# Engineering Disaster Investigation and Recurrence of the Covering Effect in a Petroleum and Gas Station in Seasonally Frozen Soil Region

Authors: Xiaohui Liu; Ruiling Zhang; Huyuan Zhang; Kai Wu; Weibin Zhou; Bo Liang; Guang Li
Journal: Geofluids
 (2022)

---

## Abstract

The impermeable engineering surface layer in the cold regions blocks the water and heat exchange between the foundation soil and the atmospheric environment. Especially in cold areas with significant temperature differences, the moisture in the foundation soil accumulates at the bottom of the structure layer to form a covering effect. This will exacerbate the occurrence of engineering freeze-thaw diseases. This paper conducts a disease survey of the Guanshan oil and gas station site, which is located in a seasonally frozen soil zone. The ponding and freeze-thaw diseases under the concrete cover are analyzed. The formation process of the pot covering effect in the lower part of the concrete surface layer was reproduced through indoor tests. In addition, a water-vapor-heat coupling model of unsaturated soil was established, which quantitatively produced the formation process of silty clay covering under the concrete slab. The results show that (1) in-situ monitoring demonstrated that the water content of the roadbed soil from 0 to 50 cm below the concrete slab gathered significantly, with the water content increasing by 5 to 30%. (2) Under the action of the indoor time-varying covering effect, the moisture content of silty clay will increase with the number of freezing-thawing cycles, with a maximum migration amount of 6%. (3) Seasonal temperature changes lead to the accumulation of water in the subgrade surface, and the maximum accumulation amount is 32%. (4) During the freezing period, the liquid water and vapor water in the subgrade migrate to the surface layer of the subgrade. As a result, the moisture content of the subgrade surface layer increases, while the melting period is the opposite. The above research results can provide theoretical support and scientific countermeasures for engineering design and disease control in cold regions.


---

## Body

## 1. Introduction

Under the action of large temperature difference in a pavement layer of embankment in cold regions, liquid water and vapor accumulate at the bottom of the waterproof cover. This phenomenon is considered as the pot cover effect or covering effect [1, 2]. The covering effect leads to the increase of the porosity of subgrade filling, the reduction of bearing capacity, and the aggravation the freezing-thawing hazard of embankment [3]. In recent years, there have been many diseases caused by the covering effect. For example, the runway at Lanzhou Zhongchuan Airport has a large amount of moisture enrichment underneath, which in turn leads to cracking of the road surface [4]; Moisture accumulation within 50 cm under the pavement structure of Changzhi Airport in Shanxi [5] moisture accumulation at the top of the subgrade fill in the Lanxin Wuwei section, the frost heave amount in winter reaches 40 mm, and the local soil moisture content is close to saturation when it melts in spring [6]. With the promotion of “the Belt and Road” strategy, more projects are being carried out in the arid and semiarid regions of the northwest, which are characterized by typical environmental features such as significant temperature differences and a low water table, thus creating the conditions for a covering effect. Therefore, the study of the formation process of the covering effect is of great importance for the prevention and control of diseases on roads and airports.Since Li et al. [3] first proposed the concept of covering effect in 2014, scholars have carried out analyses from laboratory experiments and field experiments to numerical simulations to reveal the mechanism of covering effect. In indoor experiments, Luo et al. [7] and Wang et al. [8] analyzed the covering effect under a constant temperature gradient by designing a water vapor migration test setup; Zhang et al. [9] selected calcareous sand as the experimental material to conduct a series of tests on the covering effect under different influencing factors; Teng et al. [10] also used unsaturated sandy soil to conduct an indoor test and obtained an important mechanism for the substantial increase of moisture in unsaturated soil-water vapor condenses into ice; and Gao et al. [11] and Bai et al. [12] designed unidirectional freezing experiments under open and closed systems to study the cover effect and frost heave mechanism of coarse-grained soils. In the field test, Li [13] and Gao et al. [14] took the highway pavement in Xinjiang as the research object. They analyzed the change of the water content of the roadbed under the covering layer and found that the cover effect will lead to an increase of the water content of the roadbed. Luo et al. [15–17] compared and analyzed the effect of the presence or absence of a compartment on the cover effect in Beijing Daxing International Airport. In terms of numerical simulations, Zhang [18] found that seasonal temperature changes have an impact on the roadbed covering effect; Zhang et al. [19] and Teng et al. [20] used coupled water-vapor-thermal model to simulate the formation mechanism of the covering effect; Yao et al. [21] investigated the effects of initial water contents, the boundary temperatures, and the location of the spacer on the covering effect; and Zhang et al. [22] summarized and analyzed the diseases of cold area cover effect and prospected their control measures. Chen et al. [23] and Tong [24] conducted a further simulation analysis of the mulching effect on the basis of considering time-varying evaporation simulation and unsaturated permafrost heat and mass transfer.The above summary shows that existing studies mainly analyzed the covering effects of airport runways and high-speed railway roadbeds, and mainly focused on indoor tests, while the field covering effects have been less explored. Moreover, the available indoor tests [25–28] are conducted under constant temperature boundary conditions, and there is a lack of research on the seasonal transport patterns of water vapor and liquid water in real environments, such as time-varying covering effect. Guanshan petroleum and gas station is an important node for Lanzhou-Zhengzhou-Changsha oil and gas transportation, so it is extremely important to ensure the safety and stability of the roadbed at Guanshan station. In this study, the concrete surface roadbed of Gansu Guanshan station is used as a research object. Firstly, an in situ disease investigation was carried out, and the change of water content in the lower part of the subgrade was measured. Then, the existence of the roadbed covering effect in the seasonally frozen soil zone was reproduced by indoor tests. Meanwhile, a coupled water-vapor-heat transport model is formulated and verified to analyze the forming mechanism of covering effect. Finally, the established model was used to predict the long-term stability of the roadbed under time-varying environment. The above results can provide theoretical support for the prevention and control of roadbed cover effect disasters in seasonally frozen soil areas.


## 2. Field Disaster Investigation

The Guanshan petroleum and gas station of Lanzhou Oil and Gas Transportation Branch is located in the southeast of Lanzhou, close to National Highway 309. The station is about 175 m long from east to west and 130 m wide from north to south, with a covering an area of about 239 m2. The main facilities in the station include workspace, oil pressure track farm, pump shed, substation area, and pipeline process area (Figure 1).Figure 1
Location of Guanshan station.Since the project was put into operation in 2009, different degrees of subsidence and heaving have occurred on the ground level of the station yard, roads, and pipeline process areas. In order to explore the cause of the disease, in situ drilling was carried out, and it was found that the stratum of the site was simple in lithology. The exposed strata are silty clay, loess, and sandstone in sequence. On the basis of exploring the lithology of the foundation of the site, soil replacement and reconstruction of the original panel were carried out. However, although the yard in the station has been dealt with in the winter of 2016, the yard in the station still experienced a large-scale uplift, and the broken of concrete floor between the pressure relief tank area and the pump shed area is the most serious. The ground uplift has a tendency to further intensify, which seriously affects the normal operation of the equipment in the pressure relief tank area and the pump shed area (Figure2).Figure 2
Pavement disease.
(a)
Recessed concrete panels(b)
Frost heaving of concrete panelsIn order to further clarify the causes of diseases such as frost heave and cracking of concrete slabs in Guanshan station, the water content changes of 6 exploration pits in Guanshan station were measured in January 2019. The probe deployed during detection is a 5TM temperature and moisture sensor. The size of the probe is 100 mm∗32 mm ∗7 mm (length∗width∗height), the measurement range is 0% ~ 100%, and the working temperature range is 40°C ~ 50°C. Figure 3 selects the water content of two probe pits for analysis. Compared with the water content of the subgrade soil layer when the probe was laid in 2009, the water content in the probe pit increased dramatically in 2019. The water content in the range of 0 ~ 50 cm under the concrete panel is significantly aggregated, and the water content increases by 5% ~ 30% (Figure 3).Figure 3
Moisture content monitoring.
(a)(b)


## 3. Experimental Recurrence of the Pot Cover Effect

### 3.1. Test Apparatus

To test the reproduction of the covering effect, an indoor freeze-thaw cycle laboratory device was designed. This device includes a couple of thermostats (the controlled temperature range is about -40°C to +90°C, with an accuracy of 0.1°C), a soil column (30 cm dia. and 30 cm high), and a data-logging system.The top and bottom temperatures of the soil specimen are controlled through a pair of aluminum plates, which are connected to two independent thermostats by circulating tubes. The tubes are filled with antifreezing solution (ethylene diamine chlorate glycol-based antifreeze). The soil container is a polypropylene transparent cylinder with a wall thickness of 2.5 cm. The polypropylene material is used because its coefficient of heat conduction is smaller than metal or other plastic products. There are holes in the side of the column for burying the temperature and moisture sensors (5TM). The top end of the specimen is sealed against vapor and liquid flux with a plastic film. The cylinder is surrounded by insulation material in order to effectively reduce the lateral loss of heat.The following details the temperature and moisture sensor 5TM (Figure4). 5TM is a high-resolution sensor for measuring unfrozen water content during the soil freeze-thaw cycle. Its working principle is to measure the dielectric constant of the soil and obtain the volumetric moisture content of the soil after conversion.Figure 4
5TM temperature moisture sensor.


### 3.2. Test Methods

Lanzhou Guanshan station is located in a seasonally frozen environment. This test is based on the road covering effect of concrete pavement structure in Guanshan oil station, Gansu Province. The purpose is to reproduce the formation process of the time-varying covering effect of the concrete pavement structure road in the station through the indoor test. Since the height of the test cylinder is 30 cm, the temperature of this experiment is set according to the geometric similarity ratio of 1 : 6. Therefore, this test soil column corresponds to a depth range of 1.8 m below the simulated road base surface. The test temperature is set according to the ambient temperature of the roadbed soil layer in the Guanshan area. The temperature settings of the upper and lower temperature guide plates in the experiment are shown in Table1. For the actual temperature control effect of the upper and lower temperature guide plates during the test, please refer to Reference [29].Table 1
Temperature of the upper and lower temperature guide trays.
Boundary locationTemperature and time functionUpper temperature guide plate8+12sin2πt/144+π/2Lower temperature guide plate7.7+6.3sin2πt/144+π/5The initial moisture content of the soil was taken as the optimum quality moisture content for road base filling in the Guanshan area, which is 12%. The dry density of the soil sample was 1.6 g/cm3, and the volumetric water content was about 20%.One freeze-thaw cycle was tested for 6 days, and a total of 3 freeze-thaw cycles were performed. Six 5TM probes were placed at a depth of 1.5 cm, 4 cm, 9 cm, 15 cm, 21 cm, and 26 cm from the top of the cylinder (Figure5). As the 5TM probe deployed for the test could only measure the liquid water content inside the soil, only the liquid water content inside the soil during the test was analyzed.Figure 5
Probe location placement.
(a)
Physical picture(b)
Schematic


### 3.3. Experimental Results and Analysis

Figure6 shows the variation of water content and temperature changes at different depths. It can be seen from Figure 6(a) that the liquid water content of the upper soil sample shows an overall increasing trend with the increase of the number of test cycles. Take the change of soil moisture content at the depth of 1.5 cm from the test surface as an example, and the soil moisture content was 22.6% at the end of the first cycle, 24.1% at the end of the second cycle, and 25.8% at the end of the third cycle. As the 5TM sensor deployed in the test can only measure the liquid water content in the soil, the water content in Figure 6(a) drops and corresponds to the temperature curve in Figure 6(b). Part of the liquid water freezes as ice, thus reducing the liquid water content in the soil. The moisture content of the soil layer at 9 cm and 15 cm in the middle of the soil sample remained basically unchanged at 20% of the initial volumetric moisture content during the test, while the soil moisture content at the depth of 21 cm and 26 cm in the lower part of the soil sample continued to decrease.Figure 6
Variation of water content and temperature changes at different depths.
(a)
Water content(b)
Soil temperatureFigure7(a) is a histogram of the distribution of water content at each measuring point during the test. The position of each measuring point has been described in Figure 5(b), and will not be repeated here. It can be seen that as the number of freeze-thaw cycles increases, the water content of the surface layer of the soil sample increases with the number of cycles. The moisture content of the soil layer at a depth of 1.5 cm was analyzed, and the moisture content was 22.6%, 23.2%, and 25.8% on the 6th, 12th, and 18th days, respectively. The moisture content of the surface layer of the soil column shows an overall trend towards an increase, while the moisture content of the lower soil layer of the soil sample decreases relatively. Figure 7(b) shows the humidity comparison of the upper and lower soils of the borrow column section after the test. At the end of the test, the water content of the upper soil layer was significantly higher compared to the lower soil layer. Since there is no water supply in the test, the above phenomenon can only occur because the water in the lower soil layer migrates to the upper soil layer. Based on the above analysis, it is found that under the action of seasonally freeze-thaw cycles, the soil samples will experience an obvious covering effect. The moisture content of the upper part of the soil increases with the number of freeze-thaw cycles.Figure 7
Measured volumetric water content profile.
(a)
Water content distribution along the depth(b)
Cross-sectional water content at the end of the test


## 3.1. Test Apparatus

To test the reproduction of the covering effect, an indoor freeze-thaw cycle laboratory device was designed. This device includes a couple of thermostats (the controlled temperature range is about -40°C to +90°C, with an accuracy of 0.1°C), a soil column (30 cm dia. and 30 cm high), and a data-logging system.The top and bottom temperatures of the soil specimen are controlled through a pair of aluminum plates, which are connected to two independent thermostats by circulating tubes. The tubes are filled with antifreezing solution (ethylene diamine chlorate glycol-based antifreeze). The soil container is a polypropylene transparent cylinder with a wall thickness of 2.5 cm. The polypropylene material is used because its coefficient of heat conduction is smaller than metal or other plastic products. There are holes in the side of the column for burying the temperature and moisture sensors (5TM). The top end of the specimen is sealed against vapor and liquid flux with a plastic film. The cylinder is surrounded by insulation material in order to effectively reduce the lateral loss of heat.The following details the temperature and moisture sensor 5TM (Figure4). 5TM is a high-resolution sensor for measuring unfrozen water content during the soil freeze-thaw cycle. Its working principle is to measure the dielectric constant of the soil and obtain the volumetric moisture content of the soil after conversion.Figure 4
5TM temperature moisture sensor.


## 3.2. Test Methods

Lanzhou Guanshan station is located in a seasonally frozen environment. This test is based on the road covering effect of concrete pavement structure in Guanshan oil station, Gansu Province. The purpose is to reproduce the formation process of the time-varying covering effect of the concrete pavement structure road in the station through the indoor test. Since the height of the test cylinder is 30 cm, the temperature of this experiment is set according to the geometric similarity ratio of 1 : 6. Therefore, this test soil column corresponds to a depth range of 1.8 m below the simulated road base surface. The test temperature is set according to the ambient temperature of the roadbed soil layer in the Guanshan area. The temperature settings of the upper and lower temperature guide plates in the experiment are shown in Table1. For the actual temperature control effect of the upper and lower temperature guide plates during the test, please refer to Reference [29].Table 1
Temperature of the upper and lower temperature guide trays.
Boundary locationTemperature and time functionUpper temperature guide plate8+12sin2πt/144+π/2Lower temperature guide plate7.7+6.3sin2πt/144+π/5The initial moisture content of the soil was taken as the optimum quality moisture content for road base filling in the Guanshan area, which is 12%. The dry density of the soil sample was 1.6 g/cm3, and the volumetric water content was about 20%.One freeze-thaw cycle was tested for 6 days, and a total of 3 freeze-thaw cycles were performed. Six 5TM probes were placed at a depth of 1.5 cm, 4 cm, 9 cm, 15 cm, 21 cm, and 26 cm from the top of the cylinder (Figure5). As the 5TM probe deployed for the test could only measure the liquid water content inside the soil, only the liquid water content inside the soil during the test was analyzed.Figure 5
Probe location placement.
(a)
Physical picture(b)
Schematic


## 3.3. Experimental Results and Analysis

Figure6 shows the variation of water content and temperature changes at different depths. It can be seen from Figure 6(a) that the liquid water content of the upper soil sample shows an overall increasing trend with the increase of the number of test cycles. Take the change of soil moisture content at the depth of 1.5 cm from the test surface as an example, and the soil moisture content was 22.6% at the end of the first cycle, 24.1% at the end of the second cycle, and 25.8% at the end of the third cycle. As the 5TM sensor deployed in the test can only measure the liquid water content in the soil, the water content in Figure 6(a) drops and corresponds to the temperature curve in Figure 6(b). Part of the liquid water freezes as ice, thus reducing the liquid water content in the soil. The moisture content of the soil layer at 9 cm and 15 cm in the middle of the soil sample remained basically unchanged at 20% of the initial volumetric moisture content during the test, while the soil moisture content at the depth of 21 cm and 26 cm in the lower part of the soil sample continued to decrease.Figure 6
Variation of water content and temperature changes at different depths.
(a)
Water content(b)
Soil temperatureFigure7(a) is a histogram of the distribution of water content at each measuring point during the test. The position of each measuring point has been described in Figure 5(b), and will not be repeated here. It can be seen that as the number of freeze-thaw cycles increases, the water content of the surface layer of the soil sample increases with the number of cycles. The moisture content of the soil layer at a depth of 1.5 cm was analyzed, and the moisture content was 22.6%, 23.2%, and 25.8% on the 6th, 12th, and 18th days, respectively. The moisture content of the surface layer of the soil column shows an overall trend towards an increase, while the moisture content of the lower soil layer of the soil sample decreases relatively. Figure 7(b) shows the humidity comparison of the upper and lower soils of the borrow column section after the test. At the end of the test, the water content of the upper soil layer was significantly higher compared to the lower soil layer. Since there is no water supply in the test, the above phenomenon can only occur because the water in the lower soil layer migrates to the upper soil layer. Based on the above analysis, it is found that under the action of seasonally freeze-thaw cycles, the soil samples will experience an obvious covering effect. The moisture content of the upper part of the soil increases with the number of freeze-thaw cycles.Figure 7
Measured volumetric water content profile.
(a)
Water content distribution along the depth(b)
Cross-sectional water content at the end of the test


## 4. Numerical Recurrence of the Pot Covering Effect

### 4.1. Mathematical Model

#### 4.1.1. Governing Equation

Liquid water migration driven by temperature gradients and substrate suction gradients follows the Richards equation [30]. The expression is as follows:
(1)ql=qlh+qlT=−Klh∂h∂z+1−KlT∂T∂z,where ql is the total liquid water flux; qlh is the liquid water flux due to the matrix suction gradient; qlh is the liquid water flux due to the temperature gradient(m·s-1); h for the pressure head(m); z is the spatial coordinate position (m), upward is positive; T is temperature(K); Klh (m·s-1) is the liquid water permeability coefficient under the action of the soil matrix suction gradient; and KlT(m2·K-1·s-1) is the liquid water permeability coefficient under the action of soil temperature gradient.The flow of vaporous water in soil is described by Fick’s law as [31]:
(2)qv=qvh+qvT=−Kvh∂h∂z−KvT∂T∂z,where qv is the total water vapor flux; qvh is the water vapor flux under the action of the soil matrix suction gradient; qvT is the water vapor flux under the action of the temperature gradient(m·s-1); Kvh(m·s-1) is the water vapor conductivity under the action of the soil matrix suction gradient; and KvT(m2·K-1·s-1) is the water vapor conductivity under the action of a temperature gradient.According to the principle of mass conservation, the mass conservation equation of unsaturated frozen soil is as follows [31]:
(3)∂θ∂t=∂θl∂t+∂θv∂t+ρiρw∂θi∂t=‐∂ql∂z−∂qv∂z=∂∂xKlh∂h∂z+1+KlT∂T∂z+Kvh∂h∂z+KvT∂T∂z,where θ is the total volume moisture content(m3·m-3); θl is the moisture content of liquid water(m3·m-3); θv is the equivalent water vapor moisture content(m3·m3); θi is the ice content(m3·m-3); ρi is the density of ice(kg·m-3); and ρw is the density of liquid water(kg·m-3).The energy transfer should comprehensively consider the process of water migration, evaporation, condensation, and phase change in unsaturated soil. The heat control equation of unsaturated soil is as follows [32]:
(4)CP∂T∂t−Liρi∂θi∂t+Lwρw∂θv∂t=∂∂tλ∂T∂z−Cl∂qlT∂z−Cv∂qvT∂z−Lwρw∂qv∂z,where CP is the specific heat capacity of the soil(MJ·m-3·K-1); Cl is the specific heat capacity of liquid water; Cv is the specific heat capacity of water vapor(kJ·m-3·K-1); Li is the latent heat of phase transition of water(kJ·kg-1); Lw represents the latent heat of vaporization(J·m-3); and λ represents the thermal conductivity of unsaturated frozen soils(W·m-1·K-1).


#### 4.1.2. Hydraulic Properties

Ignore the hysteresis phenomenon of soil in the process of wetting and drying cycle; in this paper, the Van Genuchten [33] model (V-G model) is used to describe the soil-water characteristic curve of unsaturated soil, and the expression is as follows:
(5)Se=θl−θrθs−θr=11+αhnmh<01h≥0,where Se is the effective saturation; θs is the saturated moisture content; θr is the residual moisture content (m3·m-3); and α and n and m are the fitting parameters of the V-G model. The unsaturated permeability coefficient Klh due to the matrix suction gradient can be calculated using the Mualem [34] model and is expressed as:
(6)Klh=KsSel1−1−Se1/mm2/Ih<0KSh≥0,where KS is the saturated hydraulic conductivity(m·s-1); I is the ice resistance coefficient; l is an empirical parameter; and Mualem [34] recommends l taking 0.5.Xu et al. [29] proposed that the unfrozen water content is a function of the initial water content and temperature and established a functional relationship. The maximum unfrozen water content θumax during freezing is expressed as:
(7)θumax=aT−273.15−b,where a and b are parameters related to soil properties [29].The expressions for liquid water content and ice content are determined as:(8)θl=θotherθumaxT<T0andθ>θumax,(9)θi=ρwρiθ−θi.


#### 4.1.3. Model Validation

To verify the validity of the numerical model developed in this paper, the calculated results in this paper are compared with the above-mentioned laboratory test results. Figure8(a) shows the temperature distribution law on the 2nd and 17th day of the test. It can be seen from the figure that the experimental value and the simulated value are in good agreement and the temperature difference is less than 0.5°C. Figure 8(b) shows the change curve of water content along the depth on the 18th day of the test. It can be seen from the figure that the variation law of water distribution during the test is basically consistent with the simulated value, and the difference in water content is less than 1%. The variation laws of soil temperature field and moisture field calculated by the numerical model in this paper are consistent with the measured results of laboratory tests. This proves the applicability and effectiveness of the numerical model established in this paper.Figure 8
Measured and simulated soil temperatures and water contents profile.
(a)
Soil temperature water content(b)
Water content


### 4.2. Recurrence of the Covering Effect

#### 4.2.1. Geometric Model and Hydrothermal Parameters

The subgrade soil at a certain depth under the concrete slab is taken to analyze the change law of water and heat transfer under the covering effect. The soil layer distribution of the site is shown in Figure9. In the figure, z represents the depth of the roadbed, 0≤z≤3m is the subgrade base composed of silty clay, and −20≤z<0m is the foundation soil layer composed of loess. The numerical simulation software COMSOL is used to analyze the causes of moisture accumulation under the concrete panel covering. The calculation model is one-dimensional, and the hydrothermal parameters input in the model are shown in Table 2.Figure 9
The soil layer distribution of the research site.Table 2
Soil hydrothermal parameters [29].
LithologyDepth of soil layerDensity (kg·m-3)α (m-1)nKs (10-6 m·s-1)Thermal conductivity (W·m-1·K-1)Heat capacity (kJ·m-3·K-1)FrozenUnfrozenFrozenUnfrozenSilty clayRoadbed21000.0493.736.111.51.48701060LoessUnsaturated region19000.0681.090.561.71.610101150


#### 4.2.2. Model Boundary Conditions and Initial Values

In the numerical simulation, the initial temperature of the foundation filling usually refers to the average temperature within 2 m below the ground surface during the actual construction process, which is about 15°C [35]. This paper also takes the value accordingly. In order to exclude the water migration caused by the difference in moisture content between the silty clay base and the loess base soil, the same initial moisture content is set to 14% in this paper. The calculation period is 20 years.Before the calculation, the initial temperature field of the loess foundation must be determined first. Therefore, in this paper, the initial temperature field of the natural site is obtained by the method of numerical calculation. Taking the soil 20 m below the natural site ground as the one-dimensional geometric model for calculation, in the one-dimensional calculation model of the natural site, the boundary under temperature is taken as the flux boundary considering the influence of geothermal (q=0.05 W/m2) [36]. The moisture boundaries of natural sites are all taken as zero-flux boundaries. The initial temperature value entered in the model is arbitrary (this value does not affect the distribution of the final stable temperature field). The above initial values and boundary conditions are brought into the model for calculation, and the model calculation time is 80 years. Take the stabilized temperature field as the initial temperature of the soil layer of the natural site. When the annual average temperature change and the maximum temperature change are both less than 0.01°C, the temperature field is considered to be stable [37]. In the process of determining the soil temperature field, the surface thermal boundary is usually based on the boundary layer principle [38]. August 1 was selected as the initial time of the simulation. According to the in-situ disease investigation, the air temperature and the natural site upper boundary temperature are shown in Equations (10) and (11), respectively.
(10)T0=8+18sin2πt8760+2π3,(11)T1=8+1.5+16sin2πt8760+2π3,where t is time (hours).Considering the endothermic effect of the subgrade surface layer, the temperature change function of the subgrade surface is:(12)T2=8+3+17sin2πt8760+2π3.Taking formula (12) as the upper boundary of foundation soil temperature, the lower boundary is the flux boundary considering geothermal effects [36] (q=0.05W/m2). The moisture boundaries are all closed, simulating the impermeable state under the covering effect.


#### 4.2.3. Simulation Results and Analysis

Figure10 shows the subgrade temperature changes with time and depth. It can be seen that the temperature of the subgrade soil layer is basically stable in the third year (Figure 10(a)). Therefore, the time-history curve of the subgrade temperature field in the third year is extracted for analysis, and the results are shown in Figure 10(b). The approximate range of the subgrade temperature field in summer and autumn is 6 ~ 23°C, of which the maximum temperature of the filling is 24°C. In spring and winter, the subgrade temperature generally ranges from -8 to 16°C, and the minimum temperature of the filling is -8°C. In the figure, 0°C is regarded as the freeze-thaw interface. It can be seen from the freeze-thaw interface at 0°C that the maximum freezing depth is 1.5 m.Figure 10
Subgrade temperature changes with time and depth.
(a)
Soil temperature at different depths(b)
Soil temperature in the third yearFigure11 illustrates the distribution of total water content for the subgrade along the depth. The total water content increases with the increase of time at the depth of 2 ~ 3 m for the subgrade but decreases at the depth of -1 m ~ 2 m for the subgrade. Generally speaking, the moisture in the soil migrates to the upper part of the subgrade year by year. As shown in Figure 11, the maximum moisture content of the soil at the subgrade surface layer can reach 30%. This is due to the moisture in the lower soil gradually migrates to the upper soil layer and finally accumulates in the surface soil of the subgrade. For the depth soil layer of -2 ~ -1 m, it is less affected by the covering effect due to the distance from the concrete surface layer, and the groundwater is too deep to supply capillary water. Therefore, the soil moisture in this depth range remains unchanged at the initial moisture content.Figure 11
Distribution of total water content with depth.In order to analyze the overall change of soil moisture accumulation at different depths of subgrade, the variations of moisture content with time at the depth of 2.9 m for the subgrade surface layer and the depth of 2.5 m, 1.5 m and 0.5 m inside the subgrade are extracted (Figure12). The soil water content at depths of 2.9 m and 2.5 m increases year by year as a whole, while the soil water content at depths of 1.5 m and 0.5 m experiences slightly decreased and then keeps stable. Additionally, Figure 12 reveals that the curve of soil moisture content at four different depths is basically stable around the 20th year. This indicates that the water content of the subgrade soil remains stable after the 20th year.Figure 12
Dependence of water content on time for different depths.Limited to space, this work only describes the variation of total moisture content of subgrade soil layer with time and depth in the 20th year, as depicted in Figure13. The soil water content changes greatly at the depth of 1 m from the subgrade surface. The soil moisture content in this depth increases from the initial 14 to 30.3%. This illustrates that the phenomenon of moisture accumulation on the subgrade surface is significant.Figure 13
Variation of total water content.Figure14 depicts the histogram of monthly average values for liquid water flux and gaseous water flux in subgrade soil layer. In this paper, the liquid water and water vapor transport upward (to the air) is defined as “+,” while the downward (to the interior of soil) is defined as “–”. In this article, the comparison of water flux refers to the absolute value of flux. Figure 14(a) shows that the liquid water flux of the subgrade soil at three different depths (z=1.5 m, 2.0 m, and 2.5 m) is basically positive during the freezing period (December to March), indicating that the liquid water migrates upward during this period. For example, the liquid water flux of the soil layer at a depth of 2.5 m in December is 0.76×10−9m/s. During the thawing period (April to November), the liquid water flux is negative, indicating that the liquid water migrates downward during this period. For example, the liquid water flux of the soil layer at a depth of 2.5 m in July is −1.15×10−9m/s. Meanwhile, the vapor water flux demonstrated in Figure 14(b) has a similar variation law with the liquid water flux. Both are positive during the freezing period and negative during the thawing period.Figure 14
Monthly average of liquid water flux and water vapor flux.
(a)
ql monthly average(b)
qv monthly averageFigure15 shows the variations of liquid water flux and water vapor flux at different depths (z= 0 m, 1.5 m, and 2.5 m) for the subgrade soil from the 18th to the 20th year. The data extracted in Figure 15 starts from August of the 18th year. Figure 15 demonstrates that the liquid water flux and water vapor flux of the soil at different depths present a sinusoidal trend with the increase of time. As shown in Figure 15(a), the liquid water flux of the soil at the depth of 2.5 m fluctuates the most dramatically. Specifically, the liquid water migrates to the interior of the subgrade soil in winter and spring, but to the surface of the subgrade soil in summer and autumn. At the same time, the smaller the depth (the farther from the subgrade surface layer), the longer the time corresponding to the peak of the liquid water flux for the soil, and the smoother the variation curve of the liquid water flux. This indicates that the liquid water content deep in the ground is less affected by seasonal temperature changes, and the migration changes are not significant. Figure 15(b) reveals that the water vapor flux of the subgrade soil also fluctuates with time. The farther from the subgrade surface (the smaller the depth), the more drastic the variation of the water vapor flux. Therefore, it can be inferred that the amount of the water vapor migration inside the subgrade soil should be greater than that in the subgrade surface. This also verifies the conclusion drawn by Teng et al. [30] that the main reason for the covering effect in cold and arid regions is the water vapor migration.Figure 15
Changes in liquid water flux and water vapor flux.
(a)
Liquid water flux(b)
Water vapor fluxFigure16 shows the variation of ice content in the 20th year after the water field is stable. It reflects the changes of ice content with time and depth in the process of freezing and thawing. It can be seen from Figure 16 that the ice content of the roadbed exists from the beginning of November to the end of March of the following year. The ice content is present at a depth range of approximately 1.5 to 3 m, which is consistent with the roadbed freezing depth of approximately 1.5 m depicted in Figure 10(b). As the subgrade depth increases, the ice content decreases. The maximum ice content occurs from December to February of the following year, and its value is 16%. The increase of ice content and volume will lead to frost heave cracking in the subgrade surface, which will seriously threaten the driving safety of vehicles. Therefore, it is important to pay attention to the generation of the covering effect in practical engineering. It is recommended that treatment measures such as soil replacement and the use of consolidated soil be used for prevention and treatment.Figure 16
Variation of ice content of roadbed with time and depth.


## 4.1. Mathematical Model

### 4.1.1. Governing Equation

Liquid water migration driven by temperature gradients and substrate suction gradients follows the Richards equation [30]. The expression is as follows:
(1)ql=qlh+qlT=−Klh∂h∂z+1−KlT∂T∂z,where ql is the total liquid water flux; qlh is the liquid water flux due to the matrix suction gradient; qlh is the liquid water flux due to the temperature gradient(m·s-1); h for the pressure head(m); z is the spatial coordinate position (m), upward is positive; T is temperature(K); Klh (m·s-1) is the liquid water permeability coefficient under the action of the soil matrix suction gradient; and KlT(m2·K-1·s-1) is the liquid water permeability coefficient under the action of soil temperature gradient.The flow of vaporous water in soil is described by Fick’s law as [31]:
(2)qv=qvh+qvT=−Kvh∂h∂z−KvT∂T∂z,where qv is the total water vapor flux; qvh is the water vapor flux under the action of the soil matrix suction gradient; qvT is the water vapor flux under the action of the temperature gradient(m·s-1); Kvh(m·s-1) is the water vapor conductivity under the action of the soil matrix suction gradient; and KvT(m2·K-1·s-1) is the water vapor conductivity under the action of a temperature gradient.According to the principle of mass conservation, the mass conservation equation of unsaturated frozen soil is as follows [31]:
(3)∂θ∂t=∂θl∂t+∂θv∂t+ρiρw∂θi∂t=‐∂ql∂z−∂qv∂z=∂∂xKlh∂h∂z+1+KlT∂T∂z+Kvh∂h∂z+KvT∂T∂z,where θ is the total volume moisture content(m3·m-3); θl is the moisture content of liquid water(m3·m-3); θv is the equivalent water vapor moisture content(m3·m3); θi is the ice content(m3·m-3); ρi is the density of ice(kg·m-3); and ρw is the density of liquid water(kg·m-3).The energy transfer should comprehensively consider the process of water migration, evaporation, condensation, and phase change in unsaturated soil. The heat control equation of unsaturated soil is as follows [32]:
(4)CP∂T∂t−Liρi∂θi∂t+Lwρw∂θv∂t=∂∂tλ∂T∂z−Cl∂qlT∂z−Cv∂qvT∂z−Lwρw∂qv∂z,where CP is the specific heat capacity of the soil(MJ·m-3·K-1); Cl is the specific heat capacity of liquid water; Cv is the specific heat capacity of water vapor(kJ·m-3·K-1); Li is the latent heat of phase transition of water(kJ·kg-1); Lw represents the latent heat of vaporization(J·m-3); and λ represents the thermal conductivity of unsaturated frozen soils(W·m-1·K-1).


### 4.1.2. Hydraulic Properties

Ignore the hysteresis phenomenon of soil in the process of wetting and drying cycle; in this paper, the Van Genuchten [33] model (V-G model) is used to describe the soil-water characteristic curve of unsaturated soil, and the expression is as follows:
(5)Se=θl−θrθs−θr=11+αhnmh<01h≥0,where Se is the effective saturation; θs is the saturated moisture content; θr is the residual moisture content (m3·m-3); and α and n and m are the fitting parameters of the V-G model. The unsaturated permeability coefficient Klh due to the matrix suction gradient can be calculated using the Mualem [34] model and is expressed as:
(6)Klh=KsSel1−1−Se1/mm2/Ih<0KSh≥0,where KS is the saturated hydraulic conductivity(m·s-1); I is the ice resistance coefficient; l is an empirical parameter; and Mualem [34] recommends l taking 0.5.Xu et al. [29] proposed that the unfrozen water content is a function of the initial water content and temperature and established a functional relationship. The maximum unfrozen water content θumax during freezing is expressed as:
(7)θumax=aT−273.15−b,where a and b are parameters related to soil properties [29].The expressions for liquid water content and ice content are determined as:(8)θl=θotherθumaxT<T0andθ>θumax,(9)θi=ρwρiθ−θi.


### 4.1.3. Model Validation

To verify the validity of the numerical model developed in this paper, the calculated results in this paper are compared with the above-mentioned laboratory test results. Figure8(a) shows the temperature distribution law on the 2nd and 17th day of the test. It can be seen from the figure that the experimental value and the simulated value are in good agreement and the temperature difference is less than 0.5°C. Figure 8(b) shows the change curve of water content along the depth on the 18th day of the test. It can be seen from the figure that the variation law of water distribution during the test is basically consistent with the simulated value, and the difference in water content is less than 1%. The variation laws of soil temperature field and moisture field calculated by the numerical model in this paper are consistent with the measured results of laboratory tests. This proves the applicability and effectiveness of the numerical model established in this paper.Figure 8
Measured and simulated soil temperatures and water contents profile.
(a)
Soil temperature water content(b)
Water content


## 4.1.1. Governing Equation

Liquid water migration driven by temperature gradients and substrate suction gradients follows the Richards equation [30]. The expression is as follows:
(1)ql=qlh+qlT=−Klh∂h∂z+1−KlT∂T∂z,where ql is the total liquid water flux; qlh is the liquid water flux due to the matrix suction gradient; qlh is the liquid water flux due to the temperature gradient(m·s-1); h for the pressure head(m); z is the spatial coordinate position (m), upward is positive; T is temperature(K); Klh (m·s-1) is the liquid water permeability coefficient under the action of the soil matrix suction gradient; and KlT(m2·K-1·s-1) is the liquid water permeability coefficient under the action of soil temperature gradient.The flow of vaporous water in soil is described by Fick’s law as [31]:
(2)qv=qvh+qvT=−Kvh∂h∂z−KvT∂T∂z,where qv is the total water vapor flux; qvh is the water vapor flux under the action of the soil matrix suction gradient; qvT is the water vapor flux under the action of the temperature gradient(m·s-1); Kvh(m·s-1) is the water vapor conductivity under the action of the soil matrix suction gradient; and KvT(m2·K-1·s-1) is the water vapor conductivity under the action of a temperature gradient.According to the principle of mass conservation, the mass conservation equation of unsaturated frozen soil is as follows [31]:
(3)∂θ∂t=∂θl∂t+∂θv∂t+ρiρw∂θi∂t=‐∂ql∂z−∂qv∂z=∂∂xKlh∂h∂z+1+KlT∂T∂z+Kvh∂h∂z+KvT∂T∂z,where θ is the total volume moisture content(m3·m-3); θl is the moisture content of liquid water(m3·m-3); θv is the equivalent water vapor moisture content(m3·m3); θi is the ice content(m3·m-3); ρi is the density of ice(kg·m-3); and ρw is the density of liquid water(kg·m-3).The energy transfer should comprehensively consider the process of water migration, evaporation, condensation, and phase change in unsaturated soil. The heat control equation of unsaturated soil is as follows [32]:
(4)CP∂T∂t−Liρi∂θi∂t+Lwρw∂θv∂t=∂∂tλ∂T∂z−Cl∂qlT∂z−Cv∂qvT∂z−Lwρw∂qv∂z,where CP is the specific heat capacity of the soil(MJ·m-3·K-1); Cl is the specific heat capacity of liquid water; Cv is the specific heat capacity of water vapor(kJ·m-3·K-1); Li is the latent heat of phase transition of water(kJ·kg-1); Lw represents the latent heat of vaporization(J·m-3); and λ represents the thermal conductivity of unsaturated frozen soils(W·m-1·K-1).


## 4.1.2. Hydraulic Properties

Ignore the hysteresis phenomenon of soil in the process of wetting and drying cycle; in this paper, the Van Genuchten [33] model (V-G model) is used to describe the soil-water characteristic curve of unsaturated soil, and the expression is as follows:
(5)Se=θl−θrθs−θr=11+αhnmh<01h≥0,where Se is the effective saturation; θs is the saturated moisture content; θr is the residual moisture content (m3·m-3); and α and n and m are the fitting parameters of the V-G model. The unsaturated permeability coefficient Klh due to the matrix suction gradient can be calculated using the Mualem [34] model and is expressed as:
(6)Klh=KsSel1−1−Se1/mm2/Ih<0KSh≥0,where KS is the saturated hydraulic conductivity(m·s-1); I is the ice resistance coefficient; l is an empirical parameter; and Mualem [34] recommends l taking 0.5.Xu et al. [29] proposed that the unfrozen water content is a function of the initial water content and temperature and established a functional relationship. The maximum unfrozen water content θumax during freezing is expressed as:
(7)θumax=aT−273.15−b,where a and b are parameters related to soil properties [29].The expressions for liquid water content and ice content are determined as:(8)θl=θotherθumaxT<T0andθ>θumax,(9)θi=ρwρiθ−θi.


## 4.1.3. Model Validation

To verify the validity of the numerical model developed in this paper, the calculated results in this paper are compared with the above-mentioned laboratory test results. Figure8(a) shows the temperature distribution law on the 2nd and 17th day of the test. It can be seen from the figure that the experimental value and the simulated value are in good agreement and the temperature difference is less than 0.5°C. Figure 8(b) shows the change curve of water content along the depth on the 18th day of the test. It can be seen from the figure that the variation law of water distribution during the test is basically consistent with the simulated value, and the difference in water content is less than 1%. The variation laws of soil temperature field and moisture field calculated by the numerical model in this paper are consistent with the measured results of laboratory tests. This proves the applicability and effectiveness of the numerical model established in this paper.Figure 8
Measured and simulated soil temperatures and water contents profile.
(a)
Soil temperature water content(b)
Water content


## 4.2. Recurrence of the Covering Effect

### 4.2.1. Geometric Model and Hydrothermal Parameters

The subgrade soil at a certain depth under the concrete slab is taken to analyze the change law of water and heat transfer under the covering effect. The soil layer distribution of the site is shown in Figure9. In the figure, z represents the depth of the roadbed, 0≤z≤3m is the subgrade base composed of silty clay, and −20≤z<0m is the foundation soil layer composed of loess. The numerical simulation software COMSOL is used to analyze the causes of moisture accumulation under the concrete panel covering. The calculation model is one-dimensional, and the hydrothermal parameters input in the model are shown in Table 2.Figure 9
The soil layer distribution of the research site.Table 2
Soil hydrothermal parameters [29].
LithologyDepth of soil layerDensity (kg·m-3)α (m-1)nKs (10-6 m·s-1)Thermal conductivity (W·m-1·K-1)Heat capacity (kJ·m-3·K-1)FrozenUnfrozenFrozenUnfrozenSilty clayRoadbed21000.0493.736.111.51.48701060LoessUnsaturated region19000.0681.090.561.71.610101150


### 4.2.2. Model Boundary Conditions and Initial Values

In the numerical simulation, the initial temperature of the foundation filling usually refers to the average temperature within 2 m below the ground surface during the actual construction process, which is about 15°C [35]. This paper also takes the value accordingly. In order to exclude the water migration caused by the difference in moisture content between the silty clay base and the loess base soil, the same initial moisture content is set to 14% in this paper. The calculation period is 20 years.Before the calculation, the initial temperature field of the loess foundation must be determined first. Therefore, in this paper, the initial temperature field of the natural site is obtained by the method of numerical calculation. Taking the soil 20 m below the natural site ground as the one-dimensional geometric model for calculation, in the one-dimensional calculation model of the natural site, the boundary under temperature is taken as the flux boundary considering the influence of geothermal (q=0.05 W/m2) [36]. The moisture boundaries of natural sites are all taken as zero-flux boundaries. The initial temperature value entered in the model is arbitrary (this value does not affect the distribution of the final stable temperature field). The above initial values and boundary conditions are brought into the model for calculation, and the model calculation time is 80 years. Take the stabilized temperature field as the initial temperature of the soil layer of the natural site. When the annual average temperature change and the maximum temperature change are both less than 0.01°C, the temperature field is considered to be stable [37]. In the process of determining the soil temperature field, the surface thermal boundary is usually based on the boundary layer principle [38]. August 1 was selected as the initial time of the simulation. According to the in-situ disease investigation, the air temperature and the natural site upper boundary temperature are shown in Equations (10) and (11), respectively.
(10)T0=8+18sin2πt8760+2π3,(11)T1=8+1.5+16sin2πt8760+2π3,where t is time (hours).Considering the endothermic effect of the subgrade surface layer, the temperature change function of the subgrade surface is:(12)T2=8+3+17sin2πt8760+2π3.Taking formula (12) as the upper boundary of foundation soil temperature, the lower boundary is the flux boundary considering geothermal effects [36] (q=0.05W/m2). The moisture boundaries are all closed, simulating the impermeable state under the covering effect.


### 4.2.3. Simulation Results and Analysis

Figure10 shows the subgrade temperature changes with time and depth. It can be seen that the temperature of the subgrade soil layer is basically stable in the third year (Figure 10(a)). Therefore, the time-history curve of the subgrade temperature field in the third year is extracted for analysis, and the results are shown in Figure 10(b). The approximate range of the subgrade temperature field in summer and autumn is 6 ~ 23°C, of which the maximum temperature of the filling is 24°C. In spring and winter, the subgrade temperature generally ranges from -8 to 16°C, and the minimum temperature of the filling is -8°C. In the figure, 0°C is regarded as the freeze-thaw interface. It can be seen from the freeze-thaw interface at 0°C that the maximum freezing depth is 1.5 m.Figure 10
Subgrade temperature changes with time and depth.
(a)
Soil temperature at different depths(b)
Soil temperature in the third yearFigure11 illustrates the distribution of total water content for the subgrade along the depth. The total water content increases with the increase of time at the depth of 2 ~ 3 m for the subgrade but decreases at the depth of -1 m ~ 2 m for the subgrade. Generally speaking, the moisture in the soil migrates to the upper part of the subgrade year by year. As shown in Figure 11, the maximum moisture content of the soil at the subgrade surface layer can reach 30%. This is due to the moisture in the lower soil gradually migrates to the upper soil layer and finally accumulates in the surface soil of the subgrade. For the depth soil layer of -2 ~ -1 m, it is less affected by the covering effect due to the distance from the concrete surface layer, and the groundwater is too deep to supply capillary water. Therefore, the soil moisture in this depth range remains unchanged at the initial moisture content.Figure 11
Distribution of total water content with depth.In order to analyze the overall change of soil moisture accumulation at different depths of subgrade, the variations of moisture content with time at the depth of 2.9 m for the subgrade surface layer and the depth of 2.5 m, 1.5 m and 0.5 m inside the subgrade are extracted (Figure12). The soil water content at depths of 2.9 m and 2.5 m increases year by year as a whole, while the soil water content at depths of 1.5 m and 0.5 m experiences slightly decreased and then keeps stable. Additionally, Figure 12 reveals that the curve of soil moisture content at four different depths is basically stable around the 20th year. This indicates that the water content of the subgrade soil remains stable after the 20th year.Figure 12
Dependence of water content on time for different depths.Limited to space, this work only describes the variation of total moisture content of subgrade soil layer with time and depth in the 20th year, as depicted in Figure13. The soil water content changes greatly at the depth of 1 m from the subgrade surface. The soil moisture content in this depth increases from the initial 14 to 30.3%. This illustrates that the phenomenon of moisture accumulation on the subgrade surface is significant.Figure 13
Variation of total water content.Figure14 depicts the histogram of monthly average values for liquid water flux and gaseous water flux in subgrade soil layer. In this paper, the liquid water and water vapor transport upward (to the air) is defined as “+,” while the downward (to the interior of soil) is defined as “–”. In this article, the comparison of water flux refers to the absolute value of flux. Figure 14(a) shows that the liquid water flux of the subgrade soil at three different depths (z=1.5 m, 2.0 m, and 2.5 m) is basically positive during the freezing period (December to March), indicating that the liquid water migrates upward during this period. For example, the liquid water flux of the soil layer at a depth of 2.5 m in December is 0.76×10−9m/s. During the thawing period (April to November), the liquid water flux is negative, indicating that the liquid water migrates downward during this period. For example, the liquid water flux of the soil layer at a depth of 2.5 m in July is −1.15×10−9m/s. Meanwhile, the vapor water flux demonstrated in Figure 14(b) has a similar variation law with the liquid water flux. Both are positive during the freezing period and negative during the thawing period.Figure 14
Monthly average of liquid water flux and water vapor flux.
(a)
ql monthly average(b)
qv monthly averageFigure15 shows the variations of liquid water flux and water vapor flux at different depths (z= 0 m, 1.5 m, and 2.5 m) for the subgrade soil from the 18th to the 20th year. The data extracted in Figure 15 starts from August of the 18th year. Figure 15 demonstrates that the liquid water flux and water vapor flux of the soil at different depths present a sinusoidal trend with the increase of time. As shown in Figure 15(a), the liquid water flux of the soil at the depth of 2.5 m fluctuates the most dramatically. Specifically, the liquid water migrates to the interior of the subgrade soil in winter and spring, but to the surface of the subgrade soil in summer and autumn. At the same time, the smaller the depth (the farther from the subgrade surface layer), the longer the time corresponding to the peak of the liquid water flux for the soil, and the smoother the variation curve of the liquid water flux. This indicates that the liquid water content deep in the ground is less affected by seasonal temperature changes, and the migration changes are not significant. Figure 15(b) reveals that the water vapor flux of the subgrade soil also fluctuates with time. The farther from the subgrade surface (the smaller the depth), the more drastic the variation of the water vapor flux. Therefore, it can be inferred that the amount of the water vapor migration inside the subgrade soil should be greater than that in the subgrade surface. This also verifies the conclusion drawn by Teng et al. [30] that the main reason for the covering effect in cold and arid regions is the water vapor migration.Figure 15
Changes in liquid water flux and water vapor flux.
(a)
Liquid water flux(b)
Water vapor fluxFigure16 shows the variation of ice content in the 20th year after the water field is stable. It reflects the changes of ice content with time and depth in the process of freezing and thawing. It can be seen from Figure 16 that the ice content of the roadbed exists from the beginning of November to the end of March of the following year. The ice content is present at a depth range of approximately 1.5 to 3 m, which is consistent with the roadbed freezing depth of approximately 1.5 m depicted in Figure 10(b). As the subgrade depth increases, the ice content decreases. The maximum ice content occurs from December to February of the following year, and its value is 16%. The increase of ice content and volume will lead to frost heave cracking in the subgrade surface, which will seriously threaten the driving safety of vehicles. Therefore, it is important to pay attention to the generation of the covering effect in practical engineering. It is recommended that treatment measures such as soil replacement and the use of consolidated soil be used for prevention and treatment.Figure 16
Variation of ice content of roadbed with time and depth.


## 4.2.1. Geometric Model and Hydrothermal Parameters

The subgrade soil at a certain depth under the concrete slab is taken to analyze the change law of water and heat transfer under the covering effect. The soil layer distribution of the site is shown in Figure9. In the figure, z represents the depth of the roadbed, 0≤z≤3m is the subgrade base composed of silty clay, and −20≤z<0m is the foundation soil layer composed of loess. The numerical simulation software COMSOL is used to analyze the causes of moisture accumulation under the concrete panel covering. The calculation model is one-dimensional, and the hydrothermal parameters input in the model are shown in Table 2.Figure 9
The soil layer distribution of the research site.Table 2
Soil hydrothermal parameters [29].
LithologyDepth of soil layerDensity (kg·m-3)α (m-1)nKs (10-6 m·s-1)Thermal conductivity (W·m-1·K-1)Heat capacity (kJ·m-3·K-1)FrozenUnfrozenFrozenUnfrozenSilty clayRoadbed21000.0493.736.111.51.48701060LoessUnsaturated region19000.0681.090.561.71.610101150


## 4.2.2. Model Boundary Conditions and Initial Values

In the numerical simulation, the initial temperature of the foundation filling usually refers to the average temperature within 2 m below the ground surface during the actual construction process, which is about 15°C [35]. This paper also takes the value accordingly. In order to exclude the water migration caused by the difference in moisture content between the silty clay base and the loess base soil, the same initial moisture content is set to 14% in this paper. The calculation period is 20 years.Before the calculation, the initial temperature field of the loess foundation must be determined first. Therefore, in this paper, the initial temperature field of the natural site is obtained by the method of numerical calculation. Taking the soil 20 m below the natural site ground as the one-dimensional geometric model for calculation, in the one-dimensional calculation model of the natural site, the boundary under temperature is taken as the flux boundary considering the influence of geothermal (q=0.05 W/m2) [36]. The moisture boundaries of natural sites are all taken as zero-flux boundaries. The initial temperature value entered in the model is arbitrary (this value does not affect the distribution of the final stable temperature field). The above initial values and boundary conditions are brought into the model for calculation, and the model calculation time is 80 years. Take the stabilized temperature field as the initial temperature of the soil layer of the natural site. When the annual average temperature change and the maximum temperature change are both less than 0.01°C, the temperature field is considered to be stable [37]. In the process of determining the soil temperature field, the surface thermal boundary is usually based on the boundary layer principle [38]. August 1 was selected as the initial time of the simulation. According to the in-situ disease investigation, the air temperature and the natural site upper boundary temperature are shown in Equations (10) and (11), respectively.
(10)T0=8+18sin2πt8760+2π3,(11)T1=8+1.5+16sin2πt8760+2π3,where t is time (hours).Considering the endothermic effect of the subgrade surface layer, the temperature change function of the subgrade surface is:(12)T2=8+3+17sin2πt8760+2π3.Taking formula (12) as the upper boundary of foundation soil temperature, the lower boundary is the flux boundary considering geothermal effects [36] (q=0.05W/m2). The moisture boundaries are all closed, simulating the impermeable state under the covering effect.


## 4.2.3. Simulation Results and Analysis

Figure10 shows the subgrade temperature changes with time and depth. It can be seen that the temperature of the subgrade soil layer is basically stable in the third year (Figure 10(a)). Therefore, the time-history curve of the subgrade temperature field in the third year is extracted for analysis, and the results are shown in Figure 10(b). The approximate range of the subgrade temperature field in summer and autumn is 6 ~ 23°C, of which the maximum temperature of the filling is 24°C. In spring and winter, the subgrade temperature generally ranges from -8 to 16°C, and the minimum temperature of the filling is -8°C. In the figure, 0°C is regarded as the freeze-thaw interface. It can be seen from the freeze-thaw interface at 0°C that the maximum freezing depth is 1.5 m.Figure 10
Subgrade temperature changes with time and depth.
(a)
Soil temperature at different depths(b)
Soil temperature in the third yearFigure11 illustrates the distribution of total water content for the subgrade along the depth. The total water content increases with the increase of time at the depth of 2 ~ 3 m for the subgrade but decreases at the depth of -1 m ~ 2 m for the subgrade. Generally speaking, the moisture in the soil migrates to the upper part of the subgrade year by year. As shown in Figure 11, the maximum moisture content of the soil at the subgrade surface layer can reach 30%. This is due to the moisture in the lower soil gradually migrates to the upper soil layer and finally accumulates in the surface soil of the subgrade. For the depth soil layer of -2 ~ -1 m, it is less affected by the covering effect due to the distance from the concrete surface layer, and the groundwater is too deep to supply capillary water. Therefore, the soil moisture in this depth range remains unchanged at the initial moisture content.Figure 11
Distribution of total water content with depth.In order to analyze the overall change of soil moisture accumulation at different depths of subgrade, the variations of moisture content with time at the depth of 2.9 m for the subgrade surface layer and the depth of 2.5 m, 1.5 m and 0.5 m inside the subgrade are extracted (Figure12). The soil water content at depths of 2.9 m and 2.5 m increases year by year as a whole, while the soil water content at depths of 1.5 m and 0.5 m experiences slightly decreased and then keeps stable. Additionally, Figure 12 reveals that the curve of soil moisture content at four different depths is basically stable around the 20th year. This indicates that the water content of the subgrade soil remains stable after the 20th year.Figure 12
Dependence of water content on time for different depths.Limited to space, this work only describes the variation of total moisture content of subgrade soil layer with time and depth in the 20th year, as depicted in Figure13. The soil water content changes greatly at the depth of 1 m from the subgrade surface. The soil moisture content in this depth increases from the initial 14 to 30.3%. This illustrates that the phenomenon of moisture accumulation on the subgrade surface is significant.Figure 13
Variation of total water content.Figure14 depicts the histogram of monthly average values for liquid water flux and gaseous water flux in subgrade soil layer. In this paper, the liquid water and water vapor transport upward (to the air) is defined as “+,” while the downward (to the interior of soil) is defined as “–”. In this article, the comparison of water flux refers to the absolute value of flux. Figure 14(a) shows that the liquid water flux of the subgrade soil at three different depths (z=1.5 m, 2.0 m, and 2.5 m) is basically positive during the freezing period (December to March), indicating that the liquid water migrates upward during this period. For example, the liquid water flux of the soil layer at a depth of 2.5 m in December is 0.76×10−9m/s. During the thawing period (April to November), the liquid water flux is negative, indicating that the liquid water migrates downward during this period. For example, the liquid water flux of the soil layer at a depth of 2.5 m in July is −1.15×10−9m/s. Meanwhile, the vapor water flux demonstrated in Figure 14(b) has a similar variation law with the liquid water flux. Both are positive during the freezing period and negative during the thawing period.Figure 14
Monthly average of liquid water flux and water vapor flux.
(a)
ql monthly average(b)
qv monthly averageFigure15 shows the variations of liquid water flux and water vapor flux at different depths (z= 0 m, 1.5 m, and 2.5 m) for the subgrade soil from the 18th to the 20th year. The data extracted in Figure 15 starts from August of the 18th year. Figure 15 demonstrates that the liquid water flux and water vapor flux of the soil at different depths present a sinusoidal trend with the increase of time. As shown in Figure 15(a), the liquid water flux of the soil at the depth of 2.5 m fluctuates the most dramatically. Specifically, the liquid water migrates to the interior of the subgrade soil in winter and spring, but to the surface of the subgrade soil in summer and autumn. At the same time, the smaller the depth (the farther from the subgrade surface layer), the longer the time corresponding to the peak of the liquid water flux for the soil, and the smoother the variation curve of the liquid water flux. This indicates that the liquid water content deep in the ground is less affected by seasonal temperature changes, and the migration changes are not significant. Figure 15(b) reveals that the water vapor flux of the subgrade soil also fluctuates with time. The farther from the subgrade surface (the smaller the depth), the more drastic the variation of the water vapor flux. Therefore, it can be inferred that the amount of the water vapor migration inside the subgrade soil should be greater than that in the subgrade surface. This also verifies the conclusion drawn by Teng et al. [30] that the main reason for the covering effect in cold and arid regions is the water vapor migration.Figure 15
Changes in liquid water flux and water vapor flux.
(a)
Liquid water flux(b)
Water vapor fluxFigure16 shows the variation of ice content in the 20th year after the water field is stable. It reflects the changes of ice content with time and depth in the process of freezing and thawing. It can be seen from Figure 16 that the ice content of the roadbed exists from the beginning of November to the end of March of the following year. The ice content is present at a depth range of approximately 1.5 to 3 m, which is consistent with the roadbed freezing depth of approximately 1.5 m depicted in Figure 10(b). As the subgrade depth increases, the ice content decreases. The maximum ice content occurs from December to February of the following year, and its value is 16%. The increase of ice content and volume will lead to frost heave cracking in the subgrade surface, which will seriously threaten the driving safety of vehicles. Therefore, it is important to pay attention to the generation of the covering effect in practical engineering. It is recommended that treatment measures such as soil replacement and the use of consolidated soil be used for prevention and treatment.Figure 16
Variation of ice content of roadbed with time and depth.


## 5. Conclusion

(1)
Onsite monitoring found that the water content of the roadbed soil from 0 to 50 cm below the concrete slab gathered significantly, with the water content increasing by 5 to 30%.(2)
Seasonal frozen soil under time-varying temperature boundary conditions, water content of silty clay increases with the number of freeze-thaw cycles. The cumulative moisture content within the maximum freezing depth is up to 6%, and the subgrade covering effect is significant(3)
Seasonal temperature changes lead to the accumulation of water in the subgrade surface, and the maximum accumulation amount is 32%. During the freezing period (December to March), the liquid water and gaseous water in the subgrade migrate upwards. The melting period (April to November) is the opposite(4)
Under seasonal temperature changes, the water accumulated within 1.5 m of the upper subgrade during freezing season will freeze into ice, and the maximum ice content can reach 16%. Therefore, corresponding measures should be taken to prevent the occurrence of covering effect



---

*Source: 2035174-2022-07-30.xml*