volumetric ice content.

According to Richard’s equation, and combined with the hindering effect of pore ice on the migration of unfrozen water, the migration law of water permafrost can be expressed as the following equation:

$${\displaystyle \frac{{\mathsf{\theta }}_{\mathrm{u}}}{\mathsf{\partial }\mathrm{t}}}+\nabla (-{\mathrm{D}}_{\left({\mathsf{\theta }}_{\mathrm{u}}\right)}\nabla -{\mathrm{K}}_{\mathrm{g}({\mathsf{\theta }}_{\mathrm{u}})})+{\displaystyle \frac{{\mathsf{\rho }}_{\mathrm{I}}}{{\mathsf{\rho }}_{\mathsf{\omega }}}}{\displaystyle \frac{\mathsf{\partial }{\mathsf{\theta }}_{\mathrm{I}}}{\mathsf{\partial }\mathrm{t}}}=0$$

(4)

where ${\mathrm{D}}_{\left({\mathsf{\theta }}_{\mathsf{\mu }}\right)}$ is the soil’s hydraulic conductivity; ${\mathrm{K}}_{\mathrm{g}({\mathsf{\theta }}_{\mathsf{\mu }})}$ is the soil permeability coefficient in the direction of gravitational acceleration; and ${\mathsf{\rho }}_{\mathrm{I}}$ is the density of ice.

The blocking effect of pore ice reduces the migration of unfrozen water, and pore ice makes the original diffusion rate and infiltration rate of water I times that of the same unfrozen water content. The blocking coefficient can reflect the difference between the diffusion of water in frozen and unfrozen soil.

$$\mathrm{D}=\mathrm{k}·\mathrm{I}/\mathrm{c}$$

(5)

$$\mathrm{I}={10}^{-10{\mathsf{\theta }}_{\mathrm{I}}}$$

(6)

where I is the impedance factor.

In this numerical simulation, the relative saturation S is used as the solution variable instead ${\mathsf{\theta }}_{\mathrm{u}}$, and the expression is as follows:

$$\mathrm{S}={\displaystyle \frac{{\mathsf{\theta }}_{\mathrm{u}}-{\mathsf{\theta }}_{\mathrm{r}}}{{\mathsf{\theta }}_{\mathrm{s}}-{\mathsf{\theta }}_{\mathrm{r}}}}$$

(7)

where ${\mathsf{\theta }}_{\mathrm{s}}$ is the saturated moisture content; ${\mathsf{\theta }}_{\mathrm{r}}$ is the residual moisture content of the soil.

Equation transformations can be obtained as follows:

$${\mathsf{\theta }}_{\mathrm{u}}=\left({\mathsf{\theta }}_{\mathrm{s}}-{\mathsf{\theta }}_{\mathrm{r}}\right)\mathrm{S} + {\mathsf{\theta }}_{\mathrm{r}}$$

(8)

The parameters included in the set of control differential equations for the temperature and moisture fields of permafrost are temperature, pore ice volume content, and unfrozen water volume content. Xu [24] concluded that the unfrozen water content is related to the initial moisture content of the soil, freezing temperature, and soil temperature, and by introducing empirical coefficients, an empirical expression for the unfrozen water content was given:

$${\displaystyle \frac{{\mathsf{\omega }}_0}{{\mathsf{\omega }}_{\mathrm{u}}}}={\left({\displaystyle \frac{\mathrm{T}}{{\mathrm{T}}_{\mathrm{f}}}}\right)}^{\mathrm{b}},\mathrm{T}<{\mathrm{T}}_{\mathrm{f}}$$

(9)

where ${\mathsf{\omega }}_0$ is the initial moisture content; ${\mathrm{T}}_{\mathrm{f}}$ is the freezing temperature of the soil (°C); b is the empirical coefficient related to the soil quality, which can be determined by test or taking the empirical value

The volume ratio of unfrozen water to pore ice in permafrost is the solid–liquid ratio of permafrost, denoted as ${\mathrm{B}}_{\mathrm{I}}$:

$${\mathrm{B}}_{\mathrm{I}}={\displaystyle \frac{{\mathsf{\theta }}_{\mathrm{I}}}{{\mathsf{\theta }}_{\mathrm{u}}}}=\left\{\begin{array}{cc}1.1{\left({\displaystyle \frac{\mathrm{T}}{{\mathrm{T}}_{\mathrm{f}}}}\right)}^{\mathrm{b}}-1.1& \hspace{1em}\hspace{1em}\hspace{1em}\mathrm{T}{<\mathrm{T}}_{\mathrm{f}}\\ 0& \hspace{1em}\hspace{1em}\hspace{1em}\mathrm{T}>>{\mathrm{T}}_{\mathrm{f}}\end{array}\right.$$

(10)

where the constant 1.1 represents the ratio belonging to the density of ice, ${\displaystyle \frac{{\mathsf{\rho }}_{\mathrm{I}}}{{\mathsf{\rho }}_{\mathsf{\omega }}}}$.

A transformation of the above equation gives the dynamic equilibrium equation for the phase change that relates unfrozen water content to ice content:

$${\mathsf{\theta }}_{\mathrm{I}}={\mathrm{B}}_{\mathrm{I}}\left(\mathrm{T}\right){\mathsf{\theta }}_{\mathrm{u}}$$

(11)

The phase transition dynamic equilibrium equations can be solved by joining the temperature and moisture fields.

5.1.3. Parameters of the Soil Layers

Combined with the engineering geological investigation report of the Shi-La highway and the research of reference scholars [25], the model’s physical parameters are shown in

Table 1. Moisture field parameters of the soil layers.

Soil Layers	${\mathbf{a}}_0$	j	l	${\mathsf{\theta }}_{\mathbf{r}}$(%)	${\mathsf{\theta }}_{\mathbf{u}}$(%)	${\mathbf{K}}_{\mathbf{s}}$(m/s)
embankment fill	2.36	0.5	0.5	0.07	0.55	6.50 × 10−6
silty clay	2.65	0.18	0.5	0.02	0.5	7.49 × 10−8
moderately weathered andesite	2.59	0.22	0.5	0.08	0.65	5.13 × 10−9

${\mathrm{a}}_0$ is the intrinsic wash; j is a model parameter; l is a model parameter; ${\mathsf{\theta }}_{\mathrm{r}}$ is the residual water content of the soil layer; ${\mathsf{\theta }}_{\mathrm{u}}$ is the unfrozen water volume content of the soil layer; and ${\mathrm{K}}_{\mathrm{s}}$ is the coefficient of permeability of the soil layer.

and

Table 2. Physical parameters of the soil layers.

Soil Layer	ρ(kg/m3)	${\mathbf{C}}_{\mathbf{u}}(\mathbf{J}/\mathbf{kg}·\mathbf{K})$	${\mathsf{\lambda }}_{\mathbf{u}}(\mathbf{W}/\mathbf{m}·\mathbf{K})$	${\mathbf{C}}_{\mathbf{f}}(\mathbf{J}/\mathbf{kg}·\mathbf{K})$	${\mathsf{\lambda }}_{\mathbf{f}}(\mathbf{W}/\mathbf{m}·\mathbf{K})$
embankment fill	1780	790	1.83	2530	2.51
silty clay	1670	1680	1.25	1620	1.41
moderately weathered andesite	2122	1840	1.93	1730	1.24

$\mathsf{\rho }$ is the density of the soil layer; ${\mathrm{C}}_{\mathrm{u}}$ is the specific heat capacity of the soil layer for melting; ${\mathrm{C}}_{\mathrm{f}}$ is the specific heat capacity of the soil layer for freezing; ${\mathsf{\lambda }}_{\mathrm{u}}$ is the thermal conductivity of the soil layer for melting; and ${\mathsf{\lambda }}_{\mathrm{f}}$ is the thermal conductivity of the soil layer for freezing.

.

5.1.4. Boundary Conditions

To simplify the actual situation, the temperature field part, the top boundary, the side slopes, and the natural ground surface undergo isothermal boundary processing. The upper boundary condition is the recorded ground temperature at 0.5 m below the surface; this can be determined by fitting the sinusoidal function. Northeast China is seeing an annual temperature increase of 0.037 °C/a due to climate change [26], and the warming rate is 0.037 °C/a. The model boundary conditions can be expressed in the following form:

$$\mathrm{T}\left(\mathrm{x},\mathrm{y},\mathrm{t}\right)={\mathrm{T}}_{\mathrm{i}}+\mathrm{Asin}\left({\displaystyle \frac{2\mathsf{\pi }\mathrm{t}}{8760}}+{\displaystyle \frac{\mathsf{\pi }}{3}}\right)+{\displaystyle \frac{0.037}{365}}\mathrm{t}$$

(12)

where t is the time variable, (d). The mean annual ground temperature ${\mathrm{T}}_{\mathrm{I}}$ and annual temperature amplitude A for each boundary are shown in

Table 3. Parameters of the temperature boundary conditions.

Boundary	${\mathbf{T}}_{\mathbf{i}}$ (°C)	A (°C)
Medial divider	2.31958	18.34224
Left toe of the slope	0.45162	2.67472
Right toe of the slope	3.12189	8.54856
Left natural hole	0.68466	4.7579
Right natural hole	0.29258	7.12944

.

Both sides of the model are set as adiabatic boundaries, and the lower boundary condition is taken to be a constant value of T = −0.6 °C.

5.1.5. Initial Conditions and Model Verification

In order to verify the correctness of the model constructed in this paper, the correctness of the model was verified by comparing the model temperature field with the existing measured ground temperature data. The simulation results at different depths with the measured temperatures were compared with the simulation results at different depths at representative dates in the freeze–thaw cycle process in the medial divider and in the right natural hole, and the results are shown in Figure 8 below.

The findings of simulation and monitoring indicate a slight variation, which is mostly attributable to temperature changes in the subgrade surface layer brought on by precipitation, snowfall, and other outside influences. Numerical simulation according to the actual monitoring data obtained from the boundary conditions and the actual situation has some differences, but the simulation results and the change rule of the actual monitoring data are basically the same, indicating that the simulation results basically conform to the actual situation. The subsequent computation and analysis can be performed using the model.

5.2. Analysis of Temperature Field Simulation Results for Frozen Road

In order to study the change in the temperature field of the permafrost subgrade with time, the distribution of the temperature field in October is analyzed according to the numerical simulation results in the 1st, 5th, 10th, and 15th years, and the contour plots are drawn. In order to better judge the permafrost table, the 0 °C contour is used as the eigenvalue, which is indicated by the red line in the graph, as shown in Figure 9.

As a whole, the temperature field shows a right-high and left-low asymmetry. The temperature on the right side of the subgrade section is higher than that on the left side. The top surface of the embankment and the right toe of the slope remain positively warm, but the temperature of the left toe of the slope has dropped below 0 °C, and the permafrost table in the lower part of the top surface of the embankment is not at the geometric center of the subgrade and is biased to the side of the right toe of the slope. The temperature of the top surface of the embankment gradually increased from 6.01 °C at the beginning of the simulation to 6.48 °C at the end of the simulation.

Under the influence of the shaded side slopes, the temperature of the soil in the lower part of the left toe of the slope is consistently low compared to the temperature of the soil in the lower part of the right toe of the slope, which results in the permafrost table in the lower part of the left toe of the slope being higher than that in the lower part of the right toe of the slope. As the simulation time increases, under the heat absorption of the subgrade, the lower permafrost table decreases for different locations in this section, in which the lower permafrost table at the medial divider and the right toe of the slope decreases significantly more than that at the right toe of the slope and at the natural ground surface, and the location of the permafrost table under the medial divider is always lower than that at the right toe of the slope. According to the contour plots, it can be seen that with the increase in simulation time, the permafrost table in the lower part of the right side of the subgrade decreases significantly more than that on the left side, which indicates that the influence caused by the sunny–shady slope effect on the temperature field of the subgrade deepens gradually with the passage of time.

As shown in

Table 4. Permafrost table at different locations on the subgrade.

Time	Medial Divider	Left Toe of the Slope	Right Toe of the Slope	Natural Ground Surface
Year 1	−5.02 m	−2.06 m	−4.52 m	−4.04 m
Year 5	−7.57 m	−4.65 m	−7.47 m	−4.96 m
Year 10	−9.49 m	−5.98 m	−9.09 m	−5.71 m
Year 15	−10.78 m	−6.67 m	−10.11 m	−6.23 m

, with the increase in simulation time, compared with the permafrost table’s location in the initial simulation stage, each location has a different degree of decline. The permafrost table at the lower part of the medial divider has decreased by 5.76 m, and the average rate of decline is 0.38 m/a, and the rate of decline is 0.51 m/a, 0.38 m/a, and 0.26 m/a in every 5 years in turn. The permafrost table at the left toe of the slope decreased by 4.61 m; the average rate of decrease was 0.31 m/a; and the rate of decrease per 5 years was 0.52 m/a, 0.27 m/a, and 0.14 m/a in the order of 0.52 m/a, 0.27 m/a, and 0.14 m/a. The permafrost table in the lower part of the right toe of the slope decreased by 5.59 m, and the average rate of decrease was 0.37 m/a, and the rate of decrease per 5 years was 0.59 m/a, 0.32 m/a, and 0.20 m/a in the order of 0.59 m/a, 0.32 m/a, and 0.20 m/a. The permafrost table in the lower part of the natural ground surface decreased by 2.19 m, with the average rate of decrease being 0.15 m/a and the rate of decrease being 0.18 m/a, 0.15 m/a, and 0.10 m/a in the order of every 5 years. It can be concluded that the rate of decline of the permafrost table in this section has been gradually slowing down, indicating that the temperature of the soil in the lower part of the subgrade has increased under the influence of the temperature of the upper boundary, but the trend of growth has been gradually decreasing.

This results in a gradual slowing down of the rate of decrease in the permafrost table for all the years in this section, indicating that the temperature of the soil in the lower part of the subgrade has increased under the influence of the temperature of the upper boundary, but the trend of increase is gradually decreasing. The permafrost table in the lower part of the medial divider decreased at the fastest rate, and the lower part of the permafrost table at the right toe of the slope decreased at a significantly faster rate than that at the left toe of the slope. This phenomenon occurs because the sunny–shady slope effect accelerates the degradation of the permafrost in the lower part of the right toe of the slope.

The simulated temperature data in October of year five at different locations were extracted, and the simulation results were compared with the measured data in October 2023. Plot the curves as shown in Figure 10.

As can be seen from Figure 9 above, the simulation results of shallow soil temperature at each location are larger than the measured data. The location of 0 °C is lower than the actual location, especially in the medial divider, and the right toe of the slope is more obvious. The main reason for this phenomenon is that the Shi-La highway has been open to traffic since 2016 after delivery, and data monitoring began in 2020. During the data monitoring period, the amount of subgrade settlement is large, and the thickness of pavement repair in the medial divider location reaches 152 cm, which reduces the accuracy of the measured data. The simulation results are one year later than the measured data, during which time soil temperatures may have risen further and the permafrost table may have fallen further. The moisture field was not well coupled in the simulation process, thus affecting the coupling results of the temperature field. There is a gap between the various physical parameters of the soil used in the simulation process and the actual conditions in the field. In general, the simulation results and the measured data have roughly the same trend: with the increase in depth, the soil temperature gradually decreases and finally tends to stabilize.

6. Numerical Simulation of the Temperature Field of a Block-Stone Subgrade

In order to ensure the normal operation of highways in permafrost areas, special subgrade structures with active cooling effects are often used to solve the problem of subgrade diseases [27]. As an actively cooling subgrade, the block-stone subgrade can use the natural convection effect of the air within the block-stone subgrade to regulate the ground temperature and enhance the table of the subgrade man-made permafrost. In this section, the finite element numerical simulation software is used to carry out a simulation of the block-stone subgrade with different working conditions to analyze the effect of block-stone on the temperature field of the permafrost subgrade.

6.1. Model Description

6.1.1. Geometric Model

To model the temperature field of the block-stone subgrade, the model dimensions are the same as the dimensions of the model without the protection measures built in the previous section. The calculation model is shown in Figure 11 for the example of a block-stone layer with a thickness of 1 m.

6.1.2. Mathematical Model

To simplify the calculations, the temperature field model of the block-stone subgrade assumes that the gas inside the blocks is incompressible, in accordance with the Boussinesq assumption. In addition to the temperature field model, a natural convection heat transfer model within the blocks is also considered. The controlling equations construct the equations in two parts. Firstly, for the soil layer zone, the controlling equations are the same as in the previous section of this paper for ordinary subgrade. Secondly, for the block-stone layer zone, which is a porous medium containing a large number of pores, the controlling equations are as follows [28].

(1)

Continuity equation

In natural convection in porous media, air is considered as an incompressible fluid, and the equation simplifies to:

$${\displaystyle \frac{\mathsf{\partial }{\mathrm{v}}_{\mathrm{x}}}{\mathsf{\partial }\mathrm{x}}}+{\displaystyle \frac{\mathsf{\partial }{\mathrm{v}}_{\mathrm{y}}}{\mathsf{\partial }\mathrm{y}}}=0$$

(13)

where ${\mathrm{v}}_{\mathrm{x}}$ and ${\mathrm{v}}_{\mathrm{y}}$ are the seepage velocity of air in the x and y directions in the block-stone subgrade, respectively (m/s).

(2)

Momentum equation

The Brinkman equation is utilized to simulate within the block-stone layer.

$${\displaystyle \frac{\mathsf{\partial }\mathrm{p}}{\mathsf{\partial }\mathrm{x}}}=-{\displaystyle \frac{\mathsf{\mu }}{\mathrm{k}}}{\mathrm{v}}_{\mathrm{x}}-\mathsf{\rho }\mathrm{B}{\left({\mathrm{v}}_{\mathrm{x}}^2+{\mathrm{v}}_{\mathrm{y}}^2\right)}^{1/2}{\mathrm{v}}_{\mathrm{x}}$$

(14)

$${\displaystyle \frac{\mathsf{\partial }\mathrm{p}}{\mathsf{\partial }\mathrm{x}}}=-{\displaystyle \frac{\mathsf{\mu }}{\mathrm{k}}}{\mathrm{v}}_{\mathrm{y}}-\mathsf{\rho }\mathrm{B}{\left({\mathrm{v}}_{\mathrm{x}}^2+{\mathrm{v}}_{\mathrm{y}}^2\right)}^{1/2}{\mathrm{v}}_{\mathrm{y}}-{\mathsf{\rho }}_{\mathrm{a}}\mathrm{g}$$

(15)

where ρ is the air density; ${\mathsf{\rho }}_{\mathrm{a}}$ is the function of temperature with respect to air density

$${\mathsf{\rho }}_{\mathrm{a}}=0.641\left[1-\mathsf{\beta }\left(\mathrm{T}-{\mathrm{T}}_0\right)\right]$$

(16)

where B is the inertia drag coefficient; k is the medium permeability (m²); μ is the aerodynamic coefficient of adhesion, 1.75 × 10⁻⁵ kg/(m∙s); β is the coefficient of thermal expansion of air, 3.50 × 10⁻³; and T is the air temperature (°C).

Since the porous medium model includes both lumped solid and fluid components, the energy equation is as follows:

$$\mathrm{C}{\displaystyle \frac{\mathsf{\partial }\mathrm{T}}{\mathsf{\partial }\mathrm{t}}}=\mathsf{\lambda }\left({\displaystyle \frac{{\mathsf{\partial }}^2\mathrm{T}}{\mathsf{\partial }{\mathrm{x}}^2}}+{\displaystyle \frac{{\mathsf{\partial }}^2\mathrm{T}}{\mathsf{\partial }{\mathrm{y}}^2}}\right)+{\mathrm{C}}_{\mathrm{L}}\left({\mathrm{V}}_{\mathrm{x}}{\displaystyle \frac{{\mathsf{\partial }}^2\mathrm{T}}{\mathsf{\partial }{\mathrm{x}}^2}}+{\mathrm{V}}_{\mathrm{y}}{\displaystyle \frac{{\mathsf{\partial }}^2\mathrm{T}}{\mathsf{\partial }{\mathrm{y}}^2}}\right)$$

(17)

where: C is the equivalent specific heat capacity of the medium layer, 1004 J/(m³∙K); λ is the air thermal conductivity, 0.02 W/(m∙K); ${\mathrm{C}}_{\mathrm{L}}$ is the specific heat capacity of air.

6.1.3. Parameters of the Soil Layers

The calculation parameters for the embankment fill, silty clay, and moderately weathered andesite portions of the block-stone subgrade are the same as for the ordinary subgrade. Based on the summary of the related literature compilation [29,30]S, regarding the air permeability, 4.4 × 10⁻⁶ m² was taken for embankment fill, 1 × 10⁻⁹ m² was taken for silty clay, and 7.7 × 10⁻⁶ m² was taken for moderately weathered andesite.

For the block-stone layer part, the block-stone size used in this section of the simulation is 4–6 cm. Additionally, 6–8 cm and 10–15 cm are the block-stone sizes used in the simulation in the next section. The specific parameters are shown in

Table 5. Physical parameters of the block-stone layer with different particle sizes.

Particle Size (cm)	k (m2)	${\mathbf{C}}_{\mathbf{v}}$ (kJ/(m3∙K))	${\mathsf{\lambda }}_{\mathbf{s}}$ (W/(m∙K))	n (%)	ρ (kg/m3)
4~6	7.6e-7	1270	0.407	45.1	2100
6~8	4.3e-6	1250	0.396	45.7	2040
10~15	8.3e-6	1180	0.385	46.2	1950

below.

6.2. Analysis of Simulation Results of Cooling Effectiveness of Block-Stone Subgrade

The distribution of the temperature field in the 5th year, 10th year, and 15th year in October is analyzed based on the simulation results. The 0 °C isotherm is marked with a red line in the contour plot, as shown in Figure 12 and Figure 13.

As the simulation time increased, the permafrost table decreased to varying degrees at all locations in the lower part of the straight-filled 1 m block-stone subgrade. The permafrost table in the lower part of the medial divider decreased by 4.99 m, with an average rate of decline of 0.33 m/a, and the rate of decline per 5 years was 0.42 m/a, 0.34 m/a, and 0.24 m/a in that order. The permafrost table in the lower part of the left toe of the slope decreased by 3.62 m, with an average rate of decline of 0.24 m/a, and the rate of decline per 5 years was 0.43 m/a, 0.21 m/a, and 0.10 m/a. The permafrost table in the lower part of the right toe of the slope declined by 4.49 m, with a descending average rate of 0.30 m/a and a descending rate of 0.48 m/a, 0.25 m/a, and 0.17 m/a every 5 years in the order of 0.48 m/a, 0.25 m/a, and 0.17 m/a. The permafrost table in the lower part of the natural ground surface declined by 1.83 m, with a descending average rate of 0.17 m/a and a descending rate of 0.16 m/a every 5 years in the order of 0.16 m/a, 0.12 m/a, and 0.08 m/a.

As the simulation time increased, the permafrost table decreased to varying degrees at all locations in the lower part of the replacement 1 m block-stone subgrade. The permafrost table in the lower part of the medial divider decreased by 4.71 m, with an average rate of decline of 0.31 m/a, and the rate of decline per 5 years was 0.40 m/a, 0.33 m/a, and 0.22 m/a,. The permafrost table in the lower part of the left toe of the slope decreased by 3.29 m, with an average rate of decline of 0.22 m/a, and the rate of decline per 5 years was 0.35 m/a, 0.21 m/a, and 0.09 m/a. The permafrost table in the lower part of the right toe of the slope declined by 4.10 m, with an average rate of decline of 0.27 m/a, and the rates of decline per 5 years were 0.45 m/a, 0.22 m/a, and 0.15 m/a. The permafrost toe in the lower part of the natural ground surface declined by 1.70 m, with an average rate of decline of 0.17 m/a, and the rates of decline per 5 years were 0.14 m/a, 0.11 m/a, and 0.09 m/a.

In order to illustrate more clearly the change in the permafrost table under ordinary and block-stone subgrades, the trend of change in the permafrost table under different locations of the subgrades over a period of 15 years was analyzed, as shown in Figure 14.

As can be seen from Figure 14, the permafrost table of block-stone subgrade in different locations is higher than that of ordinary subgrade in the same year, and block-stone subgrade can effectively lift the permafrost table and play a certain role in heat preservation. The rate of decline in the permafrost table at different locations of both types of block-stone subgrades is decreasing from year to year, with a stabilizing trend. The cooling effect of the replacement block-stone subgrade is better than the effect of the straight-filled block-stone subgrade, which is able to better maintain the stability of the soil under the subgrade. With the increase in years, the difference between the permafrost table of block-stone subgrade and ordinary subgrade showed an overall increasing trend. The rate of decrease in the permafrost table at different locations of the block-stone subgrade was obviously lower than that of the ordinary subgrade. In summary, the stability of the block-stone subgrade over time is stronger than that of the ordinary subgrade, and the block-stone subgrade can effectively slow down the influence of the upper boundary temperature on the lower permafrost. In the construction of road projects in the permafrost areas of Northeast China, the replacement block-stone subgrade should be given priority to protect the permafrost effectively.

6.3. Numerical Simulation Study of Block-Stone Subgrade with Different Working Conditions

6.3.1. Thickness of Block-Stone

According to the numerical simulation results above, the block-stone layer has the effect of heat preservation and insulation, which can effectively reduce the temperature of permafrost deep in the foundation to reduce the degradation rate and maintain the stability of the subgrade. However, the block-stone layer with a thickness of 1 m has a limited role in protecting the lower permafrost. Therefore, to study the effect of different block-stone replacement thicknesses on the temperature field of the subgrade, the numerical simulation analysis was carried out in three conditions of 2 m, 3 m, and 4 m block-stone thickness, respectively.

(1)

Analysis of ground temperature variation with depth

Figure 15 shows the temperature at the medial divider as a function of depth for block-stone layer subgrades with different replacement thicknesses on October 10, the 15th year.

As shown in Figure 15, the effect of different replacement thicknesses of the block-stone layer on the temperature of the upper part of the soil is large. The effect of the block-stone thickness on the temperature of the soil decreases with an increase in its depth. The temperature of the soil in the lower part of the subgrade is lower when the thickness of the block stone is 4 m, and the temperature of the soil in the lower part of the subgrade is relatively more stable than the other thicknesses of the block stone. Under the same depth, the thickness of the block-stone layer increases, and the temperature of the soil gradually decreases.

For example, when the depth of the soil is 5 m, the thickness of the replacement block-stone layer increases from 1 m to 2 m, the ground temperature decreases by 0.1 °C, the thickness of the replacement layer increases from 2 m to 3 m, the ground temperature decreases by 0.31 °C, and the thickness of the replacement layer increases from 3 m to 4 m, the ground temperature decreases by 0.26 °C. Comparing the increase in the thickness of block-stone from 1 m to 2 m with that from 2 m to 3 m, the decrease in the temperature of the latter is more obvious, which indicates that the moderate increase in the thickness of block-stone will have a more obvious effect on the protection of the lower permafrost.

(2)

Analysis of the process of permafrost table change

In order to deeply investigate the influence of block-stone replacement thickness on the temperature field of permafrost subgrade, contour plots were drawn according to the numerical simulation results, and the 0 °C contour was taken as the key eigenvalue, which was indicated by a red line in the contour plots, as shown in Figure 16, Figure 17 and Figure 18.

As the simulation time increased, the permafrost table decreased to varying degrees at all locations in the lower part of the replacement 2 m block-stone subgrade. The permafrost table in the lower part of the medial divider decreased by 3.64 m, with an average rate of decrease of 0.24 m/a, and the rate of decrease per 5 years was 0.30 m/a, 0.24 m/a, and 0.19 m/a. The permafrost table in the lower part of the left toe of the slope decreased by 2.52 m, and the average rate of decrease was 0.17 m/a. The rate of decrease was 0.25 m/a, 0.17 m/a, and 0.09 m/a every 5 years. The permafrost table in the lower part of the right toe of the slope declined by 3.19 m, with a descending average rate of 0.21 m/a and a descending rate of 0.48 m/a, 0.25 m/a, and 0.17 m/a every 5 years. The permafrost table in the lower part of the natural ground surface declined by 1.33 m, with a descending average rate of 0.09 m/a and a descending rate of 0.11 m/a, 0.08 m/a, and 0.07 m/a every 5 years.

As the simulation time increased, the permafrost table decreased to varying degrees at all locations in the lower part of the replacement 3 m block-stone subgrade. The permafrost table in the lower part of the medial divider decreased by 2.44 m, and the average rate of decrease was 0.16 m/a. The rate of decrease was 0.20 m/a, 0.14 m/a, and 0.14 m/a every 5 years. The permafrost table in the lower part of the left toe of the slope decreased by 1.69 m, and the average rate of decline was 0.11 m/a. The rate of decline was 0.15 m/a, 0.11 m/a, and 0.07 m/a every five years. The permafrost table in the lower part of the right toe of the slope declined by 2.10 m, and the average rate of decline was 0.14 m/a; the rate of decline was 0.22 m/a, 0.13 m/a, and 0.07 m/a every 5 years. The permafrost table in the lower part of the natural ground surface decreased by 0.90 m; the average rate of decline was 0.06 m/a; the rate of decline per 5 years was 0.08 m/a, 0.05 m/a, and 0.04 m/a.

As the simulation time increased, the permafrost table decreased to varying degrees at all locations in the lower part of the replacement 4 m block-stone subgrade. The permafrost table in the lower part of the medial divider decreased by 1.01 m, and the average rate of decrease was 0.07 m/a. The rate of decrease was 0.08 m/a, 0.06 m/a, and 0.05 m/a. The permafrost table in the lower part of the left toe of the slope decreased by 0.80 m, and the average rate of decline was 0.05 m/a. The rate of decline was 0.07 m/a, 0.05 m/a, and 0.04 m/a every five years. The permafrost table in the lower part of the right toe of the slope declined by 0.88 m, and the average rate of decline was 0.06 m/a; the rate of decline was 0.09 m/a, 0.05 m/a, and 0.04 m/a every 5 years. The permafrost in the lower part of the natural ground surface decreased by 0.43 m; the average rate of decline was 0.03 m/a; and the rate of decline per 5 years was 0.04 m/a, 0.03 m/a, and 0.01 m/a.

In order to further understand the stability of the permafrost subgrade and the degradation of permafrost within the subgrade, the permafrost table change curves under different thicknesses of block-stone replacement subgrade were plotted, as shown in Figure 19.

As shown in Figure 19, after 15 years of simulation, the permafrost table under different working conditions was decreased to different degrees with the increase in thickness of the replacement block stone. The permafrost table rose, the magnitude of the change was reduced, and the cooling effect of the block-stone layer was further enhanced. In the actual project, the thickness of the block-stone layer can be increased appropriately to increase the stability of the lower permafrost and effectively protect it.

6.3.2. Block-Stone Particle Size

One of the main reasons for the natural convection inside the block-stone layer is that the particle size of the block-stone fill is much larger than that of the subgrade fill, and there is a large porosity inside the block-stone layer, which ensures convection movement of air under the effect of the temperature gradient. In order to analyze the effect of block-stone particle size on the internal temperature of the block-stone subgrade, the block-stone subgrade with particle sizes of 4~6 cm, 6~8 cm, and 10~15 cm was established for numerical simulation and comparative analysis. Based on the block-stone subgrade model with 4 m of replacement in the paper, only the particle size of the material was changed, and the rest of the conditions, such as boundary conditions, were the same as in the previous section.

Figure 20 shows the curves of temperature at the medial divider as a function of depth for the 10th of October for different block-stone particle sizes of the replacement block-stone subgrade.

As can be seen from Figure 19, the main difference in the temperature of the lower soil of different particle sizes of the replacement block-stone subgrade is at the surface, and the temperature difference decreases with the increase in depth. By further comparing the temperatures at the same depth under different particle sizes of the block-stone subgrade, it can be obtained that the temperature of the reclaimed block-stone subgrade with 6–8 cm particle size is the lowest, the temperature of the block-stone subgrade with 10–15 cm particle size is higher, and the temperature of the block-stone subgrade with 4–6 cm particle size is the highest. The ground temperature at a depth of 3 m under the natural ground surface is 0.1 °C, 0.15 °C, and 0.19 °C, respectively, indicating that the 6–8 cm block stone has the highest cooling effect and the stability of the roadbed is better. It can be concluded that the cooling effect does not vary with increasing particle size.

In order to further understand the effect of different block-stone particle sizes on the stability of the permafrost subgrade and the degradation of permafrost within the subgrade, the change curves of the permafrost table under different working conditions were plotted as shown in Figure 21.

It can be concluded from Figure 21 that the three different particle sizes of block-stone subgrades can lift the permafrost table in the lower part of the subgrade. The 6–8 cm size block-stone subgrade lifts the permafrost table more than the 4–6 cm and 10–15 cm size block-stone subgrades. The subgrade with 4~6 cm diameter has the smallest lifting height, and the subgrade with 10~15 cm diameter is in the middle of the two. Therefore, according to the above simulation results, the 6–8 cm size of the replacement block-stone subgrade shows a better cooling effect and raises the anthropogenic permafrost table compared to the 4–6 cm and 10–15 cm sizes of the replacement block-stone subgrade. That is, in practical engineering, moderately increasing the particle size of the block-stone can enhance the natural convection effect within the block-stone layer, thus further enhancing the stability of the lower permafrost. However, excessively increasing the size of the block-stone particle may affect the other physical parameters of the block-stone layer, thus weakening the protective effect of the block-stone subgrade on the lower permafrost. This shows that the cooling effect of natural airflow on the lower soil is greater than that of changing the physical coefficient.

7. Discussion

The design, construction, operation, and maintenance of road works in permafrost areas have been a worldwide challenge. Ensuring that permafrost subgrades can maintain long-term stability is the key to solving road engineering problems in permafrost areas. However, the properties of permafrost itself determine its sensitivity to changes in external environmental factors, such as temperature rise and engineering disturbances, which can lead to the degradation of permafrost. Permafrost, as a soil with high thermal sensitivity, has thermodynamic properties that are closely related to temperature, and slight temperature changes may cause the thermodynamic properties of permafrost to change dramatically. Therefore, it is very important to propose measures to protect permafrost. In this paper, we mainly study the change process of the temperature field of roadbeds in permafrost areas and put forward the corresponding measures to protect permafrost. With the deepening of our understanding of the research work, we can continue to research the following aspects: The process of simulated hydrothermal coupling of permafrost subgrade is relatively complicated; this paper only uses the first type of boundary conditions in the simulation process and does not take into consideration the other conditions, such as radiation, wind speed, etc., and we can then establish a hydrothermal coupling model that considers a variety of boundary conditions. In this paper, only the temperature field is simulated for the block-stone subgrade, and the next step is to consider the numerical simulation of multi-field coupling. The replacement thickness of the block-stone subgrade is only calculated at 4 m, and the optimal replacement thickness of the block-stone should be discussed in the next simulation.

8. Conclusions

In this paper, the national highway G331 Shiwei–Labudalin highway permafrost subgrade K60 + 230 section is the object of study. Through the monitoring of field data, the establishment of the permafrost area of the ordinary subgrade temperature field and the block-stone subgrade temperature field finite element model, the study of different working conditions of the block-stone subgrade cooling, and based on the prevention and control of related diseases to give a reasonable proposal. The main conclusions are as follows:

(1)

During the monitoring of the four freeze–thaw cycles, the temperature of the soil at different depths showed cyclic changes, showing obvious seasonal characteristics, with the shallow soil layer of the subgrade being significantly affected by the air temperature and the soil at deeper depths responding less to changes in atmospheric temperature, due to the fact that it did not undergo a freeze–thaw cycle and was maintained in a relatively stable negative temperature state. The permafrost table in the lower part of the subgrade at all locations has decreased to different degrees, with the medial divider decreasing by 0.5 m, the left toe of the slope by 0.5 m, the right toe of the slope by 0.5 m, and the right natural hole by 2 m, which is the main reason for the uneven settlement of the subgrade. The temperature change in the soil under the subgrade has a hysteresis phenomenon with increasing depth, and the hysteresis effect in the cold season is smaller than that in the warm season. Due to the sunny–shady slope effect, the lateral difference in subgrade temperature is large. The heat gains and losses in the medial divider and the right natural hole both show heat absorption; the medial divider is more affected by external ambient temperatures as well as engineering disturbances.

(2)

According to the numerical simulation results of the ordinary permafrost subgrade, the temperature field of the subgrade shows an asymmetry of right-high and left-low due to the sunny–shady slope effect. The permafrost table decreased to different degrees at all locations during the simulation. The average rate of decrease in the permafrost table at the medial divider, the left toe of the slope, the right toe of the slope, and the natural ground surface during the 15-year period was 0.38 m/a, 0.31 m/a, 0.37 m/a, and 0.15 m/a, respectively. The decrease in the permafrost table at the medial divider was the fastest in the past few years.

(3)

Block-stone subgrades can effectively lift the permafrost table and better maintain the stability of the soil beneath the subgrade. Replacement 1 m block-stone subgrade lifts the permafrost table better compared with the ordinary subgrade top surface, the medial divider, the left toe of the slope, the right toe of the slope, and the natural ground surface lifting 1.05 m, 1.32 m, 1.49 m, and 0.49 m, respectively. The increase in the thickness of the replacement block stone can reduce the temperature of the lower soil; the thickness of the block stone increased sequentially from 1 m to 4 m, and the temperature of the soil at a depth of 5 m decreased by 0.1 °C, 0.31 °C, and 0.26 °C, respectively. In the construction of road projects in warm permafrost areas, priority should be given to the use of replacement block-stone subgrades to effectively protect the permafrost. The simulated thickness of the replacement block-stone is 1~4 m, and the cooling effect is best when the thickness is 4 m; the simulated block-stone particle size is 4~15 cm, and the cooling effect is best when the block-stone particle size is 6~8 cm. Increasing the particle size of the block stone too much may affect other physical parameters of the block-stone layer, which may weaken the protection of the block-stone subgrade against the underlying permafrost.