Introduction

Seismic activity is frequent in the western area of China, high intensity earthquake will lead to serious geological hazards and damage the stability of buildings and transportation network1. Tunnels occupy an extremely important place in ensuring normal and convenient traffic in mountainous areas of China, damage to them caused by earthquakes and faults can seriously affect the transportation network, so it is essential to ensure their safety and durability2. Although underground buildings typically suffer a lower rate of damage than buildings on the ground in a natural disaster, tunnels will also take significant damage under strong earthquake. For tunnels located in complex geological environments, their design of safety must be considered carefully.

High intensity earthquake can cause fault misalignment, although the duration of it is relatively short during the earthquake, the generated repeated shear and compression of the surrounding rock fragmentation and misalignment will produce irreversible damage to the main and portal structure of tunnel3,4. The fault movement might be divided into fault movement and seismic motion under the strong earthquake action, and both of them could make a huge impact on the stability of tunnel structure5. According to the investigation of historical strong earthquake events, the fault of the tunnel is the most vulnerable part of the tunnel during strong earthquake, including the 1999 Chi-Chi, the 2004 Mid-Niigata, the 2008 Wenchuan and the 2016 Kumamoto earthquake6,7,8. As the most common adverse geological phenomenon in tunnel construction, the area where the fault exists is one of the most unstable areas of the surrounding rock, it may lead to tunnel collapse, large deformation and other construction geological hazards. The impact of faults on tunnel construction is mainly manifested in reducing the overall strength of the surrounding rock and changing the physical and mechanical properties of the rock mass. The presence of faults significantly reduces the strength of the tunnel structure, and the damage instability of the tunnel structure is mainly caused by the shear strength of the weak structural surfaces formed by the fault zone. The strength of these structural surfaces is generally very low, and the deformation resistance and deformation modulus are also lower than those of the rock material, this leads to low strength of the surrounding rock in the fault area9. The section of the fault zone is the key paragraph for the seismic design of the tunnel.

The researches about tunnel engineering are usually carried out with the help of numerical simulation. In current numerical study, continuum and dis-continuum based numerical simulations are two major numerical techniques in tunnel engineering10, which continuum modeling is more commonly used. The continuum-based methods contain finite element method (FEM)37, and keep numerical scheme staying stable even when the physical system may be unstable. It contains six forms of unit structure in Flac3d: beam, cable and pile are three kinds of linear structure; shell, geogrid and liner are three kinds of shell structure. Each unit consists of nodes and structural elements. By linking nodes with zone or other nodes, it can simulate the simulate of soil or structure with structural elements. By defining the material parameters, earthquake motion, boundary conditions in the software, the seismic response of tunnel structures under earthquake can be accurately simulated.

Numerical model

The elastic–plastic model was established to simulate the thermal insulation and seismic effect of Sangzhuling fault-crossing tunnel under strong earthquake in high geothermal area. The height of model was 105 m and the longitudinal length was 150 m, the height, width, and burial depth of tunnel was 15, 10 and 45 m respectively. In order to eliminate the influence of boundary effects, the left and right width of the model was taken as 5 times the width of the tunnel, which was 50 m. The thickness of the bedrock at the bottom was 20 m. The dip angle of the fault zone was about 80°, and the width was 10 m. The model was meshed to divide the model into a finite number of elements which were interrelated and mutually binding and to perform numerical simulations in Flac3d. The width and height of the surrounding rock mesh size were both 4 m, and those of the rock mesh size near the tunnel were both 1 m. The hanging wall and footwall was longitudinal divided into 10 equal parts, and the fault zone was divided into 2 parts. The overall model is shown in Fig. 1.

Figure 1
figure 1

Numerical model of Sangzhuling Tunnel.

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To study the thermal insulation effect of tunnel, it needs to set the temperature field in the program. According to the geological exploration report, the temperature of the fault zone about 100 m below the tunnel is close to 90 ℃, we set it as the temperature of the fault zone at the bottom of the model in this study. After transmitting upwards from the bottom of the fault, the temperature at the top of the model were 54 ℃. The stable temperature distribution is shown in Fig. 2.

Figure 2
figure 2

Cloud map of temperature distribution.

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Test cases

A total for four test cases were taken to analyze the difference of thermal insulation and seismic effect under different seismic measures. Plain concrete and steel fiber concrete were used as different lining materials for comparative analysis. The highly damped composite structure was applied between the primary lining and the second lining, as shown in Fig. 3. The test cases of this paper are listed in Table 1.

Figure 3
figure 3

Application method of highly damped composite structure.

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Table 1 Test cases.
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Geological condition

Sangzhuling tunnel of Sichuan-Tibet railway is 16449 m long, which is one of the important railroad projects in the west of China. The tunnel is designed and constructed using the New Austrian method, with curved wall lining and composite lining structure. The primary lining is C20 shotcrete with a thickness of 0.25 m, and the second lining is C25 modeled concrete with a thickness of 0.45 m. The tunnel is located in the Yarlung Tsangpo River suture zone, where the Indian plate collides with the Eurasian plate, the environment around the tunnel exists strong and frequent geothermal activity. As adverse geology such as high soil temperature and hot water are especially common near the tunnel, the maximum surrounding rock temperature of the tunnel can reach 90 °C and the ambient temperature inside the tunnel can reach up to 56 °C. The tunnel also crosses the Waka graben east fault zone, due to the loose and fragmented surrounding rock of the fault, its high thermal conductivity leads to the heat generated by geothermal activity being easily transferred to the tunnel via the fault. According to the geological survey and current code for design of road tunnel, the surrounding rock of the tunnel are Grade IV rocks, the fault zone surrounding rock are Grade V fragile rocks, and the bedrock are Grade II hard rocks.

Highly damped composite structure

In tunnel engineering, highly damped materials are usually used in seismic measures for lining reinforcement to decrease the tunnel vibrations caused by earthquakes. The greater the dam** effect, the more energy can be dissipated in a shorter period of time. Such as applying a soft layer to cover the tunnel lining to mitigate damage during an earthquake38, injecting a kind of soft material into the interspace between the tunnel lining and the surrounding rock to reduce shear forces on the soil-tunnel interface39 and employing constrained layer dam** treatments in the design of earthquake-resistant structure to absorb seismic energy. In contrast to the above articles, in this paper we studied the difference of thermal insulation and seismic effect when using highly damped composite structure for the two materials lining.

Material parameters

The parameters of highly damped composite structure used in the study were based on Qingdao Shamu dam** Qtech-506, which is a kind of dam** coating for the concrete surface of the tunnel. It is a kind of critical material between solid and high viscosity liquid. Under the condition of room temperature (25 ℃), the viscosity is about 6 million centipoises, the dam** factor is about 0.51. Since it is a kind of dam** material, its hardness is measured by Shore A hardness and the value is 20. The Poisson’s ratio is 0.5, and the elongation at break is greater than 1000%. The material adhesion is 1.65 MPa. The thermal conductivity of dam** layer is 0.144 W/m·℃. The parameters of the surrounding rock were obtained from local geological exploration data. The necessary parameters used for the study are listed in Table 2.

Table 2 Parameters of the materials.
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Dynamic calculation

By means of writing fish language in Flac3d, the software can simulate the effects of earthquake on tunnels, and the dynamic loads can be applied directly to the external boundaries of the model. Using the actual seismic wave measured by the Wolong station in 2008 Wenchuan earthquake to simulate the situation that tunnel affected by earthquake. The original seismic waves were filtered and baseline corrected by professional seismic wave processing software, which can reduce the effect of grid size on seismic waves40. Seismic waves were transmitted from the bedrock at the bottom of the model to above, and their horizontal, vertical and longitudinal seismic waves correspond to the x, y and z directions of the model respectively, with a duration of 15 s and an acquisition interval of 0.01 s. The local dam** factor was 0.1571. Figure 4 shows the time history curves of acceleration of x direction.

Figure 4
figure 4

Time history curves of acceleration (x direction).

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Monitoring system

Flac3d can dynamically monitor data such as the displacement, the stress and strain of each unit and node during the dynamic analysis and export their cloud maps at the end of the analysis. In the study, D2 monitoring section was placed along the vertical direction of the tunnel, so as to collect the stress, temperature, displacement and other data of the tunnel structure in the earthquake. Five measuring points (i.e., vault, left spandrel, right spandrel, left sidewall, right sidewall) were set to collect the internal force data. Figure 5 shows the monitoring section of the tunnel. The layout of measuring points is shown in Fig. 6.

Figure 5
figure 5

Monitoring section of the tunnel.

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Figure 6
figure 6

Layout of measuring points.

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Consent for publication

If this article is accepted, we agree to transfer the copyright to this journal.

Results of calculation

As the surrounding rock in the fault zone is loose and fragile and has a high thermal conductivity, the tunnel structure in the fault zone is less safe and most severely affected by high ground temperature, the requirements for thermal insulation and seismic effect of the tunnel structure near the fault is the highest among the whole tunnel. The D2 section was chosen for analysis, which was a cross-fault monitoring section in the footwall.

Thermal insulation

After the numerical simulations, the cloud maps and data of temperature could be output from the Flac3d. Figure 7 shows the cloud maps of temperature for PC and SFRC. The maximum temperature values of the second lining under each case are shown in Table 3, and the results of the comparison between each seismic measure are shown in Table 4.

Figure 7
figure 7

Cloud maps of temperature: (a) PC; (b) SFRC.

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Table 3 Maximum temperature value on the right side of D2 section.
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Table 4 Comparison of thermal insulation effect on the right side of D2 section.
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Since the results of the left and right side of the tunnel was basically the same, the right half of the tunnel was taken as an example for analysis. The data in Table.3 shows that the temperature of the second lining of the tunnel is the highest when using steel fiber concrete, which are around 60 ℃. The thermal insulation effect of the remaining three seismic measures varies, while plain concrete highly damped composite structure is slightly better. It can be seen that the effect of steel fiber concrete is the worst in reducing the temperature of the second lining, and the that of plain concrete highly damped composite structure is the best in the four seismic measures.

The data in Table 4 shows that, when using different lining materials, the thermal insulation effect of SFRC compared to PC is reduced by 24.99–32.90%, and that of SFRC highly damped composite structure compared to PC highly damped composite structure is reduced by 1.97–2.34%, which shows that the thermal insulation effect of PC lining is better than that of SFRC lining.

When using highly damped composite structure, the thermal insulation effect of PC highly damped composite structure is improved by 0.30–1.53% compared to PC, and that of SFRC highly damped composite structure is improved by 19.67–23.91% compared to SFRC. The applying of highly damped composite structure could reduce the temperatures lining markedly, especially for SFRC lining.

After incorporating steel fibers to the concrete, the temperature of SFRC lining is higher than PC lining. Its incorporating leads to higher thermal conductivity of concrete and causes higher temperature of lining. The applying of highly damped composite structure is capable of counteracting the effect of fiber incorporation on thermal conductivity, it reduces the temperature transfer to the free face of tunnel.

Maximum principal stress

The maximum principal stresses of each test case were calculated separately. Figure 8 displays the cloud maps of maximum principal stress for PC and SFRC. The calculation results are shown in Table 5.

Figure 8
figure 8

Cloud maps of maximum principal stress: (a) PC; (b) SFRC.

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Table 5 Maximum principal stress and seismic effect of section D2.
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In PC group, the maximum principal stresses for PC ranges from 10.31 to 24.51 MPa, while those of PC highly damped composite structure ranges from 8.94 to 22.34 MPa. The applying of highly damped composite structure reduced the maximum principal stresses of PC lining by 8.8–38.09%. In FRC group, the maximum principal stresses for SFRC are between 10.62 and 25.78 MPa, and the stresses of SFRC highly damped composite structure are between 9.48 and 24.31 MPa. The applying of highly damped composite structure increases the seismic effect of maximum principal stress for SFRC lining by 1.62–10.73%.

It shows that the highly damped composite structure can absorb earthquake energy, it enhances the seismic effect of maximum principal stress for both PC lining and SFRC lining at all monitoring points. Besides, the maximum principal stresses of SFRC lining are larger than those of PC lining, because the steel fibers incorporated in the concrete increases the stiffness of the lining. Although the maximum principal stresses on the SFRC lining are increased, further calculations are needed to determine their safety.

After applying highly damped composite structure, its capacity of viscous seismic energy dissipation could dramatically reduce the maximum principal stress of lining. The incorporation of steel fibers increases the strength and stiffness of lining. It also enhances the inhibitory effect on the deformation of the surrounding rock, resulting in an increase in the surrounding rock pressure on the lining.

Minimum principal stress

Similar to the analysis of maximum principal stress, Fig. 9 displays the cloud maps of minimum principal stress for PC and SFRC. The calculation results are shown in Table 6.

Figure 9
figure 9

Cloud maps of minimum principal stress: (a) PC; (b) SFRC.

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Table 6 Minimum principal stress and seismic effect of section D2.
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For PC lining, the minimum principal stresses for PC ranges from − 28.64 to 1.68 MPa, and the stresses of the PC highly damped composite structure ranges from − 20.01 to 1.49 MPa, which improved the seismic effect of minimum principal stress by 8.75–66.96%. And for SFRC lining, the minimum principal stresses for SFRC varies between − 29.34 and 1.43 MPa, the minimum principal stresses of SFRC highly damped composite structure varies between − 23.67 and 1.40 MPa, its seismic effects of minimum principal stress are increased by 0.90–23.63% compared to the former.

Both the maximum principal stresses and minimum principal stresses are decreased after using highly damped composite structure in RC and SFRC lining, which shows its stable ability of decreasing the lining stress. The physical properties of damped structure enable it to share the stress from surrounding rock with the lining structure.

The characteristic of viscous seismic energy dissipation of highly damped composite structure is also helpful for reducing the minimum principal stress on lining. After enhancing the strength and stiffness of lining, the maximum and minimum principal stress are both decreased by applying highly damped composite structure.

Safety factor

Safety factor is used for the design of tunneling structures to reflect the structural safety under seismic measures. Larger safety factor means better safety of the structure. However, related data such as the axial force and the bending moment cannot directly obtained in Flac3d. Thence the axial force and the bending moment of lining is calculated according to the Eqs. (1) and (2).

$$ \begin{array}{*{20}c} {N = \frac{{E\left( {\sigma_{1} + \sigma_{2} } \right)bh}}{2}} \\ \end{array} $$
(1)
$$ \begin{array}{*{20}c} {M = \frac{{E\left( {\sigma_{1} - \sigma_{2} } \right)bh^{2} }}{12}} \\ \end{array} $$
(2)

where N is the axis force, M is the bending moment, E is the elastic modulus, σ1 is internal stress of lining, which is calculated by Eq. (3). σ2 is the external stress of lining, which is calculated by Eq. (4), b is the width of the tunnel section, h is the thickness of the tunnel section.

$$ \begin{array}{*{20}c} {\sigma_{1} = \varsigma \left( {\sigma_{n1} + \sigma_{n2} } \right) + \frac{{\varsigma \left( {\sigma_{n1} + \sigma_{n2} } \right)}}{\xi }} \\ \end{array} $$
(3)
$$ \begin{array}{*{20}c} {\sigma_{2} = \varsigma \left( {\sigma_{n1} + \sigma_{n2} } \right) - \frac{{\varsigma \left( {\sigma_{n1} + \sigma_{n2} } \right)}}{\xi }} \\ \end{array} $$
(4)

where ς is the reciprocal of lining zone layers, σn1 is the normal stress of the internal grid, σn2 is the normal stress of the external zone, σn1 and σn2 are calculated in Eq. (5)

$$ \begin{array}{*{20}c} {\sigma_{n} = \sigma_{x} \cos^{2} \left( { - \alpha } \right) + \sigma_{y} \sin^{2} \left( { - \alpha } \right) + \sigma_{xy} \sin \left( { - 2\alpha } \right)} \\ \end{array} $$
(5)

where α is the angle between the line of centroid of inner and outer elements and vertical direction, which is calculated by Eq. (6); (x1, y1) and (x2, y2) are the centroid coordinates of the inner and outer zones, respectively.

$$ \begin{array}{*{20}c} {\alpha = \arctan \left( {\frac{{x_{2} - x_{1} }}{{y_{2} - y_{1} }}} \right)} \\ \end{array} $$
(6)

According to the Code for Design of Railway Tunnel41, the safety factors of four seismic measures are calculated by Eqs. (7) and (8). The results are shown in Table 7.

$$ \begin{array}{*{20}c} {KN \le \varphi \delta R_{a} bh} \\ \end{array} $$
(7)
$$ \begin{array}{*{20}c} {KN \le \varphi \frac{{1.75R_{l} bh}}{{\frac{{6e_{0} }}{h} - 1}}} \\ \end{array} $$
(8)

where K is the safety factor, φ is the longitudinal bending coefficient, which takes 1.0 in the study, δ is the influence coefficient of axial force eccentricity, Rɑ is the ultimate compressive strength of concrete, Rl is the ultimate tensile strength of concrete, e0 is the eccentricity of section.

Table 7 Safety factor and seismic effect of section D2.
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Taking the minimum safety factors of section D2 for analysis, and compared their seismic effects. From Table 7, it shows that the minimum safety factors from PC to SFRC highly damped composite structure are raised gradually, which are 1.739, 1.820, 2.065 and 2.42. Compared to PC, the seismic effects of the other three seismic measures are improved by 4.45, 15.79 and 28.14% respectively. The seismic effect of SFRC highly damped composite structure in safety factor is the best in all seismic measures, which have an increase of 28.14%.

The steel fibers incorporated in the concrete increases the stiffness of the lining, which improves the ability of limiting the deformation of surrounding rock. The steel fibers incorporated in the concrete increases the maximum and minimum principal stress on the lining, but also improves the upper limit of the stress that the lining can withstand. The results indicate that the SFRC lining has better performance in the safety of tunnel lining, even though larger maximum and minimum principal stresses on the lining structure.

In summary, the performance of viscous seismic energy dissipation is exerted after using highly damped composite structure, it reduces the seismic force on the lining and the pressure transmitted from the surrounding rock to the lining, then enlarging the safety factors. However, the increase in safety factors is not obvious when only applying the highly damped composite structure. After using SFRC lining, the strength, stiffness and toughness of lining are increased, it also improved the ability of resisting earthquake forces and the safety of lining. Considering the thermal insulation effect of highly damped composite structure is great while its seismic effect is general, and the SFRC lining has better seismic effect and poor thermal insulation effect, the above two measures need to be used together to make the lining having both remarkable thermal insulation effect and seismic effect.

Conclusions and outlooks

In this paper, with highly damped composite structure combining with lining structure, we proposed a kind of seismic measure for fault-crossing tunnel located in high geothermal area with strong earthquake. We simulated the temperature field and dynamic waves in the finite difference software Flac3d, and then we analyzed the thermal insulation and seismic effect from PC to SFRC highly damped composite structure according to the results of temperature, stress and safety factor. Regarding the method and the results, the conclusion are as follows.

  1. 1.

    The study used finite difference method to obtain the required data by the commonly used software in tunnel engineering. The calculation methods are well developed and hold good numerical stability.

  2. 2.

    The incorporation of steel fiber leads to larger factor of thermal conductivity, resulting in higher temperature of SFRC lining, the highly damped composite structure could reduce its influence and lower the temperature of lining.

  3. 3.

    Although SFRC lining have larger stiffness and is better for tunnel supporting, the problem of high stress on lining still needs to be solved. The highly damped composite structure could significantly share and reduce the stress of SFRC lining, also for PC lining.

  4. 4.

    According to the safety factors, the SFRC highly damped composite structure have the best seismic performance while its lining temperature is basically the same with PC lining. The damped structure could enhance the seismic effect when kee** the temperature from rising.

Meanwhile, still some work needs to be done in the future. And we are considering following tests or simulations:

  1. 1.

    More tests for the application of the highly damped composite structure, considering more conditions such as temperature and geologic setting.

  2. 2.

    Further study about the coupling analysis of temperature field and stress field.

  3. 3.

    Further considering the influence of input parameters on uncertain outputs42,43, such as the difference between the accuracy of the input parameters and the effect in practical applications.