Moisture absorption characteristics and thermal insulation performance of thermal insulation materials for cold region tunnels

Construction and Building Materials 237 (2020) 117765

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Moisture absorption characteristics and thermal insulation performance of thermal insulation materials for cold region tunnels Youyun Li a, Yongmei Sun a, Junling Qiu a, Tong Liu b,⇑, Li Yang a,c, Huidong She a a

Key Laboratory of Special Area Highway Engineering, Ministry of Education, Chang’an University, Xi’an 710064, China School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China c Sichuan Expressway Construction and Development Group Co., LTd, Si’chuan 610000, China b

h i g h l i g h t s
We Investigated the suitable isothermal hygroscopicity models of two kinds of materials.
We Studied the insulation performance of insulation material after moisture absorption.
We Proposed the correction value of thickness of insulation layer.

a r t i c l e

i n f o

Article history: Received 29 July 2019 Received in revised form 27 November 2019 Accepted 29 November 2019

Keywords: Thermal insulation material Moisture absorption Thermal insulation performance

a b s t r a c t Laying thermal insulation is one of the common thermal insulation measures to prevent frost damage of tunnels in cold regions and the performance of thermal insulation material directly determines the effectiveness of freeze-proofing and insulation of thermal insulation layer. As an important parameter for evaluating the performance of thermal insulation materials, thermal conductivity is generally affected by density, humidity, temperature and other factors, therefore this paper will mainly focus on when the air humidity in the tunnel is too high, the moisture absorption of insulation materials may occur in the humid environment for a long time, which will lead to the increase of moisture content of insulation materials. Hence tunnels in cold regions, generally exhibit lower temperature conditions, thus the water inside the insulation material is easy to freeze, which will greatly improve the thermal conductivity of the material and reduce its thermal insulation effect. Therefore, it is of great significance to study the thermal insulation performance of cold-regions tunnel thermal insulation materials after moisture absorption and complete freezing. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction With the strategic westward shift of China’s economic construction and the promotion of the development policy of the central and Western regions, the number of traffic projects built in high altitude and high latitude areas is increasing, including a large number of tunnels in cold regions [25,26,30,36]. Although a lot of measures have been taken in the design and construction of waterproofing and drainage of tunnels in cold regions, the problem of tunnel leakage has not been effectively solved due to various factors [21,28,31,38]. The theory of ‘‘ten tunnels and nine leaks” reflects the universality and seriousness of the leakage problem [33,54,55], (seen as Fig. 1). There are many reasons for tunnel freezing damage in cold region, among which the main reason is ⇑ Corresponding author. E-mail address: [email protected] (T. Liu). https://doi.org/10.1016/j.conbuildmat.2019.117765 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

that the original temperature field of tunnel surrounding rock in cold region is disturbed [24,25,39,41]. In order to reduce the disturbance to the original temperature field of surrounding rock and minimize the adverse effect of temperature, the thermal insulation layer is usually laid on the lining structure of tunnels in cold regions in China [22,27,50,56], (seen as Fig. 2). Therefore, experts and scholars have done a lot of research on thermal insulation materials [13,29,40,57]. Lai verified the necessity and effectiveness of thermal insulation material for Dabanshan tunnel in Qinghai Province by considering the coupling effect of the seepage field, temperature field and stress field [3]. Ma analyzed the influence of insulation layer location on insulation effect by establishing a numerical coupled heat and moisture transfer model for tunnels in seasonally frozen soil regions [2]. After considering the temperature and water state of the soil around the tunnel, Li obtained the optimum thickness of the tunnel insulation layer through a series of simulations [1]. Feng

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Y. Li et al. / Construction and Building Materials 237 (2020) 117765

Fig. 1. Tunnel lining icicle and pavement icing [37].

Fig. 2. Installation process of insulation layer [47].

developed a model test (seen as Fig. 3) to study the temperature changes of tunnels without thermal insulation materials and tunnels with thermal insulation materials of 5 cm thickness under freezing conditions, the results show that the insulation material with 5 cm thickness can only prevent 86.5% of the lowest temperature from transferring to surrounding rock on average [7]. Feng also found that the temperature of insulation layer, lining and surrounding rock is affected by atmospheric temperature, and the cor-

relation between the thickness of insulation layer and average temperature and formation temperature is obtained by fitting analysis method [7]. In order to overcome the problem that there is no measured temperature data in tunnel construction, Xia made full use of the topographic and meteorological conditions at the entrance and exit of the tunnel, and then proposed a method for calculating the length of the insulation layer [8]. Tan studied the freeze-proof and thermal insulation measures of Galongla Tunnel in Tibet by means of numerical simulation, and pointed out that laying 6 cm thermal insulation layer can effectively prevent the freezing damage of surrounding rock of the tunnel [9]. However, at present, the research on tunnel thermal insulation layer is based on the ideal condition of the thermal insulation material in the dry state to study its thermal insulation effect, without taking into account the adverse effects of external moisture on its thermal insulation effectiveness [53]. The influence of temperature and moisture content on thermal conductivity of thermal insulation material varies with the type of thermal insulation material, which depends on the composition, performance and internal structure of the material, which also determines the heat transfer mode and the ability of the material to accumulate moisture [36,43,48]. The thermal conductivity of materials, is one of the main parameters to measure the thermal insulation performance of materials, is also a factor area that needs greater research [32,34,49]. Taking a tunnel being excavated on the Qinghai-Tibet Railway as a calculation model, Zhang analyzed the influence of thermal insulation materials with different thermal conductivity on the temperature field of tunnel’s surrounding rock in cold region and found that thermal insulation materials with different thermal conductivity will only affect the freezing (melting) degree of surrounding rock, and will not affect the freezing and thawing development law of surrounding rock [4]. In a review, Basim Abu-Jdayi obtained the thermal conductivity of polyurethane insulation materials varies with water content. For example, the thermal conductivity of polyurethane increases from 0.025 w/(mk) to 0.046 w/(mk) with the increase of water content from 0% to 10% volume [6]. Battal Dog˘an measured the thermal conductivity of polystyrene materials at different temperatures by experiments, and determined the parameters affecting the thermal conductivity of polystyrene materials by combining experi-

Fig. 3. Structural diagram of model test [7].

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mental and numerical studies [10]. Beata Loboda examined the change of thermal conductivity of mineral wool after soaking and drying at a certain time interval to a constant mass. Statistical test results showed that moisture and re-dry had little effect on thermal conductivity of mineral wool [12]. Gur’ev has conducted research on fiber materials, result shows that moisture content has a great influence on the thermal conductivity of fiber materials [17]. In particular, according to the published literature, they learned that an increase of approximately 1% in the volume of water content in the fiber structure with a density of 150 kg/m3 would lead to an increase of 8% in the thermal conductivity [51]. Maatouk Khoukhi pointed out that the thermal conductivity K value of any material is a complex function affected by many factors, such as temperature, humidity and density, therefore, he studied the comprehensive effects of working temperature and moisture content on thermal conductivity. The results showed that the moisture content of polystyrene insulation material had a significant impact on its K value at different test temperatures [11]. Abdou experimentally studied the effect of water content on thermal conductivity of common fiber thermal insulation materials and found that the relationship between K value and water content was affected by the initial regulating water content level [5]. D’Alessandro placed thermal insulation of materials such as mineral wool and polyurethane foam in the climate room under relative humidity and tested the thermal conductivity of samples by hot disc apparatus to assess the effect of water content and the effect of different materials [16]. Although these studies involve the influence of moisture content on the thermal insulation performance of thermal insulation materials, there are relatively few studies on the thermal insulation performance of thermal insulation materials for tunnels in cold regions, which mainly considering that tunnels are underground closed structures, and the design of waterproof and drainage systems for tunnels is relatively perfect. However, in rainy season, the air humidity in tunnel is relatively high. For the thermal insulation layer laid on the surface of the second lining, it is vulnerable to the influence of humid air during this period, which makes its thermal insulation performance decline. In addition, the environment of tunnels in cold regions is extremely harsh and generally the lowest temperature is below 20 C. Under these conditions, the pore water inside the insulation layer is easily converted into ice, which makes the insulation layer material ineffective and may even become counterproductive to the insulation process. Owing to tunnels in cold regions pay more attention to the thermal insulation effect of thermal insulation layer at low temperature level, it is of practical significance to study the moisture absorption characteristics and thermal insulation performance of thermal insulation materials, at negative temperature in cold- regions.

2. Moisture absorption test 2.1. Materials and instruments The thermal insulation materials referenced in this paper are polyphenolic insulation board and polyurethane insulation board. The basic performance indicators of the materials are shown in Table 1. According to the requirement of material size in the test,

the size of the sample is determined to be 100 mm  100 mm  50 mm as shown in Fig. 4. The constant temperature and humidity box are shown in Fig. 5, and some technical parameters are shown in Table 2. 2.2. Test process (1) Sample drying and wrapping (Fig. 6(a)). The working temperature of the oven is set at about 60 °C (it is found that the material will change color when the temperature of the dried material reaches above 60 °C), and then the cut sample of thermal insulation material is dried in the instrument until the weight is basically stable, and then cooled in the drying cylinder to room temperature. Samples are wrapped around and on the top with fresh-keeping film and tape to reserve the bottom. The initial mass of the sample is recorded as m0. Finally, the dried and wrapped samples are stored in sealed bags to avoid the influence of air humidity. (2) The process of moisture absorption (Fig. 6(b)). The same temperature (12 °C) and different humidity of the constant temperature and humidity chamber should be adjusted in advance before the moisture absorption test of the sample begins. The dried and wrapped samples are put into the instrument, and the hygroscopic surface of the sample is kept upward. After a period of moisture absorption, the quality of the sample is measured and recorded until the sample of thermal insulation material reaches the stable moisture absorption state. By changing the humidity of the constant temperature and humidity box and repeating the above steps, the equilibrium moisture absorption of the sample under different humidity’s can be obtained. 2.3. Results and discussions From Fig. 7, it can be seen that the water content of thermal insulation materials under 35% RH, 65% RH and 95% RH has similar relationship with time. On the whole, the moisture absorption curve is relatively smooth, which can be roughly divided into three stages: rapid moisture absorption stage, stable moisture absorption stage and moisture absorption tending to saturation stage. Under different relative humidity conditions, the higher the relative humidity is, the greater the saturated moisture absorption rate after moisture absorption stabilization, and the longer the time required. The equilibrium moisture content of the sample is related to water activity and temperature. When the temperature is constant, it is isothermal moisture absorption but when the water activity is constant, it is isobaric moisture absorption. When the moisture content is constant, it is equal moisture absorption and the Isothermal moisture absorption curve is usually used in engineering. Foreign scholars Brunauer classified and summarized five typical isothermal equilibrium adsorption curves (Fig. 8) [14]. This classification is called BDDT classification. In Fig. 8, P is the partial pressure of water vapor on the surface of the material in equilibrium state, P0 is the saturated vapor pressure of pure water at the same temperature and pressure. P / P0 can be understood as water activity. Type I equilibrium humidity curve is due to the adsorption of monolayer. Type II is more common and type II is when multilayer adsorption or hydrophilic surface interaction occurs. Type III is

Table 1 Basic performance index of thermal insulation material. Material types

Thermal conductivity (W/(mK))

Density (kg/m3)

Compressive strength (kPa)

Fireproof performance (grade)

Volumetric water absorption (%)

Temperature range (°C)

Polyphenolic Polyurethane

0.022 ~ 0.035 0.022 ~ 0.030

25 ~ 60 25 ~ 80

100 150

B1 B2

 6.5 2

196 ~ 150 50 ~ 100

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Fig. 4. Insulation material samples.

Constant temperature water tank

Humidifier Humidity controller

Fig. 5. Constant temperature and humidity box.

Table 2 Some parameters of constant temperature and humidity box. Index

Parameter

Temperature range Temperature fluctuation Temperature Resolution Relative humidity Humidity error Size

0 ~ 60 °C ±1°C 0.1 °C 45%RH ~ 99%RH <6%RH 500 mm  500 mm  750 mm

Note: Relative humidity is the ratio of absolute humidity in air to saturated absolute humidity at the same temperature.

(a) Sample drying

(b) Sample hygroscopicity Fig. 6. Test process.

relatively rare and Type III is generally the adsorption of multimolecular layer on hydrophobic surface appears. Type IV and V are mostly reflections of capillary condensation. Fig. 9 shows the moisture absorption curve of two insulation materials at 12 °C. Fig. 9(a) shows that the equilibrium moisture content of polyphenolic insulation material increases rapidly when the relative humidity is lower than 35% RH. With the increase of relative humidity, the increase rate towards equilibrium moisture content is relatively slow, and the inflection point A appears in the corresponding curve. When the relative humidity exceeds 65% RH, the equilibrium moisture content increases tremendously, and the corresponding curve appears inflection point B. Through the analysis of isothermal adsorption curve of polyphenolic insulation materials, it can be concluded that the characteristics of isothermal adsorption curve of polyphenolic insulation materials coincide with type II isothermal adsorption curve of BDDT classification. Combining with the analysis of Fig. 10, with the increase of relative humidity in 0-A stage, single-layer hygroscopicity dominates, and the adsorbed water monolayer covers the skeleton. When the relative humidity continues to increase, the single layer moisture absorption reaches saturation state, and the second layer begins to form, which is then transformed into a multi-layer adsorption state, corresponding to the A-B stage in Fig. 9 (a). At this time, the slope of the curve decreases with the relative humidity, and the equilibrium moisture content increases slowly. When the relative humidity increases to a certain extent, which is the relative humidity corresponding to point B, the multi-layer adsorption ends. Thereafter, with the rapid increase of relative humidity, the equilibrium moisture content increases significantly, which is mainly caused by capillary phenomenon. Fig. 9(b) shows that when the relative humidity of polyurethane insulation material is lower than 50% RH, the increase of equilibrium moisture content is relatively slow. When the relative humidity exceeds 50% RH, the slope of the curve increases significantly, the equilibrium moisture content increases significantly, and the corresponding curve appears inflection point C. Through the analysis of isothermal adsorption curve of polyurethane thermal insulation materials, it can be concluded that the characteristics of isothermal adsorption curve of polyurethane thermal insulation materials coincide with that of type III isothermal adsorption curve in BDDT classification. According to the analysis of Fig. 10, the interaction force between adsorbate and adsorbate in type III isothermal adsorption curve is greater than that between solid particles and adsorbate. The interaction force between water molecules is stronger than that between polyurethane thermal insulation particles and water molecules, which make the monolayer adsorption get unsaturated, and the multilayer adsorption is accompanied by formation. After inflection point C, the hygroscopicity increases significantly, which is similar to the second half of the isothermal adsorption curve of type II and it can also be explained by the phenomenon of condensation in capillaries.

Y. Li et al. / Construction and Building Materials 237 (2020) 117765

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Fig. 7. Hygroscopicity curve of thermal insulation material under different humidity.

Fig. 8. Different types of isothermal equilibrium humidity curves [14].

(b) Fig. 9. Isothermal hygroscopicity curves of two kinds of thermal insulation materials.

2.4. Isothermal hygroscopicity model 2.4.1. Selection of fitting model The equilibrium humidity curves of polyphenolic and polyurethane insulation materials were fitted by six typical equilibrium moisture absorption models (seen in Table 3) using origin. The correlation coefficient R2, rms error RMSE and residual sum of squares RSS are selected as the evaluation indexes of model fitting effect [18].

2.4.2. Evaluation of model fitting effect 2.4.2.1. Polyphenolic. The fitting curve of isothermal moisture absorption curve of polyphenolic insulation material is shown in Fig. 11 (The symbol of water activity is ‘‘Aw” and ‘‘Aw” is equal to P / PO), and the corresponding model parameters and fitting effect evaluation index are shown in Table 4. Through analysis, the correlation coefficient R2 of fitting curve is Smith < Modified BET < Henderson < Halsey < Oswin < Peleg from small to large. The rms error RMSE and residual sum of squares RSS are

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Absorbing water on skeleton surface Solid skeleton

Free water

Water inside skeleton

Saturated wet air

Pore

(a) Dry state

(b) Wet skeleton state (c) Surface hygroscopicity (d) Free water hygroscopicity (e) Water-saturated state Fig. 10. Hygroscopicity of materials at different stages.

Table 3 Isothermal hygroscopicity model. Model

Expressions

Peleg

x ¼ aAw b þ cAw d

Henderson

h

wÞ x ¼  lnð1A a

i1 b

Halsey

x ¼ ½ lnðAa w Þ

Oswin

Aw x ¼ að1A Þ w x ¼ a  blnð1  Aw Þ aAw x ¼ 1bA w

1 b

b

Smith Modified BET

Fig. 12. Two successfully fitted models.

Foster proposed if the relative error between the predicted value and the real value of the model is less than 10%, it can be considered that the model has good applicability [15]. The relative errors between the predicted and real values of Peleg and Oswin models with better fitting degree are shown in Table 5, which shows that both models can be used to predict the isothermal hygroscopicity curve of polyphenolic insulation materials. Relatively speaking, Peleg model has higher precision, and its mathematical expression is as follows:

Fig. 11. Fitting curve of polyphenolic.

Smith > Modified BET > Henderson > Halsey > Oswin > Peleg from large to small. Therefore, Peleg model has the highest fitting degree, followed by Oswin model, but all of them are acceptable. The fitting effect of Peleg model and Oswin model is shown in Fig. 12.

x ¼ 7:6049Aw 0:4423 þ 7:3985Aw 9:0496

ð1Þ

2.4.2.2. Polyurethane. Fitting curve of isothermal hygroscopicity curve of polyurethane thermal insulation material is shown in Fig. 13. The corresponding model parameters and evaluation index

Table 4 Model parameters and evaluation indexes of polyphenolic. Model

Peleg Henderson Halsey Oswin Smith Modified BET

Parameters

Evaluation indexs

a

b

c

d

R2

RSS

RMSE

7.6049 0.0206 160.343 5.5109 2.3569 11.6432

0.4423 2.0337 3.2185 0.2657 3.4292 0.0239

7.3985 — — — — —

9.0496 — — — — —

0.9987 0.9826 0.9926 0.9972 0.8996 0.9159

0.1039 1.4487 0.5085 0.2305 8.3714 7.007

0.1218 0.4548 0.2695 0.1814 1.0935 1.004

Note: In the Peleg model, a, b, c and d are constants, b < 1, d > 1 [52].

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Y. Li et al. / Construction and Building Materials 237 (2020) 117765 Table 5 Comparison of predicted results. Water activity

Measured value

0.20 0.35 0.50 0.65 0.80 0.95

3.58 5.02 5.62 6.29 7.92 12.08

Peleg

Oswin

Predicted value

Relative error

Predicted value

Relative error

3.73 4.78 5.61 6.43 7.87 12.09

4.10% 4.7% 0.17% 2.22% 0.63% 0.08%

3.81 4.67 5.51 6.49 7.96 12.05

6.42% 6.97% 1.95% 3.17% 0.51% 0.24%

3. Study on thermal conductivity 3.1. Saturated hygroscopicity test

Fig. 13. Fitting curve of polyurethane.

of fitting effect are shown in Table 6. Through analysis, the correlation coefficient R2 of fitting curve is Halsey < Smith < Oswin < Henderson < Modified BET < Peleg. The rms error RMSE and residual sum of squares RSS are Halsey > Smith > Oswin > Henderson > Modified BET > Peleg. Therefore, the fitting degree of Peleg model is the highest, followed by Modified BET model. Although the correlation coefficients of the fitting curves of the two models are above 0.999 and the fitting degree is good, Peleg model is an empirical or semi-empirical pure mathematical model and Modified BET model is developed based on BET adsorption theory and BET model of adsorption kinetics model. The parameters of Modified BET model have practical significance and can explain the hygroscopicity of materials in depth. Therefore, the Modified BET model is established to predict the isothermal hygroscopicity curve of polyurethane insulation materials. The mathematical expressions are as follows:

x¼

1:1528Aw 1  0:8819Aw

ð2Þ

The moisture absorption model of thermal insulation materials has been studied before. In order to better determine the whole moisture absorption range of thermal insulation materials and more accurately study the thermal conductivity of thermal insulation materials, the saturated humidity moisture absorption test has been added in this paper. By taking polyphenolic and polyurethane as test objects and using a self-made hygroscopic simulator and heating saturated steam humidification method, the hygroscopicity of thermal insulation materials in humid environment for a long time was simulated, and the hygroscopicity and saturated water content of thermal insulation materials were studied, which provided a basis for the follow-up study. In the process of sample hygroscopicity, the temperature of constant temperature water tank in the hygroscopicity simulator should be pre-adjusted to 45 °C. After opening the humidifier, the humidity controller should be adjusted to make the humidity in the tank exceed 99% RH. After the humidity in the chamber is stable, the dried and wrapped samples are put into the hygroscopicity test device, and the hygroscopicity surface of the sample is kept upward. After a period of hygroscopicity, the quality of the sample is measured and recorded until the sample of the thermal insulation material reaches the hygroscopicity saturation state. Fig. 14 shows the relationship between water content and time of polyphenolic insulation material and polyurethane insulation material under the condition of heating saturated steam Accelerated moisture absorption. On the whole, with the relative humidity further increased to saturated state, the saturated moisture absorption rate of the two insulation materials after moisture absorption stabilization has a considerable increase. From the second half of isothermal hygroscopicity curve of two kinds of thermal insulation materials, it can be noted that the isothermal hygroscopicity curve is trending upward instead of downward. When the relative humidity reaches saturation, theoretically, as long as there are capillaries, the adsorption layer can increase infinitely. This is because thermal insulation materials are porous structural materials, the pore size range from small to infinite and the

Table 6 Model parameters and evaluation indexes of polyurethane. Model

Peleg Henderson Halsey Oswin Smith Modified BET

Parameters

Evaluation indexes

a

b

c

d

R2

RSS

RMSE

6.6649 0.6645 0.9177 1.1932 0.3614 1.1528

6.2685 0.7877 1.4973 0.5932 2.2907 0.8819

2.0284 — — — — —

1.1723 — — — — —

0.9999 0.9985 0.9784 0.9878 0.9873 0.9991

0.0044 0.0521 0.7313 0.4117 0.4294 0.0262

0.0252 0.0863 0.3232 0.2425 0.2476 0.0612

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Fig. 14. Hygroscopic curve of thermal insulation material under saturated humidity.

increase of saturated moisture absorption caused by capillary adsorption and condensation is theoretically endless.

3.2. Experimental study on thermal conductivity at negative temperature Firstly, the samples with different moisture content (two samples with the same moisture content) obtained after saturated moisture absorption are put into 20 °C low temperature box for freezing for 48 h, and the frozen samples with different ice content are obtained. The test process of thermal conductivity of samples at negative temperature is completed in the low temperature test chamber (shown in Fig. 16). Before the test, the output power P and test time t of the probe should be set reasonably, because too long test time t or too much output power P of the probe will make the ice and water phase change and moisture migration inside the frozen sample. The ratio of thermal dispersion coefficient K, test time t and probe radius r-square of the tested sample follows kt /r 2 2 (0.3 ~ 1). Test time t is positively correlated with probe radius R. After repeatedly debugging the test parameters, the parameters of the thermal conductivity test of the sample are finally determined as shown in Table 7. Before the test, the test probe shall be placed in a low-temperature test chamber and frozen for 6 h to eliminate the influence of temperature difference between the test probe and the tested sample. Then place the test probe in the middle of the two tested samples, and cover the hood. After starting the Hot Disk Thermal Conductivity Testing System (Fig. 15), it must be preheated for more than 1 h. Then open the corresponding thermal conductivity analysis module, set the heating power and test time of the probe, and start the test process of thermal conductivity by using the hot disk test software. The test method can ensure that the test time of each group of samples is very short and the change of ice content is small. Table 8 shows that the thermal conductivity of polyphenolic insulation material in the dry state is 0.02911 W/(m K) and that of polyurethane insulation material in the dry state is 0.02608 W/(m K) at low temperature of 20 °C.

Computer Test probe Thermal constant analyser Fig. 15. Hot Disk-2500s conductivity meter.

Table 7 Test parameters. Samples

Probe type

R (mm)

P (MW)

T(s)

Polyphenolic Polyurethane

C8563 C8563

9.868 9.868

25 15

120 90

Fig. 16. Low temperature test box.

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Y. Li et al. / Construction and Building Materials 237 (2020) 117765 Table 8 Thermal conductivity in dry state. Sample

Thermal conductivity/W/(mK)

Polyphenolic Polyurethane

RSD (%)

1

2

3

4

5

Mean

0.02906 0.02604

0.02904 0.02614

0.02921 0.02618

0.02917 0.02601

0.02907 0.02603

0.02911 0.02608

0.25 0.29

Note: RSD is relative standard deviation

Table 9 Thermal conductivity of polyphenolic thermal insulation material with different ice content. Ice content (%)

Thermal conductivity W/(mK)

Ice content (%)

Thermal conductivity W/(mK)

5.76 11.87 19.56 27.42 31.26 37.38 42.09

0.03243 0.03356 0.03503 0.03543 0.03706 0.03775 0.04018

44.19 49.78 53.62 60.26 62.7 68.99

0.04081 0.04156 0.04425 0.04556 0.04756 0.04944

Table 10 Thermal conductivity of polyurethane thermal insulation material with different ice content. Ice content (%)

Thermal conductivity W/(mK)

Ice content (%)

Thermal conductivity W/(mK)

0.56 1.57 2.99 4.19 5.02 5.91 7.03 7.59

0.02708 0.0272 0.02703 0.02728 0.02703 0.02751 0.02759 0.0283

8.12 9.06 9.99 10.63 11.3 11.94 12.72

0.02841 0.02917 0.02926 0.02981 0.0297 0.0305 0.03059

Thermal conductivities of two kinds of thermal insulation materials with different moisture content under complete freezing are shown in Tables 9 and 10. (Moisture content under complete freezing is defined as ice content.) The fitting curves of the effective thermal conductivity of the two insulation materials with ice content are shown in Fig. 17. On the whole, the thermal conductivity of thermal insulation material will change abruptly once it is absorbed and frozen. This is mainly because the thermal conductivity of dried thermal

insulation material is much smaller than that of ice. When the sample contains ice, the change of thermal conductivity of thermal insulation material is more sensitive. With the increase of ice content, the thermal conductivity of the two kinds of insulation materials increases gradually, and the variation law of thermal conductivity of both kinds of insulation materials are slightly different. The fitting formula of thermal conductivity of polyphenolic insulation material is as follows:

ke ¼ 0:0321 þ 0:03193  x1:6361

ð3Þ

The fitting formula of thermal conductivity of polyurethane insulation material is as follows: When 0 6 x 6 5%, ke ¼ 0:02712

When 5% 6 x 6 14% ; ke ¼ 0:02459 þ 4:7638  102 x

ð4Þ

4. Thickness correction of thermal insulation layer considering moisture 4.1. Engineering situation As shown in Figs. 18 and 19, the Hongtushan Tunnel is located in the Hongtushan Mountain of Yushu Prefecture, Qinghai Province. It is a single-hole two-way tunnel with length of 3020 m, its snow shelter tunnel length is 60 m and its maximum depth is 277 m. The height of the tunnel site is about 4280 m, the annual average temperature is 1.4 °C, the annual maximum temperature is 11.7 °C, the annual minimum temperature is 3.2 °C, the extreme minimum temperature is 27.6 °C, and the maximum freezing depth is 2.9 m. The method of thermal insulation in the tunnel is to lay 5 cm thick rigid polyurethane thermal insulation board on the lining surface and set calcium silicate fire-proof board on the surface.

Fig. 17. Fitting curves of thermal conductivity of two thermal insulation materials with different ice content.

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Fig. 18. Hongtushan tunnel.

Fig. 19. Longitudinal section of Hongtushan tunnel [45].

by hand-held meteorological stations. Various aspects of data are collected once a week by a manual collection process.

4.2. Field test of humidity in cave 4.2.1. Test scheme The main instruments used are temperature and humidity sensors, along with hand-held weather stations, as shown in Fig. 20. Sensors are distributed symmetrically along the longitudinal direction of the tunnel, and monitoring points are added appropriately at the entrance section. In order to avoid the influence of human and other factors on sensor testing and quality of output test data, temperature and humidity sensors are installed near the entrance and at the height of 1.8 m in the tunnel, and the temperature, humidity and pressure inside and outside the tunnel are monitored

4.2.2. Results and analysis In December, the humidity of Hongtushan Tunnel is the highest. Combining with the humidity variation curve (Fig. 21), isothermal moisture absorption model and thermal conductivity prediction model of thermal insulation materials, the moisture content of polyphenolic thermal insulation materials under different relative humidity and thermal conductivity coefficient under negative temperature after moisture absorption stabilization can be obtained as

Fig. 20. The schematic diagram of test instrument installation [46].

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Fig. 21. Change of longitudinal humidity and longitudinal temperature in Hongtushan tunnel.

shown in Fig. 22, and then the thickness of external thermal insulation layer of tunnel can be corrected. As can be seen from Fig. 22, along the longitudinal direction of the tunnel, the moisture content of the polyphenolic insulation board is between 4.5% and 6%, and the freezing thermal conductivity is between 0.032 and 0.033 W/(m K) in the humidity of 33 RH% ~55 RH%. 4.2.3. Calculating and correction the thickness of insulation layer Selecting equivalent thickness exchange method to calculate the thickness of external insulation layer [19,20,42] (seen as Fig. 23), the formulas is as follows:

1 r 0 þ hf 1 r 0 þ hb 1 r0 þ hb þ he ln ¼ ln þ ln kf kb ke r0 r0 r0 þ hb

Fig. 22. Curve of ice content and thermal conductivity of polyphenolic thermal insulation along longitudinal direction of tunnel.

Fig. 23. Calculation model [44]

ð5Þ

where r0 is equivalent radius of tunnel (m); he is thickness of lining concrete(m); hb is thickness of insulation layer(m); hf is Frozen Depth of Surrounding Rock (m);ke is thermal conductivity of lining concrete (W/(mK));kb is thermal conductivity of thermal insulation materials(W/(mK));kf is thermal conductivity of surrounding rock (W/(mK)). According to the design data of hongtushan tunnel, the parameters for determining the thickness of insulation layer are shown in Table 11. The thermal conductivity of polyphenolic insulation material in a dry state is 0.0295 W/(m.K). Formula (5) calculates that the required thickness is 3.9 cm, while the thickness adopted in engineering practice is 5 cm, which is equivalent to the reserved safety surplus of 1.1 cm thickness. The thermal conductivity of thermal insulation board increases after damp. In order to achieve the same insulation effect, the thickness of the insulation board should be increased, and the thickness of the insulation layer under different humidity can also be calculated by this formula (5). As can be seen from Fig. 24 the theoretical thickness of polyphenolic insulation board along the tunnel is between 4.2 and 4.3 cm,

Table 11 Calculating parameters of insulation layer thickness. parameters

r0 (m)

hf (m)

kf (W/(mK))

he (m)

ke (W/(mK))

Value

5.35

2.9

1.16

1

1.335

12

Y. Li et al. / Construction and Building Materials 237 (2020) 117765

CRediT authorship contribution statement Youyun Li: . : Conceptualization, Resources, Funding acquisition. Yongmei Sun: Validation, Writing - original draft. Junling Qiu: Writing - review & editing. Tong Liu: Methodology, Supervision. Li Yang: Investigation, Data curation. Huidong She: Formal analysis. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This study was supported by the National Natural Science Fund of China (Grant No. 51378071), Natural Science Foundation of Shaanxi Province of China (Grant No. 2130-2116-0351). The authors are grateful to the researchers for their support for the experimental study. Fig. 24. Calculation results of thickness of longitudinal insulation layer along tunnel.

according to the different humidity conditions prevailing in the tunnel. The humidity at the entrance of the tunnel is the largest and the compensation thickness is the largest. The polyphenolic insulation board of 4.3 cm thick laid on the lining surface of the Hongtushan tunnel can meet the theoretical calculation requirements, and the compensation value equivalent to the thickness of 0.4 cm is safe and reliable. However, considering the production process of thermal insulation materials and the thickness of thermal insulation board in practical engineering, the thickness of thermal insulation board is usually an integral multiple of 0.5 cm, therefore, it is more reasonable to determine the compensation value of thickness to be 0.5 cm. In order to achieve the same thermal insulation effectiveness and ensure the same safety surplus, when considering the influence of air humidity in the tunnel, the thickness of the external thermal insulation layer of Hongtushan tunnel should be increased to 5.5 cm. 5. Conclusions 1. 1 The isothermal hygroscopicity curve of polyphenolic insulation material is reverse S-type, which belongs to type II isothermal adsorption curve of BDDT classification and Peleg model is more suitable for isothermal hygroscopicity model of this material. Isothermal hygroscopicity curve of polyurethane thermal insulation material conforms to type III isothermal adsorption curve of BDDT classification and Modified BET model is more suitable for isothermal hygroscopicity model of this material. 2. 2 When freezing at low temperature, the change curve of thermal conductivity with ice content is exponential on the whole. For polyurethane insulation materials, the change of thermal conductivity with ice content can be divided into two stages. When the ice content is between 0% and 5%, the thermal conductivity fluctuates and when the ice content exceeds 5%, the thermal conductivity increases steadily and linearly. 3. 3 Equivalent thickness exchange method is used to calculate the thickness of external insulation layer. By taking the Hongtushan tunnel in the cold region as an example, when considering the influence of air humidity on the external polyphenolic insulation board, the correction value of the thickness of the insulation layer is 0.5 cm.

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