Study on temperature field of parallel perforated ventilation subgrade in the permafrost region

Abstract

Runways in permafrost regions face significant stability challenges due to their flat geometry, wide pavement area, and pronounced heat absorption effects. To address this issue, this study proposes a novel parallel perforated ventilation system for thermal regulation. The applicability and reliability of the numerical model are validated by comparing the parallel perforated ventilation’s air velocity, crushed rock layer performance, and temperature-depth profiles with existing experimental data. Key findings demonstrate that, under combined global warming and geothermal influence, the parallel perforated ventilation system maintains subgrade temperatures below 10 m depth in a frozen state for 30 years. The cooling efficacy of parallel perforated ventilation diminishes gradually with depth and time before stabilizing, with the most pronounced effect observed in the crushed rock layer, followed by silty clay, and least in strongly weathered rock. The study offers a scientific foundation for sustainable runway construction in permafrost areas, with implications for engineering practices under climate change scenarios.

Introduction

China’s ambitious infrastructure development plans under the “Belt and Road” Initiative and the 14th Five-Year Plan call for significant expansion of aviation infrastructure in permafrost regions, with plans to construct or renovate 133 airports¹. However, these engineering projects face unique challenges due to the thermal sensitivity of permafrost soils. The alternating freeze-thaw cycles characteristic of these regions lead to substantial changes in soil strength and deformation characteristics, resulting in thaw settlement and frost heave that threaten structural stability². Compounding these natural challenges, climate change and increasing human activities are accelerating permafrost degradation, further destabilizing the thermal equilibrium of foundation soils³.

The ventilation has emerged as an effective active cooling solution for permafrost regions. These systems operate by circulating cold air to remove heat from surrounding soils, thereby preserving the frozen state of underlying permafrost⁴. Their effectiveness in blocking downward heat transfer from asphalt pavements through forced convection has been well-documented in highway and railway applications^5,6. To better guarantee the stability of the subgrade, the perforated ventilation, the ventilation with self-windward vent, the ventilation-insulation material combination, and the ventilation-crushed rock combination have appeared successively^7–9. (1) the perforated ventilation: Su et al.¹⁰ and Lai et al.¹¹ established the numerical model of ventilation to study the influence of ventilation distance, diameter, buried depth and embankment height on the cooling effect of highway based on the basic theory of heat transfer. Yu et al.¹² and Yu et al.¹³ analyzed the cooling effect of the ventilation and verified that the ventilation was suitable for the highway engineering in the permafrost region. Niu et al.^14–16 and Li et al.¹⁷ verified the cooling effect of ventilation by field engineering monitoring. They found that the heat absorption intensity of ventilation subgrade in warm season was 2.4 times of that in cold season. Jiang and Ge¹⁸ regarded the perforated ventilation subgrade as a kind of porous medium, and studied the energy mutation of the permafrost phase change process and cooling effect of the perforated ventilation subgrade by means of the numerical model. Zhang et al.¹⁹ Sun et al.²⁰ carried out indoor test based on the improved perforated ventilation subgrade, and found that the improved perforated ventilation could effectively reduce the temperature of subgrade. They also discussed the influence of open porosity, moisture content and wind speed on the cooling effect of the improved perforated ventilation subgrade, and suggested increasing the closing device of the perforated ventilation subgrade in the positive temperature period. Su et al.²¹ found that the perforated ventilation subgrade has better cooling effect than ventilation subgrade based on the monitoring results of Qinghai-Tibet railway. (2) the ventilation with self-windward vent: Li et al.²² established the numerical model of ventilation with self-windward vent based on the experimental data of Qinghai-Tibet highway and the theory of unsteady temperature field. They discussed the discussed the cooling effect of ventilation with or without self-windward vent, and found that the cooling effect of ventilation with self-windward vent was better than that of ventilation without self-windward vent. Zhang et al.²³ found that the cooling effect of the ventilation with self-windward vent was significantly enhanced in winter, and the higher of the self-windward vent the better. Yu et al.²⁴ Li et al.²⁵ explored the cooling response of the ventilation with self-windward vent based on the monitoring data of the site project. It was found that the cooling effect of the ventilation with self-windward vent was twice as high as that of the ventilation, and could make full use of natural cold energy and effective isolation of the outside hot air. (3) The ventilation-insulation material combination: Liu et al.²⁶ established a numerical model of the ventilation-insulation material combination subgrade to compared the cooling effect of the ventilation with or without insulation material. They found that the cooling effect of the insulation material was not very significant because of the insulation material blocking the heat transfer from the subgrade to the pavement and from the ventilation to the subgrade. (4) the ventilation-crushed rock combination: Zhang et al.^27,28 constructed the numerical model of the ventilation-crushed rock combination subgrade by the equivalent thermal conductivity method. They studied the cooling effect of the ventilation-crushed rock combination subgrade and the influence on the slope of the subgrade, and proved that the ventilation-crushed rock combination could effectively regulate the cooling effect and the sunny-shady slope effect of subgrade. Wu et al.²⁹ and Hou et al.³⁰ analyzed the cooling effect of ventilation, ventilation-insulation material combination, and ventilation-crushed rock combination by means of on-site engineering monitoring. They found that the sunny-shady slope effect of the above ventilation subgrade was significant and the ventilation-crushed rock combination had the best cooling effect.

While existing ventilation technologies have proven effective for linear infrastructure like highways and railways, their application to airport runways presents distinct challenges: (1) Absence of side slopes limits natural convection. (2) Larger paved areas exacerbate heat island effects. (3) More complex thermal regimes require enhanced cooling precision. Therefore, this study introduces a novel parallel perforated ventilation specifically designed for runway applications. The parallel perforated ventilation has the featuring of enhanced airflow design with dual rectangular ducts and eight additional outlets, optimized mechanical ventilation for flat, wide geometries, and comprehensive numerical modeling for long-term thermal stability prediction. This work aims to validate the parallel perforated ventilation’s applicability for runway engineering through comparative analysis, and study the temperature field response of the parallel perforated ventilation subgrade. The study bridges critical gaps between theoretical cooling methods and practical airport engineering requirements, providing scientifically-grounded solutions for sustainable aviation infrastructure in cold regions. The findings offer valuable technical support for the entire lifecycle of runway projects, from design and construction to operation and maintenance.

Theory

Three-dimensional unsteady temperature field control equation

Because the permafrost occurs freeze-thaw phase change cycle between liquid phase and solid phase with the temperature changes, the permafrost is assumed to be divided into freezing and thawing zones by the phase change interface, and satisfy the unsteady heat transfer control equations, as shown in Eqs. (1) and (2)^31–33.

Freezing zones:

1

Thawing zones:

2

Here, x, y, and z are the rectangular coordinates. t is the time. C_f and C_u are the heat capacity of soil in freezing and thawing zones, respectively. T_f and T_u are the temperature of soil in freezing and thawing zones, respectively. λ_f and λ_u are the thermal conductivity of soil in freezing and thawing zones, respectively. q_s and q_l are the heat source intensity of soil in freezing and thawing zones, respectively. L is the phase change latent heat of soil containing water.

Control equations of gas flowing in porous media and ventilation

The pores in the crushed-rock layer allows for natural or forced convection of air, facilitating heat exchange between the air in the pores and the environment. The heat transfer effect in the cold season and the “thermal shielding” effect in the warm season make the crushed-rock layer have the function of “thermal semiconductor”. Therefore, the crushed rock layer is usually regarded as a porous medium, the characteristics of pore shape, size and direction are not arranged regularly and complex structure, the flow gas in the pore changes its shape with the change of the pore. Hence, the porous medium is assumed to be an ideal continuous medium superimposed by solid and fluid, and the solid pores are filled with fluid. The averaged momentum equation of porous media is obtained by considering the inertia term and the non-slip condition of porous wall medium, as shown in Eq. (3)^31–33.

3

Here, ρ_f is the density of fluid. V’ is the average speed of fluid. µ_f is the viscosity coefficient of fluid. Φ is the porosity of porous medium. K is the permeability. F is the coefficient of inertia term, .

It is assumed that the solids and fluids in a porous medium reach a local thermal equilibrium. The energy equation can be expressed as Eq. (4) (Li et al., 2016; Hao, 2019; Liu et al., 2025).

4

Here, h_f is the specific enthalpy of fluid. λ_m is the thermal conductivity when the flow of fluid is stagnant. λ_d is the thermal conductivity of thermal dispersion. c_f is the specific heat capacity of fluid.

When Φ is equal to 1, Eqs. (3) and (4) are transformed into the Navier-Stokes equation, which are the momentum equation and energy equation of fluid flowing in the ventilation^34,35.

Boundary conditions

According to the basic principle of heat transfer, the boundary conditions of temperature can be divided into three types³⁶.

1. The first boundary condition is also called the boundary condition of temperature, as shown in Eq. (5). The temperature at the boundary is a function of time and depends on the position at the boundary.

5

• (2)The second boundary condition is also called the boundary condition of heat flux, which represents the distribution of heat flux density with time and position on the boundary. When the boundary is adiabatic, it can also be expressed by Eq. (6), and the heat flux at the boundary is 0.

6

• (3)The third boundary condition is also called the boundary condition of convection heat transfer, which represents the convective heat transfer between the outside fluid and the surface of the object, as shown in Eq. (7).

7

Here, B is the coefficient of convection heat transfer. f(t) is the temperature of outside fluid.

Numerical model

Numerical model establishment

As shown in Fig. 1, the runway structure in the airport from top to bottom is determined as: ① the upper surface layer of asphalt concrete, ② the under surface layer of asphalt concrete, ③ base layer, ④ subbase layer, ⑤ insulation layer, ⑥ crushed rock layer, ⑦ circular perforated ventilation, ⑧ rectangular duct, ⑨ clay, ⑩ silty clay, ⑪ strongly weathered rock^33,37. The parallel perforated ventilation is composed of ⑦ circular perforated ventilation and ⑧ rectangular duct, as shown in Fig. 2³³. The ventilation ducts are prefabricated pipes, typically constructed from high-density polyethylene. The ducts have a diameter of 0.5 m, a wall thickness of 0.015 m, a spacing of 6 m, and an embedment depth of 0.5 m below the crushed rock layer surface. The thermal conductivity of high-density polyethylene ducts is 1512 J/(m·h·℃), with a heat capacity of 2300 J/(kg·℃). The ventilation ducts are equipped with axial fans installed at the inlet sections (L1, L2, R1, R2) to mechanical ventilation. The ventilation time is the coldest month of every year, and the air velocity and temperate are determined according to the meteorological data of the coldest month in Mohe region of China^32,36. Hence, the conditions of the parallel perforated ventilation are set out in Table 1. The heat capacity experiences a discontinuity at the phase transition temperature, posing challenges for numerical simulations. To address this, the phase change is typically modeled as occurring within a temperature range around the nominal phase transition point. By leveraging the temperature-dependent variations in heat capacity and thermal conductivity, the phase transition between distinct materials can be approximated as property changes of a single material across different temperature intervals. Specifically, the latent heat of phase change is incorporated into the material’s heat capacity over this interval. Drawing on the research of Hao³², Qi³⁶ and Liu et al.³³, Table 2 outlines the thermal parameters of the subgrade. Given the distinct materials used in pavement structures and subgrade layers, and considering the negligible water content in pavement materials, the influence of latent heat during phase transitions can be reasonably neglected. As a result, the thermal parameters of pavement structures remain relatively stable across temperature variations, with minor fluctuations as shown in Table 3. The numerical model of the runway with the parallel perforated ventilation is established by the software of “Fluent”³³. Considering the periodicity of temperature variation, the upper boundary condition is the first boundary condition^32,33,36. The boundary on both sides of the numerical model is set as adiabatic boundary^32,33,36. The second boundary condition is selected for the bottom boundary, and a constant heat flux of 0.03℃/m is applied based on the influence of the geothermal^32,33,36. In the Fluent software, after importing the mesh, a pair of coupled surfaces-“wall” and “wall-shadow”-are automatically generated. When the “wall” surface is set as the boundary condition and the “coupled” option is selected, the numerical model of the runway can automatically achieve fluid - solid coupled heat transfer. Moreover, by setting the “interior” in the Fluent software, both fluid - solid coupled heat transfer and fluid penetration can be realized.

Fig. 1.

Three-dimensional model of runway at (a) front view, (b) vertical view, and (c) three-dimensional view³³.

Fig. 2.

Three-dimensional model of the parallel perforated ventilation³³.

Table 1.

The conditions of the parallel perforated ventilation³³.

Conditions	Inlet	Outlet	Close	Start and stop time of ventilation	Air velocity	Temperate
1	L1	R1, R2, R3, R4	L2, L3, L4	December 22 ~ December 31	5 m/s	-30℃
2	R1	L1, L2, L3, L4	R2, R3, R4	January 1 ~ January 10	5 m/s	-30℃
3	L2	R1, R2, R3, R4	L1, L3, L4	January 11 ~ January 20	5 m/s	-30℃
4	R2	L1, L2, L3, L4	R1, R3, R4	January 21 ~ January 30	5 m/s	-30℃

Table 2.

The thermal parameters of the subgrade³³.

Type	Thickness/m	Thermal parameter	-20℃	-10℃	-5℃	-2℃	-1℃	-0.5℃	0℃	20℃
Clay	1.3	Density/(kg/m3)	1870	1870	1870	1870	1870	1870	1870	1870
		Thermal conductivity/(J/(m·h·℃))	8640	8640	8640	8640	8640	8640	5544	5544
		Heat capacity/(J/(kg·℃))	835	840	850	860	870	900	1070	1070
Silty clay	2	Density/(kg/m3)	1950	1950	1950	1950	1950	1950	1950	1950
		Thermal conductivity/(J/(m·h·℃))	6500	6500	6500	6500	6500	6500	5400	5400
		Heat capacity/(J/(kg·℃))	970	1050	1090	1115	1140	1210	1285	1285
Strongly weathered rock	18	Density/(kg/m3)	2150	2150	2150	2150	2150	2150	2150	2150
		Thermal conductivity/(J/(m·h·℃))	9000	9000	9000	9000	9000	9000	7250	7250
		Heat capacity/(J/(kg·℃))	950	1060	1110	1140	1190	1250	1350	1350

Table 3.

The thermal parameters of pavement structures³³.

Number	Structure	Material	Thickness/m	Density/(kg/m3)	Thermal conductivity/(J/(m·h·℃))	Heat capacity/(J/(kg·℃))
①	The upper surface layer of asphalt concrete	AC-13 C	0.15	2300	4140	1670
②	The under surface layer of asphalt concrete	AC-20 C	0.15	2320	4320	1670
③	Base layer	Cement stabilized crushed rock	0.4	2200	3960	960
④	Subbase layer	Graded sand and stone	0.5	2100	3240	2000
⑤	Insulation layer	Expanded polystyrene board (EPS)	0.1	40	108	1400
⑥	Crushed rock layer	Particle size of 6–8 cm	1.5	1490	1426	839

Numerical model validation

The cooling effect of parallel perforated ventilation on the subgrade in the permafrost region includes the convection heat transfer between the parallel perforated ventilation and the crushed rock layer, and the convection heat transfer is closely related to the air velocity. Therefore, the reliability and validity of the numerical model of the runway in the permafrost region are verified by comparing with the velocity field and temperature field of previous studies.

When the air velocity at the inlet is 5 m/s, the temperature of air at the inlet is -30℃, and the air velocity is normal to boundary. The air velocity distributions at the inlet (AB section), middle (CD section) and outlet (EF section) of the parallel perforated ventilation are selected to verify the air velocity field of the numerical model of the runway in the permafrost region, as shown in Fig. 3. The time-history curve of air velocity in the crushed rock layer at the middle of the crushed rock layer are selected to verify the air velocity field of the numerical model of the runway in the permafrost region, as shown in Fig. 4. The temperature-depth curves at the middle of 1# and 2# perforated ventilation after the initial air velocity works for 15 days are applied to verify the temperature field of the numerical model of the runway in the permafrost region, as shown in Fig. 5.

Fig. 3.

Air velocity distribution at the (a) inlet (AB section), (b) middle (CD section), (c) outlet (EF section) of 1# and 2# perforated ventilation (The air velocity at the inlet is 5 m/s, the temperature of air at the inlet is 30℃, and the air velocity is normal to boundary).

Fig. 4.

The time-history curve of air velocity in the crushed rock layer (The position is Z = 7.5 m and Y = 19.25 m, the air velocity at the inlet is 5 m/s, the temperature of air at the inlet is 30℃, and the air velocity is normal to boundary).

Fig. 5.

The temperature-depth curves at the middle of 1# and 2# perforated ventilation after the initial air velocity works for 15 days.

Figure 3 shows that the air velocity distribution is parabolic, and in the perforated ventilation (Y = 19.0 –19.5 m) is the highest, which is consistent with the study of Jiang³⁴ and Liu et al.³⁸. Figure 3a shows that the air velocity distribution in the perforated ventilation of 1# and 2# has a slight difference, and the highest air velocity in the perforated ventilation of 1# and 2# are 4.46 m/s and 4.56 m/s, respectively. Figure 3b shows that the air velocity distribution in the perforated ventilation of 1# and 2# is basically the same, and the highest air velocity in the perforated ventilation of 1# and 2# are both 5.56 m/s. Figure 3c shows that the air velocity distribution in the perforated ventilation of 1# and 2# almost has the same shape, and the highest air velocity in the perforated ventilation of 1# and 2# are both 5.05 m/s. The reason is that the cold air from the blowing machine enters the rectangular duct firstly, then enters the crushed rock layer and circular perforated ventilation. The flow of cold air in the crushed rock layer will be subject to great resistance, which will cause a fraction of cold air in the crushed rock layer to flow into the perforated ventilation. Therefore, the air flow in the perforated ventilation is more than that at the inlet of the perforated ventilation, which leads to the air velocity at the middle (Fig. 3b) and outlet (Fig. 3c) of the perforated ventilation is greater than that of the inlet of the perforated ventilation (Fig. 3a). Moreover, because the cold air inlet (L1) entering the rectangular duct is near to the 2# perforated ventilation, the most air velocity at the inlet of 2# perforated ventilation is larger than that at the inlet of 1# perforated ventilation.

Figure 4 shows that the time-history curve of air velocity in the crushed rock layer at the inlet, middle and outlet of the parallel perforated ventilation have the same shape, and all of them gradually increase in the time of 9 h, and then become stable. The initial air velocity in the crushed rock layer is 0.46 m/s at the inlet, and near to 0.40 m/s at the middle and outlet. The stable air velocity in the crushed rock layer is 0.56 m/s at the inlet, and 0.43 m/s at the middle and outlet when the position is at the middle (Y = 19.25 m) of the crushed rock layer. The air velocity in the crushed rock layer is all at the magnitude of 10^{− 1}, which is about an order of magnitude below the initial air velocity of 5 m/s. The results in Fig. 4 are the same as the results of Fig. 3 and Liu et al.³⁸. The is because that all the boundary conditions except the inlet and outlet of the parallel perforated ventilation are non-slip boundary conditions, which leads to the air velocity at the top (Y = 20 m) and bottom (Y = 18.5 m) of the rectangular duct is smaller than that at the middle (Y = 19.25 m) of the rectangular duct. Therefore, at the AB section, the air velocity at the top (Y = 20 m) and bottom (Y = 18.5 m) of the crushed rock layer is smaller than that at the middle (Y = 19.25 m) of the crushed rock layer.

Figure 5 shows that the shape of the temperature-depth curves for the 1# and 2# perforated ventilation is similar to the studies of Hao³². Three temperature-depth curves all elevate temperature firstly, then drop steeply to the lowest temperature, finally gradually drop to a stable fluctuating temperature. However, the start and stop time of ventilation are both in winter and not the same time, which leads to the temperature at the top of the surface layer for 1# and 2# perforated ventilation is not consistent with the results of Hao³². Moreover, the structure particularity of the parallel perforated ventilation makes that the cooling effect of the parallel perforated ventilation is better than that of the existing perforated ventilation. Hence, the lowest temperature, and inflection temperature for 1# and 2# perforated ventilation are lower than that in the research of Hao³², and the temperature at the depth of 19.5 m–16.5 m for 1# and 2# perforated ventilation are also lower than that in the research of Hao³².

The results in Figs. 3, 4 and 5 shows that parameters and boundary conditions in the numerical model of the runway structure are reasonable and reliable, and the numerical model of the runway structure can be applied to analyze the temperature field of the parallel perforated ventilation subgrade in the permafrost region.

Results analysis

To explore the cooling effect of the parallel perforated ventilation on the subgrade of the runway, the temperature distribution nephograms of the parallel perforated ventilation subgrade and non-ventilation subgrade are compared. The influence of the parallel perforated ventilation on the temperature of the subgrade is analyzed in the first year. To further study the temperature field of parallel perforated ventilation subgrade in the permafrost region with the influence of the global warming, temperature-depth curves in the center of pavement structure and natural ground are discussed for 30 years.

Temperature distribution nephograms of the parallel perforated ventilation subgrade and non-ventilation subgrade

The runway structure of non-ventilation subgrade is similar to that of the parallel perforated ventilation subgrade, and is only lack of the parallel perforated ventilation in the crushed rock layer. The stop time of ventilation is January 30. The temperature distribution nephograms of the parallel perforated ventilation subgrade and non-ventilation subgrade are both extracted on January 31. The temperature distribution nephograms of the parallel perforated ventilation subgrade and non-ventilation subgrade correspond to the plane of Z = 7.5 m, as shown in Fig. 6. When the air velocity at the inlet is 5 m/s, the temperature of air at the inlet is 30℃, and the air velocity is normal to boundary. The temperature distribution nephograms of the parallel perforated ventilation subgrade and non-ventilation subgrade are shown in Fig. 7.

Fig. 6.

The plane of Z = 7.5 m.

Fig. 7.

Temperature distribution nephograms of the non-ventilation subgrade and parallel perforated ventilation subgrade in the (a) first, (b) fifth, and (c) tenth year. (The non-ventilation and parallel perforated ventilation subgrade is respectively on the top and bottom for the temperature distribution nephogram).

Figure 7a shows that the highest and lowest temperature of the crushed rock layer are − 0.23℃ and − 3.99℃ for the non-ventilation subgrade, and − 23.06℃ and − 29.93℃ for the parallel perforated ventilation subgrade, indicating a maximum temperature reduction of 25.83℃ under ventilation. In contrast, the temperature at the bottom of the silty clay layer is -0.47℃ for the non-ventilation subgrade and − 0.63℃ for the ventilated subgrade, with a maximum temperature reduction of only 0.16℃. The temperature of the strongly weathered rock remains unchanged between the two subgrades. This significant discrepancy in temperature reduction provides direct evidence for differing heat transfer efficiencies between strata, which can be quantified as follows: To compare thermal dissipation, the heat flux (energy per unit area per unit time) is calculated based on temperature changes and material properties. For the crushed rock layer, under ventilation, the large temperature drop (25.83℃ over the monitoring period) is driven by convective heat transfer—facilitated by its porous structure and air flow from the perforated ventilation. Using the formula for convective heat flux (q_conv=h·ΔT, where h is the convective heat transfer coefficient and ΔT is the temperature difference), and assuming a typical convective heat transfer coefficient of 25 W/(m²·K) for porous media with forced convection (consistent with ventilation conditions), the convective heat flux in the crushed rock layer is estimated at 646 W/m². For the silty clay layer, heat transfer is dominated by conduction. Using Fourier’s law for conductive heat flux (q_cond =k·ΔT/d, where k is thermal conductivity for silty clay (1.5 ~ 1.806 W/(m·K)), ΔT is the temperature difference (0.16℃), and d is the layer thickness (2 m), the conductive heat flux is calculated as about 0.12 ~ 0.14 W/m². This quantitative comparison reveals that the convective heat flux in the crushed rock layer is over 4000 times higher than the conductive heat flux in the silty clay layer, directly demonstrating the far higher efficiency of convection. As a result, the temperature decrease in the silty clay and strongly weathered rock (relying on conduction) is significantly smaller than in the crushed rock layer (dominated by convection).

Figure 7b and c further illustrate long-term trends: for the non-ventilation subgrade, temperatures increase by 0.7 ~ 0.9℃ from the first year to the fifth year and by 0.7 ~ 1.0℃ from the fifth year to the tenth year, likely due to cumulative heat input from global warming and geothermy. For the ventilated subgrade, temperatures decrease by 1.5 ~ 5.2℃ from the first year to the fifth year and by 0.4 ~ 3.0℃ from the fifth year to the tenth year, indicating that the heat removed by ventilation (via convection in the crushed rock layer) far exceeds heat input. The diminishing cooling amplitude over time aligns with the lower efficiency of conduction in deeper strata (silty clay and strongly weathered rock), where heat transfer is slower and more constrained by energy loss during depth-dependent conduction³⁹.

In summary, the quantified thermal dissipation—with convection in the crushed rock layer driving two orders of magnitude greater heat flux than conduction in silty clay—confirms the dominant role of convection in the crushed rock layer and the limiting effect of conduction in denser strata.

The influence of the parallel perforated ventilation on the temperature of the subgrade in the first year

To investigate the influence of parallel perforated ventilation on the temperature field of runway structure in the first year, the temperature-depth curves in the center of the perforated ventilation on the 15th of each month are drawn, as shown in Figs. 8 and 9.

Fig. 8.

The temperature-depth curves in the center of the perforated ventilation on the 15th of each month at the section of (a) AB, (b) CD, and (c) EF for the 1# perforated ventilation.

Fig. 9.

The temperature-depth curves in the center of the perforated ventilation on the 15th of each month at the section of (a) AB, (b) CD, and (c) EF for the 2# perforated ventilation.

Figure 8a shows that at the section of AB, the temperature in the perforated ventilation is not higher than that under the perforated ventilation from January to December. This phenomenon illustrates that the perforated ventilation has a cooling effect on the subgrade, keeping the subgrade temperature negative throughout the year, which is beneficial to subgrade temperature stability. From January to April, the entire runway maintains negative temperatures, with a stable temperature of -0.8℃ at the bottom of the subgrade. From May to October, pavement temperatures are positive, subgrade temperatures transition from positive to negative with increasing depth, and the stable temperature at the bottom of the subgrade remains − 0.8℃. From November to December, the entire runway is negative, with a stable temperature of -0.9℃ at the bottom of the subgrade. This is because winter spans December to February, and ventilation operates from December 22 to January 30 with an inlet temperature of -30℃ in the parallel perforated ventilation, resulting in the lowest temperatures in January. Additionally, spring (March to May) sees ambient temperatures rise from negative to positive, summer (June to August) has the highest temperatures, and autumn (September to November) sees temperatures drop from positive to negative.

Figure 8b shows that at the section of CD, the entire runway remains negative from January to March, with a stable temperature of -0.8℃ at the bottom of the subgrade. From April to May, positive temperatures occur in the surface layer, base layer, and subbase layer, while other layers remain negative, with a stable temperature of -0.8℃ at the bottom of the subgrade. In June, positive temperatures extend to the insulation layer, with other layers negative and a stable temperature of -0.8℃ at the bottom of the subgrade. In July, positive temperatures occur above the perforated ventilation, while the ventilation and underlying layers remain negative, with a stable temperature of -0.8℃ at the bottom of the subgrade. From August to September, positive temperatures include the perforated ventilation and overlying layers, with underlying layers negative and a stable temperature of -0.9℃ at the bottom of the subgrade. In October, positive temperatures are above the ventilation, with the ventilation and underlying layers negative, and a stable temperature of -1.0℃ at the bottom of the subgrade. From November to December, all temperatures are negative, with a stable temperature of -1.1℃ at the bottom of the subgrade.

Notably, the crushed rock layer temperature in Fig. 8b is lower than in Fig. 8a and c from January to August, which relates to the hysteresis of heat conduction³⁹. The ambient temperature changes first affect the upper surface layer, with deeper layers showing delayed responses, and temperature variation amplitude decreases with depth and time⁴⁰. Due to the ventilation’s cooling effect, the crushed rock layer exhibits a large temperature drop, with the perforated ventilation reaching a minimum of -30℃. The insulation layer above the crushed rock layer inhibits upward cold transfer, limiting temperature rises in the upper crushed rock. Below the crushed rock layer, silty clay (with high thermal conductivity) receives cold transfer, but heat transfer efficiency differs significantly between strata, as quantified below: The heat transfer between the perforated ventilation and crushed rock layer is dominated by convection, while that between silty clay and strongly weathered rock is dominated by conduction. To quantify this, the heat flux (energy per unit area per unit time) is calculated for both modes. For the crushed rock layer: Under ventilation, the maximum temperature difference (ΔT_conv) driven by convection is 25℃ (from typical ambient-influenced temperatures to -30℃ in the ventilation zone). Using a convective heat transfer coefficient of 25 W/(m²·K) for forced convection in porous media (consistent with ventilation conditions), the convective heat flux is q_conv=h·ΔT_conv=625 W/m². For silty clay: The maximum temperature change (ΔT_cond) due to conduction is 0.3℃ (from near − 0.8℃ to -1.1℃ at the bottom of the subgrade). With a thermal conductivity of 1.5 ~ 1.806 W/(m·K) for silty clay and a layer thickness of 2 m, the conductive heat flux is q_cond=k·ΔT_cond/d = 0.12 ~ 0.14 W/m². This comparison shows convective heat flux in the crushed rock layer is over 4000 times higher than conductive flux in silty clay, directly demonstrating the far lower efficiency of conduction. Consequently, the temperature decrease in silty clay and strongly weathered rock is smaller (≤ 0.3℃) and stabilizes earlier at the bottom of the subgrade, while the crushed rock layer exhibits larger temperature fluctuations driven by efficient convection.

Figure 8c shows that at the section of EF, temperature-depth curves vary similarly to Fig. 8a. This is because sections AB and EF are symmetric about the runway center, and the runway structure is assumed isotropic and homogeneous. Additionally, the parallel perforated ventilation operates with air intake from L1 (December 22 ~ 31), R1 (January 1 ~ 10), L2 (January 11 ~ 20), and R2 (January 21 ~ 30), with L1/L2 inlets near AB and R1/R2 inlets near EF.

The temperature-depth curves in Fig. 9 are the same to that of Fig. 8. The is because that 2# perforated ventilation and 1# perforated ventilation are symmetrically arranged on both sides of the axis of the crushed rock layer, and the distance from the inlet of air to 1# and 2# perforated ventilation is the same. Moreover, the parameters of the 1# and 2# perforated ventilation are identical. Therefore, the temperature-depth curves of 1# perforated ventilation are similar to that of 2# perforated ventilation under the condition of four inlet ventilated interactively for 10 days.

The influence of the parallel perforated ventilation on the temperature of the subgrade for 30 years

To analyze the influence of the parallel perforated ventilation on the temperature field of runway structure and natural ground with global warming, the temperature-depth curves in the center of the pavement and natural ground in the tenth, twentieth, thirtieth year are drawn, as shown in Figs. 10 and 11.

Fig. 10.

The temperature-depth curves in the center of the pavement in the (a) tenth, (b) twentieth, (c) thirtieth year.

Fig. 11.

The temperature-depth curves in the center of the natural ground in the (a) tenth, (b) twentieth, (c) thirtieth year.

The temperature-depth curves in Fig. 10 are similar to those in Figs. 8b and 9b. The temperature-depth curves in the center of the pavement are an asymmetric funnel distribution. The temperature-depth curves shift to the left from January to July, indicating the existence of low-temperature intercalation. The temperature-depth curves shift to the right from August to December, indicating the existence of high-temperature intercalation. These temperature characteristics are similar to the studies of Wang⁴¹ and Zhang⁴². There is a sudden change of temperature in the depth of 18.5 ~ 20 m. The reason is that the crushed rock layer is located in 18.5 ~ 20 m, the insulation layer is at the upper of the crushed rock layer, and the perforated ventilation is located in the depth of 19.0 ~ 19.5 m. The insulation layer prevents heat transfer as well as cold transfer. Hence, the pavement above the insulation layer is significantly affected by the ambient temperature, and shows the characteristics of seasonal temperature changes. Meanwhile, the pavement and subgrade under the insulation layer is significantly affected by the perforated ventilation, and shows the obvious cooling effect. The temperature under the insulation layer is negative all the years, and the change amplitude of temperature decreases with the increasing of depth to a stable temperature. Figure 10a shows that the stable temperature in the tenth year is about − 7.8℃ at the bottom of the subgrade. Figure 10b shows that the stable temperature in the twentieth year is about − 9.4℃ at the bottom of the subgrade. Figure 10c shows that the stable temperature in the thirtieth year is about − 9.5℃ at the bottom of the subgrade. This phenomenon shows that the parallel perforated ventilation can effectively reduce the temperature of subgrade and keep the stability of the subgrade under the condition of global warming. However, the cooling effect of the parallel perforated ventilation is not significant and the temperature of subgrade gradually becomes stable from the twentieth year to the thirtieth year. When the depth is about 10 m away from the subgrade, the influence of ambient temperature on the subgrade is very weak, and the temperature of the subgrade tends to a stable value.

Figure 11 shows that the temperature-depth curves in the center of the natural ground presents a symmetrical funnel distribution. Meanwhile, there is no the sudden change of temperature at the same depth of the perforated ventilation. Figure 11a shows that the temperature eventually stabilizes at -0.19℃ at the bottom of the subgrade. Figure 11b shows that the temperature eventually stabilizes at -0.20℃ at the bottom of the subgrade. Figure 11c shows that the temperature eventually stabilizes at 0.03℃ at the bottom of the subgrade. This phenomenon is the effects of global warming. However, Fig. 11 also shows that the existence of low-temperature intercalation is from January to July, and the existence of high-temperature intercalation is from August to December. Meanwhile, the influence of ambient temperature on the subgrade is very weak, and the temperature of the subgrade tends to a stable value when the depth is about 10 m away from the subgrade. The phenomenon is the same to the results of Fig. 10 and the research of Wang⁴¹ and Zhang⁴². Figure 11 illustrates that the influence of the parallel perforated ventilation on the temperature of the natural ground is little.

Conclusions

The applicability and reliability of the numerical model for the runway with the parallel perforated ventilation are verified by the available data from the previous studies. Based on the verified numerical model of runway with the parallel perforated ventilation, the temperature field response of the parallel perforated ventilation subgrade in the permafrost region is analyzed. The conclusions are as follow:

1. The cooling effect of the parallel perforated ventilation subgrade is significantly better than that of the perforated ventilation subgrade and non-ventilation subgrade. Although the parallel perforated ventilation is only ventilated for 40 days from December 22 to January 30, the temperature of the crushed rock layer and subgrade are negative for the whole year and the temperature of the surface layer, base layer, and subbase layer are only positive from May to October.

2. The cooling effect of the parallel perforated ventilation on pavement and subgrade is much better than that on natural ground. The cooling effect of the parallel perforated ventilation is best in the crushed rock layer, second in the silty clay, and worst in the strongly weathered rock. The reduction temperature amplitude of the parallel perforated ventilation decreases gradually and finally tends to be stable with the increase of time.

3. The cooling effect of the parallel perforated ventilation decreases gradually and finally tends to be stable with the increase of depth and time. The temperature of the parallel perforated ventilation subgrade is negative below the depth of 10 m for 30 years.

Author contributions

Study conception and design: Xiaolan Liu, Zhihua Chen; data collection: Xiaolan Liu, Chuanwei Fu; analysis and interpretation of results: Xiaolan Liu, Chao Lv; draft manuscript preparation: Xiaolan Liu. All authors reviewed the results and approved the final version of the manuscript.

Data availability

The data used to support the findings of this study are included within the article.

Declarations

Competing interests

The authors declare no competing interests.