Calculation of Subgrade Moisture Index in Seasonally Frozen Regions consideringEvapotranspiration at SubzeroTemperatures and the Pavement Coverage Effect

+e moisture index of subgrade material directly below a paved highway is typically represented by that of an uncovered slope. However, existing studies have demonstrated the existence of a significant moisture content difference between an uncovered slope and covered subgrade owing to evapotranspiration. Moreover, under the influence of solar radiation, wind, and other factors, soil evapotranspiration persists even at subzero temperatures. +is paper presents an improved method for subgrade moisture index calculation for regions that freeze seasonally. Instead of the conventional +ornthwaite method, the Food and Agriculture Organization Penman–Monteith (FAO-56 PM) method was employed to estimate the potential evapotranspiration (PE) of slope soil at subzero temperatures. Based on the moisture balance principle, the PE and water runoff and deficit were used as input parameters to calculate the moisture index of an uncovered slope. After the effect of pavement cover on subgrade humidity was defined through a correction coefficient determined via the matric suction dependence of soil water content, an optimized calculation formula was developed to estimate the moisture index of the subgrade material according to that of the corresponding slope. +e results calculated on a typical seasonally frozen region in Northeast China demonstrated the applicability and accuracy of the proposed method for predicting the subgrade moisture. +e potential evapotranspiration of an uncovered highway slope soil at subzero temperatures could reach 9.8%–15.7% of the total annual evapotranspiration. +e moisture index range for seasonally frozen regions was −14.2–57.3. +ese findings will have important implications for effective improvements in the design and construction of subgrade in regions that freeze seasonally or face similar climatic conditions.


Introduction
While subgrade material is usually unsaturated, its moisture condition is a critical factor that directly affects the strength and stiffness of the pavement structure [1,2]. Past studies have shown that the moisture of subgrade material reaches equilibrium several years after construction [3][4][5]. us, the moisture condition is an important consideration in the design of the structure and material of the subgrade.
In China, the moisture index is used to calculate the equilibrium suction of a subgrade when the equilibrium moisture is mainly dependent on the climate [6]. is calculation is commonly performed using the ornthwaite method, which is based on two concepts: potential evapotranspiration (PE) and moisture balance. However, the ornthwaite method assumes that the evapotranspiration from the soil ceases when the average temperature is below 0°C (i.e., subzero) and the calculated PE is zero [7][8][9][10]. e calculation results in the overestimation of the moisture index of the subgrade soil, leading to the adoption of a design value of the subgrade resilience modulus that is significantly high and results in excessive subgrade dehumidification measures. Although the evaporation rate of snow on an exposed subgrade or plant slope (equivalent to bare soil or tundra) is lower than that of liquid water and forest cover, it is not zero [11][12][13].
us, the use of the ornthwaite method to calculate the PE in seasonally frozen areas produces large errors, which reduces the accuracy of the determined moisture index. In recent decades, scholars have developed various PE estimation models that include the use of comprehensive radiation, temperature, and evaporation dish methods [14]. Temperature-based methods depend only on the air temperature and include the ornthwaite, Hargreaves [15], and McCloud [16] methods. e most important comprehensive approach for calculating the PE is the Penman-Monteith method, which is recommended by the United Nations Food and Agriculture Organization (FAO) for calculating the daily evapotranspiration of reference crops. e FAO Penman-Monteith (FAO-56 PM) method is the standard technique for calculating the PE and is used to evaluate other methods in regions lacking adequate measurement data [17,18]. FAO-56 PM considers five parameters: the maximum air temperature, minimum air temperature, relative humidity, mean wind speed at a height of 2 m, and sunshine hours. e minimum temperature has no limit, which makes the FAO-56 method highly accurate and versatile.
e Penman equation, which is used to calculate the transpiration forces in China's current Standard of Climatic Zoning for Highway (JTJ 003-1986) [19], is the original form of the FAO-56 PM method. In 1995, Liu (JTJ 003-1986) when studying the influence of environmental factors on pavement service performance [20]. In 2017, Li et al. also used the Penman equation to calculate evaporation when predicting the thickness of water and snow (or ice) layers gathered on the pavement surface in Jiangsu Province. e empirical coefficient of the equation was adjusted to align with the actual evaporation in Jiangsu Province [21]. us, experts in the transportation field consistently use this method to evaluate the dry and wet conditions of subgrades.
Generally, the ornthwaite method is employed to calculate the moisture index of the subgrade soil. However, when the subgrade is covered by pavement, which is usually impermeable, the rainfall infiltration and evapotranspiration of the subgrade significantly differ from those of uncovered soil. In the humid and rainy climate of Shanghai, China, a field survey showed that the average moisture content was 23.4% for slope soil at a depth of 0.5 m and only 20.3% for a subgrade located directly beneath a paved highway at the same depth. us, the subgrade had a moisture content of approximately 0.87 times that of the slope [22,23]. Xinjiang, China, experiences strong evapotranspiration, and a field survey showed that the average moisture content was 3.04% for the exposed surfaces and 5.73% for the subgrade soil. e subgrade thus had a moisture content of approximately 1.88 times that of the exposed surface [24].
ese results indicate that the moisture state of an uncovered slope does not represent that of the subgrade directly below a paved highway.
Although researchers have found that pavement coverage affects the subgrade moisture, current specifications do not provide a quantitative explanation for this phenomenon. Because soil water is generally under motion, it flows from a state of high energy to a state of low energy. However, its seepage velocity is generally slow and the kinetic energy can thus be ignored. Hence, the main factor that determines the movement of soil water is its potential energy [25].
is study aimed to develop a methodology for moisture index calculation of the subgrade in seasonally frozen regions taking into account the PE and pavement coverage effect. Accurate estimation of the PE is critical for calculating subgrade moisture content. To quantify the evapotranspiration of slope soil at subzero temperatures, which is neglected in the ornthwaite method, we applied the FAO-56 PM method to predict the PE and evaluated its prediction accuracy with respect to various influencing factors. en, the moisture index of an uncovered slope was calculated by the moisture balance principle using the PE and two extra factors as input parameters. Based on the matric suction dependence of soil water content, a method for calculating the correction coefficient of the pavement coverage effect was proposed to develop an optimized calculation formula for predicting the subgrade moisture index. e application of the proposed method to a seasonally frozen region in Northeast China was discussed as a case study. is study will not facilitate the exploitation of the subgrade moisture formation mechanism in seasonal freezing regions and other areas with similar climates and therefore establish a targeted method for estimating it, but it can also narrow the existing gap in research on subgrade design and control between seasonally frozen regions and other climatic regions.

Calculation of Potential Evapotranspiration (PE) with the FAO-56 PM Method.
Evapotranspiration is the amount of water dispersed in the air by evaporation during a certain time period and is typically expressed by the thickness of the evaporated water layer. e FAO-56 PM method considers five parameters: the maximum air temperature, minimum air temperature, relative humidity, mean wind speed at a height of 2 m, and sunshine hours. e calculation formula is as follows: where ET 0 is the daily evapotranspiration (cm), PE is the cumulative ET 0 after a month, Z and φ are the altitude and latitude, respectively, and T, T max , and T min are the average, maximum, and minimum air temperatures (°C), respectively. Furthermore, RH mean denotes the average relative humidity (%), n represents the actual sunshine hours (h), and u z is the mean wind speed at a height of 2 m (m/s). Moreover, e s and e a are the saturated and actual vapor pressures (kPa), respectively, and are calculated as follows: e s � e 0 T max + e 0 T min 2 , e a � RH mean 100 Δ is the slope of the temperature-saturated vapor pressure curve at T (kPa/°C): c is the hygrometer constant (kPa/°C): where c p is the specific heat at a constant pressure and is generally 1.013 × 10 −3 MJ·kg −1 ·C −1 . In addition, ε is the ratio of water vapor to dry air or latent heat of vaporization and is generally 2.45 MJ·kg −1 , and P is the actual local steam pressure: R n is the net radiation (MJ·m −2 ·d −1 ): R ns is the net shortwave radiation (MJ·m −2 ·d −1 ): R nl is the net longwave radiation (MJ·m −2 ·d −1 ): R s is the actual solar radiation reaching the Earth's surface (MJ·m −2 ·d −1 ): N is the maximum possible sunshine hours (h): ω s is the sunshine hour angle (rad): where φ and δ are the latitude and diurnal inclinations (rad), respectively: J is the ordinal number for the day (J � 1 on January 1 and increments by one for each additional day). R a is the solar radiation at the top of the atmosphere (MJ·m −2 ·d −1 ): R a � 37.6d r ω s sin φ sin δ + cos φ cos δ sin ω s , (13) d r is the reciprocal of the relative distance between the Sun and Earth: R so is the clear sky solar radiation that reaches the Earth's surface (MJ·m −2 ·d −1 ): Furthermore, Z is the altitude of the calculated point (m) and σ is the Stefan-Boltzmann constant and is given by σ � 4.903 × 10 − 9 MJ·K −4 m −2 d −1 . T max ,K and T min ,K are the maximum and minimum absolute temperatures, respectively, where T max ,K � T max + 273.16 and T min ,K � T min + 273. 16. Meanwhile, G is the soil heat flux and can be generally ignored because it is relatively small on the daily scale, and u z denotes the actual wind speed at the height of the weathervane (m·s −1 ):

Principle of Moisture Balance and Moisture Index of Slope
Soil. Moisture balance is a concept used in soil science and agricultural meteorology. Common models include the exponential regression model, artificial neural network model, water balance model, soil water and heat-coupling transport model for a freezing-thawing period, and soilplant-atmosphere continuum water and heat-coupling transport model [26,27]. e ornthwaite method uses the water balance model to determine the moisture balance. Li et al. [28] calculated the potential vegetation productivity in China using a dynamic soil moisture model based on the ornthwaite method. e ornthwaite moisture balance principle has been applied to subgrade moisture balance analysis [9,29,30]. e soil has a certain water storage capacity because of its complex porous structure. Water is replenished by meteorological precipitation and lost through evapotranspiration. When the precipitation is less than the evapotranspiration, all the precipitation will be evaporated, along with part of the original water in the soil. After all the original moisture in the soil evaporates, the soil assumes the deficit (DF) state. When the precipitation is greater than the PE, the soil reaches the maximum moisture state (i.e., saturated). e excess precipitation flows away in the form of runoff, and R represents the total amount of runoff produced in a month. In the following calculation, the month is used as the statistical unit. e moisture balance of the soil can be summarized by the following three states distinguished by the monthly storage of soil moisture: Advances in Civil Engineering

Existing Runoff,
where S i is the monthly water storage (cm) for month i and S max is the maximum soil water storage capacity (cm). In state 1, S i > S max , the monthly storage exceeds the maximum capacity, and not all of the water has evaporated in the current month. e surplus water can form runoff to replenish the soil in the next month. In state 2, 0 < S i ≤ S max , the monthly storage is between zero and the maximum capacity. Not all the water has evaporated in the current month; however, runoff does not form to replenish the soil in the next month. In state 3, S i ≤ 0, the monthly water storage is zero and all the water (including the monthly precipitation and the supply of the prior month) has evaporated in the current month. It should be noted that no practical condition exists in which the soil water storage is less than zero. is finding is only the result of a mathematical calculation indicating that the evaporation in the current month is much greater than the precipitation. Based on the above analysis, the calculation process of the moisture balance was optimized to that shown in Figure 1.
S i-1 represents the final water storage of the soil in the previous month, which is the initial water storage of the current month. e maximum storage capacity S max depends on the soil type and is equal to the product of the saturated volumetric moisture content θ s and thickness of the soil layer h. e influence of the rainfall depth is generally between 0.6 and 2.5 m [31].
In this study, the soil layer thickness h of a slope affected by rainfall was set to 1.2 m [31]. To calculate the moisture balance, the initial water storage capacity S 0 of the slope soil needs to be determined. e initial water storage is related to the initial moisture conditions of the soil and is equal to the initial moisture content θ 0 multiplied by the thickness of the soil layer h (i.e., 1.2 m). e moisture index is an annual index and is calculated from the moisture balance of the annual monthly precipitation and PE. e moisture index of the slope soil (I m ′ ) is given by where R y is the annual runoff (cm) of the slope soil and DF y is the annual water deficit (cm) of the slope soil. PE y is the annual total evapotranspiration (cm) of the slope soil. e above values are obtained by the accumulation of the monthly values.

Correction Coefficient for the Pavement Coverage Effect.
Because the pavement material is usually impermeable, the moisture in the subgrade directly below undamaged pavement cannot evaporate as freely as that on natural ground.
is is referred to as the pavement coverage effect. Evapotranspiration and infiltration cannot be accurately measured in the subgrade; thus, the subgrade moisture index cannot be directly calculated with equation (18). e pavement coverage effect hinders not only the transpiration of moisture in the subgrade, but also the direct infiltration of natural precipitation. When groundwater is deeply buried, the subgrade moisture is not affected by changes in the groundwater level, and the infiltration of capillary water rises. In this case, the water supply to the subgrade and the water loss from the subgrade are mainly caused by the precipitation infiltration and evapotranspiration of the slope soil. e moisture transfer force between the slope soil and subgrade is known as the matric suction force. is factor is used to establish a method for calculating the correction coefficient for pavement coverage. is method is employed to modify the moisture index of the slope soil. Accordingly, the moisture index of the subgrade can be obtained.
For a dry subgrade with a working area above the capillary wetting surface of groundwater, the subgrade moisture is not affected by the groundwater. When energy loss and longitudinal seepage flow are not considered, the subgrade moisture index (I m ) is directly proportional to the slope soil moisture index (I m ′ ) and is closely related to the pavement coverage effect: is can be expressed as where c is the correction coefficient for the pavement coverage effect. According to soil mechanics, water always flows from a state of high energy to a state of low energy, as previously mentioned. e potential energy determines the movement of water in soil; it can be divided into the gravity, pressure, matrix, and solute potentials. For unsaturated soils without salinization, the potential energy mainly comprises the gravity and matrix potentials. If the vertical distance between two points under consideration (i.e., slope soil and subgrade) is zero, then the gravity potential would be zero. e matrix potential Ψ m is mainly caused by the surface tension of the air-water interface in unsaturated soil and is calculated as When a pore is connected to the atmosphere, then u a � p a � 0. u w is the negative pore water pressure, and s is the matric suction. erefore, the main factor that causes water movement between the slope soil and the subgrade is the matric suction between them. e pavement coverage 4 Advances in Civil Engineering correction coefficient c can be defined as the ratio of the matric suctions of the slope soil and subgrade: where s sw is the matric suction of a certain point in the subgrade and s ss is the matric suction at a point in the slope soil at the same height. For unsaturated soils, the soil-water characteristic curve (SWCC) describes the relationship between the matric suction and the humidity. It is also used to estimate the dynamic resilience modulus and permanent deformation of the subgrade. For a given soil, the SWCC is monotonic within its defined interval. erefore, where θ sw is the volume moisture content of the subgrade and is equal to the optimal volume moisture content of the subgrade θ 0 . θ ss is the volume moisture content of the slope soil and is calculated according to the water stored in a unit volume of the slope soil at the end of the year: where h is the calculated thickness of the slope (h � 1.2 m) and S y is the final value of the annual water storage: When (R y − 0.6DF y )/h > 0, R y is greater than the corresponding DF y for a given year, and the slope soil has more moisture than the initial state; then, I m ′ is positive. When (R y − 0.6DF y )/h < 0, R y is less than the corresponding DF y for a given year and the slope soil contains less moisture than in the initial state, and I m ′ is negative. Depending on the positive and negative conditions of I m ′ , c can be calculated as follows:

Moisture Index (I m ) Calculation Example.
As an example, the FAO-56 PM method was used to calculate the PE at the Yanji Meteorological Station (YJ). e basic information of the meteorological stations is presented in Table 1. e initial volumetric moisture content θ 0 was 0.18, and the saturated volumetric moisture content θ s was 0.24. e meteorological data were obtained from the monthly datasets of the surface climatic standard values  published by the China Meteorological Administration, as given in Table 2. e PE calculation process is presented in Table 3. e calculation process and results for the moisture balance and slope soil moisture index I m ′ are presented in  Figure 1: Moisture balance calculation process.
Advances in Civil Engineering Table 4. e pavement coverage correction coefficient c was determined to be us, the annual moisture index of the subgrade was

Data
Currently, the Standard of Climatic Zoning for Highway classifies the eastern Changbai Mountains in Northeast China as Zone II 1 . is area is distributed over Heilongjiang, Jilin, and Liaoning Provinces and is a typical example of a seasonally frozen area. Highway projects in this area are mainly threatened by snow damage in winter and water damage in summer. e moisture index for the slope soil in this area was calculated using the FAO-56 PM method, and c was calculated using equation (26). e moisture index for the typical subgrade in the area was then calculated. e meteorological data used here were obtained from the monthly datasets of the surface climatic standard values published by the China Meteorological Administration .
e China Meteorological Data Network provides detailed data at http://data.cma.cn. Table 5 presents the values of θ 0 and θ s for different soil groups. Table 6 presents the PE values calculated for the different stations. Evapotranspiration occurred in the slope soils at subzero temperatures, which lasted for 3-5 months. e PE accounted for 9.8%-15.7% of the total evapotranspiration at subzero temperatures. Figure 2 shows the relationship between PE and mean sunshine hours of seven meteorological stations. e relationship between PE and the mean sunshine hours at subzero temperatures is depicted in Figure 3. Table 7 presents the correlation coefficient between PE and mean sunshine hours. e results indicate that the mean sunshine hours had a significant influence on the evapotranspiration of the subgrade, as shown in Figure 2. When the annual data were used for the statistical analysis, PE showed an increasing trend at the seven meteorological stations with an average rate of increase of 0.08 cm/h and an average correlation coefficient of 0.65, as shown in Table 7.

Mean Sunshine Hours.
When only subzero temperature data were used (i.e., the average temperature was less than 0°C), the mean sunshine hours showed a significant positive correlation with the evapotranspiration of the subgrade, as illustrated in Figure 3. At subzero temperatures, the mean sunshine hours were 136.8-244.1 h, while the PE values were within 0.69-4.97 cm. PE increased significantly with increasing sunshine hours,       Advances in Civil Engineering 7 with an average rate of increase of 0.03 cm/h and an average correlation coefficient of 0.83, as shown in Table 7. Figure 4 shows the relationship between PE and the mean wind speed, while Figure 5 shows the relationship between PE and the mean wind speed at subzero temperatures. Table 8 presents the correlation coefficient between PE and the mean wind speed. e results indicate that, over the course of a year, the monthly averaged PE variation with respect to the mean wind speed did not show a consistent trend among the stations, as shown in Figure 4. PE showed a decreasing trend at DD and SFH, with correlation coefficients of −0.85 and −0.8, respectively. JX and YJ also had negative correlations; however, the correlation coefficients were only −0.54 and −0.23, respectively, as shown in Table 8 Table 8. Figure 6 shows the relationship between the mean temperature and PE, while Figure 7 shows the relationship between PE and the mean temperature at subzero temperatures. Table 9 presents the correlation coefficient between PE and the mean temperature. e results indicate that the mean temperature had a significant effect on the evapotranspiration of the slope soil, as shown in Figure 6. Over the entire year, PE increased with the mean temperature at the seven meteorological stations with an average rate of increase of 0.31 cm/°C and an average correlation coefficient of 0.94, as presented in Table 9. At subzero temperatures, the mean temperature showed a significant positive correlation with the evapotranspiration of the slope soil, as depicted in Figure 7. In Zone II 1 , subzero temperatures last approximately 3-5 months. At subzero temperatures, PE was 0.69-4.97 cm with an average rate of increase of 0.19 cm/°C, and the average correlation coefficient was 0.79 at JX, as shown in Table 9. Figure 8 shows the relationship between the mean relative humidity and PE at the seven meteorological stations. Figure 9 depicts the relationship between PE and the mean relative humidity at subzero temperatures. Table 10 presents the correlation coefficient between PE and the mean relative humidity. e results and analysis of the annual data showed that the mean relative humidity did not have a significant effect on the evapotranspiration of the slope soil, as shown in Figure 8. PE showed no clear trends at the seven meteorological stations. At DD and YJ, there was a relatively linear increase in PE with the relative humidity, with correlation coefficients of 0.57 and 0.89, respectively. In contrast, the other five stations  had correlation coefficients that were less than 0.5 with an average of 0.26, as presented in Table 10. When the mean temperature was subzero, the results showed that the mean relative humidity had a significant negative correlation with the evapotranspiration of the slope soil, as shown in Figure 9. When the mean temperature was subzero, the mean relative humidity of the seven meteorological stations ranged from 53% to 73%, and the PE values were within 0.69-4.97 cm. PE  decreased significantly with increasing relative humidity, with an average rate of decrease of 0.23 cm/% and an average correlation coefficient of −0.9, as shown in Table 10.

Accuracy of Potential Evapotranspiration (PE) Estimated
with the FAO-56 PM Method. Figure 10    Mean relative humidity (%) Figure 9: Relationship between PE and the mean relative humidity at subzero temperatures.  1 , the original meteorological data indicated a large temperature difference between day and night in May and June, and the mean temperature was often only approximately 65% of the maximum temperature. e mean temperature is an influencing factor that showed an extremely positive correlation with PE, which is why the calculated values of the model were less than the measured values. Table 11 presents the calculated c values of the different soil classes at each station. e pavement coverage correction coefficient was greater than or equal to zero for the different soil classes at each station. Here, c > 1 indicates that the subgrade had more moisture than the slope; thus, the moisture movement was from the subgrade to the slope. Meanwhile, c < 1 indicated the opposite scenario.

Subgrade Moisture Index (I m ) Modified by the Pavement Coverage Effect.
e above calculation method was used to obtain the moisture balance, slope moisture index, and pavement coverage correction coefficient and to determine the moisture index of each station for different subgrade types. e results are presented in Table 12.
e Chinese standard JTJ 003-1986 has been employed since 1986 and has contributed to the improvement of highway construction in China. In 2008, Wang et al. [33] studied the natural division of humid seasonally frozen regions in eastern China and further divided Zone II 1 into four third-level zones: II 1-a , II 1-b , II 1-c , and II 1-d . eir thirdlevel zoning method combines a theoretical mathematical model and semiempirical correlation analysis to more objectively determine the boundaries. e seven meteorological stations in this study were scattered among Zone II 1-a (JX), Zone II 1-b (MDJ and SFH), Zone II 1-c (BX, LJ, and YJ), and Zone II 1-d (DD). Figure 11 compares the corrected values of the subgrade moisture index for the four third-level zones with the values based on current specifications along with the humidity coefficient K: e results indicate that I m was −14.2-0 in Zone II 1-a , −1.1-0 in Zone II 1-b , −2.9-57.3 in Zone II 1-c , and 25.7-48.5 in Zone II 1-d . e values gradually decreased from the southwest to the northeast. e average humidity coefficient was 0.67 in Zone II 1-a , 0.72 in Zone II 1-b , 0.89 in Zone II 1-c , and 1.10 in Zone II 1-d . e humidity coefficient gradually decreased from the southwest to the northeast. Zone II 1 had minimum and maximum moisture index values of −14.2 and 57.3, respectively; this range is slightly greater than that recommended by current specifications (−8.1 to 35.1).
When the FAO-56 PM method was used to calculate the slope soil PE, the moisture index of the slope soil decreased because the PE at subzero temperatures was considered. e soil moisture index of the subgrade was obtained by using the pavement coverage correction coefficient to revise the slope moisture index I m . e range was not below that of the values recommended by the current code; however, the maximum and minimum values produced a wider range. e four third-level zones in Zone II 1 showed clear differences in the subgrade moisture index. In particular, Zone II 1c had the widest range for the subgrade moisture index of −2.9 to 57.3. is zone had a wider range than Zone II 1-d and a greater maximum value. is can be explained by the natural geographical environment of Zone II 1-c , which is dominated by the core area of the Changbai Mountain Nature Reserve and contains 16 peaks that are 2500 m above sea level. e annual sunshine hours are less than 2300 h, and the evapotranspiration capacity is relatively weak. In addition, the annual precipitation in this area is between 700 and 1400 mm; thus, the surface runoff is high and leads to a high moisture index. To summarize, the third-level zoning method was used to refine the subgrade moisture index in Zone II 1 to distinguish the different influences of the climate, geological landforms, and other factors. is method was shown to be effective at improving the calculation accuracy of the subgrade moisture index.

Conclusion
Taking into account the nonnegligible evapotranspiration at subzero temperatures and the pavement coverage effect, we presented an improved method for calculating the moisture index of subgrade in seasonally frozen regions. e FAO-56 PM method was applied to estimate the PE at subzero temperatures, which is neglected by the ornthwaite method, to calculate the moisture index of an uncovered slope. e PE was found to account for 9.8%-15.7% of the total annual evapotranspiration. Based on the relationship between the matric suction and soil water content, a correction coefficient was proposed to define the pavement coverage effect. In accordance with this effect, an optimized moisture calculation formula without considering the source of the evaporated water was developed to map the moisture index of the uncovered slope to that of the covered subgrade.
e results of a case study demonstrated the validity of the proposed method in determining the subgrade moisture index of seasonally frozen regions, whose reasonable range appears to be −14.2 to 57.3 for subgrade design. is study can not only aid systematically elucidating the formation pattern of subgrade moisture in seasonally frozen regions but also shed some light on the design and operation management implications of highway subgrade to improve their operational performance. Future studies that consider the effect of ice condensation and bidirectional melting are required to further improve the subgrade moisture calculation approach.

Data Availability
All data, models, and code generated or used during the study appear in the submitted article.