1. Introduction
In recent years, more and more tunnels in high-altitude and high-latitude areas have been constructed in China, thus the problem of frost damage in old tunnels in cold regions is becoming more and more prominent [
1]. Apart from icing problems, several tunnels with a service life of more than 10 years have demonstrated the phenomena of serious cracking of the lining, brittle lining, partial peeling, and falling off near the portal [
2]. In contrast to the problem of icing in tunnels, the deterioration of the lining concrete affects the bearing structure, which will seriously threaten the safety of the tunnel structure. Additionally, the problem of the lining blocks falling off will have an even more serious impact on traffic safety than will the falling of ice. Therefore, it is very important to research the rules and influence of tunnel lining material deterioration in cold areas to increase our knowledge of maintenance and operation safety.
At present, research on the frost damage of tunnels in cold regions mainly focuses on the temperature field of the tunnel and the influence of frost damage. The analytical calculation method, model experiments, and in situ tests are the main methods used in these studies. A series of analytical solutions considering different boundary conditions, different parameters, and different models were carried out to study the frost heaving force in cold-region tunnels. Based on the initial elastic state of the surrounding rock, a semi-analytical method to calculate the stress in the plastic was proposed [
3]. Then, the entire surrounding rock was divided into four zones: the unfrozen elastic zone, the frozen elastic zone, the frozen plastic zone, and the support zone. In addition, a more complicated elastoplastic calculation model for the surrounding rock in cold-region tunnels was established [
4]. Meanwhile, based on the stochastic analysis model and the stochastic finite element method, the stochastic mechanical characteristics of tunnels in cold regions were investigated [
5]. Furthermore, an analytical elastoplastic solution for frost heaving force was recently proposed, in which an anisotropic frost heave coefficient, k, was introduced to consider transversely isotropic frost heaving [
6]. Then, a novel noncircular solution for frost heaving force was established and verified using the example of the Zhegu Mountain tunnel [
7]. Additionally, aiming at the prediction of crack initiation and propagation in brittle materials, an efficient parameter estimation framework was proposed, involving a step-wise Bayesian inversion framework for ductile fractures to provide accurate knowledge regarding the effective mechanical parameters [
8,
9]. These numerical calculation methods for the frost heaving force of tunnels include comprehensive explanations and support for the topic of freezing damage and prevention in cold-region tunnels.
On the other hand, the analytical calculation and model test were carried out to study the distribution laws and factors of the tunnel temperature field. Based on the analytical results of the temperature field in the cross-section and the longitudinal direction of tunnels [
10,
11], a three-dimensional analytical model of the temperature field was proposed [
12]. The result show that the freezing length reduced from 143 m to 70 m and the maximum radial freezing depth at the entrance is also shortened from 4.7 m to 2.4 m due to a 5 cm insulation layer. The analytical calculation of the temperature field in the tunnel has achieved a comprehensive research result. However, their analytical calculation models took the temperature function over a period of one year as the boundary condition, but the influence of daily periodic temperature change on freezing length and freezing depth was ignored. As a result, the deterioration of lining structure subjected to daily freeze–thaw cycles was ignored. Additionally, model tests to evaluate the reliability of a 5 cm-thick insulation layer were developed [
13], and a mathematical optimization model of the insulation layer’s parameters was constructed by taking the Daban mountain tunnel as an example [
14]. This extends the distribution laws and factors of the tunnel temperature field of tunnels with insulation layers.
Further, the temperature distribution of some cold-region tunnels was measured by advanced equipment and methods in 104 tunnels located in Gangwon Province of Korea [
15] and the Hongfu tunnel [
16], the Zuomutai tunnel [
17], and the Wushaoling tunnel [
18] in China. Their test results were in agreement that the air temperature in the tunnel changes periodically in the form of an approximate trigonometric function from the annual perspective. The temperature of the tunnel portal section is affected by the outside of the tunnel, and the influence of the middle section is small, which shows that the temperature fluctuation of the portal section is large and the temperature fluctuation of the middle section is small. The temperature changes in the sections at the two sides of the tunnel are different, and the temperature distributions are asymmetrical along the tunnel length. The test results of the temperature field distribution provide practical verification and theoretical support for the further understanding of the mechanism and reasonable design of tunnel frost damage. Lately, the distribution laws of daily freeze–thaw cycles in tunnels were studied [
19], and it was revealed that unsaturated freeze–thaw cycles will also damage the strength and durability of concrete cube. This again draws researchers’ attention to the deterioration of the lining structure. However, the influence of concrete deterioration on the stress and crack of lining structure has not been studied further in cold region tunnels.
In this paper, based on the analysis of the service environment and distribution of freeze–thaw cycles in cold-region tunnels, the rule of the gradual deterioration of the lining structure was proposed. An experimental system was established to simulate the deterioration of the lining structure of cold-region tunnels; it was composed of a circular tunnel models, a cold air circulation system, and a temperature test system. The initial deterioration of the lining concrete was realized after 100 unsaturated freeze–thaw cycles took place, and the temperature field of the experimental model was tested during the freeze–thaw cycles. The bearing capacity and strain of the lining models were tested. Lastly, the influence of the deterioration of the lining structure on the service tunnels was discussed in the hope of providing support for the maintenance and design of tunnels in cold regions.
2. Influence of Freeze–Thaw Cycle on Tunnels
The tunnel temperature field test was carried out on the Wushaoling Tunnel Group in Yongdeng on the Gulang expressway (G30). The tunnel group is located in the north branch of Qilian Mountain, at an altitude of 2085–3050 m. The annual minimum temperature in this area is −24 °C, and the icing period is from November to March. The location of the tunnel group is shown in
Figure 1. The Wushaoling Tunnel Group uses the construction standard of two-way separated tunnels and a design speed of 60 km/h. The tunnel group is composed of five tunnels, and three tunnels with different lengths were selected for evaluation in this study. Tunnel No. 1 is 4905 m long, tunnel No. 3 is 875 m long, and tunnel No. 5 is 2936 m long. An intelligent temperature recorder was used to test the temperature field of the tunnel. The layout of the test section is shown in
Figure 2. The sensor of the recorder was tightly attached to the lining surface, about 2.5 m from the arch foot, usually on the sidewall on the right side of the driving direction. The sampling interval of the test was 1 h. Through the temperature field test, we obtained the longitudinal distribution of the freeze–thaw cycles in the tunnels.
2.1. Distribution Law of Freeze–Thaw Cycle in the Longitudinal Direction of the Tunnel
The results show that freeze–thaw cycles occurred uniformly in medium-length highway tunnels. Additionally, there were obvious differences in the number of freeze–thaw cycles taking place in extra-long tunnels, which could occur hundreds of times at the tunnel entrance and only six times in the middle of the tunnel. The number of freeze–thaw processes occurring on the surface of the lining is shown in
Figure 3. For tunnel No. 1, which is longer than 4500 m, freeze–thaw cycles occurred six times at 3400 m, which was one twentieth of the amount of cycles occurring at the entrance. For tunnel No. 3, which is no more than 1000 m, the numbers did not change much with the increase in length. Most parts are subjected to around 60 freeze–thaw cycles; this is a relatively stable stage. For tunnel No. 5, the freeze–thaw cycles gradually declined to a low level and then climbed to the previous level. Overall, we found that the lining near the portal section could experience thousands or even tens of thousands of freeze–thaw cycles in its design life. The damage caused by undergoing a large number of freeze–thaw cycles cannot be ignored.
2.2. Distribution Law of Freeze–Thaw Cycle in Cross-Section
The continuous measurement results of the temperature field show that the daily period temperature fluctuation caused by day–night alternation is very significant and widespread. The distribution law of the freeze–thaw cycles in the tunnel cross-section was initially studied by numerical simulation; the model is shown in
Figure 4a. A composite equation with annual and daily periodic temperature variations was adopted as the temperature load on the lining surface, as shown in Formula (1) [
18].
where
t is time, by the hour;
Tb is the daily amplitude of temperature (°C);
T1 is the annual period of temperature change, which is recommended to be 8640 h;
T2 is a daily period of temperature change;
is the annual initial phase; and
is the daily initial phase. The numerical simulation result showed that the number of freeze–thaw cycles taking place at different radial depths of the tunnel secondary lining are different, as shown in
Figure 4b. It decreases rapidly with the increase in radial depth. When the number of freeze–thaw cycles on the tunnel lining surface reaches 140, the number of freeze–thaw cycles at the radial depth of 5 cm can reach 80, and it can reach 50 at the radial depth of 10 cm. The tunnel lining concrete suffers different freeze–thaw cycles at different radial depths, which also inevitably leads to the different deterioration of the concrete strength at different radial depths.
2.3. Deterioration of Tunnel Lining Concrete
In fact, tunnel lining concrete is in an unsaturated state in service, and concrete would be subjected to tens of thousands of unsaturated freeze–thaw cycles, which inevitably leads to the deterioration of the lining concrete material [
19]. The number of unsaturated freeze–thaw cycles varies gradually in the longitudinal direction, and in the cross-section of the tunnel, which leads to the deterioration of concrete, showing a gradual distribution related to the number of freeze–thaw cycles taking place. A schematic diagram of the progressive deterioration of tunnel lining concrete in cold regions is shown in
Figure 5.
In the cross-section of the tunnel, the number of unsaturated freeze–thaw cycles experienced by the lining surface is the greatest, and the deterioration degree is most serious. With the increase in radial depth, the number of freeze–thaw cycles decreases and the deterioration degree of the lining is more slight. Similarly, the number of freeze–thaw cycles decreases in the longitudinal direction of the tunnel from the tunnel portal, with the degree of deterioration of the lining becoming gradually lighter from the tunnel portal. What kind of influence will this have on the lining structure? In the following section, we will study this through a model test.
6. Discussion
The phenomenon of the falling off or peeling off of lining concrete usually occurs in cold-region tunnels after lining material degradation. Based on the loading structure method, numerical simulation was used to study the influence of lining material gradual degradation on the lining structure with ANSYS. According to the test, about 100 unsaturated freeze–thaw cycles per year occur in the lining surface in Section 1. Four working conditions were selected, as shown in
Figure 17. We found the following: (1) There is no deterioration of the lining structure in the initial stage of tunnel construction. (2) After 10 years of operation, the lining surface within 5 cm suffered 1000 unsaturated freeze–thaw cycles, showing a slight deterioration. (3) After 20 years of operation, the lining surface within 5 cm suffered 2000 unsaturated freeze–thaw cycles, showing a moderate deterioration and a mild deterioration within 5–10 cm of the lining surface. (4) After 30 years of operation, 3000 unsaturated freeze–thaw cycles occurred within 5 cm of the lining surface, showing severe deterioration and moderate deterioration within 5–10 cm of the lining surface and mild deterioration within 10–15 cm of the lining surface. The physical and mechanical properties and parameters are shown in
Table 3. A numerical simulation was carried out for the general cross-section of highway tunnels.
The simulation results show that the gradual deterioration of the lining concrete changes the stress state of the lining structure in the vault of the tunnel. Under the condition of no deterioration of the lining taking place, the section eccentricity, e0, is less than 0.2 times the height of the boundary section, and the safety of the section is controlled by the compressive strength of the concrete. With the increase in the tunnel’s operation years, the gradual deterioration of concrete leads to the upward displacement of eccentricity, and the safety of the section is controlled by the tensile strength of the concrete. The safety factor of the central section of the arch tunnel is reduced from 8.3 to 6.0 and, finally, to 3.9, as shown in
Figure 18. It can be seen that, with the increase in operation life, the safety state of the tunnel vault gradually worsens. After 30 years of operation, the concrete on the lining surface of the arch roof lining is now close to the ultimate tensile state as shown in
Figure 19. If a certain number of temperature cracks occur in the construction of the tunnel lining, with the gradual deterioration of the lining concrete these cracks will develop gradually, leading to serious cracking of the lining structure and even the peeling off and falling of blocks.
In this paper, we have used a linear analysis model to analyze the influence of the deterioration of lining concrete on the structure, and predicted the lining cracks. In actual engineering, concrete is a nonlinear material, and the results of a linear model will deviate from the actual situation. At present, there are many nonlinear simulation models and crack prediction models. In subsequent research, we will carry out nonlinear analysis on the influence of lining deterioration, and try to obtain more results.