Influence of cork-rubber gasket on the circular propagation of train-induced vibration waves in high-speed railway shield tunnels

Abstract

Shield tunnels are constructed by assembling segment, and this construction method will produce a large number of joints. As the component with the largest contact area in the joints of the shield tunnel, the cork-rubber gasket has a significant effect on the transmission of train-induced vibration waves between the segments. In order to study the influence of cork-rubber gasket on the transmission of train-induced vibration waves in the circumferential direction, based on the hammering test of high-speed railway shield tunnel, a dynamic calculation model for high-speed railway shield tunnel was constructed, and the influence of elasticity modulus of cork-rubber gasket on the propagation of train-induced vibration waves was investigated. The results show that: (1) the longitudinal joints of high-speed railway shield tunnels can weaken high-frequency vibration waves more than low-frequency vibration waves; (2) the lower the modulus of elasticity of cork-rubber gasket is, the greater the attenuation of the peak of the temporal range of vibration acceleration of train-induced vibration waves after they pass through the longitudinal joints; (3) compared with the cork-rubber gasket of high elasticity, the cork-rubber gasket with low elasticity can improve the damping effect of the longitudinal joints on low-frequency bands (0–500 Hz) effectively. This research offers new methodologies for optimising vibration isolation in shield tunnels and contributes to the advancement of tunnel design for high-speed rail systems.

Keywords

High-speed railway shield tunnel cork-rubber gasket vibration isolation

1. Introduction

The high-speed railway into the city takes the form of an underground line, aiming to minimise the occupation of the urban surface. However, the underground section of high-speed railway in the urban area will inevitably produce vibration impact problems. The vibration of high-speed railway has its outstanding characteristics, which are mainly reflected in: (1) The amplitude of quasi-static component and parametric excitation component will be significantly increased after the speed is increased. A large number of studies have shown that the shield tunnel vibration response is almost linearly positively correlated with the train speed; (2) the significant difference brought about by the increase in train speed results in a much higher eigenfrequency corresponding to the eigenwavelength, as well as an intensification of the parametric excitation effect. These differences lead to the fact that the current environmental impact assessment methods used for urban rail transit are no longer applicable to the vibration assessment of the underground section of high-speed railway in urban areas, and there is an urgent need to carry out research on the vibration propagation law of the underground section of high-speed railway in urban areas.

Vibration due to train–rail system interaction during train operation is one of the main sources of dynamic loading on tunnel structures. At present, many experts and scholars have carried out research on the vehicular response of tunnels, and the main means of research are field tests, model tests and numerical simulations. Field testing is the most intuitive and reliable method to study the structural response of tunnels and ground-level vehicular vibration. Degrande et al. (2006) found that the vibration response at the elevation arch and sidewalls was positively correlated with the train speed, and Lopes et al. (2016) proposed a numerical model based on dynamic substructures, which was verified by measuring the response of the buildings along the metro line. The vibration response of the tunnel bed (Li, 2011), standard blocks and sleeper rails (Lee and Guo 2014) as well as the dynamic deformation of the shield tunnel under train loads (Sekiya et al., 2022) are also compared and analysed by scholars through real measurements. Wang et al. (2024) conducted an in-depth analysis on hunting stability and established a mapping relationship between HC and the vehicle hunting state, validated through a rig test.

Meanwhile, numerical simulation has also been widely used to solve the vibration response by establishing a numerical model close to the actual state. Vrouwenvelder (2000, 2001) analysed the dynamic response characteristics of high-speed train tunnels with laminated foundations and tunnel structures based on a planar model of the tunnel envelope. He et al. (2018) proposed a three-dimensional analytical model for the prediction of surface vibrations in space-parallel tunnels. Noori et al. (2019) calculated the energy flow generated by the passage of a train by establishing a semi-analytical model of the track–tunnel–surface system, and Lai et al. (2016) applied a three-dimensional dynamical finite element model to analyse the vibration response characteristics of the tunnel vehicle loads and underground train loads on the shield tunnel structure and its propagation law. Other scholars have also used nonlinear finite element to establish three-dimensional models to study the dynamic response of double-layer circular tunnels (2016) and overlapping shield tunnels (2018) under train excitation.

There are also many scholars to solve complex engineering problems through indoor modelling tests. Zhang et al. (2021) investigated the mechanism of the influence of swept load on the dynamic response of the integral contact cross-channel by carrying out indoor modelling tests and using the frequency response function, and based on this, a new type of assembled contact cross-channel was proposed, and its vibration damping effect was investigated. Ding et al. (2023) conducted model tests on shield tunnels with and without typical cracks based on the Hangzhou metro line to characterise their dynamic response under train vibration loading. Tian et al. (2021) investigated the defective section of shield tunnel lining under cyclic loading through full-scale experiments and 3D numerical simulation. Yang et al. (2013a, 2013b) used a centrifuge to restore the stress field of the soil around the tunnel in a model test to investigate the vibration characteristics of the tunnel structure and the surrounding soil when the excitation loads are located at the surface and underground, respectively. Huang et al. (2015) carried out model tests to analyse the acceleration response characteristics of the tunnel up-arch and foundation. Yan et al. (2020) combined model tests and numerical simulations to investigate the dynamic response of overlapping tunnel lining structures under the action of different train speeds and different tunnel headroom distances. Yang et al. (2018, 2022) produced three types of tunnel models, namely, circular, horseshoe and rectangular, to carry out indoor model tests, and investigated the dynamic response characteristics of the tunnel models with different cross-sectional forms under train vibration loads through time domain and frequency domain analyses.

With the deepening of the understanding of the dynamic characteristics of shield tunnels, scholars have realised that segment joints give rise to dynamic characteristics of shield tunnels that are different from those of other types of tunnels, and they have gradually included segment joints in their research process; Yan et al. (2018) analysed the dynamic response of shield tunnels with and without joints under the same vibration stimulus. Zhou et al. (2019) established a 2.5D shield tunnel finite element model considering segment joints to study the dynamic response of shield tunnel in saturated soil. Zhang and Cui (2017) analysed the dynamic response of soft soil under the action of train vibration by using a model including joints. Deng et al. (2006) also analysed the displacement and velocity response in the soil by establishing a numerical model of the shield tunnel considering the shield tunnel assembly effect. Gharehdash and Barzegar (2015) compared the results of the dynamic response of the model with and without joints, and found that the dynamic response was more obvious after considering the joints, and the existence of joints must be considered in the vibration analysis of shield tunnels. Jin et al. (2023) established a dynamic calculation model for shield tunnels considering joints and analysed the propagation law of vibration waves inside the shield.

However, due to the constraints of computational efficiency and other factors, not many complex contact surfaces have been considered in HSR shield tunnels, and some scholars have used the shield tunnel model without joints to consider the influence of joints by discounting the modulus of elasticity (Ding et al., 2010) or the overall bending stiffness of the structure. Some scholars have considered the joints in their setups, but they have not comprehensively modelled the joints with the three contact surfaces of “concrete–concrete,” “sealing gasket–sealing gasket” and “cork-rubber gasket–cork-rubber gasket.” These simplifications may lead to the fact that the aforementioned shield tunnel dynamic calculation model, which takes into account the characteristics of the segment joints, does not accurately reflect the dynamic characteristics of the shield tunnel.

The connection method and composition of segment joints show a high correlation with the environmental vibrations associated with shield tunnelling. The cork-rubber gasket, as the component with the largest contact area in the segment joint, plays a crucial role in the transmission of vibration waves between segments. Therefore, this study investigates the transmission pattern of vibration waves between segments through field tests. At the same time, from the cork-rubber gasket, three types of pipe joint models are established, including “concrete–concrete,” “sealing gasket–sealing gasket” and “cork-rubber gasket–cork-rubber gasket.” The model is used to study the elastic modulus of the cork-rubber gasket. Focusing on how the modulus of elasticity of the cork-rubber gasket affects the transmission of vibration waves, the results of the study can provide a reference for the structural design and parameter selection in the pre-construction stage of the decision-making process.

2. Dynamic performance test of high-speed railway shield tunnel

2.1. Engineering background

To investigate the propagation characteristics of vibration waves in high-speed railway shield tunnels and to provide model correction data for numerical simulations that account for assembly effects, a test was conducted in these tunnels. The shield tunnel under examination has a total length of 7352 m. In the marine section, the minimum overburden is 16.56 m, corresponding to a maximum depth of 58 m. The maximum water pressure is 0.58 MPa, and the maximum overburden reaches 30.95 m. The average segment width is 2000 mm, with wedge rings on both sides featuring a wedge amount of 48 mm. Each segment includes crack-resistant reinforcement within the dowel, encased in steel sheets. Elastic sealing gasket grooves are provided on both the inner and outer arcs of the segment, with a water expansion stopping strip on the outer arc and embedded grooves on the inner arc. The structural components include 7 + 2+1/3, longitudinal 56 and annular 30 high-performance M36 bolts of grade 8.8. The test section, depicted in Figure 1(a), is located at ring number 2196. This section was selected to examine the vibration transmission characteristics of the longitudinal joint between the capping block and the adjacent block, as well as between the adjacent block and the standard block.

2.2. Test point arrangement

During the test, sensors and sensor supports were positioned at selected longitudinal joint measurement points. Each support was equipped with two acceleration sensors: one oriented perpendicular to the inner arc of the segment, pointing towards the centre of the circle, and the other directed tangentially along the inner arc. Following the connection of the acceleration sensors, vibration excitation device, data acquisition system and laptop computer, functionality of each instrument was verified. Upon confirming proper operation, the excitation device was used to apply an impulse load at the designated loading point, and the data acquisition system recorded the acceleration responses at each measurement point. This process was repeated 8–10 times for accuracy.

Test points were established based on previous experience and site conditions. Longitudinal joint test points were positioned 15 cm on either side of the longitudinal joint under examination. The locations of these joints are depicted in Figure 1(b), with red dots indicating measurement points. At each point, two acceleration sensors were placed. For convenience in installation, the sensors were not oriented in the vertical and horizontal directions as in prior tests. Instead, one sensor was perpendicular to the inner arc and directed towards the circle’s centre, while the other was aligned tangentially along the inner arc.

The test points were labelled as 1, 2, 3, 4, 5 and 6 from bottom to top. The sensor perpendicular to the inner arc and pointing towards the centre was designated with a suffix “1,” and the sensor pointing tangentially along the inner arc was designated with a suffix “2.” These designations are illustrated in Figure 2, showing the “1–1” and “2–2” test points.

2.3. Test equipment

The test data acquisition device used by the Beijing Oriental Institute of the INV3062 C distributed acquisition instrument (shown in Figure 2). 8 Ch analog input, each channel independent 24-bit AD, full parallel synchronous sampling, the highest sampling frequency of 216 KHz. Vibration excitation device used by the Beijing Oriental Institute of the DFC series of highly elastic polymerisation force hammer, and used the INV1841 miniature charge amplifier to amplify the signal generated by the force hammer.

Acceleration sensors are mainly used INV9822 general-purpose piezoelectric acceleration sensors developed and produced by Beijing Oriental Institute. There are 10 sensors with a range of 50 g, three sensors with a range of 20 g, three sensors with a range of 10 g and six sensors with a range of 3g.

2.4. Test data analysis

Figure 3 illustrates the time response of each measurement point. The data reveal two notable phenomena: (1) the acceleration response diminishes as the distance from the vibration excitation point increases, and (2) the onset time of the acceleration response is delayed with increasing distance from the excitation point. These observations align with findings from previous studies and corroborate common expectations. Additionally, the acceleration response measured perpendicular to the inner arc of the segment, directed towards the centre of the circle, is greater than the response measured tangentially along the inner arc at the same measurement point.

As shown in Figure 4, the joint exhibits a markedly greater attenuation capacity for high-frequency vibrations compared to low-frequency vibrations. Specifically, the acceleration amplitudes at measurement points 1 and 2 are reduced by over 40% in the frequency ranges of 4000–5000 Hz and 6000–7000 Hz. Conversely, at measurement points 5 and 6, the acceleration amplitude in the 1–500 Hz range shows an average reduction of approximately 0.5 m/s², also about 40%. The amplitude differences at measurement points 3 and 4 are not as pronounced when compared to adjacent joints.

Moreover, the attenuation of vibration waves is evident primarily at high frequencies, with minimal attenuation observed in the low-frequency range (500 Hz). This indicates that while the concrete portion of the segment can attenuate high-frequency vibrations, longitudinal joints remain the predominant factor influencing overall vibration attenuation in the shield tunnel.

3. Shield tunnel model for high-speed railway

3.1. Geometric modelling

Existing power calculation models for shield tunnels exhibit two primary deficiencies: they either neglect the influence of segment assembly effects for computational efficiency or fail to account for the specific differences between urban rail transit and high-speed railway shield tunnels. To address these issues, it is crucial to develop a dynamic calculation model that accurately represents high-speed railway shield tunnels and provides a basis for studying the impact of cork-rubber gaskets on vibration wave transmission. For this purpose, a high-speed railway shield tunnel has been selected as the modelling object. The shield tunnel segment has an outer diameter of 13.8 m and an inner diameter of 12.6 m. Each segment has an average width of 2000 mm, with double-sided wedge rings featuring a wedge amount of 48 mm. To accommodate the soft stratum, the shield section joints include concave and convex features on the ring joints of the segment’s contact surface, while the longitudinal joints lack such features. Both the inner and outer arcs of the segment are equipped with elastic sealing gasket grooves; the outer arc groove includes a water-swelling water stop strip, and the inner arc features embedded slots. The configuration of each pipe piece in a single ring of the shield tunnel model is illustrated in Figure 5. To more accurately and realistically simulate the tunnel’s working environment, the corresponding soil layer is incorporated around the tunnel model.

According to the design drawing data, the inner diameter of the shield tunnel is 12600 mm, the outer diameter is 13800 mm and the thickness of the segment is 600 mm. The width of the segment is 2000 mm, the capping block corresponds to a circumcentric angle of 14.94° and the adjacent and standard blocks correspond to a circumcentric angle of 38.34°.

Established studies have not constructed segment contact or only constructed rough segment contact. As a kind of multi-material composite contact surface, the shield tunnel segment contact surface obviously cannot neglect its role in the process of vibration wave transmission between segments. Therefore, as shown in Figure 6, according to the actual shield tunnel segment, the detail model of the contact surface between segment is constructed in this paper. The detail model of the contact surface is mainly composed of three parts: “sealing gasket–sealing gasket,” “cement–cement” and “cork-rubber gasket–cork-rubber gasket.”

3.2. Material parameters

The parameters of the materials used in the model are shown in Table 1. Among them, the relationship between Shore hardness and modulus of elasticity is (Gong et al., 2018):

E_{g} = (15.75 + 2.15 H_{A}) / (100 - H_{A})

(1)

Table 1.

Material parameters.

Material type	Modulus of elasticity /GPa	Shore hardness HS	Poisson’s ratio	Density /kg/m³	Rayleigh damping
Material type	Modulus of elasticity /GPa	Shore hardness HS	Poisson’s ratio	Density /kg/m³	α	β
C50 concrete	34.5	-	0.2	2420	0.11	1.91×10⁻⁶
EPDM rubber	-	65 ± 5	0.4	900	1.88	2.39×10⁻⁵
Nitrile Butadiene Rubber	-	75 ± 10	0.4	950	1.65	2.22×10⁻⁵

C50 concrete is used for the segment part, EPDM rubber is the sealing gasket constituent material, Nitrile Butadiene Rubber is the cork-rubber gasket constituent material and water-expandable rubber material is the water-expandable rubber constituent part.

After considering various factors, the segment portion of the shield tunnel was simulated using a 3D four-node tetrahedral unit. For the sealing gasket and force transmission liner, a 3D eight-node hexahedral unit was used for simulation.

3.3. Boundary conditions and loads

The buried depth of the tunnel is 20 m, the density of the soil is 1940 kg/m², the modulus of elasticity is 20 MPa, Poisson’s ratio is 0.31 and the damping ratio is 0.05. The geometric dimension of the soil model is 100 m × 50 m × 30 m. The soil is simulated by eight-node linear hexahedral cells, and the mesh size is 2 m. Taking into account of the wave reflection around the model, the boundaries at the bottom of the ground are set up to constrain the soil, and infinite cells are used around it. In addition, a vibration excitation is generated in the dynamic computational model using an impulse load with the same amplitude and position as the load used in the field tests (as shown in Figure 7).

3.4. Grids and elements

As shown in Figure 8, after considering various factors (computational efficiency, accuracy, vibration characteristics, etc.), the segment part and sealing gasket part of the shield tunnel are simulated using 3D four-node tetrahedral elements; for the remaining sealing gasket and cork-rubber gasket, 3D eight-node hexahedral elements are used for simulation. The mesh size of the segment is 0.2 m, and the mesh size of the sealing gasket and cork-rubber gasket is 0.1 m.

3.5. Response points

The test points were selected at 13 cm from the left and right sides of each joint to be tested, as shown in Figure 9. Measurement points 1 and 2 are located at 15 cm on both sides of the longitudinal joint between the adjacent block under the capping block and the standard block, measurement points 3 and 4 are located at 15 cm on both sides of the longitudinal joint between the capping block and the adjacent block under the capping block, and measurement points 5 and 6 are located at 15 cm on both sides of the longitudinal joint between the adjacent block on the capping block and the block above the capping block.

4. Analysis cases

In this paper, the modulus of elasticity of cork-rubber gasket is investigated. The modulus of elasticity of 1.08 × 10⁷ Pa was used for Case 1, and 1.08 × 10⁸ Pa and 1.08 × 10⁶ Pa modulus of elasticity were used for Cases 2 and 3, respectively. Case 1 is the initial parameter of the cork-rubber gasket, Case 2 and Case 3, are used to comparatively analyse the effect of different modulus of elasticity of the cork-rubber gasket.

5. Results

5.1. Time history analysis

As shown in Figure 10, from the analysis of the time history results, comparing the tangential time history before and after passing through the longitudinal slit, the acceleration amplitude of the response points on both sides of the longitudinal slit in Case 1 decreases from 12.6 m/s² to 0.3 m/s², with an attenuation of about 97%, while in Case 2, the acceleration amplitude decreases from 12.6 m/s² to 2.4 m/s² with an attenuation of 81%, and in Case 3, it decreases from 12.6 m/s² to 0.04 m/s², with an attenuation of 99.7%. The attenuation is 99.7%. It can be seen that with the increase of the elastic modulus of the cork-rubber gasket, the attenuation of the tangential acceleration amplitude before and after the vibration wave passes through the longitudinal joint becomes smaller and smaller.

As shown in Figure 11, the acceleration response value pointing in the radial direction is larger than the acceleration response value pointing upwards along the tangential direction of the inner arc at this measurement point. Comparing the radial time history before and after passing through the longitudinal joint, it can be found that the selection of different elastic modulus cork-rubber gasket has different effects on the model calculation results. The attenuation is about 99% for Case 1 and Case 3, and about 75% for Case 2. Same as the results of tangential time history analysis before and after passing through the longitudinal joint, the attenuation of Case 2 is the smallest.

The peak vibration acceleration values at the response points of Case 1, Case 2 and Case 3 were counted respectively as shown in Figure 12, which further illustrates that the longitudinal joints are still the main cause of vibration wave attenuation in shield tunnels, and show the trend of smaller peak vibration acceleration values for low elasticity modulus cork-rubber gaskets.

Separate statistical longitudinal joint before and after the measurement point radial vibration acceleration attenuation amplitude shown in Figure 13, with the measurement point distance from the loading point gradually increased, the vibration acceleration attenuation amplitude continues to decrease, the vibration wave attenuation amplitude in the segment is much smaller than the amplitude of the vibration wave through the attenuation of the longitudinal joint, and with the elasticity of the cork-rubber gasket modulus of the increase in the amplitude of the attenuation of the vibration wave through the longitudinal joint is reduced.

5.2. Frequency spectral analysis

Figure 14(a) shows the spectral analysis of tangential vibration acceleration at the measurement points before and after the longitudinal joint for cases 1, 2 and 3. Observing the response points 1–2, compared with Case 1, the vibration acceleration in high frequency (600 Hz ∼ 2000 Hz) of Case 2 is smaller than that of Case 1, and around 540 Hz, there is an obvious peak in Case 2 compared with Case 1, and the vibration acceleration reaches 0.2298 m/s², which is much larger than that of Case 1, which is 0.09 m/s². Compared with Case 3 and Case 1, the vibration acceleration at all frequencies in response points 1–2 Case three is smaller than that of Case 1, and the vibration acceleration amplitude in each frequency band decreases by an average of 0.003 m/s², with a decrease of about 13%.

It can be found that after passing through the longitudinal joint, the vibration acceleration at high frequency (500 Hz and above) attenuates significantly under each working case. When the frequency is 1000 Hz and above, the vibration acceleration at each measurement point tends to be close to 0. This is consistent with the results of our field tests that the longitudinal joints of shield tunnels weaken high-frequency vibration waves more than low-frequency vibration waves. Comparing Case 1 and 2, it can be clearly observed that the peak value located around 540 Hz disappears, and at the same time, it can be found that in the low-frequency band (250∼400 Hz) the vibration acceleration attenuation of Case 2 is not ideal, and the vibration acceleration amplitude near 250 Hz increases instead of decreasing, increasing from 0.0337 m/s² to 0.0671 m/s². Because the vibration acceleration of each frequency at the response point 1–2 Case 3 is smaller than that of Case 1, even after passing through the longitudinal slit, the vibration acceleration of each frequency at the observation point 2–2 Case 3 is still smaller than that of Case 1, and the vibration acceleration attenuation amplitude of the vibration wave of the two cases after passing through the longitudinal slit is still not much different, but in general the amplitude of the frequency bands is smaller than that of Case 1.

Figure 14(b) shows the spectral analysis of radial vibration acceleration at the measurement points before and after the longitudinal slit for cases 1, 2 and 3. Observing the response points 1–1, it can be found that the radial vibration acceleration for each case has obvious peaks around 145 Hz and 500 Hz, with the peaks of 0.520 m/s² and 0.908 m/s² for Case 1, and the peaks at the two locations of Case 2 and Case 3 being 0.249 m/s², respectively, 0.631 m/s² and 0.279 m/s², 0.792 m/s² respectively, the peak values around 500 Hz are significantly reduced after passing through the longitudinal joints, and the decreases of the three cases are 98%, 74% and 98% respectively, indicating that the low modulus of elasticity cork-rubber gasket will enhance the damping effect of the longitudinal joints on the frequency band around 500 Hz.

6. Conclusions

In this paper, based on the high-speed railway shield tunnel test to construct the high-speed railway shield tunnel power calculation model considering the effect of assembling, using finite element software Abaqus to calculate the mechanical analysis of the segment of the three-ring shield tunnel, through the field test and model analysis we find:

(1) The vibration wave is transmitted in the high-speed railway shield tunnel, and the concrete part of the segment has a certain high-frequency vibration weakening ability, but the longitudinal joints are still the main cause of the vibration wave attenuation in the shield tunnel. The longitudinal joints of high-speed railway shield tunnel have a stronger weakening ability for high-frequency vibration waves than for low-frequency vibration waves. This highlights the need for design improvements targeting longitudinal joints to enhance vibration control, especially for high-frequency waves.

(2) The modulus of elasticity of the cork-rubber gasket has a significant effect on tunnel vibration. For the transmission of vibration waves inside the tunnel, the lower the modulus of elasticity of the cork-rubber gasket, the smaller the vibration acceleration peak value at each measurement point, and the greater the attenuation of the vibration acceleration peak value of vibration waves passing through the longitudinal joints.

(3) From the frequency spectral analysis, the increase of the modulus of elasticity of the cork-rubber gasket reduces the damping effect of the longitudinal joint in the frequency band of about 500 Hz, and when the modulus of elasticity of the cork-rubber gasket is reduced to a certain value, it is not obvious to increase the damping effect of the longitudinal joint by continuing to reduce the modulus of elasticity.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The present study is sponsored by the National Natural Science Foundation of China (52378443) and the Tianjin Science and Technology Plan Project (22JCQNJC01710).

ORCID iDs

Hao Jin

Bolong Jiang

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