Study of the time-dependent thermal behavior of the multilayer asphalt concrete pavement in permafrost regions

Construction and Building Materials 193 (2018) 162–172

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Study of the time-dependent thermal behavior of the multilayer asphalt concrete pavement in permafrost regions Wansheng Pei a, Long Jin b,⇑, Mingyi Zhang a, Shuangyang Li a, Yuanming Lai a a b

State Key Laboratory of Frozen Soil Engineering, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou 730000, China Key Laboratory of Highway Construction & Maintenance Technology in Permafrost Regions, Ministry of Transport, CCCC First Highway Consultants Co., LTD, Xi’an 710065, China

a r t i c l e

i n f o

Article history: Received 10 October 2018 Accepted 16 October 2018

Keywords: Multilayer asphalt concrete pavement Thermal behavior Time dependence Air convective embankment Permafrost regions

a b s t r a c t Asphalt concrete is one of the widespread pavement materials. The multilayer asphalt concrete pavement (MACP) has strong heat-absorption capacity. The thermal behavior of the MACP can affect the energy exchange between atmosphere and embankment, especially for the permafrost ground which is sensitive to temperature. To investigate the thermal behavior of the MACP, an in-situ experiment was performed firstly to investigate the effect of MACP on the cooling performance of an air convection embankment used in permafrost region. Subsequently, a mathematical model was developed and validated to describe the thermal behavior. Finally, series of simulations were carried out to evaluate the time dependence of the thermal behavior. The results indicate that, (1) the asphalt pavement can alter the energy exchange between permafrost foundation and atmosphere, and reduce the cooling performance of the embankment; (2) the construction interval of MACP can strengthen the convective cooling capacity and accelerate the heat dissipation of the permafrost foundation; (3) an optimized construction interval was proposed for the simulated air convection embankment to maintain its long-term stability. The study can contribute to the construction control of air convection embankment with MACP in permafrost regions. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction The asphalt concrete (AC) has been a widely used pavement material [1,2]. To enhance the performance of asphalt concrete pavement (ACP), researches have conducted numerous experimental and numerical studies [1–4]. Present results indicate that the ACP has strongly heat storage behavior [4,5]. Thus, the ACP can change the energy exchange between the underlying stratum and the atmosphere. The thermal behavior of ACP is significant for the embankment stability in permafrost regions [6,7]. Permafrost is widely distributed on the Earth [8–11]. It is very sensitive to geotemperature changes [11]. Highway embankments with multilayer asphalt concrete pavement (MACP) constructed in permafrost regions alter the natural ground-surface energy balance and accumulate thermal energy during warm periods due to the increased solar absorption and reduced surface moisture [12]. In addition, climate warming also accelerates permafrost degradation, particularly for the high-altitude permafrost on the QinghaiTibet Plateau (QTP) [9].

⇑ Corresponding author. E-mail address: [email protected] (L. Jin). https://doi.org/10.1016/j.conbuildmat.2018.10.147 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.

To meet the demand of the engineering stability in permafrost regions, air convective embankments have been proposed to stabilize the underlying permafrost, i.e. the two-phase closed thermosyphon embankment, the duct-ventliated embankment, and the crushed-rock embankment [11,12,14–17]. Crushed-rock embankment (CRE) is one of extensively used air convection embankments, which can effectively prevent the thaw settlement of permafrost stratum due to the natural/forced convective cooling effect of the permafrost-porous layer-atmosphere system [12–16,18–21]. In cold seasons, the temperature at the top of the crushed-rock layer is warmer than that at the bottom [21]. Thus, air convection could occur within the porous layer due to the existence of unstable air pressure/temperature gradient [13]. Numerous experiments and simulations have been performed to evaluate the cooling performance of the crushed-rock layer. Previous studies illustrate that some parameters of the crushed-rock layer, i.e. particle size [21,23,24], boundary condition [19,24,25], thickness [20], inclination angle, width-to-thickness ratio [26], and paving location [27], can affect its convective cooling performance. Based on these researches, the CRE has been optimized and developed dramatically in permafrost regions. Applications of the CRE include the Qinghai-Tibet Railway (QTR) and the

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Qinghai-Tibet Highway (QTH) in China, the Taylor Highway in the USA, the Baikal-Amur Railway in Russia, and the Hudson Bay Railway in Canada [11,14,22]. However, studies illustrate that the delayed construction of embankment fill upon the crushed-rock layer can affect the cooling behavior of the CRE for the QTR [28]. Ma et al. suggested that the crushed-rock layer should be constructed at the end of September, and the upper fill should be paved on May in the next year for the QTR [29]. For the highway, the problem becomes significant due to the strongly heat-absorption capacity of dark-colored and wide MACP [30,31]. Filed investigations show that the MACP can reduce the convective cooling effect of the CRE in warm permafrost regions [31]. Consequently, how to reduce the thermal effect of heat-absorption MACP on the cooling effect of the underlying crushed-rock layer is important to enhance the thermal stability of embankment in permafrost regions. In this paper, a field experiment of a CRE with the MACP in permafrost region of the QTP was performed. Based on the geotemperature variation caused by the construction of the MACP, we revealed the influence mechanism of the MACP on the thermal stability of the CRE. Then, a convective heat transfer model was developed to describe the thermal effect of the MACP. Based on the model, series of numerical simulations were carried out to analyze the time-dependent thermal behavior of the MACP. Finally, an optimized construction interval of the MACP was proposed for the simulated embankment to enhance its long-term stability.

2. Field experiment 2.1. Experimental design A field investigation is conducted to observe the influence of the MACP on the cooling effect of CRE. The elevation of the test site is 4340 m in the QTP (site A in Fig. 1). The mean annual geotemperature at the depth of 15 m is nearly
0.6 °C. This site is a warm and ice-rich permafrost region. The embankment structure and monitoring system are shown in Figs. 2 and 3. According to the geolog-

ical drilling, there are three soil layers under the embankment within the depth of 30.0 m (Fig. 3), including the silty clay layer (0–1.2 m), the sandy soil layer (1.2–3.6 m), and the highly weathered mudstone layer below 3.6 m. The height of the embankment is 2.5 m with a 12.25-m wide pavement. During construction, a 1.2-m crushed-rock layer with the mean particle size of 0.2 m (diameter range from 0.1 m to 0.3 m) was constructed. Subsequently, the 0.35-m embankment fill layer was completed on October 2012. However, the MACP was not laid until October 2013. To evaluate the thermal effect of the MACP on the cooling performance of the CRE, the monitoring cross section is shown in Fig. 3. In Fig. 3, the precision of the temperature sensor is ±0.05 °C. 2.2. Experimental results and analyses 2.2.1. Heat transfer within the crushed-rock layer Fig. 4 shows the variation of temperature at the slope surface of the crushed-rock layer. The temperature variation can be expressed by the following function in Eq. (1).




T slope ¼ 0:5 þ 13sin

2pt þ a0 365



ð1Þ

where a0 is the initial phase angle, and t is time (day). In each year, the ambient is usually the coldest on January 15, and it is the warmest on July 15 (Fig. 4). Therefore, the temperature distributions within the crushed-rock layer on two typical seasons from 2013 to 2016 are analyzed (Fig. 5). When the ambient temperature is the highest on July 15 each year, thermal energy in the ambient will transfer into embankment. Thus, the air convection cannot occur within the crushed-rock layer. The isotherms are approximately parallel to the top surface of the embankment (Fig. 5b, d, f, and h). However, the top temperature of this layer is obviously higher than the bottom temperature mainly because the porous crushed-rock layer can reduce its effective thermal conductivity. The temperature difference can reach 6.0–8.0 °C. Meanwhile, the top temperature of the crushed-rock layer before the construction of the MACP

Fig. 1. Permafrost distribution in the QTP and field site (Source: Cheng and Wu [9]).

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Fig. 2. Photos of the tested crushed-rock embankment.

Fig. 3. Cross section of the CRE (P-P´). The MACP is made up of five layers from top to bottom, including the 0.04-m asphalt concrete marked as AC-13C, the 0.05-m asphalt concrete marked as AC-20C, the 0.18-m asphalt treated base marked as ATB-25, the 0.18-m cement stabilized base (CSB), and the 0.2-m graded sand-gravel cushion (GSC).

25 20

Fitted data

Measured data

15

Temperature /

10 5 0 -5 -10 -15 -20 -25 12-10-26

R2=0.842 13-07-29

14-05-01 15-02-02 Time /year-mm-dd

15-11-05

16-08-08

Fig. 4. Variation of temperature at the slope surface of the crushed-rock layer.

(Fig. 5b) is slightly lower than that under the MACP due to the strong heat-absorption ability of the pavement. It can be confirmed by the appearance of +14.0 °C isotherms (Fig. 5d and f). The slope surface temperature is the coldest on January 15 each year (Fig. 4). The heat conduction ability between the ambient and embankment is obviously reduced after the construction of the

MACP due to its low thermal conductivity (Fig. 5c, e, and g). Thus, the top temperature of the crushed-rock layer rises significantly after the construction of the MACP (from
16.0 °C in Fig. 5a to
10.0 °C in Fig. 5c, e, and g). Meanwhile, the curved isotherms indicate that slight air convection forms within the crushed-rock layer in cold seasons. The convection process can accelerate the heat release into the ambient, especially in the central zone of the porous crushed-rock layer (from X =
4.0 m to X = +4.0 m). However, the decreasing temperature gradient between the top and bottom of the crushed-rock layer caused by the MACP can reduce the convection cooling performance (Fig. 5c, e, and g). In addition, the isotherms within the crushed-rock layer are slightly asymmetric. This is mainly resulted from the shady-sunny slope effect. The left side slope absorbs more solar energy than the right side slope (Fig. 5). Fig. 6 shows the variation of temperature at the bottom center of the crushed-rock layer. The bottom temperature at the center of the crushed-rock layer reaches its minimum and maximum values in January and July, respectively. However, the minimum temperature is
3.1 °C, which is nearly 1.0 °C lower than that after the construction of MACP. In addition, the maximum temperature before the construction of MACP (5.9 °C on July 13, 2013) is also

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Heat release

Heat absorption

Fig. 5. Temperature distributions within the crushed-rock layer on January15 and July 15 each year (Unit: °C). a), c), e) and g) are January 15; b), d), f) and h) are July 15.

8 Without asphalt pavement

Temperature /

6 4 2 0 -2 -4 12-10-01

After the construction of asphalt pavement

13-07-08

14-04-14 15-01-19 Time /yy-mm-dd

15-10-26

16-08-01

Fig. 6. Variation of temperature at bottom center (Y = 0.2 m) of the crushed-rock layer.

lower than that after the construction of pavement (7.3 °C on July 13, 2014). Consequently, the construction of strongly heat-absorption MACP can change the endothermic process in warm seasons and the exothermic process in cold seasons. Specifically, in warm seasons, the heat-absorption ability is enhanced due to the small albedo of the black-colored MACP [4]. In cold seasons, the low thermal conductivity of the MACP can reduce the cold solar energy absorption.

2.2.2. Thermal conditions of the stratum soil The permafrost degeneration rate can directly indicate the effect of MACP on the cooling performance of the crushed-rock layer. Fig. 7 shows the variation of ground temperatures along the centerline of the embankment with time. The permafrost temperature continues to rise since the construction of the embankment due to the thermal disturbance of embankment although the annual surface temperatures are almost the same (Fig. 4). However, the permafrost degradation rate accelerates significantly after

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Original natural ground surface 0.21 m/year

Without asphalt pavement After the construction of asphalt pavement

Fig. 7. Variation of geotemperatures with time along the centerline of the embankment (Unit: °C).

the construction of MACP. The movement rate of the permafrost table after the construction of MACP (0.64 m/year) is nearly three times higher than that before the construction of MACP (0.21 m/year) (Fig. 7). The increase of degradation rate of the permafrost table further demonstrates that the heat-absorption MACP can weaken the cooling performance of the porous crushed-rock layer. 3. Mathematical model and validation The in-situ investigations objectively reflected that the construction of MACP can weaken the cooling performance of an air convection embankment in permafrost regions. Therefore, the time-dependent thermal effect of the MACP should be considered during the construction to enhance the cooling capacity of a CRE. However, not all experiments can be conducted in situ due to the engineering limitations and high cost. To make full discussion of the time dependence, series of numerical simulations were performed. 3.1. Mathematical model The model of a CRE can be divided into three zones (Fig. 3), including the crushed-rock layer, the pavement structure layer and the soil layers. The computational equations for each zone are described as follows: 3.1.1. The convective heat transfer model for crushed-rock layer Convective heat transfer of the air within the crushed-rock layer occurs under air pressure gradients [18–20,32–35]. In the simulation, we assume that only the motion of interstitial air is considered, and the air inside the crushed-rock layer is incompressible. Therefore, the convective heat transfer process can be described by the mass, momentum and energy conservation equations in Table 1:

where

3.1.2. The conductive heat transfer model for pavement materials and soil layers Based on the related references [36–39], the convective heat transfer in soil layers can be ignored since heat conduction is 102-103 times greater than convective heat transfer in these layers. Therefore, only the heat conduction process with phase change is considered in these layers. The heat transfer process can be described as:

Ce



 @T @ @T @ @T ¼ ke þ ke @t @x @x @y @y

Momentum conservation Energy conservation

k ¼

   @T C e @t

¼0

(1)

v x
qa Bjvjv x ; v y
qa Bjvjv y
qa g

(2)

  @T  @   @T  @ @T ¼ @x ke @x þ @y ke @y
C a qa v x @T @x þv y @y

(3)

ð5Þ

where the superscript e means equivalent, C and k are the volumetric heat capacity and thermal conductivity of the media, respectively. If the phase change of soil occurs in a range of temperature (Tm ± DT), the heat capacity and thermal conductivity of the media could be taken as a constant when T is beyond phase-transition zone, otherwise, they change according to Eqs. (6) and (7) in phase-transition zone [37]:

e

Equation

ð4Þ

where qa0 and T0 are reference values for density and temperature, and b is the thermal expansion coefficient of air.

Table 1 Convective heat transfer model for crushed-rock layer [15,33–35].

@v y @v x @x þ @y l @p @x ¼
k l @p @y ¼
k

vyqare the x and y components of air velocities, ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v 2x þ v 2y ; B is the inertial resistance factor of

qa ¼ qa0 ½1
bðT
T 0 Þ

C ¼

Mass conservation

and

non-Darcy flow; k is permeability of the crushed-rock layer; l is dynamic viscosity of air; p is air pressure; qa is air density; qa Bjvjv x is the inertia-turbulent term; Ca is air specific heat at constant pressure; C e and ke are effective volumetric heat capacity and effective thermal conductivity. It is assumed that the relationship between qa and T matches the Boussinesq approximation [35]:

e

Term

vx

respectively; jv j ¼

8 > < :

8 > < > :

T < T m
DT

Cf

l > 2D T

þ

C f þC u 2

T m
DT 6 T 6 T m þ DT

kf kf þ

ku
kf 2DT

ð6Þ

T > T m þ DT

Cu

T < T m
DT

½T
ðT m
DT Þ T m
DT 6 T 6 T m þ DT ku T > T m þ DT

ð7Þ

where the subscripts f and u represent the frozen and unfrozen states; and l is the latent heat per unit volume. For the material of the multilayer pavement, the phase change in Eq. (5) can be ignored.

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Fig. 8. Variations of temperatures at the bottom center (Y = 0.2 m) of the crushed-rock layer.

3.2. Solution method The control volume integration (CVI) method is used to solve the highly nonlinear equations. The spatial and temporal discretization for the general format is carried out according to Lai et al [37] and Tao [38]. Then, the successive under-relaxation method is utilized to solve the discrete equations for every time interval [15,38]. All the concrete details about the numerical method in this work can be found in Tao [38]. 3.3. Model validation To investigate the applicability of the above model in engineering practice, the monitoring embankment is selected. Before the

simulation, the observed temperatures on October 15, 2012 are selected as the initial values. The simulated and observed temperatures at the bottom center of the crushed-rock layer are given in Fig. 8. Fig. 8 indicates that the simulated curve can fit the observation well although there exists difference between the simulated and observed temperatures. The difference is mainly caused by factors such as the simplified geography and boundary conditions in the numerical simulation (Figs. 3 and 4). Actually, the geography and weather are complex in the field [40], including the undulating surface, irregular ponding, solar radiation and so on. In general, the mathematical model can be applied to analyze the time-dependent thermal effect of the MACP in permafrost regions.

Table 2 Construction schemes of the MACP. Construction

The construction of MACP

Time

The 1st year

The 1st year

The 2nd year

Jul.15

Oct.15

Jul.15

Oct.15

Jul.15

Oct.15

Jul.15

Oct.15

0 Case 1

3 Case 2

12 Case 3

15 Case 4

24 Case 5

27 Case 6

36 Case 7

39 Case 8

Time intervals (Month) Cases

The 3rd year

The 4th year

Fig. 9. Geometrical model of a CRE with MACP. (PartⅠis embankment fill layer, Part Ⅱ is crushed-rock layer, Part III is silty clay layer, Part Ⅳ is sandy soil, and Part V is highly weathered mudstone. S is monitored point during the simulation).

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Table 3 Thermal parameters of pavement materials and soil layers [15,32,33,37,39,41]. Physical variable

kf (W/m°C)

Cf (J/m3°C)

ku (W/m°C)

Cu (J/m3°C)

  l J=m3

AC-13C AC-20C ATB-25 CSB GSC Fill soil Silty clay Sandy soil Weathered mudstone

1.300 1.300 1.100 1.100 1.100 1.980 1.351 2.550 1.824

2.256  106 2.256  106 1.760  106 1.680  106 1.680  106 1.913  106 1.879  106 1.825  106 1.846  106

1.300 1.300 1.100 1.100 1.100 1.919 1.125 2.180 1.474

2.256  106 2.256  106 1.760  106 1.680  106 1.680  106 2.227  106 2.357  106 2.456  106 2.099  106

0 0 0 0 0 2.04  107 6.03  107 1.38  107 3.77  107

4. Numerical simulations

embankment surfaces and ground surfaces can be described by the following expression:

To fully reveal the time-dependent thermal disturbance caused by the MACP, different construction schemes of the pavement (Table 2) are simulated with the assumption that the substructure is constructed on the warmest season (July 15) considering the most unfavorable thermal disturbance conditions during the constructions. In Table 2, 8 cases are designed. The construction interval between the substructure and the MACP varies from 0 to 39 months.


 2p p T ¼ T 0 þ Asin t h þ þ a0 8760 2

4.1. Computational domain According to the field experiment and the Specifications for Design of Highway Asphalt Pavement [42], the geometrical model is illustrated in Fig. 9.

ð8Þ

where th is the time in hours, a0 is the phase angle which is determined by the finishing time of embankment. The mean annual temperature T0 and the annual amplitude of temperature A for different surfaces are shown in Table 6. The lateral boundaries AH and DG are assumed to be adiabatic since the computational domain is extended to be wide enough. Geothermal heat flux at boundary GH is q = 0.06 W/m2 according to references [32,33,37]. In these simulations, the initial temperature distributions under natural ground surface (Parts III, Ⅳ, and V in Fig. 8) are obtained through a long-term transient solution with the upper boundary condition (Eq. (8)).

4.2. Physical parameters 5. Results and analyses In the simulations, the material parameters are listed in Table 3. The related parameters of crushed-rock layer are given in Table 4. The physical parameters of air are shown in Table 5.

5.1. Analysis of temperature variations

4.3. Boundary conditions According to the field monitoring data and related studies [15,37,40,41], the thermal boundary conditions for the air,

Table 4 Physical parameters of crushed rock [34,38]. Physical variable Crushed-rock layer

C (J/(m3°C)) 1.015  10

The service life of a MACP is 15 years according to the related Specifications [32]. Therefore, the thermal states during 15 years after construction of the embankment are analyzed.

6

k (W/(m°C))

1.66  10

0.387

B (m
1)

k (m2)
5

41.20

Table 5 Physical parameters of air [15]. Physical variable

Ca J/(m3°C)

k W/(m°C)

l kg/(ms)

Air

0.644  103

0.02

1.75  10
5

Table 6 Thermal boundary parameters of different surfaces [16,34,38,41]. Surface

Natural ground surfaces: AB and CD Asphalt pavement surface: OP Slope surfaces: BM and NC Soil shoulder surface: OM and NP

Parameter T0(oC)

A(oC)


0.6 2.5 0.5

12.0 15.0 13.0

To analyze the cooling performance of the crushed-rock layer in different cases, the temperature variations at point S (Fig. 9) are shown in Fig. 10. Fig. 10a indicates that the temperatures in different construction cases are discrepancy during the first seven years (stage I). After the 7th operation year (stage II), the temperature variations are nearly the same. During the cold seasons in stage I (Fig. 10b), the temperature at point S in case 1 (time interval is 0) is obviously higher than those in other cases, especially in the first three years. However, the temperature in case 8 (time interval is 39 months) is the lowest in cold seasons. Therefore, the time interval between the construction of the MACP and the underlying fill layer can affect the cooling capacity of the crushed-rock layer in permafrost regions. Meanwhile, the cooling capacity of the crushed-rock layer increases with the increasing time interval. In addition, the impact is the most prominent if the MACP is constructed without any time interval (case 1). Two cases (on July 15 and October 15) are compared with 3month interval in each year. It can be found that the construction scheme on October 15 is better than that on July 15 in the same year. The maximum temperature difference at point S between such two cases at the same time can reach 1.1 °C (cases 1 and 2). However, the effect of the MACP on the convective cooling performance in such cases reduces with time and almost disappears within two years after the construction of the MACP. Because the maximum thaw depth of an embankment usually occurs on October 15 (Fig. 7), the variations of permafrost table

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W. Pei et al. / Construction and Building Materials 193 (2018) 162–172 4 Case 1 Case 5

Case 2 Case 6

Case 3 Case 7

Case 4 Case 8

2

Temperature /

0

-2

-4

-6

Stage

(a) Case 1

Stage

-8 0

1

2

3

4

5

6

7 8 Time /Year

9

10

11

12

13

14

15

(a) Geotemperature variations within 15 operation years. Case 1 Case 5

Case 3 Case 7

Case 4 Case 8

Jul. 15

Case 2 Case 6

Oct. 15

-2

Oct. 15

Oct. 15

Temperature /

0

Jul. 15

Jul. 15

Jul. 15

2

Oct. 15

4

(b) Case 8

-4

Fig. 12. Geotemperature distributions under embankments on October 15 in the 4th year after construction in two cases (Unit: oC). (a) Case 1; (b) Case 8.

-6 -8 -10 0

1

2

3

4

5

6

7

Time /Year

(b) Geotemperature variations within the first 7 operation years. Fig. 10. Geotemperature variations at the center of the original natural ground (Point S). (a) Geotemperature variations within 15 operation years; (b) Geotemperature variations within the first 7 operation years.

at the centerline on October 15 after the 2nd year in different cases are illustrated in Fig. 11. The maximum thaw depth in case 1 is the largest in the first few years. Therefore, the cooling performance of the crushed-rock layer can be significantly weakened by the MACP without considering the time interval during its construction. However, the thermal disturbance caused by the MACP reduces with time. Meanwhile, the permafrost table moves up obviously when the time interval exceeds 12 months (cases 3–8). In addition, the impact on the cooling performance of the crushed-rock can be reduced by changing the construction time of pavement from July 15 to October 15 in the same year.

-0.2

Depth /m

-0.4

-0.6 Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

Case 8

-0.8

1

2

3

4 Time /Year

5

6

7

Fig. 11. Variations of permafrost table with time at the centerline of the embankment on October 15 each year.

Fig. 12 shows the discrepancy of geotemperature distributions under embankments in two cases (cases 1 and 8) before the construction of the MACP in case 8. The geotemperature in case 8 with 39-month intervals is lower than that in case 1 without any time intervals, which can be confirmed by the existence of
1.0 °C isotherm in case 8 (Fig. 12b). Therefore, the construction of the MACP without considering time interval will weaken the cooling performance of the crushed-rock layer. The warm permafrost in case 1 is disadvantageous to the long-term thermal stability of embankment with strong heat-absorption ability. Meanwhile, there exist waved isotherms under embankment in case 1 (
0.3 °C and
0.5 °C isotherms in Fig. 12a). The transverse difference in geotemperature can cause uneven deformation under traffic loads because the mechanical behavior of permafrost varies with temperature [37,43]. Consequently, the long intervals before the construction of the MACP can effectively enhance the embankment stability in permafrost regions. To directly evaluate the impact of the construction interval of the MACP on the cooling performance of the underlying crushedrock layer, the variation of effective cooling range on October 15 in different cases are illustrated in Fig. 13. Considering the limit of test precision for temperature in engineering practices, we define the effective cooling range as a change in geotemperature of
0.1 °C or less compared to that without the embankment at the same time [44]. Therefore, the isoline for a geotemperature variation of
0.1 °C is selected as the boundary of the effective cooling range caused by the crushed-rock layer. The isolines for the symmetrical structure are illustrated in Fig. 13 because the geotemperatures are symmetrically distributed under the embankment (Fig. 12). For cases 1–6 with the construction interval less than three years after the completion of the fill layer, the cooling range gradually increases with time in each case, especially in the depth direction (Fig. 13a–13f). Meanwhile, the construction of MACP can reduce the expanding rate of cooling range. In addition, the cooling range in the second year almost unchanged in different cases due to the effect of accumulated heat within embankment fill. It expands with the increased construction interval of the MACP after the second year (Fig. 13a–h). The variation of effective cooling range further demonstrates that the

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Construction on Jul. 15, 1a

Time interval: 0

Construction on Oct. 15, 1a

Time interval: 3 months

Construction on Jul. 15, 2a

Construction on Oct. 15, 2a

2a

5a 4a

5a

Time interval: 12 months

Time interval: 15 months

Construction on Jul. 15, 3a

Construction on Oct. 15, 3a

2a

5a 7a

Time interval: 24 months

Time interval: 27 months

Construction on Jul. 15, 4a

Construction on Oct. 15, 4a

2a 3a

7a 5a

Time interval: 36 months

Time interval: 39 months

Fig. 13. Isolines for geotemperature change of
0.1 °C under the symmetrical structure of embankment in different cases. Isolines are labeled in years (a) after construction.

construction interval of the MACP can impact the cooling performance of the crushed-rock layer. However, when the construction interval exceeds three years, the maximum cooling range occurs in the 4th year (Fig. 13g and h). Then, the cooling range narrows

down from the 4th to 7th year. In the 7th year, the maximum cooling depth of
0.1 °C isoline in case 8 is approximately 0.5 m deeper than that in case 6. Therefore, the construction interval no less than 27 months (the third cold season after the completion of fill layer)

W. Pei et al. / Construction and Building Materials 193 (2018) 162–172

(a) Case 1

(b) Case 8 Fig. 14. Air convection within the crushed-rock layer on January 15 in the 4th year after constructions in two cases. (a) Case 1; (b) Case 8.

in case 6 is a recommanded construction scheme considering the long-term stability of embankment and the time limit in engineering practice.

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(1) The thermal effect caused by the MACP can reduce the longterm stability of the CRE. Specifically, the MACP can strengthen the heat absorption into permafrost stratum by changing the endothermic process in warm seasons and the exothermic process in cold seasons. Meanwhile, construction of the MACP can also weaken the convective cooling capacity of the underlying crushed-rock layer by altering the convective vortexes characteristics. (2) The construction interval between the MACP and substructure can enhance the cooling performance of the CRE by adjusting the convective characteristics. (3) Considering the long-term stability of embankment and the time limit in engineering practice, a construction interval no less than 27 months (in the third cold season after the completion of fill layer) is recommanded for the simulated CRE. The study of time-dependent thermal effect of the MACP indicates that the reasonable construction interval is an effective technique to control geotemperature in permafrost regions. Therefore, the construction control technique could also have wide applications in other thermal control engineering. Conflict of interest None. Acknowledgements

5.2. Analysis of air convection characteristics The cooling performance of the crushed-rock layer with impermeable boundaries mainly depends on the Rayleigh-Benard convection behavior [13,34]. Therefore, we give the air convection characteristic within the crushed-rock layer for two cases with different construction intervals (Fig. 14). In cold seasons, the temperature at the bottom boundary of the crushed-rock layer is higher than that at the top boundary. Rayleigh-Benard convection occurs within this layer under the temperature gradient, which can strengthen the heat dissipation from underlying permafrost to the ambient. Fig. 14 indicates that clockwise and counterclockwise convective vortexes form in sequence for both cases. However, the numbers of convective vortex for two cases are different due to the discrepancy in the construction interval. For case 1 without any time intervals before the construction of the MACP, there exist 14 convective vortexes within the porous crushed-rock layer, including two large vortexes under the embankment slopes (Fig. 14a). Meanwhile, the maximum air velocity (0.031 m/s) occurs under two slopes. For case 8 with 39-month construction interval, 20 vortexes form although the maximum air velocity is 0.029 m/s under two slopes (Fig. 14b). More convective vortexes can strengthen the heat dissipation process from the permafrost into the cold ambient. Additionally, the smaller convective vortexes under slopes in case 8 can accelerate the heat release rate. Therefore, the cooling performance of the crushed-rock layer considering construction interval of the MACP is better (Fig. 12).

6. Conclusions To maintain the long-term stability of a crushed-rock layer embankment (CRE) in permafrost regions, a field experiment and series of numerical simulations were performed to analyze the geotemperature control technique by using the time-dependent thermal effect of the MACP. Base on the study, the following conclusions can be drawn:

This research was supported by the National Key Research and Development Program of China (grant no. 2018YFC0809605), the National Science Fund for Distinguished Young Scholars (grant no. 41825015), the National Natural Science Foundation of China (grant nos. 41672315, 41471063, 41701070), the Key Research Program of Frontier Sciences of Chinese Academy of Sciences (QYZDY-SSW-DQC015), the West Light Foundation of the Chinese Academy of Sciences (Dr. Wansheng Pei), the Program of the State Key Laboratory of Frozen Soil Engineering (nos. SKLFSE-ZQ-38, SKLFSE-ZT-26), the STS Program of Chinese Academy of Sciences (grant no. HHS-TSS-STS-1502), and the Natural Science Foundation of Gansu Province of China (grant no. 1508RJZA100). References [1] S. Sreedhar, E. Coleri, S.S. Haddadi, Selection of a performance test to assess the cracking resistance of asphalt concrete materials, Constr. Build. Mater. 179 (2018) 285–293. [2] H. Qasrawi, I. Asi, Effect of bitumen grade on hot asphalt mixes properties prepared using recycled coarse concrete aggregate, Constr. Build. Mater. 121 (2016) 18–24. [3] X.Q. Fang, J.Y. Tian, Elastic-adhesive interface effect on effective elastic moduli of particulate-reinforced asphalt concrete with large deformation, Int. J. Eng. Sci. 130 (2018) 1–11. [4] Z.Q. Zhang, Q.B. Wu, Y.Z. Liu, Z. Zhang, G.L. Wu, Thermal accumulation mechanism of asphalt pavement in permafrost regions of the Qinghai-Tibet Plateau, Appl. Therm. Eng. 129 (2018) 345–353. [5] T. Asaeda, V.T. Ca, A. Wake, Heat storage of pavement and its effect on the lower atmosphere, Atmos. Environ. 30 (3) (1996) 413–427. [6] Q.B. Wu, Z.Q. Zhang, Y.Z. Liu, Long-term thermal effect of asphalt pavement on permafrost under an embankment, Cold Reg. Sci. Technol. 60 (3) (2010) 221– 229. [7] J.P. Li, Y. Sheng, Analysis of the thermal stability of an embankment under different pavement types in high temperature permafrost regions, Cold Reg. Sci. Technol. 54 (2) (2008) 120–123. [8] O.B. Andersland, B. Ladanyi, Frozen Ground Engineering, John Wiley & Sons, 2004. [9] G.D. Cheng, T.H. Wu, Responses of permafrost to climate change and their environmental significance Qinghai-Tibet Plateau, J. Geophys. Res. Earth Surf. 112 (F2) (2007). [10] X. Li, G.D. Cheng, A GIS-aided response model of high-altitude permafrost to global change, Sci. China, Ser. D Earth Sci. 42 (1) (1999) 72–79. [11] G.D. Cheng, A roadbed cooling approach for the construction of Qinghai-Tibet Railway, Cold Reg. Sci. Technol. 42 (2) (2005) 169–176.

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