Effect of increased linings on micro-pressure waves in a high-speed railway tunnel

Tunnelling and Underground Space Technology 52 (2016) 62–70

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Effect of increased linings on micro-pressure waves in a high-speed railway tunnel Feng Liu, Song Yao ⇑, Jie Zhang, Yi-ben Zhang Key Laboratory of Traffic Safety on Track of Ministry of Education, Central South University, Changsha 410075, PR China

a r t i c l e

i n f o

Article history: Received 23 December 2014 Received in revised form 16 November 2015 Accepted 25 November 2015 Available online 14 December 2015 Keywords: High-speed railway tunnel MPW Increased lining technology Full-scale measurement Numerical simulation Moving-model experiment

a b s t r a c t A micro-pressure wave (MPW) is generated when a train enters a tunnel at high speed, which causes a strong impact on the environment around the tunnel. The increased lining used to repair damage in high-speed railway tunnels changes cross-sections and has a strong influence on the MPW at the tunnel exit. In this paper, the methods of full-scale measurement, numerical simulation and moving-model experiments are used to study the MPW generated in a tunnel whose lining is increased. The rules governing the effect of increased linings on MPWs are obtained, which can be used as a reference for the Tunnel Damage Regulation Project in China. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Tunnel damage is a worldwide problem (Wang et al., 2001) that not only threatens traffic safety in tunnels but also shortens the maintenance cycle and service life of the tunnels. Increased lining technology is a common method to repair tunnel damage in ordinary-speed railways. It adds concrete with a certain thickness to the surface of the original lining, which can prevent the development of crack damage (Pei et al., 2013). In recent years, increased lining technology has been widely applied in high-speed railways in China because of the serious tunnel damage. However, the impact of increased lining on the aerodynamic effect in a highspeed railway is more obvious than that in an ordinary-speed railway. It is necessary to study how the increased lining impacts the aerodynamic effect. An important part of the aerodynamic effect in a high-speed railway tunnel (Raghunathan et al., 2002) is that the MPW is formed as a consequence of the steepening of the nose entry wave and results in the generation of a sonic boom at the exit of the tunnel, which can be sufficiently strong to disturb local inhabitants by, for example, rattling the windows of their houses (Baron et al., 2006; Vardy, 2008). According to previous studies, many factors affect the MPW significantly: the nose of the train (Bellenoue and Kageyama, 2002; Kikuchi et al., 2011; Ku et al., 2010), the hood at the tunnel portal ⇑ Corresponding author. E-mail addresses: [email protected] (F. Liu), [email protected] (S. Yao), [email protected] (J. Zhang), [email protected] (Y.-b. Zhang). http://dx.doi.org/10.1016/j.tust.2015.11.020 0886-7798/Ó 2015 Elsevier Ltd. All rights reserved.

(Liu et al., 2010; Murray and Howe, 2010; Uystepruyst et al., 2013; Xiang and Xue, 2010), shafts (Miyachi et al., 2014; Ricco et al., 2007; Yoon et al., 2001), cross passages (N’Kaoua et al., 2006), track form (N’Kaoua et al., 2006), and so on. However, the effect of increased lining on the MPW has been little studied. Traditional methods of studying the aerodynamic phenomenon of high-speed trains are full-scale measurement (Iida et al., 2001; Ko et al., 2012; Sakuma et al., 2010), numerical simulation (Choi and Kim, 2014; Muñoz-Paniagua et al., 2014; Uystepruyst et al., 2011) and model experiments (Gilbert et al., 2013; Liu et al., 2010; Miyachi et al., 2014; Zhou et al., 2014). This paper studies the MPW of tunnels with increased linings using all three methods. The results can be used as a reference for the Tunnel Damage Regulation Project in China.

2. Methodology 2.1. Full-scale measurement The Pingtu Tunnel, selected for our study, is located on a passenger-dedicated line between Chenzhou City and Lechang City in China. The length of the tunnel is 1921 m, and the crosssectional area is 100 m2. Although it is a double-track railway, we only study the direction of travel from Chenzhou to Lechang. The entrance and exit of the tunnel have a windowed hood and a hat oblique hood, respectively. A new lining is located 475 m away from the tunnel entrance, for which the length and the thickness

F. Liu et al. / Tunnelling and Underground Space Technology 52 (2016) 62–70

are 90 m and 0.3 m, respectively. There exists a gradual transition of 1 m in length between the new lining and the original one. To analyse the influence of the new lining on the transient pressure, pressure sensors (model 8515C-15, Endevco) were installed in the side walls of different sections around the new lining. To study the amplitudes of the MPW, low-frequency microphones (model 4193, B&K) were installed 20 m and 50 m from the tunnel exit. A multi-channel IMC recording system and a PULSE (3560C) analyser were used for data acquisition and storage. The tunnel structure and the arrangement of test points are shown in Fig. 1. This passenger-dedicated line was officially operated in 2009, and the highest operating speed is 350 km/h. Two common electric multiple units (EMUs), the CRH2C double-connection EMU and the CRH380A EMU, were selected for measurement (Fig. 2 and Table 1). The test speed of the EMUs ranged from 250 km/h to 350 km/h, and three repetitions were undertaken for each speed. Measurement uncertainty mainly came from the repeatability of measurement, the pressure sensor or the microphone and the data acquisition equipment. The measurement uncertainties for pressure and for the MPW in our full-scale measurement were under 1.8% and 1.2%, respectively, which guarantees reliability. 2.2. Numerical simulation It is not practical or economic to rely only on full-scale measurement. In this paper, the influence of the new lining on the

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MPW is further analysed by means of numerical simulation and a moving-model experiment. 2.2.1. Numerical domain and boundary conditions To understand the aerodynamic phenomenon of the tunnel entry problem, a three-dimensional, viscous, compressible, unsteady, turbulent model was applied (Liu et al., 2010). The numerical domain is shown in Fig. 3(a). The external domain is simulated as two rectangular bodies. A sliding mesh technique (Chu et al., 2014) is used to simulate the relative motion between the train and its surroundings. The no-slip solid-wall boundary condition was used for the tunnel walls, the train body and the ground. The far-field boundary condition was used for the external domain and the tunnel extremity. At the beginning of the computation, the train was placed 50 m from the tunnel entrance to ensure the stability of numerical simulation. 2.2.2. Geometrical model and mesh The calculation model for the tunnel was obtained by simplifying the real geometrical structure of the Pingtu Tunnel. The windowed hood at the entrance and hat oblique hood at the exit were retained, but the curvature radius and the track gradient were ignored in the model. Similarly, the EMU calculation model was obtained by simplifying the geometrical structure of the CRH380A (Fig. 2(c)). This simplification means ignoring some small but complex structures, such as pantographs, lights and door handles. In

Fig. 1. (a) Profiles of the tunnel, (b) arrangement of the test points near the new lining and (c) cross-section of the tunnel.

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Fig. 2. (a) CRH2C double-connection EMU, (b) CRH380A EMU, (c) CRH380A EMU for numerical simulation and (d) CRH380A EMU for the moving-model experiment.

Table 1 Details of the EMUs. Types of EMU

Length (m)

Formation (car)

Length of the nose (m)

Cross-section (m2)

CRH380A CRH2C DC

200.0 402.8

8 16

12.00 9.55

11.12 11.20

around the train body was 0.05 m, and the total number of meshes was 5,071,139. The mesh independence was checked by comparing the simulation results of the mesh set with 8,024,331 meshes against that with 5,071,139 meshes. The difference in the amplitudes of the MPW was 1.6%. Therefore, the mesh set with 5,071,139 meshes was adopted for the rest of the simulation. 2.2.3. Numerical details The governing equations were solved by the commercial software package Fluent 6.3.26. The computational domain was discretized by the finite volume method. The standard k–e turbulence model was used. The convection and diffusion terms were discretized with the second-order upwind scheme. The time derivative was discretized with the second-order implicit scheme for unsteady flow calculation. The time step was 0.001 s. According to previous studies (Chu et al., 2014; Liu et al., 2010; Muñoz-Paniagua et al., 2014), the aerodynamic pressure and the MPW generated by high-speed trains travelling through a tunnel can be simulated effectively by the method adopted in this paper. In addition, the comparisons for the MPW between the experimental data and the numerical results are shown in Section 3.3. 2.3. Moving-model experiments Scale model experiments were carried out on the movingmodel rig at Central South University. This moving-model rig can be used for a variety of aerodynamic investigations. It consists of 164-m-long tracks along which reduced-scale model vehicles can be propelled at speeds of up to 139 m/s (500 km/h). The same facilities have also been used in previous studies, including Liu et al. (2010) and Zhou et al. (2014), who both obtained reasonable and reliable results.

Fig. 3. (a) Numerical domain and (b) mesh of a cut plane.

this way, the mesh quality can be improved and the calculation results are not affected (Chu et al., 2014; Uystepruyst et al., 2013). The domain near the train was discretized by a non-structured mesh and the other domain by a structured mesh. A cut plane view of the volume mesh is shown in Fig. 3(b). The smallest mesh size

2.3.1. Experimental models The scale ratio of the models used in our experiment was 1:31, and some photographs of this experiment are shown in Fig. 4. The model of the tunnel was established from scaled drawings of the Pingtu Tunnel. The length and cross-sectional area of the tunnel model are 61.968 m and 3.226 m2, respectively. The hoods at the tunnel portals are retained, and the installation of new lining is

F. Liu et al. / Tunnelling and Underground Space Technology 52 (2016) 62–70

achieved by increasing the thickness of the wall of the tunnel model. The model of the high-speed train was built from scaled drawings of the CRH380A. Fig. 2(d) shows a photograph of the train model mounted in the moving-model rig. The train model is grouped in eight coaches, which are 6.452 m long, 0.109 m wide and 0.119 m high. 2.3.2. Test system The test system is used for real-time measurement of the running speed of the train model and the amplitudes of the MPW at the exit of the tunnel. As the maximum pressure of the MPW is always used as a measure of acceptability and the maximum will always be dominated by lower-frequency components of the radiated waves (Vardy, 2008), a low-frequency microphone (model 4193, B&K) and a PULSE (3560C) analyser were utilised in our experiments. These provide a satisfactory level of rationality and precision for the measurement of the MPW (Yang et al., 2014).

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The distance from the installed microphone to the tunnel exit is 0.645 m (corresponding to 20 m in full scale). For each experimental configuration, 25–30 repetitions were undertaken. Each run was examined for its acceptability in terms of train speed, and accuracy within 0.5% of the target train speed was the desired criterion. The five runs with the best results were picked, and the ensemble-average amplitudes of the MPW were obtained for each experiment case. The measurement uncertainty for the MPW in our model experiment was less than 0.8%, which guarantees the reliability of the measurement. 2.3.3. Similarity conditions To validate the results of the model experiment, similarity conditions should be ensured. This means some important similarity parameters should be equal between the experiment and the real phenomenon. For the train model experiments, the important similarity parameters are as follows (Auvity et al., 2001; Gilbert et al., 2013):

Fig. 4. Lining structure in the tunnel model. (a) Windowed hood in the entrance, (b) hat oblique hood in the exit, (c) without new lining and (d) with new lining.

train Mach number. train-tunnel blockage ratio. scaling of the train geometry and the tunnel geometry. Reynolds number.

In our experiment, the first three parameters met the similarity conditions, but the last did not. When the train speed was 300 km/ h, the Reynolds numbers of the full-scale measurement and model experiment based on the hydraulic diameter of the tunnel were 4.9 ⁄ 107 and 1.6 ⁄ 106, respectively. However, past studies, such as Ogawa and Fujii (1997), show that the effect of viscosity on pressure waves generated by a train is not significant. In addition, there are many devices (Bellenoue et al., 2001; Doi et al., 2010; Miyachi et al., 2014; Ricco et al., 2007) for studying the aerodynamics of a tunnel with reduced-scale models whose scales are close to or less than 1:31. Therefore, the scaling for the Reynolds number was not taken into account in our experimental model. 3. Results and discussion 3.1. Full-scale measurement 3.1.1. Transient pressure near the new lining The peak pressures are mainly decided by tunnel length, train length, train speed and location of test points. Fig. 5 shows the peak-to-peak value (maximum-minimum) of the pressure at Point 5. From the test results, the peak-to-peak value of the pressure is proportional to the square of the train speed. The CRH2C doubleconnection, with a longer train formation, has a higher peak-topeak pressure value than the CRH380A does. From previous research (Baron et al., 2006; Vardy, 2008), the MPW is mainly influenced by the maximum gradient of the initial compression wave. Fig. 6 shows the maximum gradients of the initial compression wave for the test points near the new lining. For both the CRH2C double-connection or CRH380A, the maximum gradient of the initial compression wave increases as the train speed increases. When the EMUs are running at the same speed, the maximum gradient of the initial compression wave for the CRH2C is greater than that for the CRH380A. During the propagation of the initial compression wave, the main change in the pressure gradient occurs at the point where the tunnel cross-section is about to change, whereas there is little change in other places. For example, when the initial compression wave arrives at the beginning of the new lining, a new compression wave is reflected because of the decrease in the cross-section of the tunnel. The reflected wave and the original compression wave are superimposed and intensified in front of the new lining (point 3); therefore, the pressure gradient of the corresponding test point increases. Similarly, when the initial compression wave arrives at

Pressure (kPa)

CRH2C Double Connection

Maximum of Pressure Gradient (kPa/s)

The The The The

CRH380:

Train Speed (km/h) Fig. 5. Peak-to-peak pressure value at Point 5 versus EMU speed.

300km/h

330km/h

350km/h

330km/h

350km/h

(a) 250km/h

300km/h

Testing Point

(b) Fig. 6. Maximum gradients of the initial compression wave for the different test points. (a) CRH2C DC and (b) CRH380A.

the end of the new lining, a new expansion wave is reflected because of the increase in the cross-section of the tunnel. The reflected wave can weaken the intensity of the original compression wave near the end of the new lining (point 6), so the pressure gradient of the corresponding test point decreases. 3.1.2. MPW at the exit of the tunnel Fig. 7 shows the MPW when the EMU passes through the Pingtu Tunnel at different speeds. The MPW increases with the increase of train speed. Although the two EMUs vary greatly in length, the MPWs show little difference because of their similar crosssectional areas. When the EMU passes through the tunnel at 350 km/h, the MPW at 20 m from the tunnel exit is 25.32 Pa, which is below the limit value of 50 Pa according to the ‘Technical Regulations for Dynamic Acceptance for High-speed Railway Construction’ (TB10761-2013). Alternately, an excellent train head shape can decrease the gradient of the initial compression wave

CRH380A

CRH2C:

250km/h

Testing Point

Maximum of Pressure Gradient (kPa/s)

1. 2. 3. 4.

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Micro-Pressure Wave (Pa)

66

CRH2C Double Connection-20m CRH2C Double Connection-50m CRH380A-20m CRH380A-50m

CRH2C-20m: CRH380A-20m: CRH2C-50m:

CRH380A-50m:

Train Speed (km/h) Fig. 7. MPW versus EMU speed.

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effectively and improve the MPW. Therefore, the MPW, especially at the point 20 m from the exit, is smaller for the CRH380A than the CRH2C. This is because the CRH380A has a better head shape and a longer nose.

3.2.1. Influence of the EMU on the surface pressure When the compression wave encounters a sudden contraction in its cross-sectional area (such as when the wave travels through the new lining), the reflected wave is in phase with the incident one, whereas a sudden expansion of the cross-section causes an out-of-phase reflection, as shown in Fig. 8 (Baron et al., 2001). Fig. 9 compares the time history of the pressure change on the EMU surface. The initial compression wave, caused by the head of the EMU, reflects when it encounters the start of the new lining. As the reflected compression wave propagates to the EMU, the pressure increases (corresponding to k in Fig. 9). When the initial compression wave encounters the end of the new lining, an expansion wave will be reflected. As the reflected expansion wave propagates to the EMU, the pressure decreases (corresponding to l in Fig. 9). Similarly, for the initial expansion wave caused by the end of the EMU and the other pressure waves reflected in the tunnel portal, the corresponding change and reflection will occur whenever these waves travel through the new lining. However, the changes of the pressure waves are mainly decided by the sectional ratio (upstream cross-sectional area/downstream cross-sectional area). From Fig. 9, the pressure change caused by the new lining is within 100 Pa. This is because the sectional ratio changes little after increased lining. 3.2.2. Results of the calculations of the MPW for different linings The compression wave is reflected when it travels through the new lining, and the energy of the wave is separated during the reflection. Therefore, the new lining can influence the gradient of the initial compression wave and change the MPW. Table 2 shows the change of MPW for linings with different thicknesses. The amplitude of the MPW decreases slightly with increasing

b- - without lining

Pressure (kPa)

3.2. Numerical simulations

a- - with lining

Time (s) Fig. 9. Comparison of pressure at the measurement point on the CRH380A EMU.

thickness. The MPW is reduced by 0.697% for an increased lining thickness of 0.5 m compared with the original condition. Table 3 shows the change of the MPW for linings with different lengths. The amplitude of the MPW decreases as the length of the new lining increases from 0 m to 60 m. When the length of the lining continues increasing, the MPW remains almost unchanged. The MPW for the increased 400-m-long lining decreases by 0.149% compared with that without increased lining. It can be concluded that the length of the lining has little effect on the MPW when the length exceeds a certain value. Table 4 shows the change of the MPW for linings with different length transitions. The MPW changes slightly as the transition length increases from 0 m to 2.5 m, and the amplitude fluctuation is within 0.071%. It can be concluded that the length of the lining transition has no effect on the MPW. Table 5 shows the change of the MPW for linings located at different positions. The MPW increases by 3.601% when the lining is increased at the tunnel entrance, whereas the MPW decreases by 7.366% when the lining is increased at the tunnel exit. When the lining is increased in the other positions, the MPW decreases by from 0.094% to 0.157% compared with the case without increased

Fig. 8. Propagation and reflection of a compression wave at an abrupt change in the tunnel cross-section (adapted from Baron et al. (2001)).

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Table 2 Results of the MPW calculations for linings with different thicknesses (VEMU = 300 km/h, Llining = 90 m, Llocation = 475 m, Ltransition = 1 m).

Amplitude of the MPW (Pa) MPW change rate (%)

Original lining

Thickness of new lining (m) 0.1

0.2

0.3

0.4

0.5

12.775

12.774

12.770

12.757

12.724

12.686

0.008

0.039

0.141

0.399

0.697

0

b

Pressure (kPa)

Item

c a- - 0m b- - 0.3m c- - 0.5m

Table 3 Results of the calculations of the MPW for linings with different lengths (VEMU = 300 km/h, Llocation = 475 m, Lthickness = 0.3 m, Ltransition = 1 m). Item

Amplitude of the MPW (Pa) MPW change rate (%)

Original lining

Length of new lining (m) 30

60

90

180

300

12.775

12.762

12.758

12.757

12.756

12.756

0

0.102

0.133

a

Time (s) Fig. 10. Initial compression wave for linings with different thicknesses.

0.141

0.149

Table 6 Results of the calculations of the MPW for linings with different thicknesses (VEMU = 300 km/h, Llining = 90 m, Llocation = 0 m, Ltransition = 1 m).

0.149

Item

Amplitude of the MPW (Pa) MPW change rate (%)

lining. It can be concluded that the position of the new lining has little effect on the MPW when the lining is not in the tunnel portals. 3.2.3. Results of the calculations of the MPW when the linings are increased in the entrance As noted in Section 3.2.2, new lining located in the middle or at the exit of the tunnel can reduce the MPW, whereas new lining located at the tunnel entrance can increase the MPW. This is because the new lining in the entrance can cause a greater initial compression wave gradient when the wave is generated. Therefore, the new lining in the entrance was analysed further. Fig. 10 shows the change in the initial compression wave for new linings with different thicknesses located in the tunnel entrance. Table 6 shows the results for the MPW. With the increase in the thickness of the new lining, the peak of the initial compression wave is obviously changed and the MPW increases linearly. The MPW increases by 9.119% for the lining with a thickness of 0.5 m compared with the case without increased lining. Adding the new lining in the tunnel entrance should therefore be avoided. Table 7 shows the change of the MPW for linings with different transitions located at the tunnel entrance. The amplitude of the MPW decreases as the length of the transition increases. The MPW resulting from increasing the 2.5-m-long transition is reduced by 0.340% compared with the case without the transition.

Original lining

Thickness of new lining (m) 0.1

0.2

0.3

0.4

0.5

12.775

12.980

13.203

13.400

13.655

13.940

1.605

3.350

4.892

6.888

9.119

0

It is worth noting that, besides the MPW (which is called the entrance MPW) generated when the EMU goes into the entrance of the tunnel, a new one (which is called the lining MPW) can be generated when the EMU enters the new lining. In this paper, we only study the entrance MPW because the amplitude of the lining MPW is quite small. 3.3. Moving-model experiment Fig. 11 shows the change in the MPW of the model experiment for the new lining located in different positions. The amplitude of the MPW increases when the train speed increases. When the new lining is at the entrance, the MPW is greater, whereas the MPW is smaller when the new lining is at the exit. When the new lining is in the middle of the tunnel, it has little effect on the MPW. Full-scale measurement, numerical simulation and the movingmodel experiments are three common methods used to study train aerodynamics. Full-scale measurement plays an important role in the assessment of a scientific phenomenon. However, it is not

Table 4 Results of the calculations of the MPW for linings with different transitions (VEMU = 300 km/h, Llining = 90 m, Llocation = 475 m, Lthickness = 0.3 m). Item

Amplitude of the MPW (Pa) MPW change rate (%)

Original lining

Length of transition (m)

12.775 0

0

0.5

1

1.5

2

2.5

12.754 0.164

12.756 0.149

12.757 0.141

12.755 0.157

12.756 0.149

12.754 0.164

Table 5 Results of the calculations of the MPW for linings with different locations (VEMU = 300 km/h, Llining = 90 m, Lthickness = 0.3 m, Ltransition = 1 m). Item

Original lining

Amplitude of the MPW (Pa) MPW change rate (%)

12.775 0

Distance from the entrance (m) 0

195

475

675

915

1155

1395

1635

1819

13.235 3.601

12.755 0.157

12.757 0.141

12.757 0.141

12.759 0.125

12.758 0.133

12.763 0.094

12.761 0.110

11.834 7.366

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F. Liu et al. / Tunnelling and Underground Space Technology 52 (2016) 62–70 Table 7 Results of the calculations of the MPW for linings with different transitions (VEMU = 300 km/h, Llining = 90 m, Llocation = 0 m, Lthickness = 0.3 m). Item

Original lining

Amplitude of the MPW (Pa) MPW change rate (%)

12.775 0

in the middle

in the entrance

0

0.5

1

1.5

2

2.5

13.427 5.104

13.419 5.041

13.400 4.892

13.375 4.697

13.375 4.697

13.376 4.705

in the exit

Micro-Pressure Wave (Pa)

without lining

Length of transition (m)

Train Speed (km/h) Fig. 11. MPW for linings with different locations in the moving-model experiment.

Table 8 Results of the three methods for the MPW (VEMU = 300 km/h, Llining = 90 m, Lthickness = 0.3 m, Ltransition = 1 m). Types of EMU

Types of lining

Model experiment (Pa)

Numerical calculations (Pa)

Full-scale measurement (Pa)

CRH2C DC

Llocktion = 475 m

–

12.819

13.4

CRH380A

Without lining Llocktion = 475 m Llocktion = 0 m Llocktion = 1819 m

13.8

12.775

–

13.8

12.757

13.3

14.2 12.8

13.400 11.834

– –

economic, and the test process is hard to control. Numerical simulation has a distinct advantage for studying the regularity of a phenomenon. However, the disadvantage is that there are many assumptions and simplifications in it. A moving-model experiment can often replace a full-scale measurement and provide the foundations for numerical simulation; in addition, it can also be used for studying the regularity of a phenomenon directly. Table 8 shows a comparison for the MPW obtained by the three methods. There is a difference of 3.8% between the experimental results and the full-scale results, possibly because of the simplification of the real structure and the measurement uncertainty; in addition, there is a difference of 4.4% between the numerical simulation results and the full-scale results, possibly caused by a numerical dissipation in the three-dimensional numerical calculation for simulating the long tunnel. Overall, the difference in the MPW between the three methods is within 8%, and the rules of the MPW obtained are basically consistent. 4. Conclusions From the results that have been presented above, the following major conclusions can be drawn. (1) The three methods supplement and verify each other, and the rules of the MPW obtained are basically consistent.

(2) When the CRH2C double-connection EMU or the CRH380A EMU travels through the Pingtu Tunnel at a speed of 350 km/h, the maximum MPW 20 m from the exit of the tunnel is 25.3 Pa, which is below the reference limit value of 50 Pa; the MPW for the CRH2C double-connection EMU is greater than that for the CRH380A EMU. (3) When the new lining is increased in the middle of the tunnel, it has little effect on the MPW; changes in the thickness of the lining, the length of the lining or the length of the transition lead to less than 1% changes of the MPW. When the lining is increased in the portals of the tunnel, the change is more obvious; when a 0.3-m-thick lining was increased in the tunnel entrance or the tunnel exit, the MPW increased by 3.601% and 7.366%, respectively. (4) In addition to the MPW, the train-tunnel aerodynamic effects also include the aerodynamic pressure, the gusts in the tunnel, the aerodynamic drag and so on. In this paper, the MPW is mainly studied; the influence of the other aerodynamic effects will be studied in future work. If only the MPW is considered, increased lining technology could be used to repair tunnel damage in high-speed railways, but installing the lining in the portals of the tunnel should be avoided.

Acknowledgments This work was sponsored by China’s Ministry of Railways. The first author was supported by the Exploration and Innovation Funds of Central South University (No. 2014ZZTS038). Thanks are extended to Professor Xifeng Liang for his constructive comments on and suggestions for the calculation model and to Professor Mingzhi Yang for his guidance on the moving-model experiments.

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