International Journal of Heat and Mass Transfer 127 (2018) 1178–1188 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt Thermal performance of a novel crushed-rock embankment structure for expressway in permafrost regions Minghao Liu a, Wei Ma a, Fujun Niu a,b,⇑, Jing Luo a, Guoan Yin a a b State Key Laboratory of Frozen Soil Engineering, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, Gansu 730000, China South China Institute of Geotechnical Engineering, School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, Guangdong 510641, China a r t i c l e i n f o Article history: Received 20 March 2018 Received in revised form 21 June 2018 Accepted 30 July 2018 Keywords: Thermal performance Convection heat transfer Crushed-rock interlayer Expressway Permafrost Porous media a b s t r a c t The current crushed-rock interlayer structure, which was successfully adopted in construction of the Qinghai-Tibet Railway, cannot maintain the foundation stability of expressways in permafrost regions because of the strong heat absorption of the wide and dark-colored asphalt pavement surface. To satisfy the higher cooling requirement of expressways, a novel crushed-rock interlayer structure, which especially focuses on enhancing the cooling performance on the embankment core, is presented. A heat transfer model, which includes air convection in the crushed-rock interlayer and the heat conduction with a phase change in the soil layers, was developed to simulate the temperature evolution of a full-scale testing expressway embankment section built in Huashixia, the Qinghai-Tibet Plateau. The numerical results indicated that the new structure has a significant cooling performance and especially plays an effective role in lowering the permafrost temperature beneath the centerline of the expressway. Moreover, the new structure has the benefit of maintaining symmetry of the embankment temperature distribution. Therefore, it can be concluded that the new structure is an effective method to prevent permafrost degradation under expressways and can ensure the long-term thermal stability of embankments under the climate warming. The study provides reference and guidance for expressway design and construction in permafrost regions, such as the planned Qinghai-Tibet Expressway. Ó 2018 Published by Elsevier Ltd. 1. Introduction The Qinghai-Tibet Plateau (QTP), which has an average elevation of more than 4000 m a. s. l., contains the largest lowlatitude permafrost area on the earth  (Fig. 1). With the rapid economic development in China, many pivotal engineering projects have traversed the special regions of the QTP, e.g., the Qinghai-Tibet Railway (QTR), the Qinghai-Tibet Highway, and the Qinghai-Tibet Power Transmission Line. However, engineering problems frequently occur, including frost heave and thaw settlement of foundation soils, leading to damage, malfunction or infrastructure failures [2,3], and the problems will be exacerbated under the climate warming [4,5]. Under combination of the climate warming and thermal disturbances from engineering constructions, infrastructures on the degrading permafrost in the QTP are at a clear risk . The QTR is the first transportation infrastructure designed in the plateau permafrost region of China to take climate warming into consideration . This roadway project has resulted ⇑ Corresponding author at: State Key Laboratory of Frozen Soil Engineering, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, Gansu 730000, China. E-mail address: firstname.lastname@example.org (F. Niu). https://doi.org/10.1016/j.ijheatmasstransfer.2018.07.146 0017-9310/Ó 2018 Published by Elsevier Ltd. in the introduction of a roadbed cooling approach and the development of various special embankment structures with cooling features, including crushed rocks, ventilation ducts, thermosyphons, and sun-shadings, to protect the permafrost from warming and thawing beneath the railway embankments [7,8]. A crushed-rock embankment, which is a cost-effective mitigation technique to reduce the effects of permafrost degradation, has been widely applied in the QTR construction in permafrost regions, and its ability of protecting the underlying permafrost has been validated by numerous field experiments and numerical simulations [9–12]. Experimental embankments with crushedrock materials on the Alaska Highway in the USA and at the Beaver Creek test site in Canada have also demonstrated the excellent cooling performances [13,14]. A crushed-rock embankment is usually constructed using coarse, poorly-graded rocks with a high porosity, which allows natural/forced air convection to occur within them and can accelerate heat extraction from the embankment and underlying soil during winter. In summer, the heat transfer within the porous layer primarily occurs through conduction because the crushed-rock layer has a lower thermal conductivity than the typical embankment material , and thus less heat is conducted to the underlying soil. In summary, its cooling mecha- M. Liu et al. / International Journal of Heat and Mass Transfer 127 (2018) 1178–1188 1179 Nomenclature m m q P k c B k T b C L velocity (ms1) dynamic viscosity (Pas) density (kgm3) pressure (Pa) thermal conductivity (Wm1°C-1) specific heat capacity (Jkg1°C1) inertial resistance factor (m1) permeability of the medium (ms1) temperature (°C) thermal expansion coefficient of air volumetric heat capacity (Jm3°C1) latent heat (Jm3) nism results from the increased winter cooling rates and decreased summer warming rates . Although a crushed-rock embankment has been used as a mainstream technique to maintain the road foundation stability of railways and ordinary highways on the plateau [9–11], the current structure used for the QTR cannot satisfy the higher cooling requirement of an expressway, which has a wider and darkcolored asphalt pavement. This is mainly because of the adoption of an asphalt pavement and the much wider (more than 20 m wide) road surface [16,17], both of which significantly increase the heat absorption and decrease the heat dissipation from the top surface compared with railway and ordinary highway embankment, causing more severe permafrost thaw settlement . Based on the data from several monitoring units installed along the newly built Gonghe-Yushu Expressway in the east part of the QTP, obvious permafrost warming trends were observed under some crushed-rock embankments, especially under the centerlines , indicating that the crushed-rock configuration used for the QTR cannot be directly applied to expressway construction in t q time (s) heat flux (Wm2) Subscripts/superscripts x x-direction y y-direction a air ⁄ equivalent f frozen u unfrozen H height permafrost regions. According to the proposed development project by China’s Ministry of Transport, the plan is for the Qinghai-Tibet Expressway (QTE) to run across the largest plateau permafrost region in China, and it is expected to play an important role in promoting the economic development of Tibet . The QTE will face more severe permafrost degradation problems than the QTR, especially under impacts of the climate warming. Some composite embankments that combine crushed-rock and other cooling measures such as a forced-air ventilation duct, L-shaped thermosyphons, and insulating material for better cooling performances have been developed, and their effects in increasing the thermal stability of expressway embankments have been verified by laboratory tests or numerical experiments [20,21]. However, the combining of two or more cooling measures multiplies the construction costs. Nanofluid can be selected as an ideal working fluid to enhance the convection heat transfer efficiency in porous media [22–24], but such a material at present cannot be directly applied in the construction of crushed-rock embankment in permafrost regions. Fig. 1. Permafrost distribution and embankment section with new design at Huashixia in QTP. The data in this permafrost map was from the China Cold and Arid Scientific Data Center (http://westdc.westgis.ac.cn/). 1180 M. Liu et al. / International Journal of Heat and Mass Transfer 127 (2018) 1178–1188 This paper presents a novel crushed-rock interlayer embankment (CRIE) for expressways in permafrost regions. This new embankment structure focuses on enhancing the convection cooling performance of a large-width expressway, especially the embankment center. To evaluate the cooling effect of the new CRIE on the permafrost, a full-scale embankment section for an expressway using the new design located in a warm permafrost region with an elevation of 4500 m at Huashixa in the QTP was selected for study. A numerical heat transfer model, which included the air convection heat transfer in the crushed-rock layer and heat conduction with a phase change in the soil layers, was developed to simulate the temperature evolution of the embankment section with the new design, followed by model verification. This model was used to forecast the long-term cooling performance of the new structure based on the assumption that the air temperature in the QTP will warm up by 2.6 °C in the next 50 years . It is hoped that this work would provide guidance for expressway design and constructions in permafrost regions. below which there is ice-rich permafrost. The mean annual ground temperature ranges from 1.0 °C to 0.5 °C. This warm and icerich permafrost condition is typical in the QTP and is troublesome for engineering infrastructures. 3. Numerical model A coupled heat transfer model was developed to investigate the thermal performance of the new designed embankment for an expressway. In the model, the embankment model is divided into three zones based on the different heat transfer characteristics of the different media, i.e., the air zone outside the crushed-rock layer, crushed-rock zone, and soil layer zone. The crushed-rock zone was taken as porous media because of its highly permeability. Based on the heat and mass transfer theories, the air convection heat transfer in the crushed-rock layer and heat conduction with a phase change in the soil layers were considered in the model. 3.1. Physical model 2. New embankment design and site description Fig. 2 presents photos and structural diagram of the new CRIE. Compared with the traditional structure, a layer of crushed rock was added to the central portion of the current crushed-rock interlayer to form a connective reverse T-shaped crushed-rock frame. The open boundary of this layer was intended to improve the ventilation capacity of a wider crushed-rock layer, especially in the center. Thus, it was expected to enhance the air convection heat transfer in winter time within the layer and results in greater heat dissipation from the embankment. The added crushed-rock layer is located in the central isolation of the expressway. Therefore, it will not influence driving safety. The studied embankment with the new design, which was completed in August 2014, is located at Huashixia, with an elevation of approximately 4500 m a. s. l. on the QTP (Fig. 1). The site is an open area and is close to the Qing-Kang Highway. The vegetation cover in the site is less than 50%. The soil types mainly consist of silty clay, sand with gravel in the upper layers, and a highly weathered mudstone layer. The permafrost table is nearly 2.0 m in depth, The physical model of the new embankment was established based on the full-scale embankment located at Huashixia, which has an elevation of approximately 4500 m a. s. l. on the QTP, as shown in Fig. 3. A traditional CRIE was also studied for comparison. In practical permafrost engineering problems, the rock layer can be considered infinitely long in the longitudinal direction. Thus, the simulation model was established in a 2-D cylindrical coordinate system. In the model, the new CRIE has side slopes of 1:1.5, a width of 24.0 m at the crest of the driving surface, and a height of 2.5 m, including a 1.2 m thick crushed rock layer at its bottom and a 1.2 m wide crushed-rock layer in the center. There was no central crushed-rock layer in the traditional embankment model. As shown in Fig. 3, the numerical model has 30 m wide horizontal extensions from the right and left slope toes, which were designed to eliminate the boundary effect. In the vertical direction, the model has a 30 m deep extension, which includes a 1.0 m thick silty clay layer, 6.0 m thick sandy soil layer with gravel, and 23 m thick strongly weathered mudstone layer. Fig. 2. The full-scale testing expressway embankment section with the new CRIE design in Huashixia. (a) Crushed-rock in the basement; (b) crushed-rock in the center; and (c) structural diagram. 1181 M. Liu et al. / International Journal of Heat and Mass Transfer 127 (2018) 1178–1188 J I Air flow K A L N M O P 1.2m .5 1:1 Q R B H G C F 23m 6m 1m 30m 24m 1.2m Inlet 1.3m 30m Outlet D E Part I- embankment fill; Part II- crushed-rock layer; Part III- silty clay; Part IV- gravel soil; Part Vweathered mudstone; Part VI- air Fig. 3. Physical model of new CRIE for expressway. 3.2. Governing equations 3.2.1. Air zone outside crushed-rock layer The airflow/wind is considered to be a turbulent flow outside the crushed-rock layer . Because the air is assumed to be an incompressible fluid with constant physical properties, the influence of the air temperature on the airflow velocity is negligible. Consequently, the physical problem can be described by the Reynolds averaged equations, and we have the following governing equations for the airflow’s turbulent heat transfer process . Continuity: @v x @v y þ ¼0 @x @y ð1Þ where v x and v y are the x and y components of the air velocity, respectively. Momentum: ! @ mx @ðmx mx Þ @ðmy mx Þ @p @ 2 mx @ 2 mx ¼ þl þ q þ 2 þq @x @y @x @t @x2 @y @m @ðmx my Þ @ðmy my Þ @p @ 2 my @ 2 my ¼ þl þ q yþq þ 2 @x @y @y @t @x2 @y ð2Þ qa g @T @ @T @ @T @ðmx TÞ @ðmy TÞ ¼ ka þ ka qc a þ @t @x @x @y @y @x @y ð3Þ ð4Þ where ka and ca are the thermal conductivity and specific heat capacity of air at a constant pressure, respectively. 3.2.2. Crushed-rock layer zone Air convection inside the crushed-rock layer can occur when unstable air pressure gradients exist. Thus, crushed-rock layer in the embankment model can be considered as porous media . In the model, only the motion of the interstitial air is considered. Therefore, the governing equations can be written as follows : Continuity: @v x @v y þ ¼0 @x @y @p l ¼ mx qBjmjmx @x k ð6Þ @p l ¼ my qBjmjmy qa g @y k ð7Þ where jmj ¼ qa ¼ q0 ½1 bðT T 0 Þ ð8Þ where T0 is the corresponding temperature of q0, and b is the thermal expansion coefficient of air. Energy: @x @ @T @ @T @ @ðmx TÞ @ðmy TÞ ¼ k þ k qca þ @t @x @x @y @y @x @x @y ð9Þ where C⁄ and k⁄ are the effective volumetric heat capacity and effective thermal conductivity, respectively. 3.2.3. Soil layers and embankment fill zones Based on the assumption that the heat conduction is far larger than the convective heat transfer in the soil layers , the convective heat transfer in these layers can be ignored. Thus, only the heat conduction and phase change in the soil layers are considered. The heat transfer process in the soil layers can be described as follows [27,30]: C @x @ @T @ @T ¼ k þ k @t @x @x @y @y ð10Þ We assume that the phase change of the media occurs in a range of temperatures ðT m DTÞ. Based on the sensible heat capacity method, C⁄ and k⁄can be expressed as follows: ð5Þ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ m2x þ m2y , B is the Beta factor of the non-Darcy flow, k is the permeability of the porous medium, m is the dynamic viscosity of air, p is the air pressure, and qBjmjmx is the inertia-turbulent term. Because the air is incompressible, its density qa is a function of the temperature and obeys the Boussinesq approximation: C ! where m is the dynamic viscosity of air, q is the air density, and p is the air pressure. Energy: qca where v x and v y are the x and y components of the air velocity in the porous medium, respectively. Momentum: C ¼ 8 > < L > 2D T : Cf C f þC u 2 þ Cu T < ðT m DTÞ ðT m DTÞ 6 T 6 ðT m þ DTÞ T > ðT m þ DTÞ ð11aÞ 1182 k ¼ M. Liu et al. / International Journal of Heat and Mass Transfer 127 (2018) 1178–1188 8 > < > : T < ðT m DTÞ kf kf þ ku kf 2DT Table 2 Temperature parameters of air, natural ground surfaces, and embankment surfaces. ½T ðT m DTÞ ðT m DTÞ 6 T 6 ðT m þ DTÞ T > ðT m þ DTÞ ku ð11bÞ where the subscripts f and u represent the frozen and unfrozen states, respectively; C and k are the volumetric heat capacity and thermal conductivity of the media, respectively; and L is the latent heat per unit volume. Based on the measured data and previous laboratory test results , the related thermal parameters are given in Table 1. The mean particle size of the crushed rock is approximately 20.0 cm (diameter range from 10 cm to 30 cm), which accords with the construction of the studied embankment section. The permeability and inertial resistance factor are k = 1.39 105 m2 and B = 211.20 m1, respectively [29,32]. The specific heat of air at an elevation of more than 4500 m is ca = 1.004 103 Jkg1°C1, the thermal conductivity is ka = 2.0 102 Wm1°C1, the air density is qa = 0.641 kgm3, and the dynamic viscosity is l = 1.75 105 kgm1s1. 3.4. Boundary and initial conditions 3.4.1. Boundary conditions In the computational model, temperatures are used as the thermal boundary conditions, including the air and the natural ground surface and embankment surface. Based on the observed data and adherent layer theory , the thermal boundary conditions can be expressed as follows: 2p p t þ þ a0 8760 2 þ DT t 8760 ð12Þ where T0 and A are the mean annual temperature and annual amplitude of the temperature, respectively; t is the time in hours; and a0 is the phase angle, as determined by the completion time for the embankment. Based on a widely accepted climate warming scenario for the plateau , an increase rate of DT = 0.052 °Ca1 is taken into account for the mean annual air temperature. The mean annual air temperature is 4.5 °C in this region, and based on the adherent layer theory  and field observations, the values of T0 and A for different surfaces in Eq. (12) are listed in Table 2. Based on the in-situ observed data for the wind at Huashixia on the QTP, the ambient wind velocity outside the embankment can be expressed as follows: m10 ¼ 4:6 þ 1:52 sin T0 (°C) A Air (IH) Natural ground surface (AK and RH) Asphalt pavement (MN and OP) Side slope surfaces (LM and PQ) Median strip surface (NO) 4.5 0.52 2.0 0.2 0.2 11.5 12 15 13 13 mH ¼ m10 3.3. Physical parameters T ¼ T 0 þ A sin Variables 2p 3p tþ þ a0 8760 2 a H 10 ð14Þ where a is the power law exponent, and a value of a = 0.16 was obtained in this study. A constant heat flux of q = 0.06 Wm2 is applied to the bottom surface of the computational model. The lateral boundaries in Fig. 3 are assumed to be adiabatic. 3.4.2. Initial conditions The construction of the studied embankment took place in summer, thus it is assumed that the embankment was constructed on July 15 when the warmest time of the year occurs. The initial temperature fields of underneath the embankment (Parts III, IV and V in Fig. 3) on July 15 were obtained through a long-term transient solution with the upper boundary condition of natural ground surface (Eq. (12)) without considering climate warming. According to numerous numerical simulation tests, the stable thermal regime can be obtained after 100 years of computations. The initial temperature fields of embankment (Parts I and II in Fig. 3) were determined by the air temperature at the construction time. The initial wind temperature is taken as air temperature on that date. The initial velocity field of the airflow on July 15 is calculated by using a wind boundary condition (Eqs. (13) and (14)) without considering the effect of thermal boundary conditions. 3.5. Solution method Because the governing equations in the model are highly nonlinear, a numerical solution must be employed. The spatial and temporal discretization of the above governing equations is carried out by using the Control Volume Integration Method . The discrete coupled equations are solved in an iterative manner using a Successive Under-Relaxation Method for every time interval Dt , and the iteration sequence is continued until the maximum normalized changes of all variables are less than 103, Using these methods, we can obtain the variable fields of the three zones. Additional details concerning this numerical method used in this model can be found in Refs. [26,27]. ð13Þ where m10 is the wind velocity at a height of 10 m. On the basis of the ‘‘power law for the wind profile” of the atmospheric surface layer , the wind velocity at a height of H from the natural ground surface at boundary IH can be simplified as follows: 3.6. Model validation To validate the aforementioned numerical model, the ground temperatures at a natural borehole and a central borehole of the new embankment were monitored, and a comparison between Table 1 Thermal parameters of different materials in computational model (k: thermal conductivity; C: heat capacity; L: latent heat of freezing; subscript f: frozen; subscript u: unfrozen). Physical variables kf Wm1°C1 Cf Jm3°C1 ku Wm1°C1 Cu Jm3°C1 L Jm3 Embankment fill (I) Crushed-rock layer (II) Silty clay (III) Gravel soil (IV) Weathered mudstone (V) Air (VI) 2.053 0.442 1.351 2.610 1.824 0.020 1.625 106 1.016 106 1.879 106 1.863 106 2.122 106 0.644 103 1.794 0.442 1.125 1.910 1.474 0.020 1.982 106 1.016 106 2.357 106 2.401 106 2.413 106 0.644 103 2.04 107 0 6.03 107 2.32 107 3.81 107 0 M. Liu et al. / International Journal of Heat and Mass Transfer 127 (2018) 1178–1188 1183 Fig. 4. Comparison of measured and simulated ground temperatures: (a–b) natural ground boreholes and (c–d) embankment center boreholes. the computed and measured temperatures is given in Fig. 4. The results indicated that the computed temperatures agreed well with the measured data for the permafrost layer. A large difference between the measure data and simulated data was found for the active layer because a perfect condition was considered for the temperature boundary, whereas it is actually variable and complex on the QTP. In general, the numerical model is reasonable for simulating the thermal regime of a crushed-rock embankment in a permafrost region. 4. Results and analysis 4.1. Thermal regime evolution in warm seasons 4.1.1. Traditional CRIE Fig. 5a–d shows the evolutions of the geothermal regimes of the traditional CRIE on October 15 in the 2nd, 5th, 20th, and 30th years after construction, respectively. The 0 °C isotherm is defined as the permafrost table because the maximum seasonal thaw depth usually occurs in October on the QTP. From Fig. 5a, the temperature field of the traditional CRIE is basically symmetrical in the 2nd year after construction and when the permafrost table under the embankment elevates to near the original ground surface. However, the permafrost table beneath the embankment center is relatively deeper than that under the embankment shoulders, indicating a higher heat absorption in the center. The permafrost temperature beneath the embankment increases, as shown by the descending lines for 0.5 and 0.6 °C. This is mainly caused by the thermal disturbance from embankment construction in the warm season. As shown in Fig. 5b, the traditional CRIE begins to show a weak cooling effect on the underlying permafrost after five years of operation. However, a marked asymmetry for the temperature distribution is observed at this time, as shown by the asymmetrical distribution of the 0.8 °C isotherms under the embankment. In M. Liu et al. / International Journal of Heat and Mass Transfer 127 (2018) 1178–1188 1 -0.8 -0.6 -15 -25 -20 -10 -5 10 15 20 25 0 -10 -5 5 0 10 15 Y/m 20 25 5 0 1 -0.5 -5 0 4 0 1 -0.8 -10 -15 -25 -20 -15 -10 -5 5 0 2 10 15 20 25 0 -5 4 -20 2 1 0 0 -0.8 -15 -10 4 -0.5 1 .8 -20 -15 -10 -5 0 5 10 20 25 X/m Fig. 5. Thermal regimes of traditional CRIE on October 15 in 2nd (a), 5th (b), 20th (c), and 30th (d) years after construction (unit: °C). the 20th year after construction, a 1.0 °C isotherm occurs under the embankment as a result of the cooling effect of the CRIE, but the asymmetry of the temperature distribution intensifies. This implies that the cooling performance of the traditional CRIE is obviously weakened from the windward side to the leeward side because of the much wider embankment for the expressway. In the 30th year after construction, the 1.0 °C isotherm disappears beneath the embankment, which indicates that the permafrost temperature obviously increases as a result of climate warming. The warm permafrost may cause instability in the embankment because the deformation of the permafrost is promoted by the increase in temperature. Therefore, the traditional CRIE structure cannot satisfy the higher cooling requirement of an expressway with a wide and dark-colored asphalt pavement, and the serious asymmetry of its ground temperature distribution will be intensified with an increase in the width of the embankment and may cause uneven thaw settlement. 4.1.2. New CRIE Fig. 6 shows the geotemperature distributions of the new CRIE on October 15 in the 2nd, 5th, 20th, and 30th years after construc- 0 -0.5 -1 -5 5 0 10 15 20 25 5 -1 0 -0.5 -1.5 -20 -15 -10 -5 5 0 1 0 10 15 20 25 X/m (d) 5 2 -5 0 5 6 -15 -25 4 0 -1 -0.5 1 2 -0.5 -1.5 -10 15 1 -1.5 -1.5 1 -0 25 (c) 0 2 -0.5 -0.5 -10 -15 -25 1 20 X/m -15 -25 5 15 1 -1 -5 5 6 4 -1 X/m (d) 10 4 3 1 -10 -1 -1 5 0 (b) 0 -0.5 -5 -10 -5 5 (c) 1 -0.6 -0.8 X/m -15 -25 X/m -0.5 0 -0.5 -10 -0.8 -15 -15 -0.5 0 -0.8 -20 -20 -0.5 -0.8 -0.5 3 1 -0.6 0 Y/m 5 1 4 4 1 0 -0.8 -15 -25 1 -0.5 0 -15 -25 -5 5 4 -10 Y/m 5 5 -5 Y/m 0 (b) 1 3 1 -10 X/m 0 Y/m -15 (a) 0 1 -0.5 -0.6 -0.8 0 -10 5 1 0 -0.5 -5 5 3 Y/m 4 0 Y/m 5 (a) Y/m 5 -1 1184 -1 -20 -15 -10 -5 0 5 10 15 20 25 X/m Fig. 6. Thermal regimes of new CRIE on October 15 in 2nd (a), 5th (b), 20th (c), and 30th (d) years after construction (unit: °C). tion. Significant differences in the ground temperature field evolution can be observed for the two different embankment structures. As shown in Fig. 6a, similar to the traditional structure, a weak warming of the underlying permafrost caused by the heat disturbance associated with embankment construction occurs in the initial two years after construction. However, the permafrost table under the embankment moves upward near the original ground surface, especially under the center line, with a magnitude that is nearly 1.0 m higher than the same position in the traditional CRIE. The ground is significantly cooled by the new embankment structure in the 5th year after construction, as indicated by the existence of 1.0 °C and 1.5 °C isotherms under the embankment center, as shown in Fig. 6b. In addition, the new CRIE improves the symmetry of the ground temperature field. In the 20th year after construction, the cold-temperature zone of 1.0 °C expands and covers most of the area under the embankment (Fig. 6c). This indicates that the warm permafrost experiences a significant cooling process as a result of the cooling performance of the new embankment structure. After 30 years of operation, the permafrost beneath the embankment warms slightly under the impact of climate warming. M. Liu et al. / International Journal of Heat and Mass Transfer 127 (2018) 1178–1188 1185 Fig. 7. Variations in permafrost table beneath centerlines of new structure and traditional CRIE. However, the foundation soil is still cooler than that under the natural ground surface. As shown in Fig. 6d, the 1.0 °C and 1.5 °C isotherms are still found under the embankment, and the permafrost table is also kept near the bottom of the embankment in the 30th year after construction. As a result, the ground temperature is clearly lower under the new embankment than under the traditional one, with a difference of nearly 0.7 °C. The differences demonstrate that the new CRIE has a better cooling effect than the traditional one, and its thermal regime is beneficial to maintain the long-term thermal stability of an expressway in a permafrost region. To clearly show the variations in the permafrost tables beneath the embankments, Fig. 7 summarizes the depths of the permafrost tables in the centerlines of the two embankments over a period of 30 years after their construction. As shown, considerable upward movements of the permafrost tables occur under the two embankments in the 2nd year after construction. In particular, the permafrost table beneath the new embankment structure shows a sharper uprising of 2.8 m and then enters the interior of the embankment in only 2 years after construction, implying that the seasonal freeze-thaw process will only occur in the embankment body. Although a slight downward movement of the permafrost table occurs as a result of climate warming, it is also kept above the original ground surface in the 30th year after construction. This result clearly indicates the effectiveness of the new embankment structure design in cooling the permafrost stratum under the expressway, especially under the embankment center. Fig. 8. (a) Variations of outside air temperature and air temperature in crushedrock layer; (b) variations of instantaneous heat fluxes at bottom of new structure and traditional CRIE in 5th year after construction. During the warm seasons from April to October, the positive heat fluxes at the bottom of the embankments are similar for the new structure and traditional one, and the maximum heat flux values are both approximately 3.0 Wm2. However, during the cold seasons, the negative heat fluxes are different. The heat flux of the new structure increases with the air temperature and reaches a maximum value of approximately 8.0 Wm2 in January when the lowest air temperature occurs. In contrast, for the traditional structure, the maximum heat flux in winter is less than 7.0 Wm2. The negative heat flux is clearly larger in the new embankment than in the traditional one in winter, with a mean annual difference of nearly 0.6 Wm2, demonstrating the superior convection heat transfer of the new embankment in winter. Therefore, compared with the traditional CRIE, the new structure has a stronger cooling capacity and can effectively stabilize the permafrost stratum under an expressway in a permafrost region. 4.2. Heat fluxes Fig. 8 illustrates the air temperatures outside and inside the rock layer, along with the instantaneous heat fluxes at the bottom of the new structure and traditional CRIE in the 5th year after construction when the embankment is in a relatively stable state. It can be found that the air temperature in the rock layer decreases with a decrease in the air temperature outside in cold seasons, with a minimum temperature of approximately 7.5 °C. The long and cold winter on the QTP increases the convection cooling rate of the crushed-rock layer. The variations of the instantaneous heat fluxes at the bottom of the new CRIE and traditional CRIE in the 5th year after construction are shown in Fig. 8b, where positive values stand for heat absorption and negative values stand for heat release. Data of the instantaneous heat fluxes in this figure were computed and collected during the numerical computation. It can be seen that the change processes for the heat fluxes are consistent with the air temperature variation, and both the new and traditional CRIE experience strong heat release processes in the 5th year after construction. 4.3. Cooling performances of crushed-rock interlayers with new and traditional structures in cold seasons The active cooling effect of a crushed-rock layer comes from a heat insulation effect during summer and a convection cooling effect during winter caused by the air convection heat transfer through its pore structure . Fig. 9 shows the temperature distribution of the traditional CRIE on January 15 in the 2nd, 5th, 20th, and 30th years after construction. As shown, the cold energy enters the crushed-rock interlayer from the air inlet in the right toe and first cools the foundation soil under this region, as indicated by the descending line for 0.8 °C (Fig. 9b). The cooling trend for the permafrost continues in the 20th year after construction because of the performance of the crushed-rock interlayer, which can be seen in the existence of the 1.0 °C isotherm (Fig. 9c). However, the low-temperature zone of 1.0 °C only exists under the right hand portions (windward side) of the embankment, implying that the traditional structure cannot effectively cool the foundation soil under the left hand portion of the embankment because of the 1186 M. Liu et al. / International Journal of Heat and Mass Transfer 127 (2018) 1178–1188 5 -8 -4 -4 -8 .5 -1 -0 -0.5 -0.5 -0 -15 -25 5 -0 -15 -5 -10 5 0 10 20 25 (b) -10 -4 -8 -1 -8 -15 -25 -0.8 -10 -8 -1 -5 0 -4 -0. 8 -0 -15 -25 -20 -15 -5 -10 0 5 10 15 20 25 -1 -8 -4 -0.5 0 -8 -1 -4 -0.5 5 10 15 20 25 -0 -1 -0.5 -0.7 .5 -0 -5 -0 .5 -4 -0 .7 -15 -5 -10 5 0 10 15 20 25 (c) -10 -8 -1 -10 -8 -4 -8 -0.7 -4 -0.5 -1.5 -0 -1.5 -20 -15 -10 -5 -8 -1 -1.5 -0.5 0 5 .7 10 15 20 25 (d) -5 -1 -8 -8 -4 -0.5 -8 -4 -1.5 -10 -4 -8 -1 -0.5 -1 -0.7 -0 .7 -15 -25 -8 -1.5 X/m -10 -10 -1. 5 -1 0 -1 -4 -8 -0.7 -0.5 -10 -8 -4 .7 -20 -5 5 -10 -4 25 X/m Y/m -8 -4 -1 20 -1 -15 -25 X/m 0 15 -1 0 (d) -8 Y/m -5 -10 10 -0. 7 -15 5 0 -1 -20 -5 -1 -10 -0.7 -15 -25 5 -1 -0.7 -10 -10 -10 .7 -5 -0.5 -0.7 -10 -0.7 -15 -0 Y/m 0 -4 -0.7 -4 -8 -10 -1 -15 -25 Y/m -8 -10 -0.7 -0.5 .7 (b) 5 (c) -4 -0.5 -5 X/m 5 -0.5 X/m -10 .8 -10 -10 -8 -0.7 -4 -0.5 -20 5 -4 -8 -1 -0.5 -1 -10 15 -10 -8 -5 X/m 0 Y/m -20 -10 -0.7 -4 -0 .7 .7 -10 0 -4 -8 -0.5 -0.7 -5 (a) -10 -1 Y/m 0 -10 Y/m (a) Y/m 5 -20 -15 -10 -5 0 5 10 15 20 25 X/m Fig. 9. Thermal regimes of traditional CRIE on January 15 in 2nd (a), 5th (b), 20th (c), and 30th (d) years after construction (unit: °C). large-width pavement of the expressway. Under the effect of climate warming, the cooling performance of the traditional structure in winter is significantly reduced, and the 1.0 °C isotherm disappears in the 30th year after construction (Fig. 9d) compared with that in the 20th year. The permafrost temperature under the traditional embankment becomes warmer, and reaches approximately 0.7 °C as a result of its ineffective cooling process. The warm permafrost at this temperature lacks thermal stability. All of these facts indicate that the cooling of the traditional CRIE for the expressway is relatively limited and cannot produce cooling effects strong enough to influence the underlying permafrost, especially under the leeward side of the expressway. In Fig. 10, after the thermal disturbance caused by the embankment construction dissipates, the new CRIE begins to show its cooling performance. In cold seasons, air convection occurs in the rock layer, and cold energy is transferred from the cold air to underlying soils. As a result, the permafrost beneath the centerline of the embankment is cooled first, as shown by the decline of the 1.0 °C and 1.5 °C isotherms in Fig. 10b, which is significantly different from the cooling characteristic of the traditional structure (Fig. 8b). In the 20th year, the 1.0 °C and 1.5 °C isotherms both expand -15 -25 -20 -15 -10 -5 0 5 10 15 20 25 X/m Fig. 10. Thermal regimes of new CRIE on January 15 in 2nd (a), 5th (b), 20th (c), and 30th (d) years after construction (unit: °C). beneath the embankment as a result of the cooling effect of the new structure (Fig. 10c), which reveals that the underlying permafrost experiences an obvious cooling process in cold seasons. Although the cooling capacity of the new structure is slightly weakened by the effect of climate warming, the low-temperature 1.0 °C zone covers most of the area under the embankment in the 30th year. This demonstrates the effectiveness of the new design in cooling the permafrost under the expressway, especially the embankment center. Furthermore, the geotemperature distribution is also symmetric after 30 years of operation. This implies that the new CRIE can not only provide a good cooling performance, but also eliminate the thermal asymmetry induced by the wind direction on the QTP. To differentiate the cooling performances of the crushed-rock interlayers in the new and traditional structures, Fig. 11a and b show time series of the ground temperatures at depths of 6 and 15 m relative to the original ground surface beneath the centerline and right shoulders of the two embankments. It can be found that the cooling performance of the new CRIE significantly reduces the soil temperatures at these two depths, and makes the fluctuation of the temperature larger than that in the traditional CRIE, M. Liu et al. / International Journal of Heat and Mass Transfer 127 (2018) 1178–1188 1187 Fig. 11. Time series of ground temperatures at 6 and 15 m beneath (a) centerline and (b) right shoulders of two embankments, and (c) variation of ground temperature with depth at centerlines of two embankments on October 15th in 30th year after construction. revealing an obvious influence on the thermal status of the underlying permafrost of the new structure. Furthermore, the permafrost temperature at the depth of 15 m beneath the centerline of the new CRIE is obviously lower than that under the traditional structure, with a large difference of nearly 1.0 °C (Fig. 11a), which is significantly larger than the value of approximately 0.4 °C at the same depth under the right shoulders of the two embankments (Fig. 11b). This similarity could also be observed in the permafrost at a depth of 6 m. It demonstrates the superior cooling effect of the new design on the embankment center. Fig. 11c shows the temperature profiles at the centerlines of the two embankments on October 15, in the 30th year after construction. As shown, although the traditional CRIE can cool the permafrost to some extent, its cooling scope and magnitude are limited, resulting in an obvious warming of the permafrost beneath the embankment centerline under climate warming. The degeneration of the permafrost at temperatures higher than 1.0 °C results in poor stability. However, if the new structure is adopted for an expressway, the permafrost beneath the embankment experiences considerable cooling processes after construction. In the 30th year, the permafrost temperature at a depth of up to 15 m beneath the centerline of the new embankment is still lower than 1.0 °C, and the lowest temperature is nearly 1.7 °C at a depth of 5 m, which is approximately 1.0 °C lower than that of the traditional structure. The cold temperature condition implies that the effects of climate warming and embankment construction cannot accelerate the permafrost degradation beneath the new CRIE because of its significant cooling performance. The comparison of these temperature profiles further confirms the advantages of the crushedrock interlayer structure used in the new design, compared to the traditional one, and demonstrates the effectiveness of the new design in improving the thermal stability of expressways in permafrost regions. expressway in a permafrost region under the effect of climate warming. The following conclusions can be drawn: 5. Conclusions Acknowledgements This paper presented a novel crushed-rock embankment structure for an expressway. A heat transfer model was developed to investigate the cooling performance of the new design for an This research was supported by the National Natural Science Foundation of China (Grant No. 41701067, 41730640, 41630636), the Science and Technology Service Network Initiative of the (1) The cooling of the traditional CRIE for an expressway is relatively limited and cannot produce cooling effects strong enough to influence the underlying permafrost. The largewidth embankment surface and significant heat absorption caused by the asphalt pavement greatly weaken the cooling capacity of the CRIE on the permafrost under the embankment center and leeward side, resulting in an obvious permafrost degradation and asymmetrical geotemperature distribution. Thus, this structure cannot maintain the thermal stability of an expressway in permafrost regions. (2) In contrast, the new CRIE produces a significant cooling performance and especially plays an effective role in lowering the permafrost temperature beneath the centerline of the expressway. Moreover, the new structure shows the effect of improving the symmetry of the embankment temperature distribution. Therefore, the new embankment structure can effectively protect the underlying permafrost and ensure its long-term thermal stability even under the climate warming. 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