Research status and progress of tunnel frost damage

j o u r n a l o f t r a f fi c a n d t r a n s p o r t a t i o n e n g i n e e r i n g ( e n g l i s h e d i t i o n ) 2 0 1 9 ; 6 ( 3 ) : 2 9 7 e3 0 9

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Review Article

Research status and progress of tunnel frost damage Yanbin Luo, Jianxun Chen* School of Highway, Chang'an University, Xi'an 710064, China

highlights
The local and foreign research results of cold region tunnels are systematically concluded.
The defects of existing research on cold region tunnels are comprehensively analyzed.
The direction of frost damage level classification is proposed.
The major prevention and control technologies of frost damage are concluded and analyzed.

article info

abstract

Article history:

The problems of frost damage in cold region tunnels have been systematically analyzed

Received 19 June 2017

and studied by local and foreign scholars. A series of important achievements has been

Received in revised form

proposed. In this paper, the research results on mechanism of frost damage, analysis of

13 September 2018

temperature field, classification of frost damage levels, and frost prevention technologies

Accepted 17 September 2018

are summarized. The principles and limitations of the three major theories of frost damage

Available online 17 April 2019

mechanism are elaborated, and the importance of structural damage research on shotcrete in cold region tunnels is emphasized. Two major defects of current research on temper-

Keywords:

ature field are concluded. The present situation of research on frost damage classification

Cold region tunnel

of cold region tunnels is discussed. The directions of further studies for tunnel temperature

Frost damage mechanism

field and frost damage classification are proposed. The prevention technologies for tunnel

Temperature field

frost damage in foreign countries, and the advantages and disadvantages of the four major

Tunnel frost damage classification

prevention technologies in China and their applicable conditions, are concluded and

Prevention measure

analyzed. Meanwhile, the importance of frost damage classification is highlighted. Therefore, the local and foreign research results for cold region tunnels are systematically concluded, the defects of the researches are comprehensively analyzed, and the directions of further study are proposed. They are significant to solve the problems of tunnel frost damage in the future. © 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).

1.

Introduction

Many cold region tunnels have been constructed in northeastern and northwestern China, Japan, Europe, Norway, and

Russia (Zhang et al., 2002a, b). However, frost damage in tunnels is serious. Even, such phenomena that the main structure of tunnel was scrapped and serious traffic accidents occurred during operation resulting from serious frost damage (Sun,

* Corresponding author. Tel.: þ86 29 82334887. E-mail addresses: [email protected] (Y. Luo), [email protected] (J. Chen). Peer review under responsibility of Periodical Offices of Chang'an University. https://doi.org/10.1016/j.jtte.2018.09.007 2095-7564/© 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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2005). Based on the Japanese National Railway statistics in 1979, 1100 of 3800 railway tunnels in the country endangered the driving safety during winter operation owing to frost damage; 104 of 302 highway tunnels in Hokkaido had serious frost damage. Electric heating devices were installed in some tunnels as treatment measures to eliminate ice in the side walls and arch. But, these measures were costly (Kojima and Asakura, 1996). In the European Scandinavian Peninsula and the Alps Mountain, frost damage phenomena in tunnels often occurred. In order to prevent frost damage in winter, some road tunnels adopted heating measures, and the cost was also quite high (Lu¨lttger and Poyda, 1992). In Norway, 630 cold region tunnels have been constructed in 1990 with a total length of 60 km. All the tunnels had a wide range of leakage and icicle (Gronhaug, 1988). The operation of many railway projects in the former Soviet Union (Krasnoyarsk, Outer Baikal, and East Siberia railways) and the Federal Republic of Germany, Sweden, and France were affected by frost damage in winter (ТруЪчиков, 1990). In the cold region of China, because of the frost damage, some of the tunnels cannot be used for up to 8e9 months in a year (Luo, 2010). For example, the northwest of the Wushaoling Tunnel, Kuixiandaban Tunnel, Guanjiao Tunnel and the Qidaoliang Tunnel have encountered typical frost damage. The Yuxi-Molegai Tunnel in No. 217 National Highway in Xinjiang Tianshan was abandoned after few years of operation, owing to the serious frost damage of ice jam in the tunnel (Sheng et al., 1996; Su, 2007). Since 1949, dozens of cold region tunnels have been constructed in the northeast high-latitude area of China, such as the Lingding Tunnel of the Yalin line, the Xiling No. 1 and No. 2 Tunnels of the Nenling line, the Xiluoqi No. 2 Tunnel, the Baikaer Tunnel, and the Tumenling Tunnel of the Katu line. Considering the cold weather and insufficient knowledge on the characteristics of tunnel engineering in cold areas, many tunnels had had serious frost damage during construction. And, after a few years of operation, even 10 years or more, new frost damage still occurred in succession. The frost damage became more and more serious (Railway Third Survey and Design Institute, 2002; Zhang, 2006). In recent years, a large number of long tunnels in highaltitude and extremely cold areas have been built in China, such as the Dabanshan highway tunnel (3790 m altitude, 30  C lowest temperature), the Zhegushan highway tunnel (3300 m altitude, 31.1  C lowest temperature), the Kunlunshan railway tunnel (4600 m altitude, 36  C lowest temperature), and the Fenghuoshan railway tunnel (4800 m altitude, 37  C lowest temperature) (Su, 2007). Several scholars have investigated these tunnels from construction to operation and provided valuable data for research. In this paper, the results of the said works are summarized to serve as references for the design and construction of cold region tunnels, and the research on frost damage prevention.

2.

Mechanism of tunnel frost damage

The frost heave pressure in rock mass is usually considered in tunnel frost damage, as tunnel frost damage caused by frost heave pressure leads to the cracking of tunnel lining concrete

(Chen et al., 2005). Therefore, early scholars have studied the tunnel frost heave mechanism and formed the following three theories (Hu and Wang, 2002; Lai et al., 2000; Zhang, 2006).

2.1.

Frost heave of weathering layer with water

In the 1980s, Japanese scholars investigated frost damage in numerous tunnels in Hokkaido and northeast areas, and found that rock mass around the lining is surrounded by 10e20 cm weathering layer in any tunnel with frost damage. In winter, there are ices that are free and thin sandwiched in the weathering layer. However, there is barely ice in the weathering layer in the tunnel vault, although the thickness of the weathering layer is up to 50 cm. Therefore, the inward convergence deformation of the side wall lining is quite large, which can reach 20e30 mm, due to the horizontal frost heave force. And, some horizontal cracks occur in the side wall lining. However, the deformation of tunnel crown is small, because there is hardly frost heave. Therefore, it can be believed that the frost heave of lining is caused by the freezing of water in the weathered layer. The water content in the weathering layer in the side wall is much larger than that in the crown. Therefore, frost heave occurs mostly on the side wall, and rarely on the vault. Zhang and Wang (2004) affirmed the theory. They replaced the frost heave force by side pressure, and simplified it into a one-dimensional spring problem. The formula for frost heave force was deduced, as follow Pb ¼

daK1 K2 K1 þ K2

(1)

where d is the thickness of frost heave layer of rock mass, Pb is the frost heave force acting on the lining, a is the volume expansion coefficient of rock mass after freezing, K1 is the circumferential deformation stiffness of the tunnel lining, K2 is the elastic resistance of the rock mass out of the weathering layer. The result has been included in the “Guidelines for Design of Highway Tunnel” (JTG/T D70-2010).

2.2.

Frost heave of freezing and thawing lithosphere

The theory of frost heave of freezing and thawing lithosphere was proposed by the Institute of Environment and Engineering of China Academy of Sciences based on the Ministry of Communications research project entitled “The Construction Technology of Tunnel Engineering in High-altitude and Cold Area.” Based on the actual situation of the Dabanshan Tunnel, this theory is introduced for loose and weak rock mass tunnels. The theory indicates that the frost heave of freezing and thawing lithosphere is formed by certain depth range of rock mass surrounding the tunnel lining. Given that the pore in rock of the lithosphere is homogeneous and saturated, the water in the lithosphere can change to ice and its volume can expand entirely, thereby producing frost heave force on the tunnel lining. Based on the theory, some Chinese scholars simplified tunnel into a circular shape, and established the calculation model of frost heave force (Fig. 1), in order to deduce the calculation formula of frost heave force.

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In Fig. 1, a is the lining inner diameter, b is the lining outer diameter (i.e., inner diameter of the freezing lithosphere), c is the outer diameter of freezing lithosphere (i.e., inner diameter of the original unfrozen rock), d is the outer diameter of the original unfrozen rock, Pc is the expansive force acting on the outer unfrozen rock mass resulting from frost heave, P0 is the original force inunfrozen rock mass. In 1996, Sheng et al. (1996) obtained an elastic solution of frost heaving force. In 1999, Lai et al. (1999a) regarded both the tunnel rock mass and lining structure as homogeneous, isotropic elastomers, and assumed that they met the conditions of axisymmetric plane-strain problem. Meanwhile, the frost heave force at the interfaces satisfied the continuity equation. The formula of frost force with respect to time in the lining - frozen rock mass - unfrozen rock mass system were derived through Laplace transform, based on the principles of elasticity. The specific formula of the frost heave force is as follows.
 ð1 þ m2 Þðc2 þ b2  2m2 c2 Þ 1 þ m3 1 þ Pb ¼ e0 ð1 þ m2 Þ 2 2 E2 ðc  b Þ D E3 
  2 1  m22 c2 1 ð1 þ m3 Þ e0 ð1 þ m2 Þ þ P0  D E3 E2 ðc2  b2 Þ

ð1þm1 Þ½2m1 b2 ðb2 þa2 Þð1þm3 Þ E1 E3 ðb2 a2 Þ



ð1þm2 Þð1þm3 Þðb2 þc2 2m2 b2 Þ E2 E3 ðc2 b2 Þ

  II   uIII r r¼c ur r¼c ¼ Dh

(3)

where e0 is the linear strain for frost heave, m1 , m2 , and m3 are the Poisson ratio of the lining, freezing lithosphere, and

(4)

where ur is the radial displacement. Then, the elastic solution of the frost heave force acting on the lining was obtained, as follows

(2)

ð1þm1 Þð1þm2 Þ½2m1 b2 ðb2 þa2 Þðc2 þb2 2m2 c2 Þ E1 E2 ðb2 a2 Þðc2 b2 Þ  2 2 2 ð1þm2 Þ ðb þc2 2m2 b2 Þðc2 þb2 2m2 c2 Þ 4 1m22 c2 b2 þ 2  2 2 E22 ðc2 b2 Þ E2 ðc2 b2 Þ þ

unfrozen original rock, respectively, E1 , E2 , and E3 are the elastic modulus of the lining, freezing lithosphere, and unfrozen original rock, respectively. According to the corresponding principle of elasticity and viscoelastic, the viscoelastic analytic solution of frost heave force can been given by the Bao Aiding-Tomson viscoelastic constitutive model. Wu et al. (2003) and Zhang et al. (2003a, b) introduced the expansion quantity Dh of freezing lithosphere. The original unfrozen rock mass was regarded as an infinite plane without force, which was different from Lai et al. (1999a). The displacement at the interface of the frozen lithosphere and the unfrozen rock mass met the following continuous conditions.

Pb ¼

D¼

299

naE2 pq þ ðm2 þ 1Þ½eðm1  m1 Þ þ ðm2  m2 Þ

8 b2 þ a2 > m1 ¼ 2 > > > b  a2 > > > > > > c2 þ b2 > > m 2 ¼ 2 > > c  b2 > < 2b2 > p¼ 2 > > > c  b2 > > > > > 2c2 > > q¼ 2 > > > c  b2 > : e ¼ E2 =E1

(5)

(6)

where n is the integrity coefficient of the rock mass. The result has also been included in the “Guidelines for Design of Highway Tunnel” (JTG/T D70-2010). In 2012, Gao et al. (2012) resolved the frost heave displacement Dh1 at the interface of the freezing lithosphere and tunnel lining, and the displacement Dh2 at the interface of the freezing lithosphere and original unfrozen rock mass. The continuity conditions of the two displacements should be met as 

  uIIr r¼b uIr r¼b ¼ Dh1 II   uIII r r¼c ur r¼c ¼ Dh2

(7)

Then, the solution of the frost heave force was obtained. In 2015, Huang et al. (2015) thought the frost heave of the rock mass was uneven. They introduced the circumferential stress sq and radial stress sr of rock mass, and circumferential strain eq and radial strain er. Similarity, according to the elastic mechanics, the displacements of Dh1 and Dh2 were obtained, and the analytical solution of frost heave force was deduced.

2.3.

Fig. 1 e Mechanical model of frost heave force of a tunnel.

Frost heave of stagnant water

The theory of frost heave of stagnant water was proposed by China Railway Southwest Research Institute based on the study of the QinghaieTibet railway tunnel. This theory states that frost heave force is caused mainly by the freezing of

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stagnant water at the back of the lining. The space of stagnant water is located between the lining and rock mass, resulting from uneven excavation and support surfaces and weak construction of the waterproof plate layer. The frost heave force occurs when stagnant water freezes. Based on the above, Wang and Hu (2004) established the frost heave model for a triangle space with water, and obtained the analytical solution of the frost heave force on the tunnel lining. Deng (2012) proposed a constrained frost heave model of water storage space. The theoretical formula of frost heave force was given, and the frost heave force for a tetrahedron space with water was analyzed and discussed. The frost heave forces obtained from the above three theory and the corresponding calculation formulas are different in numerical size, and the magnitude is quite large. However, their accuracy cannot be validated due to the lack of on-site measured data and related physics mechanical parameters of rock mass. The reference of the former Soviet Union showed that the frost force can be up to 15 MPa when the water intruding into the rock cracks is freezing, and the freezing force of ice is 211 MPa when sealing vessel is used under no volume expansion condition. However, the frost heave force measured in the Chaoyang No. 2 railway tunnel in the Nenlin line servicing the northeast forest is only 25e200 kPa (Ding, 2008). Some tunnels are located in cold areas without frost heave damage. Tunnel frost damage is caused by many factors, such as frost damage of lining concrete, frost heave damage of stagnant water located in parts of tunnel, frost heave damage of rock mass, frost heave damage of fissure water filled in existing cracks, imperfect design of drainage system, cavity located in the back of tunnel lining, and insufficient thickness of tunnel lining (Chen et al., 2005; Su, 2007). The frost damage of cold region tunnels is complex because of the individual or joint effects of the said factors. Thus, just taking the frost force as the cause of tunnel frost damage is not appropriate. The mechanism of tunnel frost damage in cold region is currently investigated comprehensively by analyzing and studying from the macroscopic and microscopic aspects. At the macroscopic aspect, the basic conditions to cause tunnel frost damage are mainly considered, including temperature, hydrology, rock mass and engineering measures. At the microscopic aspect, moisture migration, water phase change, and structural damage are mainly considered. The problem of structural materials influenced by repeated freezing and thawing in engineering is becoming increasingly prominent; thus, scholars have studied the freezing and thawing damage of geotechnical and concrete materials. The development of industrial CT technology has facilitated comprehensive research on the mechanism of microscopic and submicroscopic damage of geotechnical and concrete materials. The shotcrete structure is a main support unit of a tunnel, besides rock mass and concrete structure. The structural damage of shotcrete under freezeethaw cycles is rarely explored in China, and only freezing and thawing cycle tests on slope shotcrete and simple tests of dynamic mode and quality change have been conducted in Japan. Therefore, the research of the mechanical properties, frost resistance, and durability of shotcrete under freezeethaw cycle is necessary

(Luo et al., 2012). In the current work, the frost resistance durability of tunnel shotcrete under freezeethaw cycles is investigated using CT scan technology (Chen et al., 2014, 2015, 2017). The study results can serve as a basis for research on the structural damage of shotcrete, so as to further reveal the mechanism of frost damage in cold area tunnel.

3.

Temperature field in cold region tunnel

The temperature field in cold region has been studied for more than 170 years, particularly on the problems of frozen soil, including temperature field, seepage field, stress field, and other related problems. Research on cold region tunnels are rare and only increased during the gradual construction of such tunnels between the 1980s and 1990s.

3.1.

Regularity of temperature field of cold region tunnel

CRREL (Johansen et al., 1988)of the United States conducted long-term observations on a multi-year permafrost tunnel in Alaska since 1963 and acquired a series of valuable research results. In the design and construction seminar of the former Soviet Beiagan mountain railway tunnel (ТруЪчиков, 1990), the scholars analyzed the temperature variation regularity of the tunnel with different lengths, and found that the entrance temperature of the tunnel is related to the climatic conditions and the running direction of train. With regard to local studies, Nie (1988) conducted a systematic air temperature observation in the Xiuoqil No. 2 Tunnel in the permafrost regions of the Daxinganling region, the Ducao Tunnel, and the Kuixiandaban tunnel in Xinjiang Tianshan. The results showed that temperature increases with distance from the tunnel entrance in the cold season, whereas the opposite is observed in the summer season. In addition, Wu et al. (2003) summarized the temperature variation regularity of cold region tunnels relying on the Qinghai Daban Mountain Tunnel and combining with the test data of the Quixian Tunnel in Xinjiang Tianshan, the Ducao Tunnel, Xibuluoqi No. 2 Tunnel and Cuiling No.2 Tunnel in Daxinganling, and the Helanshan Tunnel in Gansu. The results showed that for the abovementioned single-track railway tunnels built in China in early times, the temperature inside the tunnel is much higher than that at the portal in the cold seasons, because of the small crosssectional area, low driving speed and low traffic flow. That is to say, the longer the distance from the portal, the higher the temperature will be. But it is opposite in the warm seasons. Therefore, it is proposed that anti-freezing and thermal insulation measures should be taken and strengthened in certain section of tunnel portal in order to prevent frost damage. The construction of numerous cold region tunnels has started the temperature field tests and analyses on these tunnels. Wang et al. (2001) tested and analyzed the temperature field of the Xiaopanling Tunnel on the YanjieTumen Secondary Highway in Jilin Province. They found that the freezing depth outside the tunnel was larger than that inside the tunnel. And, the temperature variation of

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the rock mass at a certain depth from the lining surface lags behind the air temperature. Using the air and ground temperature test data of the Kunlunshan Tunnel of the QinghaieTibet Railway, Huang (2003) analyzed the variation regularity of temperature field around the freezing and thawing lithosphere of permafrost tunnels. It was found that the influence of air temperature in the tunnel on the rock mass temperature decreased with the increase of the depth of rock mass. Zhang (2005) analyzed the distribution characteristics of air temperature and ground temperature in the tunnel. It was found that the influence of the air temperature inside the tunnel on the ground temperature of the rock mass decreased as the depth of the rock mass increased. The temperature field of the Tiziling Tunnel in the QineQing Highway, Hebei Province was tested and analyzed by Chen (2004). The air temperature outside and inside tunnel, and the temperature in rock mass in the Zhegushan Tunnel in Sichuan Province were monitored and analyzed by Xie et al. (2004). It was found that the farther away from the tunnel portal in the longitudinal direction was, the higher the temperature of the tunnel rock mass and lining structure was, and the temperature of the measurement point at the same depth was less affected by the outside air temperature and more stable. The temperature field of the Xiangyunling Tunnel in Chengde City, Hebei Province was tested and analyzed by Chen and Luo (2008). The distribution regularity of temperature field in cold region tunnel was summarized. The temperature field of the Fenghuoshan Tunnel in the QinghaieTibet Railway was observed and researched by Zhang et al. (2007). And, it was found that when the temperature inside the tunnel was higher than that outside the tunnel during construction, the melting depth of the rock mass would be greater than the upper limit of natural permafrost. However, after the tunnel construction is completed, the depth of the rock mass freeze-thaw circle would be lower than the upper limit of natural permafrost, when thermal insulation measures were taken. The temperature field of the Qingshashan Tunnel in the east of the QinghaieTibet Plateau was measured and analyzed by Lai et al. (2007). The variation law of the temperature inside tunnel rock mass was revealed. Cheng (2009) tested the air temperature inside and outside tunnel and the temperature field in the rock mass in Alatan Tunnel in Inner Mongolia, and the results were analyzed and summarized. The relationships between the variation laws of air temperature inside and outside the tunnel, and between the variation law of the temperature in the tunnel rock mass and the air temperature inside the tunnel and the geological conditions, were revealed. Song (2015) conducted field tests of temperature field in Houanshan Tunnel in JilinTumen-Hunchun passenger dedicated railway line. The distribution laws of radial temperature field in tunnel lining and rock mass, and the longitudinal temperature field inside tunnel were revealed. Jia (2016) conducted a series of temperature field tests inside and outside Wafangdian Tunnel in Beijing-Shenyang passenger dedicated railway line. The distribution law of temperature field inside tunnel was revealed, and the relevant influencing factors of temperature at tunnel portal and the natural wind speed were analyzed. It was found that the temperature at the

301

portal of tunnel and the equivalent natural wind speed have a greater impact on the temperature field of the tunnel in cold regions, and have a mutually reinforcing role. Yang (2016) found that the higher the thermal diffusivity of rock mass was, the faster the heat conduction, and the decrease of temperature and cooling rate of the rock mass would be, based on the radial temperature test results of different sections in the Wafangdian Tunnel combined with numerical simulation analysis. The radius of the tunnel freezing and thawing lithosphere increased with the increase of the thermal conductivity of the rock mass and the heat transfer coefficient of the tunnel lining, and decreased with the increase of the initial geothermal temperature, specific heat and density. Most scholars have conducted temperature field test of a single tunnel and obtained some regularities of tunnel temperature. However, the summary and analysis on the distribution regularity of temperature field in cold region tunnels is rare. To the best of our knowledge, only Wu et al. (2003) examined several single-line railway tunnels, including the Dabanshan Tunnel. However, the results could not fully reflect the temperature field distribution law for the current two-lane, three-lane and four-lane highway tunnels and high-speed railway tunnels with large cross section, large traffic volume and high traffic speed. In addition, the different distribution laws of temperature field inside different types of tunnels, including the permafrost, local permafrost, and non-permafrost tunnels, were revealed by Luo (2010). The distribution law of temperature field in different types of tunnels is different; thereby more attention and data accumulation and systematic analysis of tunnel temperature field are needed.

3.2. Calculation and simulation of temperature field in cold region tunnel The temperature field in cold region tunnels is currently calculated and simulated extensively. Regarding foreign studies, the numerical solution of temperature field of phasechange heat conduction was proposed by Bonacina et al. (1973). The non-linear problem of phase-change heat conduction of temperature field was analyzed by Comini et al. (1974) using the finite element method. Takumi et al. (2008) established tunnel temperature field computing model based on thermal convection and heat conduction theories, and the results of the calculation were compared with the measured results. Suneet et al. (2008) deduced the doubleseries solution of transient temperature field in polar coordinates with multilayer annulus in the radial direction. With regard to local studies, the temperature field of tunnel rock mass was analyzed by He et al. (1996, 1999) based on the tunnel wall temperature altered with the cyclical change in air temperature. The change trend of frost and thaw condition of tunnel rock mass was also analyzed and predicted using the coupling model of gas and solid convection heat transfer and solid heat conduction under the situations of air flow in tunnel of laminar and turbulent flows separately. Lai et al. (1999b, 2001) derived differential control equations of the coupling of temperature and seepage fields with phase transition in accordance with the theories of heat transfer and

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seepage. The finite element formula of this problem was deduced by the Galerkin method, and the heat conduction equations of the frozen and unfrozen areas were simplified depending on the actual conditions of the frozen soil region. The analytical solution of the temperature field of circular cross-section tunnel in cold region was obtained using the dimensionless and perturbation technique. Zhang et al. (2002b, 2003b, 2004) deduced the finite element formula using the Galerkin method based on the thermal equilibrium differential control equations with phase transition transient temperature field problems. The computational software was developed on the working platform of ANSYS software, and the calculation software was used to predict the thawing of the Kunlunshan Tunnel during construction. Zhang et al. (2005) established the three-dimensional computational model of air and rock mass convection heat transfer and rock mass heat conduction in cold region tunnels, based on the basic theories of hydrodynamics, frozen soil, and heat transfer. The finite element analysis was carried out with the Galerkin method, and the finite element calculation program was compiled. Three-dimensional non-linear analysis of air and rock mass convective heat transfer and rock mass heat conduction of the QinghaieTibet railway tunnel was also performed. Zhang et al. (2006b) compiled the calculation procedure and conducted the finite element analysis of temperature field in cold region tunnels using the finite difference method. The FLAC3D 2.1 software was used as the platform, and the built-in Fish language of the software as the tool. The time-dependent heat conduction for tunnel in cold region with nonhomogeneous outer boundary conduction was divided into transient heat conduction with periodic function boundary and constant heat conduction with constant temperature boundary condition by Xia et al. (2010). Through combining the separation variable and the Laplace transform technique, the explicit analytical solution of tunnel transient temperature field with thermal insulation layer was obtained. Based on the basic principles of fluid mechanics, heat transfer and aerodynamics, a temperature field model considering the influence of ventilation for cold region tunnel was developed by Tan et al. (2013). And, the temperature field changing law of the Galongla Tunnel in Tibet under the condition of ventilation was analyzed. Feng and Jiang (2014) established a calculation model for the temperature field of multi-layer medium cold region tunnel, considering the difference between the annual mean air temperature and the temperature of rock mass and the airsolid convective heat transfer. The Laplace transform and Den Iseger numerical inversion were adopted to make the solution of the model. Then, the effect of thermal conductivity and convective heat transfer coefficient on tunnel temperature field was analyzed. It can be found that the smaller the convective heat transfer coefficient is, the greater the difference between the solid surface temperature and the air temperature is. If the convective heat transfer coefficient is constant, the larger the thermal conductivity of the solid is, the greater the difference of the temperature between the solid surface and the air is. Zhou et al. (2016) established unsteady-state finite-difference equations for

heat transfer and heat convection to calculate the temperature field of a cold region railway tunnel considering natural wind, train-induced wind and mechanical ventilation wind. The characteristics of temperature distributions in the tunnel lining structure and rock mass were revealed, under natural wind, train-induced wind and mechanical ventilation wind as well as the influence of wind temperature, wind speed and wind direction.

3.3. Coupling of temperature, seepage, and stress fields in tunnel Local and foreign studies on the three-field coupling of temperature, seepage, and stress of rock and soil have developed from single field and factor to multiple fields and factors, and from porous medium to fissure medium. The three-field coupling is extensively investigated, but that in cold region tunnels is unexplored. Harlan (1973) proposed the popular Harlan equation. The mathematical model of thermal mass transfer in the freezing process of soil was first used to analyze the coupling of seepage and temperature fields. In domestic, Huang and Yang (1999) and Huang et al. (1999) preliminarily established the mathematical model of coupling effect of temperature and seepage fields of the rock mass through equal continuous treatment of permeability and thermal physical properties of the fractured rock mass in tunnel. The model was applied to the Qinling tunnel engineering. Lai et al. (1999b, c) carried out the non-linear analysis of coupling of seepage and temperature fields in cold region tunnels, as well as the three-field coupling. Li et al. (2004) analyzed the elastoplastic analytical solution of the stress and displacement around the tunnel by considering the effect of seepage field with the simple circular tunnel as the research object. Zhang et al. (2006a) established the three-dimensional mathematical model of coupling of seepage and temperature fields of permafrost based on the basic theory of heat transfer and seepage mechanics, and considered the coupling effect of seepage and temperature fields in permafrost. The finite element program was compiled by the Galerkin method, and the shallow buried section of the Kunlunshan Tunnel of the QinghaieTibet Railway was analyzed. It was found that under the coupling effect of seepage field and temperature field, the phenomenon of water leakage in Kunlunshan Tunnel was consistent with the actual situation on-site. Therefore, the seepage field has a great influence on the temperature field of the rock mass in tunnel. And, in the design of the tunnel in cold regions, the coupling effect of the seepage field and the temperature field should be considered. Yang et al. (2006) proposed the common numerical solution of moisture and heat coupling for soft rock in cold region tunnel, and applied FEMLAB software to simulate temperature field and moisture field of Dabanshan Tunnel. It was found that the migration of water largely affected the distribution of the temperature field in the rock mass. The freezing depth decreased, as the permeability coefficient of rock mass increased. The thermo-hydro-mechanical-damage coupled model of rock mass in cold region tunnel under ventilation

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was established by Tan (2010), considering the influence of volume strain on the temperature and seepage field of rock mass, and the effect of temperature gradient, seepage pressure and frost heave force on the mechanical field of rock mass. Thereby, the frost heave process of the cold region tunnel was simulated and analyzed; he combined the temperature-seepage coupling model, the wind field turbulence model and the freeze-thaw damage constitutive model to establish a temperature-seepage-stress-damage coupling model that can reflect the actual working conditions of the cold region tunnel. Hu (2014) proposed a computing model of temperature field in cold region tunnel, considering the ventilation-seepage coupling, by which the temperature field of Balangshan Tunnel in Sichuan Province was simulated, and the characteristics of temperature field under the effect of ventilation and seepage were revealed. Sun et al. (2016) simulated the temperature field of a highway tunnel in Liaoning Province in China by establishing a calculation model under the coupling action of fluid and solid. It was found that the higher the initial temperature of the rock mass was, the greater the temperature difference between the inner and outer sides of the lining would be, and the higher the thermal conductivity of the rock mass was, the greater the influence range of the low temperature air on rock mass would be. In most of the above studies, the temperature of tunnel wall was taken as the boundary to calculate and simulate the tunnel temperature field. However, this temperature was always obtained through field test. Thus, it is vital to predict and test the air temperature of tunnel entrance and inside tunnel to obtain the actual distribution law of tunnel temperature. It is worth mentioning that Japanese scholars have conducted statistical regression analysis for 335 tunnels in the Hokkaido and northeast Shinkansen, and found the relationship between the temperature of tunnel entrance and the locations where the temperature was 0  C and 5  C in cold region tunnel.

4.

Classification of tunnel frost damage

The condition of tunnel frost should be scientifically evaluated and the degree of tunnel frost damage should be determined to develop remedial schemes and preventive measures for tunnel frost damage. Proper classification is a key to scientifically evaluate the condition of tunnel frost damage. The situation of frost damage can be comprehensive analyzed and the state of frost damage can be scientifically evaluated only by properly classifying the degree of tunnel frost damage. Domestic and foreign scholars classified tunnel frost damage using various methods. Japanese scholars researched on the lining variation and deterioration in operating tunnels, and developed the corresponding classification criteria. In 1997, China's railway sector promulgated the industry standard “Railway Bridge and Tunnel Building Deterioration Assessment Standards-Tunnel” (T2820.2e1997), and developed a classification standard based on the impact of frost damage on tunnel operating function. However, the tunnel frost damage is a kind of security hazard, and the development process of frost damage is both regular and random. It is

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insufficient to make a classification of tunnel frost damage according to the final form of tunnel disease including lining variation, deterioration and displacement rate of clearance convergence. A more scientific and practical method is needed considering some basic conditions of frost damage such as temperature and groundwater. Relevant regulations on technical design and construction of new tunnels in cold region are lacking. Only the industry standard “the interim provisions on engineering design of the QinghaieTibet Plateau frozen soil” made the general design and construction for tunnel engineering in permafrost regions based on the characteristics of permafrost in the QinghaieTibet Plateau. The state codes of “Highway Tunnel Design Code” (JTG D70-2004) (Chongqing Traffic Research and Design Institute, 2004) only provided several regulations; for example, the drainage channel should be buried under the tunnel pavement deeply when the average temperature of the coldest month of the tunnel with groundwater is below 10  C, and the drainage tunnel should be set under the tunnel to prevent frost damage when the average temperature of the coldest month is below 25  C. These regulations cannot satisfy the needs of the design and construction of cold region tunnels. Therefore, the degree of tunnel frost damage should be classified to formulate the corresponding prevention measures of frost damage. At present, “Technical Manual of Railway Engineering Design-Tunnel” (China Railway Eryuan Engineering Group, 1995), cold region tunnels were divided according to average temperature of the coldest month and maximum freezing depth. Different forms of drainage channel were proposed, and the situation of groundwater invasion into tunnel. The average temperature of the coldest month and freezing depth are the two characteristic values of the regional climate cold degree and low temperature state. Luo (2010) made a classification of tunnel cold degree, based on the average temperature of the coldest month and freezing depth. Meanwhile, combined with the groundwater conditions, frost damage levels were divided into five using a comprehensive evaluation method. In addition, he proposed that the hazard degree of groundwater to tunnel frost damage should be quantified in the further study to realize a reliable and feasible classification. Based on the above, the classification of tunnel frost damage should be further researched to be more scientific and practical, considering tunnel disease characteristics including the lining variation, deterioration and the displacement rate of clearance convergence, and the conditions of frost damage including the cold climate and groundwater. In addition, in the future study, the factors of buried depth and geological conditions of rock mass that influence the temperature distribution in tunnel lining and rock mass also can be taken into account to make the classification more specific.

5. Preventive measures for tunnel frost damage Several countries conducted much development and research according to their own national conditions and

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characteristics, and formed various preventive measures for tunnel frost damage (Chen et al., 2005).

5.1.

Prevention measures for frost damage abroad

In the former Soviet Union (Makаpob et al., 1993; ТруЪчиков, 1990), an integrated waterproof and drainage measure system (including waterproof layer, lining drainage pipes, and drainage channel) was used to prevent tunnel frost damage. The drainage measures are generally set in rock mass surface outside the seasonal freezing range. If the freezing depth is large, then the insulation layer should be set in contact between support and rock mass or in the surface of drainage facilities. The drainage channel should be manually heated by hot water or steam. Partial heating should also be employed for the leaking lining, such as the use of air insulation board or infrared radiation and other methods. The lining surface thermal insulation layer is used to reduce the thermal stress of the lining surface. For long tunnels, a service tunnel parallel to the main tunnel usually exists. When the outside air temperature is less than 0  C in the winter, it is heated to 2  C by an electric heater installed near the shaft. Meanwhile, the heated air passes through the ventilated shaft to the ventilated tunnel. Then, it is taken into the service tunnel by forced ventilation. The warm air flows along the service tunnel to the main tunnel portal direction. By the way, the temperature of the main tunnel is heated. In Norway (Graphic Division NPRA, 2004; Gronhaug, 1990), the shelter of waterproof and anti-freezing was used to prevent tunnel frost damage. The aluminum and asbestos boards were usually used in the early. However, the installation of the aluminum board was costly and time consuming. Therefore, it was developed later that the plastic foam was sandwiched between aluminum boards, steel boards or glass fiber reinforced polyester boards to form a plate components. A doubledecked door for cold protection was applied in a few tunnels. This door can be opened by use of an automatic device when the train is near the tunnel and can then be closed after the train passes. In the United States, insulation drainage system was used to prevent tunnel frost damage (Elliot et al., 1996; ТруЪчиков, 1990). Closed micro-porous polyurethane material was made into plate affixed to the rock or masonry lining surface. Many measures were used in drainage system to prevent tunnel frost damage; for example, insulation was used in the portal of drainage tunnel, foam insulation was used in drainage channel, and heating cable was employed in drainage pipes. In France, separation wall board was used to prevent tunnel frost damage (Jaby, 1990). The back of the wall board is made of polyethylene foam, whereas the front is made of reinforced concrete. In Japan (Kurokawa, 1980; Kojima and Asakura, 1996), thermal insulation and heating methods were used to prevent tunnel frost damage. As for thermal insulation method, the insulation material is set on the lining surface or between the initial support and secondary lining. This method includes Uprofile groove combined with insulation material method, surface thermal insulation method, and composite lining thermal insulation method. For some local sites where the frost damage is extremely serious, the heating methods are used, for example the electric heating or warm tube method.

Fig. 2 e Anti-freezing drainage tunnel system. From the above, we can see that cold region tunnel frost damage preventions applied in foreign were mainly based on thermal insulation, drainage and active heating. Setting the insulation materials on the surface of rock mass or lining concrete is an effective thermal insulation measure to reduce the heat exchange between tunnel structure and cold air. Thereby, the frost heave of groundwater in tunnel is prevented, and the freeze-thaw damage of the lining structure and rock mass is reduced. In addition, the set of thermal insulation door can reduce the intrusion of cold air into tunnel, which is also an effective thermal insulation measure. For the drainage of tunnel, the drainage channels should be set outside the freezing range, or lay thermal insulation material on the channels to ensure that the tunnel drainage is smooth without ice clogging. The above measures are at low cost, and the effect is remarkable. Therefore, they are widely applied in many countries. However, for the active heating method, such as electric heating and warm pipe, the cost is very high. It is always used in the section of severe frost damage, or partial use in the extreme cold environment.

5.2.

Local preventive measures for frost damage

Chinese tunnel scholars have made many efforts to solve tunnel frost damage. Tunnel frost damages are mainly waterproof and drainage and anti-freezing problems. Current local preventive measures for tunnel frost damage are discussed below (Chen, 2006a,b,c; Chen and Luo, 2007; Luo, 2007). (1) Anti-freezing drainage tunnel Anti-freezing drainage tunnel is a key measure to dewater groundwater. This tunnel is located under the main tunnel and is similar to a small tunnel with drainage holes. Drainage tunnel comprises a drainage system with vertical drainpipes, drainage holes, heading tunnel, checked shaft, and portal of drainage with vertebral body for insulation. The groundwater behind the lining in the rock mass is collected by the drainage system in the drainage tunnel, and then discharge to the outside. Drainage tunnel can significantly reduce or eliminate tunnel frost

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Fig. 3 e A warm conical mound of drainage outlet (unit: cm). (a) Plane. (b) IeI cutaway.

damage, such as groundwater as spring, hanging ice, and frost heave. An example of a drainage system is shown in Fig. 2. Drainage tunnel is suitable for cold region with the mean temperature of the coldest month below 20  C and the freezing depth of rock of 5e6 m. The buried depth of drainage tunnel depends on the freezing depth of rock mass. The suitable depth is 5 m in general, as shown in Fig. 2. If the thickness of the soil above the tunnel is less than the freezing depth, then the insufficient part should be filled with embankment. A warm conical mound of drainage outlet (Fig. 3) can be adopted to ensure the outlet being unfrozen in cold seasons. (2) Central deep-buried drain Central deep-buried drain is a drainage facility buried under the main tunnel at the depth exceeding the freezing depth of rock mass and uses the ground temperature to keep the water in the drainage unfrozen, as shown in Fig. 4. Central deep-buried channel is generally applicable to cold regions, wherein the location of the freezing depth of rock mass is between 1.5 and 2.5 m and water exists in winter. Central deep-buried drain and drainage tunnel are basically similar with few differences. Drainage tunnel is always used for deep-freezing regions and constructed by underground excavation method. However, central deep-buried channel is buried shallow and constructed by cut-and-cover method. The major advantage of central deep-buried channel is the excellent drainage effect because of the strong penetration of loose backfilled. This method is limited by the impact on the finished tunnel structure of lining and substrate during excavation, which can bring security risks to the project. The disadvantages of this method outweigh its benefits.

portal sections of 150e400 m length, because the middle section of tunnel exhibits no frost damage owing to its high temperature. The length of the drainage channel for frost prevention should be appropriately selected in low-temperature tunnels, as shown in Fig. 5. The drainage channel for frost prevention generally adopts a side ditch system. The upper part of the channel is covered by double slabs, the insulation material is filled between the upper and lower slabs, the thickness of insulation is generally more than 30 cm, and water flow in the channel is set in the lower part. However, for some severe and extreme cold tunnels, the method is not feasible, such as the Baikaer tunnel in Nenlin railway where the average temperature of the coldest month is down to 28  C. Asphalt glass wool was adopted as the insulation material. However, the water in the channel was frozen in winter. To prevent the failure of this channel, the 450 mm steam pipe was reserved under the channel during construction, and equipped with a boiler with an evaporation amount of 0.4 T/h to warm the channel. The boiler started to work from the beginning of the winter in 1977, thereby finally solving the channel freezing problem. However, the human, material, and energy consumption are costly. The drainage channel for frost prevention is unsuitable to cold regions but is suitable to moderate-freezing damage regions. In addition, in the Qidaoliang tunnel in Gansu Province, a boiler was installed outside the tunnel and connected with heating pipes installed in the drainage channel inside

(3) Drainage channel for frost prevention The drainage channel for frost prevention is buried shallow in the freezing depth of rock mass. Insulation measures are applied in the channel to prevent water freezing. The drainage channel for frost prevention is generally suitable for cold regions with average temperature of the coldest month from 10  C to 15  C, local freezing depth of rock mass of 1.0e1.5 m, and possible existence of water in winter. When the tunnel is long, the insulation should be set only on both

Fig. 4 e Central deep-buried drain.

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Fig. 5 e Drainage channel for frost prevention. tunnel to prevent the channel from freezing. However, the human, material, and energy consumption are costly. Therefore, the drainage channel for frost prevention is unsuitable to heavy and serious cold regions but is suitable to the moderate or light cold regions. (4) Thermal insulation layer The heat exchange between cold air and rock mass is the major cause of frost damage in cold region tunnels. The set of thermal insulation layer can decrease the freezeethaw range of tunnel, and ensure the water behind the lining is unfrozen and avoid the frost heave. The thermal insulation layer can be installed in two ways. One is to install the thermal insulation layer on the inner surface of the lining. Fig. 6 shows the Dabanshan Tunnel in the National Highway 227 (Xining to Zhangye) in China, in which the polyurethane foam board is installed on the lining surface. The other is to install the thermal insulation layer between two lining structures. For example, in the Fenghuoshan Tunnel constructed by New Austrian Tunneling Method (NATM) in Qinghai-Tibet

Railway, the thermal insulation layer is installed between the initial support and the secondary lining. A surface spraying method can also be adopted to complete the thermal insulation layer, for example in Wusongling Tunnel in Suifenhe-Manzhouli Highway (G015). At present, the construction methods of thermal insulation layer include surface spray method, surface laying method, and intermediate laying method. However, the construction technology and related design parameters need to be further studied. The material, thickness, and length of thermal insulation layer were explored and a systematic design method of thermal insulation layer has been formed (Lai et al., 1999c; Li et al., 2004; Tan, 2010; Yang et al., 2006; Zhang et al., 2006b). But, some key technology problems are still unsolved, for example the appropriate length determination of thermal insulation layer. Now, the commonly used calculation formula is from the research result of Kurokawa (1980) in Japan. It is a fitting formula for the temperature at tunnel portal and the distance between the tunnel portal and the location where the temperature is 0  C. However, the length of thermal insulation layer is related to not only the temperature but also the geological condition, distribution of groundwater, direction of tunnel portal, and slope of drainage. Many tunnels with thermal insulation layer have been constructed in China, which has been the first option in the construction and treatment of cold region tunnels. However, thermal insulation layer should be combined with necessary drainage measures depending on the actual situation of tunnel. The types of drainage systems mentioned above have their own advantages and disadvantages and specific scope of application. Thus, the choice of drainage should be flexible on the basis of local conditions of tunnel. For examples, although the drainage tunnel has the disadvantages of construction difficulties and high cost, it is an effective and reliable antifreezing drainage measure in permafrost and severe or extreme cold regions. When there is a large amount of groundwater in tunnel, the drainage tunnel should be preferred. The use of central deep-buried channel is limited because it will affect the stability of the tunnel side wall due to the high buried depth. In addition, a lot of engineering practice has proved that the central deep-buried channel can affect the

Fig. 6 e Thermal insulation layer of the Dabanshan Tunnel.

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stability of the finished tunnel lining and basement structure and threaten the safety of the project. A shallow-buried side ditch can also be used in the cold area tunnel if the thermal insulation measures are strengthened and the frost prevention effect is ensured. It is also suitable to take heating measures in the areas where heat sources are cheaper. Each frost prevention measure has its own advantages and disadvantages. Therefore, it is necessary to take appropriate prevention measures for frost damage, according to different frost damage degrees and actual situation of tunnel. Apart from the preventive measures for frost damage above, the temperature within the tunnel can also be increased by other measures. For example, the cold-proof door or cold-proof curtain can be installed at tunnel entrance, if the traffic volume of the tunnel is low. A cold-proof curtain was used in the Xinganling Tunnel and showed a good effect. A cold-proof door was also used in the Dabanshan Tunnel, thereby improving the inside temperature of the tunnel. Such installation measures should be linked to the station signal to automatically open and close and thus prevent traffic accidents.

6.

Conclusions

Frost damage is a major hazard in highway and railway transport and is a complex problem. Local and foreign scholars have systematically studied the mechanism of frost damage, law of temperature field, classification of frost damage, and preventive and control measures. Some suggestions and conclusions are proposed and served as theoretical support and valuable engineering reference for the design of highaltitude cold region tunnels. However, a few issues on the frost damage of cold region tunnels remain to be further explored. (1) The frost heave force value calculated by the frost damage mechanism of three theories differs from the measured value. The three theories only determine the cause of frost damage. However, many factors to cause frost damage are neglected. Therefore, a new comprehensive theory of frost damage mechanism should be actively explored and developed by tunnel scholars. (2) The structure damage of shotcrete as the main support unit of tunnel under the freezeethaw cycle is rarely examined. Therefore, further research and breakthroughs on this area are needed. (3) Studies on temperature field of cold region tunnels have obtained regular results. However, the summary and analysis research on the distribution regularity of temperature field in cold region tunnels is rare and should be given much more attention. (4) The classification of tunnel frost damage should be more scientific and practical through the combination of the tunnel disease characteristics including the lining variation and deterioration from Japanese research results and the displacement rate of clearance convergence, and the conditions of frost damage including the climate and groundwater. Meanwhile, the factors of buried depth and geological conditions of rock mass

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should be taken into account in the future study to make the classification more specific. (5) Existing prevention and control technologies of frost damage present their own advantages and disadvantages and can adapt to different levels of frost damage. Therefore, the prevention and control technologies of frost damage should be selected depending on the different levels of frost damage and different engineering conditions.

Conflict of interest The authors do not have any conflict of interest with other entities or researchers.

Acknowledgments The authors would like to acknowledge the financial support provided by the National Key Research and Development Plan of China (Grant No. 2016YFC0802202); the National Natural Science Fund Project of China (Grant Nos. 51108034 and 51678063); the China Postdoctoral Science Foundation (Grant No. 2016M602738); the Chang Jiang Scholars Program (Grant No. T2014214), the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2017JM5051); and the Traffic Science and Technology Project in Jilin Province (Grant No. 2014-4-2-14).

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Prof. Yanbin Luo is a professor in the Institute of Geotechnical and Tunnel Engineering in School of Highway, Chang'an University, Xi'an, China. He received a PhD in underground engineering from Beijing Jiaotong University. His research interests include theory and technology of frost damage prevention in cold region tunnel, stability theory and control technology in large-span tunnel and weak rock mass tunnel, and design theory and construction technology of loess tunnel. He has hosted and participated in more than 17 research projects, published more than 42 journal papers, and obtained 13 patents.

Prof. Jianxun Chen is in the Institute of Geotechnical and Tunnel Engineering in School of Highway, Chang'an University, Xi'an, China. He received a PhD in underground engineering from Beijing Jiaotong University. His main researches have focused on the theory and technology of frost damage prevention in cold region tunnel, stability theory and control technology in large-span tunnel and weak rock mass tunnel, and design theory and construction technology of loess tunnel. He has hosted more than 50 research projects, published more than 100 journal papers, and obtained 25 patents.