Deformation Response of Tunnel Lining in Geological Area of Coal Seam Group Caused by Explosion Stress Wave

Transportation construction is an important cornerstone of a country’s economic development. Tunnels play an important role in the process of traffic network construction. Especially in mountainous and hilly areas, tunnels account for a larger proportion of traffic routes. At present, in the process of highway tunnel construction, the commonly used tunnel excavation method is still drilling and blasting [1–4]. The advantage of the drilling and blasting method is that the construction period is short and the efficiency is high, but the disturbance to the surrounding rock is also great, especially when the tunnel passes through certain special geological areas, such as weak fracture zones, karst areas, and layered geological areas. In these cases, when constructing the tunnel using the drilling and blasting method, special attention should be paid to the deformation of surrounding rock under the action of blasting disturbance to avoid causing engineering accidents [5–8].

In the process of drilling and blasting, the explosion stress wave, as the main disturbance load, propagates in and thus disturbs the surrounding rock [9, 10]. At present, academic research on the damage to the surrounding rock caused by the explosion stress wave mainly includes theoretical analysis, numerical simulation, and model testing. Chu et al. analysed the damage and failure mechanism of coal caused by the blasting stress wave by using damage theory and fracture mechanics. They also carried out simulation experiments to analyse in detail the formation and propagation of cracks in the area near the blasting hole, but their research only studied the rock-breaking process of explosive stress waves in a single-medium rock mass [11]. Based on numerical analysis, Wang et al. studied the crack propagation caused by an explosion under the conditions of different degrees of fragmentation and different angles of layering. They discussed the effects of particle velocity, maximum principal stress, and delay time on crack propagation at different positions from the blasting hole. However, they only considered the failure process of the surrounding rock near the blasting hole and did not consider the transmission effect of the explosion stress wave in the whole of the surrounding rock [12]. Mainak and Sayan studied the vibration of a reinforced concrete lining in a tunnel under explosive load. They analysed the vibration reduction performance of intermittent foam-filled grooves by using a three-dimensional nonlinear finite element method. Their research mainly optimised the technical parameters and did not consider the influence of the change of the surrounding rock medium on the propagation of the explosive load [13]. Guan et al. used finite element software to study the stability of underground water transfer tunnels with different cross-section shapes under blasting loads. They mainly studied the amount of explosive and the surrounding rock medium around the tunnel without considering the effect of medium conversion [14]. Kumar et al. compared the data obtained from the simulation of blasting in numerical software with field monitoring data and studied the response of different blasting loads under different formation conditions. They mainly analysed the ground vibration and did not make an in-depth study of the propagation of the explosion stress wave in the rock mass [15]. Tian et al. carried out a blasting vibration test to study the propagation of the explosion stress wave in a superlarge cross-section shallow tunnel [16]. Paswan et al. carried out 50 blasting tests in the field to study the influence of the joint spacing and strike on the rock crushing effect. They considered the failure law of the explosion stress wave in different surrounding rock media, but they relied only on the test data to make engineering suggestions [17]. Blair combined his study with the DFEM-MCWSM model and constructed an approximate model of explosion vibration propagation in a jointed rock mass. He studied the transmission of blasting vibration after the local geological change in the rock mass, to select the appropriate delay time series to reduce the blasting vibration [18]. Guan et al. based their study on the high-order local modal analysis method. They studied the structural damage and stress response of the tunnel under explosive loading and combined this analysis with field data. Their research content was mainly based on numerical simulation analysis, and the theoretical research was not deep [19]. Based on the measured data, Jiang et al. constructed a theoretical model and numerical model of explosion stress wave attenuation. They studied the stability of the surrounding rock and adjacent pipelines under blasting load vibration [20].

Scholars have done a lot of research on the influence of explosion stress waves on the disturbance of the surrounding rock. However, the existing research has mainly focused on the damage caused by the explosion stress wave near to the blasting hole, the transmission and attenuation of the stress wave, the damage caused by the stress wave to the surrounding rock, the crack propagation in the surrounding rock, and so on. Their research methods were mainly numerical simulations and field tests. Results on the theoretical research of explosive stress waves are extremely scarce. There are even fewer results concerning the influence of explosion stress wave propagation in multimedium surrounding rock and the law of stress wave propagation. Therefore, based on Tianchengba tunnel, this paper constructs the calculation theory of explosion stress wave deformation of the tunnel lining in coal seam geological area and analyses the deformation response of the tunnel lining in the process of stress wave propagation in different media. The study of this paper can provide a theoretical basis and data reference for the design and construction of tunnels in multimedium areas.

After the tunnel is excavated by blasting, the explosion stress wave will propagate in all directions into the surrounding rock, with the explosion source as the centre. The main purpose of this paper is to study the influence of the explosion stress wave on the tunnel lining. When studying the mechanical response of the tunnel lining under blasting, the explosion stress wave propagating along the direction of tunnel excavation is mainly considered [21–23]. In this paper, we will use the basic theory of random vibration to analyse the explosion stress wave response of the tunnel lining. Using the coherence function model, this paper studies response of the tunnel lining in the cross-section (tunnel cross-section direction) and longitudinally (tunnelling direction) to the explosion stress wave. Meanwhile, we use a viscoelastic medium to replace the surrounding rock near the tunnel [24, 25].

Before constructing the explosion vibration equation, we need to simplify the calculation model. This paper is constructed to study the influence of the explosion stress wave on the tunnel lining, and we simplify the tunnel lining to a thick-walled cylinder. When studying the longitudinal vibration of the thick-walled cylindrical tunnel lining (TWCTL), we connect it through a longitudinally movable hinge support (as shown in Figure 1).

In Formula (5), $ωn$ is the natural frequency; $ξn$ is the damping ratio; and $τ$ is the generalized force.

When studying the transverse vibration of the TWCTL, we connect it through a transversely movable hinge support (as shown in Figure 2).

In Formula (10), $kh$ is the shear stiffness of the surrounding rock near the TWCTL, $EH$ is the compressive stiffness of the surrounding rock near the TWCTL, and $uhx,t$ is the transverse displacement of the tunnel field.

In Formula (4), $Au$⁠, $Bu$⁠, $Cu$⁠, $Du$⁠, $Eu$⁠, and $Fu$ are undetermined coefficients.

In practical engineering, the geological condition of the tunnel crossing area is not a single medium, but in a multimedium geological area. When the tunnel passes through a multimedium area, the disturbance of the surrounding rock caused by the explosion stress wave is different from that of a tunnel passing through a single-medium area, and the failure form is also different. It is not suitable to use the single-medium calculation model to study the tunnel lining disturbance caused by blasting under any geological conditions [26–29].

In Formula (11), $i$ represents the segmentation of different surrounding rock media, $i=0,1,2,⋯,n$⁠; $mi$ is section $i$ TWCTL mass; $νix,t$ is section $i$ TWCTL longitudinal displacement; $ηi$ is the viscosity coefficient of the section $i$ surrounding rock near the TWCTL; $kνi$ is the shear stiffness of section $i$ surrounding rock near the TWCTL; $EZi$ is the compressive stiffness of section $i$ surrounding rock near the TWCTL; and $ννix,t$ is the section $i$ TWCTL in the longitudinal displacement of the tunnel field.

If we know the corresponding boundary conditions, we can calculate the undetermined coefficients $Avi$⁠, $Bvi$⁠, $Cvi$⁠, and $Dvi$ in Formula (12).

If we know the corresponding boundary conditions, we can calculate the undetermined coefficients $Aui$⁠, $Bui$⁠, $Cu$⁠, $Dui$⁠, $Eui$⁠, and $Fui$ in Formula (16).

This paper takes the Tianchengba tunnel in Zheng’an-Xishui Expressway as an example. The tunnel is a double-lined separated extralong tunnel. The length of the left tunnel is 4255 m, the length of the right tunnel is 4280 m, and the maximum buried depth is 518.41 m. The coal stratum that the Tianchengba tunnel passes through is 128.6 m. The tunnel passes through 10 coal seams, of which there are 7 outburst coal seams, and the maximum thickness of a single coal seam is 11.2 m (as shown in Figure 5). The surrounding rocks in the tunnel crossing area are mainly coal and dolomite. The main mechanical parameters of the surrounding rock and the tunnel lining structure are shown in Table 1.

The TWCTL will experience transverse vibration and longitudinal vibration under the action of the explosion stress wave. As can be seen from Formula (19), the calculation expressions of $ux,t$ and $vx,t$ are very similar. According to the mechanical characteristics of the tunnel lining structure, we find that the influence of stress waves on the transverse vibration of the tunnel lining is greater than that on the longitudinal one. Therefore, in the following example, we only analyse the lateral vibration of the TWCTL.

The stress waves formed by the explosion of different explosives have different propagation velocities in different media and cause different vibrations in the TWCTL. Based on the single-factor analysis method, taking the acceleration of the stress wave (⁠$a=3.5$ cm/s², $a=35$ cm/s², $a=350$ cm/s², and $a=3500$ cm/s²) and the grade of the surrounding rock as variables, we study the vibration of the explosion stress wave on the TWCTL in a single medium. The mechanical parameters of the different grades of the surrounding rock and the kinetic parameters of the lining are shown in Table 2.

In a single medium, the relationship between $uTx,t$ and $uCx,t$ formed by the TWCTL with different accelerations and distances from the explosion point is shown in Figures 6 and 7. We can see from Figure 6 that the explosion stress wave propagates in a single medium, as the research point is gradually further away from the explosion point, and $uTx,t$ increases slowly in reverse and then decreases and then increases. The first trough and peak appear in the relation curve of $uTx,t$ and $x$⁠. At this time, the research point is close to the explosion point. The medium absorbing the explosion stress wave energy is less. The stress wave propagates fast, and the vibration frequency is high. The refraction and reflection of the stress wave are weak. When the stress wave has not yet had a substantial impact on the lining, it has spread far away. Therefore, in the area close to the explosion point, $uTx,t$ formed by the stress wave acting on the TWCTL is smaller. As the research site gets further away from the explosion point, $uTx,t$ first decreases slowly and then accelerates to increase, and the increasing trend is obvious. When the distance from the explosion point is about 65 m, $uTx,t$ has the largest value. Then, the curve of the relationship between $uTx,t$ and $x$ decreases at the same speed, and a second trough and peak appear. When the distance from the explosion point is about 82 m, $uTx,t$ decreases to 0 and then continues to increase in reverse until the third trough appears. However, the numerical value of $uTx,t$ at the third trough is smaller than at the second peak. The calculation results show that the explosion stress wave does not have the greatest influence on $uTx,t$ formed by the TWCTL closer to or farther away from the explosion point, but at a specific distance. The reason is that when the research point is close to the explosion point, the explosion stress wave propagates fast, the vibration frequency is high, and the refraction and reflection are weak. Almost no energy is absorbed by the medium. The explosion stress wave has little effect on $uTx,t$ formed by the TWCTL. The distance between the research site and the explosion point is moderate. The medium absorbs a small amount of energy from the explosion stress wave, and the refraction and reflection of the stress wave are obvious. The interference between the incident wave and the previous reflected wave is small, and the disturbance effect on the surrounding rock is gradually strengthened. The effect of the stress wave on $uTx,t$ formed by the TWCTL appears gradually, and the maximum disturbance area is formed. As the distance increases, the medium absorbs more stress wave energy. At the same time, after the incident wave and the previous reflected wave interfere with each other, the stress wave reduces the disturbance to the surrounding rock. Therefore, after passing through the peak area with the greatest influence of disturbance, the effect of the stress wave on $uTx,t$ formed by the TWCTL is gradually weakened. At the same time, with the increase of stress wave propagation acceleration, $uTx,t$ increases in the region near to the explosion point and decreases in the far region. From the calculation results, we know that the disturbance to the surrounding rock increases with the increase of the acceleration of the explosion stress wave. Therefore, in the process of blasting operations, it is necessary to make a careful selection of explosives to avoid an excessive detonation speed that might cause construction accidents.

After the explosion stress wave has its main vibration influence on the surrounding rock medium in the tunnel crossing area, the TWCTL will also be affected by a later creep effect. The main purpose of this paper is to study the effect on the TWCTL after the creep effect in the surrounding rock at a certain time. We can see from Figure 7, in the area closer to the explosion point, that the damage of the explosion stress wave to the surrounding rock is great, and the creep effect is also very obvious. With the change of the distance from the explosion point, $uCx,t$ caused by the creep takes the form of a cosine function but is relatively small. The main reason is that when the explosion stress wave propagates in the medium, it does so in the form of a cosine wave. Although the stress wave is refracted and reflected in the medium, the incident wave is the main influence on the creep process of the rock mass, so the functional relationship between $uCx,t$ and the explosion point takes the form of a cosine function. In addition, from the calculation, it is found that the change of acceleration of the explosion stress wave has little influence on $uCx,t$⁠. This shows that the main reason for the longitudinal displacement of the TWCTL caused by the creep effect after tunnel drilling and blasting excavation is not from the explosion stress wave, but from the lithology of the surrounding rock medium itself.

In a single medium, when the acceleration of the explosion stress wave is constant, the relationship between $uTx,t$ and $uCx,t$ formed by the TWCTL with different surrounding rock grades and the distance of the explosion point is shown in Figures 8 and 9. We can see from Figure 8 that the surrounding rock grade is better, the influence of the stress wave on the TWCTL is greater, and $uTx,t$ is also greater. The reason is that the better the mechanical parameters of the surrounding rock, the less easily the energy of the stress wave is absorbed when it is transmitted in the surrounding rock. The range of influence of the stress waves is greater. The maximum value of $uTx,t$ moves backwards. We can see from Figure 9 that the explosion stress wave acts on the surrounding rock, and the better the surrounding rock grade is, the more obvious the creep effect is. The main reason is that the surrounding rock grade is better. The effect of the stress waves in the surrounding rock is more obvious. Compared with the low-grade surrounding rock, the energy produced by the stress wave is absorbed and attenuated less, and the disturbance of the stress wave to the surrounding rock is relatively large.

In a soft medium and hard medium, the relationship between $uTx,t$ and $uCx,t$ formed by the TWCTL and the distance of the explosion point is shown in Figures 10 and 11. When the explosion stress wave changes from a soft medium to a hard medium and from a hard medium to a soft medium, there is a great difference in the TWCTL vibration caused by the wave. We can see from Figure 10 that in the range of 0~50 m from the explosion point, when the explosion stress wave propagates in the soft medium, $uTx,t$ formed by the TWCTL is smaller than in the hard medium. The reason is that as the stress wave propagates in the soft medium, and the energy will be absorbed more and will be refracted and reflected leaving less energy. Therefore, the vibration caused by the TWCTL is small. However, when the stress wave passes through a junction between different media, $uTx,t$ will suddenly change. The reason is that after the change of lithology, the transmission mode of the stress wave changes greatly, and the vibration caused by the TWCTL also changes abruptly. After the transition of the stress wave from the soft medium to the hard medium, the energy fluctuates briefly. In a certain range of propagation, the stress wave forms a short-term energy-accumulating vibration, $uTx,t$ increases sharply in the reverse direction and reaches its peak. The stress wave then decreases gradually. The reason is that when the stress wave propagates in the soft medium where the surrounding rock medium is soft, the energy propagates slowly, the energy dissipation is larger, and the energy is smaller. $uTx,t$ shows a trend of slow growth. When the medium changes from soft to hard, the energy will produce a “nest effect” on the interface between the soft and hard media. The energy forms a short-term energy accumulation, and $uTx,t$ will abruptly decrease. When a certain amount of energy has accumulated, the energy propagates further into the hard medium in an excited state. The stress wave will vibrate greatly in the hard medium. When the stress wave propagation medium changes from hard to soft, $uTx,t$ will surge abruptly. In the hard medium, $uTx,t$ increases positively with increase of the stress wave propagation distance, until it reaches the peak value; then, it decreases gradually. The reason is that when the stress wave propagates in the hard medium, the surrounding rock medium is better, the energy dissipation is smaller, and the increasing trend of $uTx,t$ is larger than that in the soft medium. However, when there is a sudden transition from a hard to a soft medium and the medium in the process of larger energy propagation is suddenly converted, the stress wave will produce huge vibration of the TWCTL at the junction of the soft and hard media, and the energy transfer process will not be like the stress wave from the soft medium to the hard medium. The energy will be better absorbed, the transfer process will be very smooth, and there will be no “nest effect.” $uTx,t$ will have a sudden surge. With further propagation of the energy in the soft medium, $uTx,t$ shows a normal growth trend. However, a large amount of energy will be absorbed in the process of propagation, and the growth trend of $uTx,t$ will gradually decrease. As can be seen from Figure 10, the peak value of $uTx,t$ formed by the TWCTL vibration caused by the stress wave entering the soft medium from the hard medium is smaller than that from the soft medium into the hard medium. Therefore, if the surrounding rock medium changes in the tunnel crossing area, the builders need to constantly monitor the vibration of the lining in the area of this change. When the surrounding rock medium changes from good to bad, special attention is required.

As can be seen from Figure 11, the creep effect of the surrounding rock caused by the explosion stress wave is mainly caused by residual energy. The peak value of $uCx,t$ formed by the action of residual energy on the TWCTL is the same. The main difference is that the medium transformation is different, and the maximum peak of $uCx,t$ appears in different regions, but all appear in hard rock. The residual energy is smaller. In the medium transition zone, when the stress wave enters the soft rock from the hard rock, the residual energy will be absorbed more after entering the soft medium, and the refraction and reflection of the energy are weak, which makes $uCx,t$ decrease rapidly. When the energy passes from soft rock to hard rock, $uCx,t$ increases rapidly. The energy is small, and the “nest effect” formed at the junction of medium conversion is not obvious. The energy will break through the interface and continue to propagate, and the increasing trend of $uCx,t$ is larger. This phenomenon further shows that when the surrounding rock medium in the tunnel crossing area changes from good to bad, the constructors need to pay special attention to the lining vibration.

The explosion stress wave propagates with different accelerations from the soft medium to the hard medium and from the hard medium to the soft medium. The relationship between $uTx,t$ and $uCx,t$ and the distance from the explosion point formed by the stress wave acting on the TWCTL are shown in Figures 12–15. The influence of the acceleration of the explosion stress wave on the TWCTL in different media is similar to that in a single-medium area, and we will not repeat it here. The construction team only needs to pay attention to the vibration of the TWCTL in the medium conversion area.

From our on-site research, we find that there is a great difference in the vibration of the tunnel lining in the area where the medium changes in the tunnel’s surrounding rock. Especially during the transition from coal to dolomite, the lining is collapsed and cracked by explosive stress waves (as shown in Figure 16). For safe tunnel blasting vibration monitoring, we only monitor the tunnel lining which is 70 m away from the explosion point. The on-site vibration monitoring of the tunnel lining is shown in Figure 17. As the stress wave propagates away from the explosion point, the vibration of the lining first increases and then decreases. In addition, we find that the vibration amplitude of the lining increases after the stress wave propagates from the coal rock to the dolomite, while it decreases after the stress wave propagates from the dolomite into the coal rock. In order to make a complete study of the influence of the stress wave on the deformation of the tunnel lining, according to the actual working conditions (as shown in Figure 18), we substitute the mechanical parameters of coal and dolomite and the specific parameters of different surrounding rock media into the theoretical calculation formula. From the alternating conversion of different surrounding rock media, we obtain the relationship between $uTx,t$ and $uCx,t$ formed by the explosion stress wave at the TWCTL and the distance of the explosion point, as shown in Figures 19 and 20.

As can be seen from Figure 19, in the process of stress wave propagation in the surrounding rock medium, $uTx,t$ increases slowly in the early stage, then increases rapidly. With the dissipation of stress wave energy, $uTx,t$ decreases gradually in the later stage. The mechanical property of dolomite is better than that of coal rock. Before reaching the maximum peak value of $uTx,t$⁠, as the stress wave propagates from dolomite to coal rock, $uTx,t$ will increase abruptly. When the stress wave propagates from coal to dolomite, $uTx,t$ will abruptly decrease. The reason is that after the stress wave enters the soft rock from the hard rock, the excessive energy in the hard medium suddenly enters the soft medium, which makes the energy transfer more smoothly and will not produce the “nest effect.” The energy produces great vibration in the surrounding rock at the junction of the soft medium and the hard medium. The deformation of the surrounding rock causes a huge squeeze on the TWCTL, and $uTx,t$ suddenly increases. As the stress wave continues to propagate in the soft medium, the energy dissipation is obvious. At the same time, when the stress wave propagates from the soft medium to the hard medium, the energy accumulates briefly at the junction of the two media, the disturbance of the stress wave to the surrounding rock is small, and $uTx,t$ decreases rapidly.

As can be seen from Figure 20, as the stress wave propagates from dolomite to coal rock, $uCx,t$ will suddenly decrease, and when it propagates from coal rock to dolomite, $uCx,t$ will suddenly increase. The formation of $uCx,t$ mainly depends on the residual stress wave. After the residual energy enters the soft medium from the hard medium, the energy is absorbed, the energy dissipation is large, the creep effect of the residual energy is not obvious, and $uCx,t$ is small. After the stress wave propagates from the soft medium to the hard medium, the energy accumulates briefly at the medium interface. The residual energy passes through the hard medium. The creep effect is obvious, and $uCx,t$ increases sharply.

In the initial design of the Tianchengba tunnel, the initial supporting concrete strength was C25 and the thickness was 20 cm, and the secondary lining concrete strength was C30 and the thickness was 50 cm. After construction according to these design parameters, in the surrounding rock medium conversion zone with poor surrounding rock conditions, and under the action of stress wave vibration, lining damage continues. According to the above research results, combined with the on-site vibration monitoring data, we make the following suggestions for the design parameters of the on-site lining. In the exchange area between coal and dolomite, the strength of the initial supporting concrete is unchanged, but the thickness is changed to 25 cm, the strength of the secondary lining concrete is changed to C35 while the thickness is unchanged, and the lining construction parameters of the other sections remain unchanged. The reason for changing the parameters is that there is direct contact between the initial support and the surrounding rock. If the strength of the concrete is enhanced, the stress wave will be absorbed less in the process of propagation and cause great damage to the secondary lining. In order to ensure the stability of the structure and increase the propagation distance of the stress wave, for more energy dissipation of the stress wave, it is only necessary to thicken the initial supporting concrete. When the stress wave propagates to the secondary lining, it needs to go through the initial support. The strength of the initial supporting concrete is lower than that of the secondary lining, and a large amount of reflection will appear when the stress wave propagates to the surface of the secondary lining concrete. In order to further ensure the safety of the secondary structure, after strengthening the secondary lining concrete, it can reflect more energy and reduce the damage to the secondary lining structure to a greater extent. After the proposed scheme is used in the field, vibration collapse and cracking of the lining concrete are greatly reduced, and the effect of the application is very good.

• (1)

  The explosion stress wave propagates in a single medium. When the research point is close to the explosion point, the stress wave propagates fast, the vibration frequency is high, and the refraction and reflection are weak. At the same time, the disturbance to the surrounding rock increases with the increase of the acceleration of the explosion stress wave. In addition, the better the grade of the surrounding rock, the more obvious the creep effect formed by the explosion stress wave, which is more damaging to the tunnel lining. When the distance between the research point and the explosion point is moderate, the interference between the incident wave and the reflected wave is small, the disturbance to the surrounding rock is strong, and the maximum disturbance area is formed. The farther away from the explosion point, the more energy will be absorbed by the medium in the energy propagation. The influence of stress waves on the surrounding rock is weakened

• (2)

  When the stress wave propagates from a soft medium to a hard medium. In the early stage, the energy propagates slowly and dissipates greatly, and $uTx,t$ shows a slow growth trend. When the propagation medium changes from soft to hard and the energy produces a “nest effect” at the interface between the soft medium and the hard medium, there is a short-term energy accumulation at the interface, and $uTx,t$ abruptly decreases; when a certain amount of energy has accumulated, the energy propagates further into the hard medium as excited state energy, which vibrates greatly in the hard medium. When the stress wave propagates from the hard medium to the soft medium, in the early stage, the energy dissipation is small. When there is a sudden transition from a hard to a soft medium, the stress wave will produce huge vibration in the TWCTL at the junction of the soft and the hard media, and there will be no “nest effect”

• (3)

  The peak value of $uCx,t$ formed by the creep effect of the surrounding rock caused by the explosion stress wave is the same, and the maximum peak appears in hard rock. When the stress wave propagates from the hard rock to the soft rock, $uCx,t$ decreases rapidly, and when the stress wave propagates from soft rock to hard rock, $uCx,t$ increases rapidly, and when the surrounding rock medium in the tunnel crossing area changes from good to bad, the constructors need to pay special attention to the lining vibration

The relevant data used in this paper are available from the authors upon request.

The authors declare that they have no conflicts of interest.

This paper is sponsored by the National Natural Science Foundation of China (Grant No. 52064008).