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Design of electric heat pipe embedding schemes for snow-melting pavement based on mechanical properties in cold regions
Cold Regions Science and Technology 165 (2019) 102806
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Cold Regions Science and Technology journal homepage: www.elsevier.com/locate/coldregions
Design of electric heat pipe embedding schemes for snow-melting pavement based on mechanical properties in cold regions
T
⁎
Kai Liua, , Chaoliang Fua, Hongzhou Xiea, Fang Wangb, Xuancang Wangc, Haijian Baia a
School of Automobile and Traffic Engineering, Hefei University of Technology, Hefei 230009, China School of Civil Engineering, Anhui Jianzhu University, Hefei 230601, China c College of Highway, Chang’an University, Xi’an 710061, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Snow-melting pavement Embedding schemes Mechanical properties Finite element Cold regions
To obtain reasonable electric heat pipe embedding schemes (EHP-ES) of the snow-melting pavement in cold regions, the mechanical properties of the snow-melting pavement with electric heat pipe (SMP-EHP) were investigated by laboratory experiments and finite element simulations. The bending experiments and melting experiments were conducted to analyze the effect of EHP-ES on the mechanical properties of the concrete slab. Additionally, the finite element model was established to simulate the actual SMP-EHP in cold regions. The allowable flexural tensile strength of cement concrete was used as the judgment index to determine the reasonableness of EHP-ES. In this case, the mechanical properties of concrete slabs with different EHP-ES were studied under two most unfavorable conditions. Based on the experimental and simulated results, the design criteria of the EHP-ES was proposed, and the reasonable EHP-ES (embedding depth: 14.0-16cm, embedding spacing: 12.0 cm-18.0 cm) were obtained. Finally, a test road in Tibet was paved to verify the feasibility of the above reasonable EHP-ES further. The research results could enrich the design of EHP-ES for snow-melting pavement in cold regions from the aspect of the mechanical properties of the concrete slab.
1. Introduction In winter, accumulated snow and ice on the road is difficult to sweep, which seriously affect the transportation and hinder economic development, especially in cold regions. To mitigate these problems, many methods, such as mechanical, chemical (Kelly et al., 2010; Aghazadeh et al., 2012; Gutchess et al., 2016; Lee et al., 2017) or thermal, have been made in the past time and alternatives are still being investigated. In recent years, the thermal method, which including solar energy (Daniels et al., 2019; Pan et al., 2015), circulating heat fluid (Xu and Tan, 2015; Asfour et al., 2016), geothermal energy and heat pump (Wang et al., 2017; Kong et al., 2019; Balbay and Esen, 2013; Lai et al., 2018), electric heating system (Vo et al., 2015; Lai et al., 2016; Li et al., 2013; Nuijten and Hoyland, 2017) has been drawn more and more attention. In the above mentioned thermal method, the snow-melting pavement with the electric heating system (SMP-EHS) has offered an efficient and easily controllable way to solve the problems mentioned above. In the open literature, for the design of the embedding schemes of SMP-EHS, researchers conducted extensive studies on these aspects of snow-melting efficiency (Lai et al., 2014; Abdualla et al., 2016),
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energy consumption (Li et al., 2013; Yang et al., 2012; Liu et al., 2017a) and temperature distribution (Won et al., 2014; Zhao et al., 2011; Lai et al., 2015). Lai et al. proposed the reasonable embedded depth of carbon fiber grille and embedded spacing of heating wires and applied the criterion of snow-free area ratio to evaluate snow-melting performance (Lai et al., 2014). Abdulla et al. identified the requirements of an electrically conductive concrete heated pavement system and tested to determine its performance (Abdualla et al., 2016). Li et al. investigated a self-deicing road system with electro-thermal materials and validated its low energy consumption (Li et al., 2013). Yang et al. developed the design of the heating panel with carbon fiber tape and conducted a deicing experiment to examine the energy consumption of the system (Yang et al., 2012). Liu et al. analyzed the relationship between energy consumption and embedded depth and embedded spacing in two phases through thermal simulation and experiments (Liu et al., 2017a). Won et al. studied the temperature distribution of the early-opening conductive heated pavement system through heat transfer and investigated the embedded spacing of copper plates (Won et al., 2014). Zhao et al. studied the temperature distribution on a representative section for the different embedded spacing of carbon fiber heat wires and determined the maximum allowed the embedded spacing of carbon
Corresponding author. E-mail address: [email protected] (K. Liu).
https://doi.org/10.1016/j.coldregions.2019.102806 Received 11 September 2018; Received in revised form 21 April 2019; Accepted 4 June 2019 Available online 11 June 2019 0165-232X/ © 2019 Elsevier B.V. All rights reserved.
Cold Regions Science and Technology 165 (2019) 102806
K. Liu, et al.
fiber heating wires (Zhao et al., 2011). Lai et al. systematically investigated the structure type, heating power and temperature field distribution of snow-melting heated pavement in the tunnel portal and presented the embedded spacing of heat cable (Lai et al., 2015). In a word, most researchers designed the embedding schemes of SMP-EHS from the aspects of snow-melting efficiency, energy consumption, temperature distribution and so on. However, the temperature difference between the internal high temperature, which caused by the electric heating system, and external low temperature of pavement surface will significantly increase the pavement temperature extreme stress and accelerate pavement damage (Joško et al., 2014; Liu et al., 2017b). In this case, it is necessary to design the embedding schemes of SMP-EHS from the aspect of mechanical properties, to enrich the existing research. In this paper, the laboratory experiments will be conducted to study the influence of the embedded depth and embedded spacing on concrete slab mechanical properties. A model of snowmelting pavement with electric heat pipe (SMP-EHP) will be established, which includes all the actual properties of the components of an existing test road. Then the finite element simulations of the model were studied under two most unfavorable conditions. Finally, a test road will be paved in Tibet. The research results will provide the foundation for the design of electric heat pipe embedding schemes (EHP-ES) in cold regions based on mechanical properties.
structure was preferred. Therefore, for the design of SMP-EHP, the range of h (6 cm-20 cm) was selected as the initial range. Additionally, according to the Specifications for the design of highway cement concrete pavement (JTG D40-2011), the minimum embedded spacing of steel bars should be twice the maximum particle size of aggregates. In this paper, the maximum particle size of aggregate was 2.6 cm. Then the maximum transverse embedded spacing of plain round bars was 30cm. Therefore, the range of d1 (6 cm-30 cm) was selected as the initial range. Based on the initial range of h and d1, the pre-embedding schemes were obtained, as shown in Table 2. 3. Laboratory experiments 3.1. Bending experiments 3.1.1. Materials preparation and methods The cement used in this study was the 42.5-grade ordinary Portland cement. Two kinds of gravel with a particle size of 5-20 mm and 10-30 mm were used in the experiment. Among them, 5-20 mm gravel accounted for 53% of the quality of synthetic aggregate. The ratio of cement, sand and stone is 1:1.73:3.35, and the water-cement ratio is 0.41. The amount of water reducing agent is 0.75% by weight of the cement. Four groups of concrete beam specimen (550 mm×150 mm×250 mm) were prepared, of which only three groups were embedded with an electric heat pipe in the symmetrical center position. The value of h was 8 cm, 12 cm and 16 cm respectively. The electric heat pipe (diameter: 12 mm, length: 550 mm) was parallel to the length (550 mm) of the specimens. There were three parallel specimens (A, B, C) in each group. The specimens would be taken out after seven days of standard curing. The universal testing machine was applied, and the loading rate was 0.08 MPa/s. The flexural tensile strengths of concrete beam specimens were calculated as follows:
2. Structure and pre-embedding schemes 2.1. Structure of SMP-EHP The three-dimensional structure of SMP-EHP was shown in Fig. 1. From the bottom to top, the layers are, in order, frozen soil, subgrade, graded crushed stone subbase, cement stabilized macadam base, extruded polystyrene (XPS) slabs and pavement concrete. The electric heat pipes, which were perpendicular to the direction of the vehicle, were embedded in the pavement concrete (size: 4 m×3 m). The XPS slabs, which can mitigate the downward heat transfer and protect the frozen soil from melting, were paved below the pavement concrete. The parameters of the materials in the model were shown in Table 1 (Qin and Hiller, 2011; Liu et al., 2015).
f = FL/ bH 2
(1)
where f was the flexural tensile strength of specimen (Mpa); F was the failure load of the specimen (N); L was the distance between two fulcra (450 mm); b was the width of the specimen (150 mm); H was the height of the specimen (250 mm), as shown in Fig. 3 (a).
2.2. The electric heat pipe pre-embedding schemes
3.1.2. Analysis of experimental results The second group B was used as the research object to analyze the development of cracks during the experiment. The load-deformation curve of second group B was as shown in Fig. 3 (b). According to Fig. 3 (b), the value of deformation increases as the load increases at the beginning stage. With the increase of the load, there was an obvious crack at the bottom of the specimen. The load at this time was defined as the failure load. Then, the load was rise and fall as the deformation increases. At this point, the bending experiment was completed. The average failure load of the three specimens (A, B, C) was taken as the failure load of this group. The bending experimental results of the concrete specimens were as shown in Table.3. From Table 3, the flexural tensile strength of the second-fourth group is greater than that of the first group, and the flexural tensile strength of concrete specimen increases as the h increases. This is because the heat pipe is added to the concrete specimens similar to the steel bar added to the cement specimens, which can improve the flexural tensile strength of the concrete. Additionally, when h increases from 8 cm to 12 cm, the failure load of concrete beam specimens increases by 8.5 kN, and when h increases from 12 cm to 16 cm, the failure load of concrete beam specimens increases by 16.2 kN. It can be seen that the increment of the failure load of the concrete specimen was relatively small when h ≤ 12 cm. Therefore, to significantly improve the flexural tensile strength of concrete, 12 cm < h ≤ 20 cm is preferred, where the maximum value is the upper limit of the initial h in section 2.2.
The EHP-ES used in laboratory experiments and simulations were called pre-embedding schemes. The layout scheme of the electric heat pipe in the concrete slab was as shown in Fig. 2. The d1 represents the embedded spacing of electric heat pipe. The d2 represents the distance between the transverse joint of the concrete slab (size: 4×3×0.25 m) and the center of the electric heat pipe. The h was used to represent the embedded depth of the electric heat pipe. The electric heat pipe can be regarded as the steel bar in the concrete. Its safety and life were very important to the SMP-EHP. By consulting the code for design of concrete structure (GB 50010-2010), the minimum concrete cover thickness (5 cm) of the reinforced concrete
Fig. 1. Schematic diagram of the SMP-EHP. 2
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Table 1 Material properties of the SMP-EHP. Pavement structure
Pavement concrete XPS slab Cement stabilized macadam base Graded crushed stone subbase Subgrade Electric heat pipe
Density (g·cm)
Elastic modulus (Mpa)
Poisson ratio
3
Thermal conductivity [W/ (m·K)]
Linear expansion coefficient (10-5/°C)
Specific heat [J/ kg·K]
25 5 20
2.50 0.05 2.30
30000 15 1500
0.12 0.01 0.20
2.00 0.03 1.40
1.0 7.0 1.0
1005 38 900
20
2.10
250
0.30
1.00
0.5
840
600 1.2(diameter)
1.70 7.93
40 206000
0.35 0.30
1.00 12.10
0.5 1.6
2010 1.6
Thickness (cm)
The embedded depth of temperature strain gauges, which parallel to the electric heat pipe and close the 2#pipe, was 5 cm, 10 cm, 16 cm and 20 cm, respectively, as shown in Fig. 5. The density of snow is 300 kg/ m3. The heating time was 5 hours. The thickness of the snow is 5 cm. The weight of the snow was 12.15 kg. The snow-melting target is to melt all the snow in five hours. To melt all the snow in 5 hours, 2.43 kg of snow per hour should be melted at least. Therefore, it is necessary to calculate the total energy Q required to melt snow and the heating power P required for each slab, which can be expressed by formula (2) and (3):
Q = CM ΔT + MHS
(2)
P = Q/(3600 × t )
(3)
where C was the specific heat capacity of snow (J /(kg°C)); M was the weight of snow (kg); ΔT was the temperature difference between the initial temperature of snow and 0 °C (°C); HS was the heat of fusion (J/ kg); t was the heating time (hour). The minimum power of each concrete slab is 231.8 W by using formula (2) and formula (3). However, the heat of the concrete slab will be lost to the air after heating. Considering the effect of snow-melting, the minimum power required for snow–melting can be set at 40% to 70% of the actual working power of the slab (Wangzhi, 2014). Therefore, the range of heating power of concrete slabs in the experiments was 416.9 W (I), 335.9 W (II), 591.7 W (III) and 414.3 W (IV), respectively.
Fig. 2. Layout scheme of the electric heat pipe (unit: m).
3.2. Melting experiments 3.2.1. Materials preparation and methods The cement used in this study was the 42.5-grade ordinary Portland cement. The mass ratio of the material required for a concrete slab as shown in Table 4. Four concrete slabs were prepared based on Specification for Design of Highway Cement Concrete Pavement (JTG D402011). The size of each slab was 0.9 × 0.9 × 0.25 m. The embedding schemes were I-IV in Table 2. The preparation of concrete slabs and the experimental process were shown in Fig. 4. In the experiments, the surface temperatures of the concrete slabs and the electric heat pipe were measured by the thermocouples, and the temperature strain gauges were embedded in the concrete slab to monitor the strain of the concrete slab, as shown in Fig. 4 (3). To reduce heat loss, the XPS slabs were placed at the bottom of the concrete slabs, and the insulation foams were wrapped around the concrete slabs, as shown in Figs. 4 (4) and 4 (5). The walls of the containers of snow were formed by the XPS slabs. Then the plastic film was covered on the surface of the containers of snow to ensure that there was no leak around the container of snow, as shown in Fig. 4 (6). Finally, a water outlet was reserved for the containers of snow, and a container of water was placed at the water outlet to collect the water melted from snow. The experiments were completed at an ambient temperature of -1 °C to -4 °C.
3.2.2. Analysis of experimental results The compressive strains of the concrete slab were shown in Fig. 6. It can be seen that the maximum compressive strain of the scheme I appear at 16 cm, while the maximum compressive strain of the other three schemes appears at 10 cm. This is because the h in scheme II-IV is 12 cm, and the temperature strain gauge at 10 cm is the closest to the heat pipe. The closer to the heat source, the higher the temperature. As a result, the compressive strain caused by the internal high temperature is also greater. Additionally, the compressive strain of scheme II and scheme III is the smallest and largest respectively. Among them, the maximum compressive strain of the scheme III is 70.5με.This is attributed to the fact that the d1 of scheme III and scheme II is the smallest and largest respectively. As the d1 decreases, the amounts of electric
Table 2 Pre-embedding schemes of heat pipes. Simulations
1 2 3 4 5 6 7
Experiments
I II III IV V / /
d1/cm
18.0 25.0 12.0 18.0 16.7 18.0 18.0
h/cm
d2/cm
16.0 12.0 12.0 12.0 14.0 8.0 6.0
11.0 12.5 8.0 11.0 7.95 11.0 11.0
3
Number of the electric heat pipe 4×3×0.25 m
0.9×0.9×0.25 m
22 16 24 22 24 22 22
5 4 7 5 6 / /
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Fig. 3. Bending experiments of concrete beam specimen: (a) Experimental equipment and specimen (unit: mm) (b) Load-deformation curve of second group B.
heat pipes and the heating power increase. At the same heating time, the growth rate of the temperature difference between the interior and exterior of the concrete slab of scheme III is faster than other schemes. Therefore, the compressive strain of scheme III is the largest. Similarly, the scheme II is the smallest. In the open temperature, Liu et al. used the CDP model to reveal the relationship between compressive strains and damage factor D. Based on their research, it can be found that when the compressive strain of the concrete slab is 70.5με, the damage factor D is 0.025, which is much smaller than the damage factor when it reaches complete failure (when D = 1, it means that the material is failure completely.) (Liu et al., 2017b). Table 5 illustrates the melting rate of the concrete slab. It can be found that scheme II does not meet the snow-melting target, while scheme I, scheme III and scheme IV can meet the snow-melting target. Among them, the melting rate of scheme III is the largest, which is consistent with the law of compressive strain. This is because the heating power of scheme I, scheme III and scheme IV is larger than that of scheme II, and the heating rate and melting rate of concrete slabs are positively correlated with the heating power. It is also interesting to note that the melting rate of the scheme I is less than that of scheme IV. This is because the d1 of the scheme I and scheme IV is 18 cm, but the h of the scheme I and scheme IV is 16 cm and 12 cm respectively. The time required for heat to reach the surface of the concrete slab increases with the increase of h. As a result, the melting rate becomes slower. In a word, to reduce the stress damage of concrete slab, the larger d1 is preferred. If the melting efficiency is considered, the smaller d1 is preferred. Therefore, it is necessary to determine the appropriate range of d1 to balance the contradiction between melting efficiency and pavement damage. The d1 is 12 cm when the heating power is 591.7 W. In this case, increasing the heating power of concrete slabs (reducing the d1) will not only waste energy but also greatly affect the stability of frozen soil in cold regions and the mechanical properties of the pavement structure. Therefore, 12 cm is chosen as the lower limit of d1 can not only meet the melting efficiency but also minimize the pavement damage. The d1 is 18 cm when the heating power is 414.3 W. In this
Table 4 Ratio of the material required for a concrete slab. Material
Mass
Water/kg
43
Cement/kg
93
Sand/kg
159.5
Gravel/kg
Water reducer/kg
5-20mm
10-30mm
164
145.5
0.07
case, reducing the heating power of concrete slabs (increasing the d1) affect its melting efficiency. Therefore, 18 cm is chosen as the upper limit of d1. Actually, it can be seen from the above experiments that when the 12 cm ≤ d1 ≤ 18 cm, the melting efficiency is not satisfied when h > 16 cm. Therefore, regardless of the other factors, 6 cm ≤ h ≤ 16 cm is preferred, where the minimum value is the lower limit of the initial h in section 2.2. 4. The stress analysis of concrete slab for SMP-EHP under different most unfavorable conditions 4.1. Judgment index and modeling hypothesis 4.1.1. Judgment index of finite element simulation The first strength theory was applied in this paper. This theory holds that the maximum tensile stress was the decisive factor for brittle fracture of materials. Regardless of the stress state of materials, the brittle fracture would occur if the first principal stress (σ1) reaches the extreme stress (σb) of materials. Considering the safety factor (n), the allowable flexural tensile stress (fr) can be calculated: fr = σb/n. Therefore, the fractured condition of the brittle materials can be expressed by: σ1≤fr. Meanwhile, the concrete slab is brittle material, and its compressive strength is greater than the flexural tensile strength. Therefore, the flexural tensile strength is the decisive factor for the concrete slab, which is to meet the requirement of the first strength theory. In a word, σ1 of the concrete slab was compared with the fr of the concrete slab to
Table 3 Bending experiments results of concrete beam specimen. Specimen
h /cm
Failure load /kN
Average failure load /kN
Average flexural tensile strength /Mpa
Variance
66.5
3.18
0.15
68.4
3.28
0.16
76.9
3.69
0.17
93.1
4.47
0.16
Flexural tensile strength/Mpa First group
None
Second group
8
Third group
12
Fourth group
16
56.5 (A) 2.71 (A) 78.9 (A) 3.78 (A) 87.4 (A) 4.20 (A) 103.6 (A) 4.97 (A)
76.1 3.65 67.8 3.25 77.2 3.71 92.8 4.45
(B) (B) (B) (B) (B) (B) (B) (B)
66.9 3.19 58.5 2.81 66.1 3.17 82.9 3.98
(C) (C) (C) (C) (C) (C) (C) (C)
4
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Fig. 4. The snow-melting experiments of concrete slab.
Fig. 5. Concrete slab used in the melting experiment: (a) Planform of the concrete slab (b) I-I section of concrete slab.
Design of Highway Cement Concrete Pavement (JTG D40-2011), the design characteristic minimum value of cement concrete flexural tensile strength was 5.0 MPa. Combined with the experimental results in 3.1 section: The electric heat pipe can improve the flexural tensile strength of concrete. Therefore, the fr was chosen as 5.5 MPa. The mathematical relationship between σ1 and fr can be expressed: σ1 ≤ fr = 5.5MPa.
determine whether there was a fracture possibility of the concrete slab, the mathematical relationship can be expressed: σ1 ≤ σ = fr. To obtain fr, the bending experiments of the concrete specimens were conducted. The Portland cement was used in these experiments. The nine groups of concrete specimens (550× 150×150 mm) with the different W/C and sand rate were prepared at 28 days. There were three parallel specimens in each group. The experimental design and the corresponding bending experimental results were presented in Table 6. According to the results, the average flexural tensile strength of all the specimens was close to 5.5 MPa. Meanwhile, in the Specification for
4.1.2. Modeling hypothesis The three-dimensional finite element model established with ABAQUS. The size of pavement concrete was 4×3×0.25 m. The 5
Cold Regions Science and Technology 165 (2019) 102806
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Fig. 6. Strain of concrete slab: (a) scheme I (b) scheme II (c) scheme III (d) scheme IV.
modeling is performed based on the following hypothesis:
Table 5 The melting rate of the concrete slab. Experimental schemes
Heating power of concrete slab/W
Ambient temperature/°C
Melting rate/ kg/h
I II III IV
416.9 335.9 591.7 414.3
-1~-4 -1~-4 -1~-4 -1~-4
2.482 1.701 2.974 2.564
(1). The theory of elastic half-space foundation thin plate is adopted. Pavement structure layer is assumed uniform in thickness and infinite in the horizontal direction. The material of each layer is homogeneously isotropic and a linear elastic body. (2). The deadweight of pavement materials is negligible. (3). The stress and strain of concrete slab at work were mainly studied without considering the load transfer capacity between slabs.
Table 6 The bending experiment results of the concrete specimens.
4.2. The stress analysis for SMP-EHP under the extreme steady melting state
Group
Sand rate
W/C
I
II
III
Average flexural tensile strength/Mpa
Variance
1 2 3 4 5 6 7 8 9
32 34 36 32 34 36 32 34 36
0.39 0.39 0.39 0.41 0.41 0.41 0.43 0.43 0.43
5.06 5.65 5.72 4.97 5.44 5.81 5.54 5.45 5.25
5.74 5.12 5.45 5.84 4.96 5.43 5.17 5.71 5.71
5.43 5.52 5.24 5.39 5.86 5.23 5.61 5.20 5.51
5.41 5.43 5.47 5.40 5.42 5.49 5.44 5.45 5.49
0.077 0.051 0.039 0.126 0.135 0.058 0.037 0.043 0.035
4.2.1. Definition of the extreme steady melting state The temperature gradient between the internal high temperature, which caused by the electric heat pipe, and the external low temperature of pavement surface will significantly increase the pavement temperature stress. Temperature stress increases as the temperature gradient increases. Therefore, the minimum temperature of the pavement surface and the maximum temperature of the electric heat pipe were coupled to simulate an extreme steady melting state. If the concrete slab containing electric heat pipe can meet the requirement under this most unfavorable condition: σ1 ≤ fr = 5.5MPa, the schemes can be regarded as qualified. When the SMP-EHP works, the temperature of the pavement structure gradually increases until the pavement surface temperature meets the melting requirement. The temperature change of the electric heat pipe and pavement surface was a dynamic process. For the 6
Cold Regions Science and Technology 165 (2019) 102806
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Fig. 7. Schematic diagram of the temperature measurement position of the electric heat pipe and concrete slab (unit: cm).
pavement surface was set as 1 °C, and the temperature of the electric heat pipe was set as 35 °C. The frozen soil temperature below 1.4m for subgrade surface was set as -1.5 °C. The constraints were added to the X direction (X=0) and the Y direction (Y=0) respectively. The constraints were added to the bottom of the subgrade (X=0, Y=0, Z=0).
convenience of calculation and analysis, it was assumed that the melting process had reached a steady melting state after a period, namely the temperature change range of the electric heat pipe and the pavement surface was very small during the melting period. The heat exchange of the SMP-EHP has entered an equilibrium state. To obtain the temperature change range of the electric heat pipe and pavement surface in the steady melting state, the snow-melting experiments of the concrete slab were conducted, as shown in the 3.2 section. To ensure the accuracy of the experimental data, the thermocouple was placed in the position of 25 cm, 55 cm and 85 cm of each electric heat pipe, respectively, and the average value of them was taken as the real-time temperature. The thermocouple was used to measure the surface temperature of the concrete slab, and the average value of all test points was taken as the real-time surface temperature. The temperature measurement position of the electric heat pipe and concrete slab were shown in Fig. 7. In these experiments, the snow-melting process had reached a steady melting state after two hours of heating. When entering the steady melting state, the temperature of the electric heat pipe and concrete slab were measured every half an hour (0h, 0.5h, 1h, 1.5h, 2h, 2.5h, 3h), as shown in Fig. 8. Among them, 0 hour means just entering the steady melting state. From Fig. 8, the temperature range of the electric heat pipe is 25 °C-35 °C, and the surface temperature range of the concrete slab is 1 °C-3 °C for the I-IV schemes. Therefore, the maximum temperature of the pavement surface is 35 °C, and the minimum temperature of the electric heat pipe is 1 °C. The above surface temperature of the concrete slab and the temperature of the electric heat pipe were coupled to simulate an extreme steady melting state, which defined as the most unfavorable condition.
4.2.3. Simulation results and analysis Through the stress analysis of the concrete slab for the SMP-EHP under the most unfavorable conditions, σ1 of the concrete slab with different pre-embedding schemes were obtained, as shown in Table 6. The temperature stress field of scheme 2 was as shown in Fig. 9. From Table 2, the d1 in schemes 1, 4, 6 and 7 are all 18cm, so they are chosen to study the effect of h on the stress of the concrete slab. As shown in Table 7, the σ1 increases as the h decreases and its variation are larger. Additionally, there is a possibility of slab fracture for scheme 6 and 7 because σ1 has exceeded 5.5 MPa. Therefore, the larger h is preferred, and the change of h has a great influence on σ1. The h in schemes 2, 3 and 4 are all 12 cm, so they are chosen to study the effect of d1 on the stress of the concrete slab. As shown in Table 7, the σ1 decreases as the d1 decreases and its variation are smaller. Therefore, the smaller d1 is preferred, and the change of d1 has litter influence on σ1. In a word, the change of h has a great influence on σ1, while the change of d1 has a relatively small influence on it. Therefore, the design criteria of EHP-ES was proposed: the range of h should be considered firstly, followed by the range of d1. The EHP-ES in the extreme steady melting state were obtained, as shown in Table 8. To obtain the EHP-ES, firstly, the initial EHP-ES were informed by coupling the initial range of d1 and the initial range of h. Secondly, the σ1 of the concrete slab was calculated with different initial EHP-ES under the extreme steady melting state. Then, the numerical relationship between σ1 and fr were compared. If the concrete slab containing the electric heat pipe can meet the requirement under this most unfavorable condition: σ1 ≤ fr = 5.5MPa, the schemes can be regarded as qualified. Finally, the extreme EHP-ES were obtained. Based on the extreme EHP-ES, the range of h and the range of d1 can be obtained under the extreme steady melting state. According to the design criteria of electric heat pipe embedding schemes for SMP-EHP, the range of h should be considered firstly, followed by the range of d1. In other words, the range of d1 needs to be determined by the range of h. From Part I in Table 7 and the initial range of h, the range of h was 12.0-20.0 cm. Based on the range of h obtained above and part II, the range of d1 was 15.4 cm-30.0 cm.
4.2.2. Boundary conditions of finite element simulation Under the most unfavorable condition, the temperature of the
4.3. The stress analysis for SMP-EHP under extreme temperature drop condition 4.3.1. Definition of extreme temperature drop condition The test road was paved between Maizhokunggar and Gongbo’gyamda in Tibet, where the altitude (4700m) is high and the
Fig. 8. The temperature of the electric heat pipe and concrete slab surface at a different phase of steady melting state (unit: °C). 7
Cold Regions Science and Technology 165 (2019) 102806
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Fig. 9. Temperature stress field of scheme 2 (unit: MPa).
between day and night in winter was 25 °C. If the concrete slab of SMPEHP can meet the above expression (σ1 ≤ fr = 5.5MPa) under the most unfavorable condition, the scheme can be regarded as qualified.
Table 7 First principal stress of concrete slab under the extreme steady melting state. Scheme
1
2
3
4
5
6
7
σ1/Mpa
3.970
4.562
5.068
4.845
4.304
5.552
5.972
4.3.2. Boundary conditions of finite element simulation According to the Fig. 10 (b), the average value of wind speed (V) was 4 m/s. The relationship between the convective heat transfer coefficient (Z) of a concrete slab and the wind speed can be expressed by the following formula (Clarke, 1985):
Table 8 The EHP-ES under the extreme steady melting state. Part I
Part II
Z = 5.678 × [a + c (V /0.304) N ] Minimum value of h /cm
σ1/Mpa
h /cm
Minimum value of d1 /cm
σ1/Mpa
6.0 10.0 14.0 18.0 30
12.0 10.0 7.7 5.3 3.8
5.5001 5.4989 5.5002 5.4997 5.4999
6.0 10.0 14.0 18.0 20.0
19.5 16.8 13.3 6.9 4.2
5.4988 5.4981 5.5021 5.4928 5.4902
(4)
when 0 ≤ V ≤ 4.88, a= 1.09, c=0.23, N=1; When 4.88 ≤ V ≤ 30.48, a=0, c=0.53, N=0.78. Therefore, the convective heat transfer coefficient was 24 W/(m2·°C). The temperature of the pavement surface was set as 1 °C, and the temperature of the heat pipe was set as 35 °C. The frozen soil temperature below 1.4 m for subgrade surface was set as -1.5 °C. The constraints were added to the X direction (X=0) and the Y direction (Y=0) respectively. The constraints were added to the bottom of the subgrade (X=0, Y=0, Z=0). The ambient temperature was reduced from 5 °C to -20 °C within 12 hours.
temperature difference between day and night (25°C) is relatively large in winter. Additionally, the mechanical properties of a special structure for SMP-EHP have a strong sensitivity to temperature, so it is necessary to analyze the influence of temperature difference on the mechanical properties of the concrete slab. To obtain the temperature data of the test road, a mini-type weather station was set up, as shown in Fig. 10 (a). According to the temperature data from the mini-type weather station for five years, the maximum value of the temperature difference between day and night in winter usually occurs from January each year. Therefore, the temperature change of these seven days of January was taken as a representative environment condition to study the stress distribution of the concrete slab under the extreme temperature drop condition. From the Fig. 10 (b), the maximum value of temperature difference
Wind speed/m/s
4.3.3. Simulation results and analysis Through the stress analysis of concrete slab for the SMP-EHP under the most unfavorable conditions, σ1 of the concrete slab was obtained by simulating the working conditions of the concrete slab with different pre-embedding schemes, as shown in Table 8. The temperature stress field of scheme 2 was shown in Fig. 11. From Table 2, the d1 in schemes 1, 4, 6 and 7 are all 18cm, so they are chosen to study the effect of h on the stress of the concrete slab. As shown in Table 9, the σ1 increases as the h decreases and its variation are larger. Additionally, the σ1 of scheme 7 is close to 5.5MPa. It shows that the larger h is preferred and the change of h has a great influence on the σ1. 6
30
Wind speed
25
4
20
2
15
Temperature
0
10 5
-2
0
-4
-5 -10
-6
-15
-8 -10 00:00
-20 24:00
48:00
72:00
96:00
Temperature/°C
d1 /cm
-25 120:00 144:00 168:00
Time/h
(a)
(b)
Fig. 10. Mini-type weather station and the testing data: (a) Mini-type weather station (b) Test date from the mini-type weather station in winter. 8
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Fig. 11. Temperature stress field of scheme 2 (unit: MPa).
6. Field experiment
Table 9 First principal stress of concrete slab under the extreme temperature drop condition. Scheme
1
2
3
4
5
6
7
σ1/MPa
3.064
4.693
5.481
4.816
4.445
5.117
5.492
6.1. SMP-EHP construction in Tibet To further verify the feasibility of the reasonable EHP-ES for SMPEHP, a test road was paved in Tibet, as shown in Fig. 12. Two different sizes of concrete slabs were designed. One of the concrete slabs has a size of 0.9 × 0.9 × 0.25 m, which is consistent with the size of the concrete slab used in the laboratory experiments. The other concrete slabs have a size of 4 × 3 × 0.25 m, which is consistent with the size of the concrete slab used in the finite element simulation. The pre-embedding schemes of field experiment as shown scheme V in Table 2. The mix proportion design of concrete slab was the same as that of laboratory experiments.
The h in schemes 2, 3 and 4 are all 12cm, so they are chosen to study the effect of d1 on the stress of the concrete slab. As shown in Table 9, the σ1 increases as the d1 decreases and its variation are smaller. Additionally, there is a possibility of slab fracture for scheme 3 because the σ1 of concrete slab has exceeded 5.5 MPa. It shows that the larger d1 is preferred and the change of d1 has small influence on the σ1. In the same way as the method above (in 4.2.3 section), the EHP-ES under the extreme temperature drop condition were obtained, as shown in Table 10. Based on the design criteria and Table 10, the range of h was 14.0 cm-20.0 cm and the range of d1 was 11.7 cm-30.0 cm is preferred.
6.2. Snow-melting experiments The snow-melting experiments were conducted to evaluate the reasonableness of EHP-ES. The thickness of the accumulated snow was 5 cm. The heating time was 5 hours. The heating power of the concrete slab in the experiments was 533 W. The snow-melting experiments of the small concrete slab were completed at an ambient temperature of -1 °C to -4 °C. The process of snow-melting of small concrete slab was as shown in Figs. 13 (a) and 13 (b). The process of snow-melting of large concrete slab was as shown in Figs. 14 (a) and 14 (b). Figs. 13 (c) and 14 (c) illustrates the compressive strain changes of the two kinds of concrete slabs. To keep in line with the laboratory experiments, the results of small concrete slabs are selected and analyzed in this paper. It could be observed that the maximum compressive strain appears at 16 cm, while the minimum compressive strain appears at 5 cm. This phenomenon is consistent with the compressive strain variation in laboratory experiments. Namely the closer to the heat source, the greater the compressive strain of the concrete slabs. It is also found that the maximum compressive strain of concrete slabs during heating is 40.5με. Based on the related research (Liu et al., 2017b), it can be found that when the compressive strain of the concrete slab is 40.5με, the damage factor D is 0.015, which is much smaller than the damage factor when it reaches complete failure (when D = 1, it means that the material is failure completely.). Additionally, the snow on the concrete slab can melt completely within 5 hours, and more than 70% of the area on the concrete slab surface is in a dry state. The snowflakes melted into water as soon as it fell on the concrete slab. Therefore, EHPES are reasonable and feasible. The research results could efficiently guide the design of EHP-ES from the aspect of mechanical properties in cold regions.
5. Recommendations for reasonable EHP-ES In a word, it can be clearly seen that the phenomenon of "internal expansion and external contraction" caused by internal high temperature and external low ambient temperature has a great impact on pavement structure. Based on the results of the bending experiments of concrete beam specimens, it can be found that the heat pipe can increase the flexural tensile strength of the concrete, and the flexural tensile strength increases as the h increases. However, the snow-melting experiment of the concrete slab found that when the 12 cm ≤ d1 ≤ 18 cm, the melting efficiency is not satisfied when h > 16 cm. It is also interesting to note that the compressive strain of concrete slabs increases with the decrease of d1 when h is fixed. Additionally, based on the finite element simulation results under the extreme conditions, the design criteria of EHP-ES was proposed: the range of h should be considered firstly, followed by the range of d1. Finally, the reasonable EHPES were obtained based on the finite element simulations and the laboratory experiments, as shown in Table 11.
Table 10 The EHP-ES under the extreme temperature drop condition. Part I
Part II
d1 /cm
Minimum value of h /cm
σ1/MPa
h /cm
Minimum value of d1 /cm
σ1/MPa
6.0 10.0 14.0 18.0 30.0
14.0 13.2 10.4 5.4 3.6
5.4999 5.4939 5.5040 5.5004 5.499
6.0 10.0 14.0 18.0 20.0
18.0 15.2 11.7 6.0 4.2
5.5002 5.4999 5.5001 5.5001 5.5002
7. Conclusion To obtain reasonable EHP-ES in cold regions, the mechanical properties of the concrete slab for SMP-EHP were studied by laboratory experiments and simulations. The feasibility of the reasonable EHP-ES was verified by the test road in Tibet. The main conclusions are as 9
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Table 11 The reasonable EHP-ES. Type
Laboratory experiments
Research content Research results Recommendation results
h/cm d1/cm
Finite element simulations
Bending experiments
Melting experiments
Extreme steady melting state
Extreme temperature drop condition
Flexural tensile strength 12.0-20.0 / 14.0 cm ≤ h ≤ 16cm 12.0 cm ≤ d1 ≤ 18.0 cm
Compressive strain 6.0-16.0 12.0-18.0
First principal stress 12.0-20.0 15.4-30.0
First principal stress 14.0-20.0 11.7-25.0
Fig. 12. SMP-EHP construction: (a) Base paving (b) Placing XPS slab (c) Finished casting.
follow:
• The
•
bending experiments results show that the flexural tensile strengths of concrete beam specimens can be improved by an electric heat pipe, and its flexural tensile strengths increase with the increasing of h. The melting experiments results show that the absolute value of the compressive strain of the concrete slab increases with the decreases of the d1. Through the finite element analysis of the SMP-EHP model under
•
two most unfavorable conditions, it was found that the σ1 of concrete slab increases with the decrease of h and d1 of the electric heat pipe. At the same time, the design criteria of the EHP-ES were summarized: The h should be considered firstly, followed by the d1. Based on the results of the laboratory experiments and finite element method, the reasonable EHP-ES were obtained: 14.0 cm ≤ h ≤ 16cm, 12.0 cm ≤ d1 ≤ 18.0 cm. Additionally, the feasibility of the reasonable EHP-ES was verified by a test road in Tibet.
Appendices Nomenclature
a,c,N b C d1 d2 EHP-ES f
The calculation coefficients for the convective heat transfer coefficient The width of the specimen (mm) The specific heat capacity of snow (J /(kg°C)) The embedded depth of electric heat pipe (cm) The distance between the transverse joint of the concrete slab and the center of the electric heat pipe (cm) Electric heat pipe embedding schemes The flexural tensile strength of beam specimen (Mpa)
Fig. 13. Snow-melting experiments of small concrete slab: (a) Initial time (b) 5hour heating (c) Compressive strain of concrete slab. 10
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Fig. 14. Snow-melting experiments of large concrete slab: (a) Initial time (b) 5hour heating (c) Compressive strain of concrete slab. fr F h H HS L M n P Q SMP-EHP SMP-EHS t V Z σ1 σb ΔT
The allowable flexural tensile stress (MPa) The failure load of the beam specimen (N) The embedded depth of electric heat pipe (cm) The height of the specimen (mm) The heat of fusion of snow (J/kg) The distance between the two fulcra (mm) The weight of snow (kg) Safety factor Heating power of snow-melting experiments (W) Total energy required to melt snow (J) Snow-melting pavement with electric heat pipe Snow-melting pavement with electric heating system Heating time of snow-melting experiments (hour) The wind velocity (m/s) The convective heat transfer coefficient (W/m2∙K) First principal stress (MPa) Extreme stress (MPa) The temperature difference between the initial temperature of snow and 0 °C (°C)
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Design of electric heat pipe embedding schemes for snow-melting pavement based on mechanical properties in cold regions
T
⁎
Kai Liua, , Chaoliang Fua, Hongzhou Xiea, Fang Wangb, Xuancang Wangc, Haijian Baia a
School of Automobile and Traffic Engineering, Hefei University of Technology, Hefei 230009, China School of Civil Engineering, Anhui Jianzhu University, Hefei 230601, China c College of Highway, Chang’an University, Xi’an 710061, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Snow-melting pavement Embedding schemes Mechanical properties Finite element Cold regions
To obtain reasonable electric heat pipe embedding schemes (EHP-ES) of the snow-melting pavement in cold regions, the mechanical properties of the snow-melting pavement with electric heat pipe (SMP-EHP) were investigated by laboratory experiments and finite element simulations. The bending experiments and melting experiments were conducted to analyze the effect of EHP-ES on the mechanical properties of the concrete slab. Additionally, the finite element model was established to simulate the actual SMP-EHP in cold regions. The allowable flexural tensile strength of cement concrete was used as the judgment index to determine the reasonableness of EHP-ES. In this case, the mechanical properties of concrete slabs with different EHP-ES were studied under two most unfavorable conditions. Based on the experimental and simulated results, the design criteria of the EHP-ES was proposed, and the reasonable EHP-ES (embedding depth: 14.0-16cm, embedding spacing: 12.0 cm-18.0 cm) were obtained. Finally, a test road in Tibet was paved to verify the feasibility of the above reasonable EHP-ES further. The research results could enrich the design of EHP-ES for snow-melting pavement in cold regions from the aspect of the mechanical properties of the concrete slab.
1. Introduction In winter, accumulated snow and ice on the road is difficult to sweep, which seriously affect the transportation and hinder economic development, especially in cold regions. To mitigate these problems, many methods, such as mechanical, chemical (Kelly et al., 2010; Aghazadeh et al., 2012; Gutchess et al., 2016; Lee et al., 2017) or thermal, have been made in the past time and alternatives are still being investigated. In recent years, the thermal method, which including solar energy (Daniels et al., 2019; Pan et al., 2015), circulating heat fluid (Xu and Tan, 2015; Asfour et al., 2016), geothermal energy and heat pump (Wang et al., 2017; Kong et al., 2019; Balbay and Esen, 2013; Lai et al., 2018), electric heating system (Vo et al., 2015; Lai et al., 2016; Li et al., 2013; Nuijten and Hoyland, 2017) has been drawn more and more attention. In the above mentioned thermal method, the snow-melting pavement with the electric heating system (SMP-EHS) has offered an efficient and easily controllable way to solve the problems mentioned above. In the open literature, for the design of the embedding schemes of SMP-EHS, researchers conducted extensive studies on these aspects of snow-melting efficiency (Lai et al., 2014; Abdualla et al., 2016),
⁎
energy consumption (Li et al., 2013; Yang et al., 2012; Liu et al., 2017a) and temperature distribution (Won et al., 2014; Zhao et al., 2011; Lai et al., 2015). Lai et al. proposed the reasonable embedded depth of carbon fiber grille and embedded spacing of heating wires and applied the criterion of snow-free area ratio to evaluate snow-melting performance (Lai et al., 2014). Abdulla et al. identified the requirements of an electrically conductive concrete heated pavement system and tested to determine its performance (Abdualla et al., 2016). Li et al. investigated a self-deicing road system with electro-thermal materials and validated its low energy consumption (Li et al., 2013). Yang et al. developed the design of the heating panel with carbon fiber tape and conducted a deicing experiment to examine the energy consumption of the system (Yang et al., 2012). Liu et al. analyzed the relationship between energy consumption and embedded depth and embedded spacing in two phases through thermal simulation and experiments (Liu et al., 2017a). Won et al. studied the temperature distribution of the early-opening conductive heated pavement system through heat transfer and investigated the embedded spacing of copper plates (Won et al., 2014). Zhao et al. studied the temperature distribution on a representative section for the different embedded spacing of carbon fiber heat wires and determined the maximum allowed the embedded spacing of carbon
Corresponding author. E-mail address: [email protected] (K. Liu).
https://doi.org/10.1016/j.coldregions.2019.102806 Received 11 September 2018; Received in revised form 21 April 2019; Accepted 4 June 2019 Available online 11 June 2019 0165-232X/ © 2019 Elsevier B.V. All rights reserved.
Cold Regions Science and Technology 165 (2019) 102806
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fiber heating wires (Zhao et al., 2011). Lai et al. systematically investigated the structure type, heating power and temperature field distribution of snow-melting heated pavement in the tunnel portal and presented the embedded spacing of heat cable (Lai et al., 2015). In a word, most researchers designed the embedding schemes of SMP-EHS from the aspects of snow-melting efficiency, energy consumption, temperature distribution and so on. However, the temperature difference between the internal high temperature, which caused by the electric heating system, and external low temperature of pavement surface will significantly increase the pavement temperature extreme stress and accelerate pavement damage (Joško et al., 2014; Liu et al., 2017b). In this case, it is necessary to design the embedding schemes of SMP-EHS from the aspect of mechanical properties, to enrich the existing research. In this paper, the laboratory experiments will be conducted to study the influence of the embedded depth and embedded spacing on concrete slab mechanical properties. A model of snowmelting pavement with electric heat pipe (SMP-EHP) will be established, which includes all the actual properties of the components of an existing test road. Then the finite element simulations of the model were studied under two most unfavorable conditions. Finally, a test road will be paved in Tibet. The research results will provide the foundation for the design of electric heat pipe embedding schemes (EHP-ES) in cold regions based on mechanical properties.
structure was preferred. Therefore, for the design of SMP-EHP, the range of h (6 cm-20 cm) was selected as the initial range. Additionally, according to the Specifications for the design of highway cement concrete pavement (JTG D40-2011), the minimum embedded spacing of steel bars should be twice the maximum particle size of aggregates. In this paper, the maximum particle size of aggregate was 2.6 cm. Then the maximum transverse embedded spacing of plain round bars was 30cm. Therefore, the range of d1 (6 cm-30 cm) was selected as the initial range. Based on the initial range of h and d1, the pre-embedding schemes were obtained, as shown in Table 2. 3. Laboratory experiments 3.1. Bending experiments 3.1.1. Materials preparation and methods The cement used in this study was the 42.5-grade ordinary Portland cement. Two kinds of gravel with a particle size of 5-20 mm and 10-30 mm were used in the experiment. Among them, 5-20 mm gravel accounted for 53% of the quality of synthetic aggregate. The ratio of cement, sand and stone is 1:1.73:3.35, and the water-cement ratio is 0.41. The amount of water reducing agent is 0.75% by weight of the cement. Four groups of concrete beam specimen (550 mm×150 mm×250 mm) were prepared, of which only three groups were embedded with an electric heat pipe in the symmetrical center position. The value of h was 8 cm, 12 cm and 16 cm respectively. The electric heat pipe (diameter: 12 mm, length: 550 mm) was parallel to the length (550 mm) of the specimens. There were three parallel specimens (A, B, C) in each group. The specimens would be taken out after seven days of standard curing. The universal testing machine was applied, and the loading rate was 0.08 MPa/s. The flexural tensile strengths of concrete beam specimens were calculated as follows:
2. Structure and pre-embedding schemes 2.1. Structure of SMP-EHP The three-dimensional structure of SMP-EHP was shown in Fig. 1. From the bottom to top, the layers are, in order, frozen soil, subgrade, graded crushed stone subbase, cement stabilized macadam base, extruded polystyrene (XPS) slabs and pavement concrete. The electric heat pipes, which were perpendicular to the direction of the vehicle, were embedded in the pavement concrete (size: 4 m×3 m). The XPS slabs, which can mitigate the downward heat transfer and protect the frozen soil from melting, were paved below the pavement concrete. The parameters of the materials in the model were shown in Table 1 (Qin and Hiller, 2011; Liu et al., 2015).
f = FL/ bH 2
(1)
where f was the flexural tensile strength of specimen (Mpa); F was the failure load of the specimen (N); L was the distance between two fulcra (450 mm); b was the width of the specimen (150 mm); H was the height of the specimen (250 mm), as shown in Fig. 3 (a).
2.2. The electric heat pipe pre-embedding schemes
3.1.2. Analysis of experimental results The second group B was used as the research object to analyze the development of cracks during the experiment. The load-deformation curve of second group B was as shown in Fig. 3 (b). According to Fig. 3 (b), the value of deformation increases as the load increases at the beginning stage. With the increase of the load, there was an obvious crack at the bottom of the specimen. The load at this time was defined as the failure load. Then, the load was rise and fall as the deformation increases. At this point, the bending experiment was completed. The average failure load of the three specimens (A, B, C) was taken as the failure load of this group. The bending experimental results of the concrete specimens were as shown in Table.3. From Table 3, the flexural tensile strength of the second-fourth group is greater than that of the first group, and the flexural tensile strength of concrete specimen increases as the h increases. This is because the heat pipe is added to the concrete specimens similar to the steel bar added to the cement specimens, which can improve the flexural tensile strength of the concrete. Additionally, when h increases from 8 cm to 12 cm, the failure load of concrete beam specimens increases by 8.5 kN, and when h increases from 12 cm to 16 cm, the failure load of concrete beam specimens increases by 16.2 kN. It can be seen that the increment of the failure load of the concrete specimen was relatively small when h ≤ 12 cm. Therefore, to significantly improve the flexural tensile strength of concrete, 12 cm < h ≤ 20 cm is preferred, where the maximum value is the upper limit of the initial h in section 2.2.
The EHP-ES used in laboratory experiments and simulations were called pre-embedding schemes. The layout scheme of the electric heat pipe in the concrete slab was as shown in Fig. 2. The d1 represents the embedded spacing of electric heat pipe. The d2 represents the distance between the transverse joint of the concrete slab (size: 4×3×0.25 m) and the center of the electric heat pipe. The h was used to represent the embedded depth of the electric heat pipe. The electric heat pipe can be regarded as the steel bar in the concrete. Its safety and life were very important to the SMP-EHP. By consulting the code for design of concrete structure (GB 50010-2010), the minimum concrete cover thickness (5 cm) of the reinforced concrete
Fig. 1. Schematic diagram of the SMP-EHP. 2
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Table 1 Material properties of the SMP-EHP. Pavement structure
Pavement concrete XPS slab Cement stabilized macadam base Graded crushed stone subbase Subgrade Electric heat pipe
Density (g·cm)
Elastic modulus (Mpa)
Poisson ratio
3
Thermal conductivity [W/ (m·K)]
Linear expansion coefficient (10-5/°C)
Specific heat [J/ kg·K]
25 5 20
2.50 0.05 2.30
30000 15 1500
0.12 0.01 0.20
2.00 0.03 1.40
1.0 7.0 1.0
1005 38 900
20
2.10
250
0.30
1.00
0.5
840
600 1.2(diameter)
1.70 7.93
40 206000
0.35 0.30
1.00 12.10
0.5 1.6
2010 1.6
Thickness (cm)
The embedded depth of temperature strain gauges, which parallel to the electric heat pipe and close the 2#pipe, was 5 cm, 10 cm, 16 cm and 20 cm, respectively, as shown in Fig. 5. The density of snow is 300 kg/ m3. The heating time was 5 hours. The thickness of the snow is 5 cm. The weight of the snow was 12.15 kg. The snow-melting target is to melt all the snow in five hours. To melt all the snow in 5 hours, 2.43 kg of snow per hour should be melted at least. Therefore, it is necessary to calculate the total energy Q required to melt snow and the heating power P required for each slab, which can be expressed by formula (2) and (3):
Q = CM ΔT + MHS
(2)
P = Q/(3600 × t )
(3)
where C was the specific heat capacity of snow (J /(kg°C)); M was the weight of snow (kg); ΔT was the temperature difference between the initial temperature of snow and 0 °C (°C); HS was the heat of fusion (J/ kg); t was the heating time (hour). The minimum power of each concrete slab is 231.8 W by using formula (2) and formula (3). However, the heat of the concrete slab will be lost to the air after heating. Considering the effect of snow-melting, the minimum power required for snow–melting can be set at 40% to 70% of the actual working power of the slab (Wangzhi, 2014). Therefore, the range of heating power of concrete slabs in the experiments was 416.9 W (I), 335.9 W (II), 591.7 W (III) and 414.3 W (IV), respectively.
Fig. 2. Layout scheme of the electric heat pipe (unit: m).
3.2. Melting experiments 3.2.1. Materials preparation and methods The cement used in this study was the 42.5-grade ordinary Portland cement. The mass ratio of the material required for a concrete slab as shown in Table 4. Four concrete slabs were prepared based on Specification for Design of Highway Cement Concrete Pavement (JTG D402011). The size of each slab was 0.9 × 0.9 × 0.25 m. The embedding schemes were I-IV in Table 2. The preparation of concrete slabs and the experimental process were shown in Fig. 4. In the experiments, the surface temperatures of the concrete slabs and the electric heat pipe were measured by the thermocouples, and the temperature strain gauges were embedded in the concrete slab to monitor the strain of the concrete slab, as shown in Fig. 4 (3). To reduce heat loss, the XPS slabs were placed at the bottom of the concrete slabs, and the insulation foams were wrapped around the concrete slabs, as shown in Figs. 4 (4) and 4 (5). The walls of the containers of snow were formed by the XPS slabs. Then the plastic film was covered on the surface of the containers of snow to ensure that there was no leak around the container of snow, as shown in Fig. 4 (6). Finally, a water outlet was reserved for the containers of snow, and a container of water was placed at the water outlet to collect the water melted from snow. The experiments were completed at an ambient temperature of -1 °C to -4 °C.
3.2.2. Analysis of experimental results The compressive strains of the concrete slab were shown in Fig. 6. It can be seen that the maximum compressive strain of the scheme I appear at 16 cm, while the maximum compressive strain of the other three schemes appears at 10 cm. This is because the h in scheme II-IV is 12 cm, and the temperature strain gauge at 10 cm is the closest to the heat pipe. The closer to the heat source, the higher the temperature. As a result, the compressive strain caused by the internal high temperature is also greater. Additionally, the compressive strain of scheme II and scheme III is the smallest and largest respectively. Among them, the maximum compressive strain of the scheme III is 70.5με.This is attributed to the fact that the d1 of scheme III and scheme II is the smallest and largest respectively. As the d1 decreases, the amounts of electric
Table 2 Pre-embedding schemes of heat pipes. Simulations
1 2 3 4 5 6 7
Experiments
I II III IV V / /
d1/cm
18.0 25.0 12.0 18.0 16.7 18.0 18.0
h/cm
d2/cm
16.0 12.0 12.0 12.0 14.0 8.0 6.0
11.0 12.5 8.0 11.0 7.95 11.0 11.0
3
Number of the electric heat pipe 4×3×0.25 m
0.9×0.9×0.25 m
22 16 24 22 24 22 22
5 4 7 5 6 / /
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Fig. 3. Bending experiments of concrete beam specimen: (a) Experimental equipment and specimen (unit: mm) (b) Load-deformation curve of second group B.
heat pipes and the heating power increase. At the same heating time, the growth rate of the temperature difference between the interior and exterior of the concrete slab of scheme III is faster than other schemes. Therefore, the compressive strain of scheme III is the largest. Similarly, the scheme II is the smallest. In the open temperature, Liu et al. used the CDP model to reveal the relationship between compressive strains and damage factor D. Based on their research, it can be found that when the compressive strain of the concrete slab is 70.5με, the damage factor D is 0.025, which is much smaller than the damage factor when it reaches complete failure (when D = 1, it means that the material is failure completely.) (Liu et al., 2017b). Table 5 illustrates the melting rate of the concrete slab. It can be found that scheme II does not meet the snow-melting target, while scheme I, scheme III and scheme IV can meet the snow-melting target. Among them, the melting rate of scheme III is the largest, which is consistent with the law of compressive strain. This is because the heating power of scheme I, scheme III and scheme IV is larger than that of scheme II, and the heating rate and melting rate of concrete slabs are positively correlated with the heating power. It is also interesting to note that the melting rate of the scheme I is less than that of scheme IV. This is because the d1 of the scheme I and scheme IV is 18 cm, but the h of the scheme I and scheme IV is 16 cm and 12 cm respectively. The time required for heat to reach the surface of the concrete slab increases with the increase of h. As a result, the melting rate becomes slower. In a word, to reduce the stress damage of concrete slab, the larger d1 is preferred. If the melting efficiency is considered, the smaller d1 is preferred. Therefore, it is necessary to determine the appropriate range of d1 to balance the contradiction between melting efficiency and pavement damage. The d1 is 12 cm when the heating power is 591.7 W. In this case, increasing the heating power of concrete slabs (reducing the d1) will not only waste energy but also greatly affect the stability of frozen soil in cold regions and the mechanical properties of the pavement structure. Therefore, 12 cm is chosen as the lower limit of d1 can not only meet the melting efficiency but also minimize the pavement damage. The d1 is 18 cm when the heating power is 414.3 W. In this
Table 4 Ratio of the material required for a concrete slab. Material
Mass
Water/kg
43
Cement/kg
93
Sand/kg
159.5
Gravel/kg
Water reducer/kg
5-20mm
10-30mm
164
145.5
0.07
case, reducing the heating power of concrete slabs (increasing the d1) affect its melting efficiency. Therefore, 18 cm is chosen as the upper limit of d1. Actually, it can be seen from the above experiments that when the 12 cm ≤ d1 ≤ 18 cm, the melting efficiency is not satisfied when h > 16 cm. Therefore, regardless of the other factors, 6 cm ≤ h ≤ 16 cm is preferred, where the minimum value is the lower limit of the initial h in section 2.2. 4. The stress analysis of concrete slab for SMP-EHP under different most unfavorable conditions 4.1. Judgment index and modeling hypothesis 4.1.1. Judgment index of finite element simulation The first strength theory was applied in this paper. This theory holds that the maximum tensile stress was the decisive factor for brittle fracture of materials. Regardless of the stress state of materials, the brittle fracture would occur if the first principal stress (σ1) reaches the extreme stress (σb) of materials. Considering the safety factor (n), the allowable flexural tensile stress (fr) can be calculated: fr = σb/n. Therefore, the fractured condition of the brittle materials can be expressed by: σ1≤fr. Meanwhile, the concrete slab is brittle material, and its compressive strength is greater than the flexural tensile strength. Therefore, the flexural tensile strength is the decisive factor for the concrete slab, which is to meet the requirement of the first strength theory. In a word, σ1 of the concrete slab was compared with the fr of the concrete slab to
Table 3 Bending experiments results of concrete beam specimen. Specimen
h /cm
Failure load /kN
Average failure load /kN
Average flexural tensile strength /Mpa
Variance
66.5
3.18
0.15
68.4
3.28
0.16
76.9
3.69
0.17
93.1
4.47
0.16
Flexural tensile strength/Mpa First group
None
Second group
8
Third group
12
Fourth group
16
56.5 (A) 2.71 (A) 78.9 (A) 3.78 (A) 87.4 (A) 4.20 (A) 103.6 (A) 4.97 (A)
76.1 3.65 67.8 3.25 77.2 3.71 92.8 4.45
(B) (B) (B) (B) (B) (B) (B) (B)
66.9 3.19 58.5 2.81 66.1 3.17 82.9 3.98
(C) (C) (C) (C) (C) (C) (C) (C)
4
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Fig. 4. The snow-melting experiments of concrete slab.
Fig. 5. Concrete slab used in the melting experiment: (a) Planform of the concrete slab (b) I-I section of concrete slab.
Design of Highway Cement Concrete Pavement (JTG D40-2011), the design characteristic minimum value of cement concrete flexural tensile strength was 5.0 MPa. Combined with the experimental results in 3.1 section: The electric heat pipe can improve the flexural tensile strength of concrete. Therefore, the fr was chosen as 5.5 MPa. The mathematical relationship between σ1 and fr can be expressed: σ1 ≤ fr = 5.5MPa.
determine whether there was a fracture possibility of the concrete slab, the mathematical relationship can be expressed: σ1 ≤ σ = fr. To obtain fr, the bending experiments of the concrete specimens were conducted. The Portland cement was used in these experiments. The nine groups of concrete specimens (550× 150×150 mm) with the different W/C and sand rate were prepared at 28 days. There were three parallel specimens in each group. The experimental design and the corresponding bending experimental results were presented in Table 6. According to the results, the average flexural tensile strength of all the specimens was close to 5.5 MPa. Meanwhile, in the Specification for
4.1.2. Modeling hypothesis The three-dimensional finite element model established with ABAQUS. The size of pavement concrete was 4×3×0.25 m. The 5
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Fig. 6. Strain of concrete slab: (a) scheme I (b) scheme II (c) scheme III (d) scheme IV.
modeling is performed based on the following hypothesis:
Table 5 The melting rate of the concrete slab. Experimental schemes
Heating power of concrete slab/W
Ambient temperature/°C
Melting rate/ kg/h
I II III IV
416.9 335.9 591.7 414.3
-1~-4 -1~-4 -1~-4 -1~-4
2.482 1.701 2.974 2.564
(1). The theory of elastic half-space foundation thin plate is adopted. Pavement structure layer is assumed uniform in thickness and infinite in the horizontal direction. The material of each layer is homogeneously isotropic and a linear elastic body. (2). The deadweight of pavement materials is negligible. (3). The stress and strain of concrete slab at work were mainly studied without considering the load transfer capacity between slabs.
Table 6 The bending experiment results of the concrete specimens.
4.2. The stress analysis for SMP-EHP under the extreme steady melting state
Group
Sand rate
W/C
I
II
III
Average flexural tensile strength/Mpa
Variance
1 2 3 4 5 6 7 8 9
32 34 36 32 34 36 32 34 36
0.39 0.39 0.39 0.41 0.41 0.41 0.43 0.43 0.43
5.06 5.65 5.72 4.97 5.44 5.81 5.54 5.45 5.25
5.74 5.12 5.45 5.84 4.96 5.43 5.17 5.71 5.71
5.43 5.52 5.24 5.39 5.86 5.23 5.61 5.20 5.51
5.41 5.43 5.47 5.40 5.42 5.49 5.44 5.45 5.49
0.077 0.051 0.039 0.126 0.135 0.058 0.037 0.043 0.035
4.2.1. Definition of the extreme steady melting state The temperature gradient between the internal high temperature, which caused by the electric heat pipe, and the external low temperature of pavement surface will significantly increase the pavement temperature stress. Temperature stress increases as the temperature gradient increases. Therefore, the minimum temperature of the pavement surface and the maximum temperature of the electric heat pipe were coupled to simulate an extreme steady melting state. If the concrete slab containing electric heat pipe can meet the requirement under this most unfavorable condition: σ1 ≤ fr = 5.5MPa, the schemes can be regarded as qualified. When the SMP-EHP works, the temperature of the pavement structure gradually increases until the pavement surface temperature meets the melting requirement. The temperature change of the electric heat pipe and pavement surface was a dynamic process. For the 6
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Fig. 7. Schematic diagram of the temperature measurement position of the electric heat pipe and concrete slab (unit: cm).
pavement surface was set as 1 °C, and the temperature of the electric heat pipe was set as 35 °C. The frozen soil temperature below 1.4m for subgrade surface was set as -1.5 °C. The constraints were added to the X direction (X=0) and the Y direction (Y=0) respectively. The constraints were added to the bottom of the subgrade (X=0, Y=0, Z=0).
convenience of calculation and analysis, it was assumed that the melting process had reached a steady melting state after a period, namely the temperature change range of the electric heat pipe and the pavement surface was very small during the melting period. The heat exchange of the SMP-EHP has entered an equilibrium state. To obtain the temperature change range of the electric heat pipe and pavement surface in the steady melting state, the snow-melting experiments of the concrete slab were conducted, as shown in the 3.2 section. To ensure the accuracy of the experimental data, the thermocouple was placed in the position of 25 cm, 55 cm and 85 cm of each electric heat pipe, respectively, and the average value of them was taken as the real-time temperature. The thermocouple was used to measure the surface temperature of the concrete slab, and the average value of all test points was taken as the real-time surface temperature. The temperature measurement position of the electric heat pipe and concrete slab were shown in Fig. 7. In these experiments, the snow-melting process had reached a steady melting state after two hours of heating. When entering the steady melting state, the temperature of the electric heat pipe and concrete slab were measured every half an hour (0h, 0.5h, 1h, 1.5h, 2h, 2.5h, 3h), as shown in Fig. 8. Among them, 0 hour means just entering the steady melting state. From Fig. 8, the temperature range of the electric heat pipe is 25 °C-35 °C, and the surface temperature range of the concrete slab is 1 °C-3 °C for the I-IV schemes. Therefore, the maximum temperature of the pavement surface is 35 °C, and the minimum temperature of the electric heat pipe is 1 °C. The above surface temperature of the concrete slab and the temperature of the electric heat pipe were coupled to simulate an extreme steady melting state, which defined as the most unfavorable condition.
4.2.3. Simulation results and analysis Through the stress analysis of the concrete slab for the SMP-EHP under the most unfavorable conditions, σ1 of the concrete slab with different pre-embedding schemes were obtained, as shown in Table 6. The temperature stress field of scheme 2 was as shown in Fig. 9. From Table 2, the d1 in schemes 1, 4, 6 and 7 are all 18cm, so they are chosen to study the effect of h on the stress of the concrete slab. As shown in Table 7, the σ1 increases as the h decreases and its variation are larger. Additionally, there is a possibility of slab fracture for scheme 6 and 7 because σ1 has exceeded 5.5 MPa. Therefore, the larger h is preferred, and the change of h has a great influence on σ1. The h in schemes 2, 3 and 4 are all 12 cm, so they are chosen to study the effect of d1 on the stress of the concrete slab. As shown in Table 7, the σ1 decreases as the d1 decreases and its variation are smaller. Therefore, the smaller d1 is preferred, and the change of d1 has litter influence on σ1. In a word, the change of h has a great influence on σ1, while the change of d1 has a relatively small influence on it. Therefore, the design criteria of EHP-ES was proposed: the range of h should be considered firstly, followed by the range of d1. The EHP-ES in the extreme steady melting state were obtained, as shown in Table 8. To obtain the EHP-ES, firstly, the initial EHP-ES were informed by coupling the initial range of d1 and the initial range of h. Secondly, the σ1 of the concrete slab was calculated with different initial EHP-ES under the extreme steady melting state. Then, the numerical relationship between σ1 and fr were compared. If the concrete slab containing the electric heat pipe can meet the requirement under this most unfavorable condition: σ1 ≤ fr = 5.5MPa, the schemes can be regarded as qualified. Finally, the extreme EHP-ES were obtained. Based on the extreme EHP-ES, the range of h and the range of d1 can be obtained under the extreme steady melting state. According to the design criteria of electric heat pipe embedding schemes for SMP-EHP, the range of h should be considered firstly, followed by the range of d1. In other words, the range of d1 needs to be determined by the range of h. From Part I in Table 7 and the initial range of h, the range of h was 12.0-20.0 cm. Based on the range of h obtained above and part II, the range of d1 was 15.4 cm-30.0 cm.
4.2.2. Boundary conditions of finite element simulation Under the most unfavorable condition, the temperature of the
4.3. The stress analysis for SMP-EHP under extreme temperature drop condition 4.3.1. Definition of extreme temperature drop condition The test road was paved between Maizhokunggar and Gongbo’gyamda in Tibet, where the altitude (4700m) is high and the
Fig. 8. The temperature of the electric heat pipe and concrete slab surface at a different phase of steady melting state (unit: °C). 7
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Fig. 9. Temperature stress field of scheme 2 (unit: MPa).
between day and night in winter was 25 °C. If the concrete slab of SMPEHP can meet the above expression (σ1 ≤ fr = 5.5MPa) under the most unfavorable condition, the scheme can be regarded as qualified.
Table 7 First principal stress of concrete slab under the extreme steady melting state. Scheme
1
2
3
4
5
6
7
σ1/Mpa
3.970
4.562
5.068
4.845
4.304
5.552
5.972
4.3.2. Boundary conditions of finite element simulation According to the Fig. 10 (b), the average value of wind speed (V) was 4 m/s. The relationship between the convective heat transfer coefficient (Z) of a concrete slab and the wind speed can be expressed by the following formula (Clarke, 1985):
Table 8 The EHP-ES under the extreme steady melting state. Part I
Part II
Z = 5.678 × [a + c (V /0.304) N ] Minimum value of h /cm
σ1/Mpa
h /cm
Minimum value of d1 /cm
σ1/Mpa
6.0 10.0 14.0 18.0 30
12.0 10.0 7.7 5.3 3.8
5.5001 5.4989 5.5002 5.4997 5.4999
6.0 10.0 14.0 18.0 20.0
19.5 16.8 13.3 6.9 4.2
5.4988 5.4981 5.5021 5.4928 5.4902
(4)
when 0 ≤ V ≤ 4.88, a= 1.09, c=0.23, N=1; When 4.88 ≤ V ≤ 30.48, a=0, c=0.53, N=0.78. Therefore, the convective heat transfer coefficient was 24 W/(m2·°C). The temperature of the pavement surface was set as 1 °C, and the temperature of the heat pipe was set as 35 °C. The frozen soil temperature below 1.4 m for subgrade surface was set as -1.5 °C. The constraints were added to the X direction (X=0) and the Y direction (Y=0) respectively. The constraints were added to the bottom of the subgrade (X=0, Y=0, Z=0). The ambient temperature was reduced from 5 °C to -20 °C within 12 hours.
temperature difference between day and night (25°C) is relatively large in winter. Additionally, the mechanical properties of a special structure for SMP-EHP have a strong sensitivity to temperature, so it is necessary to analyze the influence of temperature difference on the mechanical properties of the concrete slab. To obtain the temperature data of the test road, a mini-type weather station was set up, as shown in Fig. 10 (a). According to the temperature data from the mini-type weather station for five years, the maximum value of the temperature difference between day and night in winter usually occurs from January each year. Therefore, the temperature change of these seven days of January was taken as a representative environment condition to study the stress distribution of the concrete slab under the extreme temperature drop condition. From the Fig. 10 (b), the maximum value of temperature difference
Wind speed/m/s
4.3.3. Simulation results and analysis Through the stress analysis of concrete slab for the SMP-EHP under the most unfavorable conditions, σ1 of the concrete slab was obtained by simulating the working conditions of the concrete slab with different pre-embedding schemes, as shown in Table 8. The temperature stress field of scheme 2 was shown in Fig. 11. From Table 2, the d1 in schemes 1, 4, 6 and 7 are all 18cm, so they are chosen to study the effect of h on the stress of the concrete slab. As shown in Table 9, the σ1 increases as the h decreases and its variation are larger. Additionally, the σ1 of scheme 7 is close to 5.5MPa. It shows that the larger h is preferred and the change of h has a great influence on the σ1. 6
30
Wind speed
25
4
20
2
15
Temperature
0
10 5
-2
0
-4
-5 -10
-6
-15
-8 -10 00:00
-20 24:00
48:00
72:00
96:00
Temperature/°C
d1 /cm
-25 120:00 144:00 168:00
Time/h
(a)
(b)
Fig. 10. Mini-type weather station and the testing data: (a) Mini-type weather station (b) Test date from the mini-type weather station in winter. 8
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Fig. 11. Temperature stress field of scheme 2 (unit: MPa).
6. Field experiment
Table 9 First principal stress of concrete slab under the extreme temperature drop condition. Scheme
1
2
3
4
5
6
7
σ1/MPa
3.064
4.693
5.481
4.816
4.445
5.117
5.492
6.1. SMP-EHP construction in Tibet To further verify the feasibility of the reasonable EHP-ES for SMPEHP, a test road was paved in Tibet, as shown in Fig. 12. Two different sizes of concrete slabs were designed. One of the concrete slabs has a size of 0.9 × 0.9 × 0.25 m, which is consistent with the size of the concrete slab used in the laboratory experiments. The other concrete slabs have a size of 4 × 3 × 0.25 m, which is consistent with the size of the concrete slab used in the finite element simulation. The pre-embedding schemes of field experiment as shown scheme V in Table 2. The mix proportion design of concrete slab was the same as that of laboratory experiments.
The h in schemes 2, 3 and 4 are all 12cm, so they are chosen to study the effect of d1 on the stress of the concrete slab. As shown in Table 9, the σ1 increases as the d1 decreases and its variation are smaller. Additionally, there is a possibility of slab fracture for scheme 3 because the σ1 of concrete slab has exceeded 5.5 MPa. It shows that the larger d1 is preferred and the change of d1 has small influence on the σ1. In the same way as the method above (in 4.2.3 section), the EHP-ES under the extreme temperature drop condition were obtained, as shown in Table 10. Based on the design criteria and Table 10, the range of h was 14.0 cm-20.0 cm and the range of d1 was 11.7 cm-30.0 cm is preferred.
6.2. Snow-melting experiments The snow-melting experiments were conducted to evaluate the reasonableness of EHP-ES. The thickness of the accumulated snow was 5 cm. The heating time was 5 hours. The heating power of the concrete slab in the experiments was 533 W. The snow-melting experiments of the small concrete slab were completed at an ambient temperature of -1 °C to -4 °C. The process of snow-melting of small concrete slab was as shown in Figs. 13 (a) and 13 (b). The process of snow-melting of large concrete slab was as shown in Figs. 14 (a) and 14 (b). Figs. 13 (c) and 14 (c) illustrates the compressive strain changes of the two kinds of concrete slabs. To keep in line with the laboratory experiments, the results of small concrete slabs are selected and analyzed in this paper. It could be observed that the maximum compressive strain appears at 16 cm, while the minimum compressive strain appears at 5 cm. This phenomenon is consistent with the compressive strain variation in laboratory experiments. Namely the closer to the heat source, the greater the compressive strain of the concrete slabs. It is also found that the maximum compressive strain of concrete slabs during heating is 40.5με. Based on the related research (Liu et al., 2017b), it can be found that when the compressive strain of the concrete slab is 40.5με, the damage factor D is 0.015, which is much smaller than the damage factor when it reaches complete failure (when D = 1, it means that the material is failure completely.). Additionally, the snow on the concrete slab can melt completely within 5 hours, and more than 70% of the area on the concrete slab surface is in a dry state. The snowflakes melted into water as soon as it fell on the concrete slab. Therefore, EHPES are reasonable and feasible. The research results could efficiently guide the design of EHP-ES from the aspect of mechanical properties in cold regions.
5. Recommendations for reasonable EHP-ES In a word, it can be clearly seen that the phenomenon of "internal expansion and external contraction" caused by internal high temperature and external low ambient temperature has a great impact on pavement structure. Based on the results of the bending experiments of concrete beam specimens, it can be found that the heat pipe can increase the flexural tensile strength of the concrete, and the flexural tensile strength increases as the h increases. However, the snow-melting experiment of the concrete slab found that when the 12 cm ≤ d1 ≤ 18 cm, the melting efficiency is not satisfied when h > 16 cm. It is also interesting to note that the compressive strain of concrete slabs increases with the decrease of d1 when h is fixed. Additionally, based on the finite element simulation results under the extreme conditions, the design criteria of EHP-ES was proposed: the range of h should be considered firstly, followed by the range of d1. Finally, the reasonable EHPES were obtained based on the finite element simulations and the laboratory experiments, as shown in Table 11.
Table 10 The EHP-ES under the extreme temperature drop condition. Part I
Part II
d1 /cm
Minimum value of h /cm
σ1/MPa
h /cm
Minimum value of d1 /cm
σ1/MPa
6.0 10.0 14.0 18.0 30.0
14.0 13.2 10.4 5.4 3.6
5.4999 5.4939 5.5040 5.5004 5.499
6.0 10.0 14.0 18.0 20.0
18.0 15.2 11.7 6.0 4.2
5.5002 5.4999 5.5001 5.5001 5.5002
7. Conclusion To obtain reasonable EHP-ES in cold regions, the mechanical properties of the concrete slab for SMP-EHP were studied by laboratory experiments and simulations. The feasibility of the reasonable EHP-ES was verified by the test road in Tibet. The main conclusions are as 9
Cold Regions Science and Technology 165 (2019) 102806
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Table 11 The reasonable EHP-ES. Type
Laboratory experiments
Research content Research results Recommendation results
h/cm d1/cm
Finite element simulations
Bending experiments
Melting experiments
Extreme steady melting state
Extreme temperature drop condition
Flexural tensile strength 12.0-20.0 / 14.0 cm ≤ h ≤ 16cm 12.0 cm ≤ d1 ≤ 18.0 cm
Compressive strain 6.0-16.0 12.0-18.0
First principal stress 12.0-20.0 15.4-30.0
First principal stress 14.0-20.0 11.7-25.0
Fig. 12. SMP-EHP construction: (a) Base paving (b) Placing XPS slab (c) Finished casting.
follow:
• The
•
bending experiments results show that the flexural tensile strengths of concrete beam specimens can be improved by an electric heat pipe, and its flexural tensile strengths increase with the increasing of h. The melting experiments results show that the absolute value of the compressive strain of the concrete slab increases with the decreases of the d1. Through the finite element analysis of the SMP-EHP model under
•
two most unfavorable conditions, it was found that the σ1 of concrete slab increases with the decrease of h and d1 of the electric heat pipe. At the same time, the design criteria of the EHP-ES were summarized: The h should be considered firstly, followed by the d1. Based on the results of the laboratory experiments and finite element method, the reasonable EHP-ES were obtained: 14.0 cm ≤ h ≤ 16cm, 12.0 cm ≤ d1 ≤ 18.0 cm. Additionally, the feasibility of the reasonable EHP-ES was verified by a test road in Tibet.
Appendices Nomenclature
a,c,N b C d1 d2 EHP-ES f
The calculation coefficients for the convective heat transfer coefficient The width of the specimen (mm) The specific heat capacity of snow (J /(kg°C)) The embedded depth of electric heat pipe (cm) The distance between the transverse joint of the concrete slab and the center of the electric heat pipe (cm) Electric heat pipe embedding schemes The flexural tensile strength of beam specimen (Mpa)
Fig. 13. Snow-melting experiments of small concrete slab: (a) Initial time (b) 5hour heating (c) Compressive strain of concrete slab. 10
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Fig. 14. Snow-melting experiments of large concrete slab: (a) Initial time (b) 5hour heating (c) Compressive strain of concrete slab. fr F h H HS L M n P Q SMP-EHP SMP-EHS t V Z σ1 σb ΔT
The allowable flexural tensile stress (MPa) The failure load of the beam specimen (N) The embedded depth of electric heat pipe (cm) The height of the specimen (mm) The heat of fusion of snow (J/kg) The distance between the two fulcra (mm) The weight of snow (kg) Safety factor Heating power of snow-melting experiments (W) Total energy required to melt snow (J) Snow-melting pavement with electric heat pipe Snow-melting pavement with electric heating system Heating time of snow-melting experiments (hour) The wind velocity (m/s) The convective heat transfer coefficient (W/m2∙K) First principal stress (MPa) Extreme stress (MPa) The temperature difference between the initial temperature of snow and 0 °C (°C)
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