Experimental Study of Dynamic Responses of Special Tunnel Sections under Near-Fault Ground Motion

Abstract

Data surveys show that near-fault ground motion does great damage to tunnel structures, especially the portal section and fault zone. In this paper, a series of shaking table model tests of near-fault tunnels were conducted and the surrounding-rock fault-zone-lining model of the near-fault tunnel was established. Accelerometers and strain gauges were arranged at specific locations, and the experimental process of earthquake occurrence was simulated by inputting seismic waves of different working conditions, which obtained the characteristics of stress, damage and deformation of the tunnel model. The tested results showed that the acceleration response of the tunnel portal section was close to the wave shape of the inputted seismic wave, and the acceleration response of the arch shoulder, arch waist and arch foot was more prominent. The internal force of lining at the arch shoulder and arch foot was greater than that at the arch crown, and the peak internal force appeared at the arch foot. The internal force and the maximum or minimum principal stress of the lining under impulse ground motion were larger than those under non-impulse ground motion. Additionally, the surrounding rock had a filtering effect on the high-frequency band of seismic waves. Meanwhile, when the geological characteristics of the fault zone were poor, and the tensile damage first appeared at the arch foot, the compressive damage appeared at the junction of the surrounding rock and fault zone. This study will offer a practical guidance for tunnel engineering earthquake damage.

1. Introduction

Near-fault ground motion has been a hot research field in seismic engineering and seismology over the past 20 years [1,2]. The tunnels, bridges and long-span buildings will be inevitably affected by the earthquake fault especially. The damaged life projects will bring huge losses to the national economy and social life. In recent years, these earthquakes disasters including the Northridge earthquake (1994), Kobe earthquake in Japan (1995), Chi Chi earthquake in Taiwan (1999), Kocaeli earthquake in Türkiye (1999), etc., have had a huge influence on the whole world [3,4,5]. The results of the survey show that the near-fault ground motion has obvious long-period velocity and displacement pulses, which makes the structural damage in these areas more serious than that in the far-fault area [6,7]. As the country with the largest number of strong earthquakes in the mainland, China has a large number of seismic zones and seismic faults, and a considerable number of cities are located near the faults or seismic zones. Therefore, it is of great significance to study the near-fault seismic response.

Data surveys show that earthquake disasters have a huge destructive effect on tunnel structures. The damage to the near-fault is more serious, especially the special tunnel section, such as the portal section and fault zone. The portal section belonging to the exposed part of the tunnel is easier to be damaged than the main body of the tunnel under seismic action [8,9,10]. The basic reason is that the buried depth of the portal section is shallow, and the geological conditions are poor (mostly strongly weathered broken rock mass or loose accumulation). Once the tunnel is subjected to a strong earthquake, the side and front slopes of the portal section are prone to collapse, cracking and other seismic disasters, which will block the portal, interrupt traffic and directly cause different degrees of seismic damage to the tunnel opening and lining structure, affecting the stability and availability of the tunnel structure. Therefore, the study of near-fault ground motion to tunnel damage is essential, and it is also urgent to establish a systematic theoretical system. Due to its own particularity, the research methods of the seismic responses of underground structures are quite different from those of ground structures. These research methods can be mainly divided into prototype observation, model testing and theoretical analysis. The related content will be introduced [11,12]. Han et al. [13] considered the influence of near-fault ground motion with different characteristics on the dynamic response of isolated structures, and the forward-directional effect velocity pulse, slip impact effect velocity pulse and no velocity pulse were inputted into the shaking table tests. Experimental results showed that the dynamic response of near-fault ground motion with pulses was significantly greater than that without pulses, and the response with pulses was related to the structural period. Wang et al. [14] studied the seismic response of the tunnel by a series of shaking table tests. Tao et al. [15] conducted shaking table tests to verify the analytical solution of the single free surface slope model, which can provide a reference for the seismic design of the tunnel portal section in mountainous areas and had a positive impact on the reasonable interpretation of the seismic response characteristics of this section. Moreover, there is no systematic research on the acceleration response and stress–strain relationship of tunnel structures caused by near-fault ground motion [16,17]. Hacıefendioğlu [18] investigated the deconvolution effect of the random near-fault earthquake ground motion on the stochastic dynamic response of tunnel-soil deposit interaction systems. The analyses showed that the standard rigid-base input model is inadequate to evaluate the stochastic dynamic response of tunnel–soil deposit interaction systems subjected to the random near-fault earthquake ground motion. El-Nabulsi et al. [19] constructed the seismic wave equation in fractal dimensions based on the concept of product-like fractal measures introduced recently by Li and Ostoja-Starzewski in their formulation of anisotropic media. Liu et al. [20] presented numerical studies on seismic waves, considering the propagation effect, and aimed to illustrate the response principle and structural failure mechanism of tunnel structures under long-period ground motion. Zhou et al. [21] studied the dynamic response of the lining structure in a long tunnel passing through an adverse geological structure zone subjected to a non-uniform seismic load. Meanwhile, some scholars have also studied the damping control of tunnel dynamic responses [22,23,24,25]. Yan et al. [26] proposed a compartment-type particle damper and its design method suitable for immersed tube tunnel, and a shaking table test on the model tunnel before and after setting the particle damper was performed. Jin et al. [27] investigated a passive Tuned Mass Damper (TMD) to dampen resonant motions of a Submerged Floating Tunnel (SFT) in waves and earthquakes. The results showed that TMD played a crucial role in controlling SFT vibrations when environmental loads were close to the system’s fundamental lateral natural frequency under both wave and seismic excitations and also enhanced the comfort of passengers and reduced static and dynamic mooring tensions. We can know that scholars also have continuously studied the relationship between these characteristics and earthquake damage distribution, providing reliable basic data for a deeper understanding of the earthquake generation process. However, there are no systematic studies on the acceleration response and stress–strain relationship of tunnel structures caused by near-fault ground motion. Therefore, it is of great scientific significance and engineering application value to carry out a systematic study on the analysis of seismic response characteristics of near-fault tunnels and improve the design of tunnel construction systems.

In this paper, the seismic response characteristics of near-fault tunnels were studied through shaking table model tests. Considering the basic characteristics of near-fault ground motion, such as the slip impact effect, directivity effect, velocity pulse, hanging and footwall effect, vertical effect, etc., the biggest differences between the near-fault ground motion and ordinary ground motion are the long period and large amplitude velocity pulse, which are the main reasons for more serious damage to engineering structures caused by near-fault earthquakes. In view of the above reasons, the acceleration response, stress and strain analysis of near-fault tunnel structure lining and surrounding rock and special tunnel section under near-fault ground motion were studied in this paper.

2. Shaking Table Model Test of Near-Fault Tunnels

2.1. Prototype Selection

We adopted the standard section of single tunnels with two lanes at a design speed of 60 km/h in the Specifications for Design of Highway Tunnels (JTG D70-2004) as the prototype selection of the tunnel, as shown in Figure 1. The surrounding rock prototype of this test was Grade IV surrounding rock with poor quality. The simulated materials of the fault fracture zone were the same as that of ordinary surrounding rock. In order to further meet the elastic modulus and unit weight required by the test, some wood chips with a small mass and large modulus were added to the geotechnical material.

2.2. Experimental Apparatus

The following model test was conducted in the shaking table equipment, which consisted of the main body of the shaking table, servo motor drive system, controllers and control software, as shown in Figure 2A. Its main performance parameters are shown in

Table 1. The main parameters and technical indicators of the vibrating table.

Technical Parameter	Standards	Technical Parameter	Standards
Platform size	1.6 m × 1.2 m	Amplitude	150 mm
Maximum load weight	15 kN	Acceleration	0.5 g
Working frequency	Sinusoidal wave 0.01–10 Hz	Degrees of freedom	Single degree of freedom

. It is notable that the shaking table test was carried out with a rigid model apparatus and flexible boundary conditions, which have the advantage of high rigidity and no deformation during excitation. We can know from previous studies that the experimental results are good when the transverse dimension of the model box is greater than 5 times the tunnel diameter. The length, width and height of the model box were 1.38 m, 0.73 m and 1.005 m, respectively. The sectional dimension of the prototype tunnel was 10.28 m, which will be converted with a similar ratio of 1:50 to meet the requirements. The main frame was aluminum alloy, and the lateral walls were made of toughened glass for easy observation, as shown in Figure 2B.

In order to more accurately simulate the response of the tunnel under earthquake damage, the boundary of the model box must be processed. The bottom plate was made as a friction boundary by paste gravel to increase the friction resistance between the soil mass and the bottom, as shown in Figure 2B. The unidirectional vibration was loaded in the test. A 10-cm-thick polystyrene foam plate was pasted on the inner surface of tempered glass perpendicular to the excitation direction to reduce the reflection of waves from the inner wall of the model box. Additionally, a layer of plastic film was pasted on the inner wall of tempered glass parallel to the vibration direction to reduce the resistance between the rock and soil mass and the inner wall of the model box glass, as shown in Figure 2B.

2.3. Similarity Scales

We can know that under ideal conditions, the similarity relationship of the conventional static model must be satisfied. Besides, the shaking table model test must also conform to the similarity relationship of the dynamic model. However, it is impossible to achieve complete similarity due to various factors in the model experiment test, such as the tested materials, model test instruments, test costs and human operation errors.

According to Bukingham’s π theorem, we assumed that the similarity scale of strain is 1 [28,29,30], and the shear modulus similarity scale can be obtained from the classical dynamic equation, as follows:

$$\rho {\partial }^{2}u/\partial t^2=(\lambda +G)\partial \epsilon /\partial x+G{\nabla }^{2}u$$

(1)

where, $\rho ,u,t$ are density, displacement and time, respectively. $\mathit{\lambda },G,x$ are Lame’s constant, shear modulus and location coordinates, respectively.

For a dimensional analysis, it can be expressed as:

$$(\rho {\partial }^{2}u/\partial t^2-\lambda \partial \epsilon /\partial x)/(\partial \epsilon /\partial x+{\nabla }^{2}u)=G$$

(2)

where the units of $\rho$, ${\partial }^{2}u/\partial t^2$, $\lambda$, $\partial \epsilon /\partial x$, ${\nabla }^{2}u$, $G$ are $\mathrm{kg}\cdot {\mathrm{m}}^{-3}$, $\mathrm{m}\cdot {\mathrm{s}}^{-2}$, $\mathrm{kg}\cdot {\mathrm{m}}^{-1}\cdot {\mathrm{s}}^{-1}$, ${\mathrm{m}}^{-1}$, ${\mathrm{m}}^{-1}$ and $\mathrm{kg}\cdot {\mathrm{m}}^{-1}\cdot {\mathrm{s}}^{-1}$, respectively.

The similarity scale is obtained through dimensional analysis, that is, the similarity scale of density is $S_{\rho }$. The similarity scales of ${\partial }^{2}u/\partial t^2$, $\partial \epsilon /\partial x+{\nabla }^{2}u$, $G$ are $S_a$, $S_l^{-l}$ and $S_G$. The units of $\lambda \partial \epsilon /\partial x$ and $\rho {\partial }^{2}u/\partial t^2$ are the same. Therefore, the similarity relationship can be expressed as follows:

$$G_d^m(\gamma )/G_d^p(\gamma )=S_{G_d}=S_l\cdot S_{\rho }\cdot S_a$$

(3)

where $G_d^{}$ is dynamic shear modulus, $\gamma$ is shear strain and $G_d^{}$ is similarity scale of dynamic shear modulus, respectively. $m$ and $p$ are the model and prototype, respectively. $S_l$, $S_{\rho }$ and $S_a$ are the similarities of geometry, density and acceleration, respectively.

In this study $S_l$, $S_{\rho }$ and $S_{Gd}$ are 1/50, 1 and 1/50, respectively [28,29,30]. Other similitude ratios used in the paper are listed in

Table 2. Model test similarity.

Physical Quantity	Similarity Index	Similarity Scales
Stain	Sε	1
Geometric length	Sl	1/50
Density	Sρ	1
Elastic modulus	SGd	1/50
Speed	Sv = SGd1/2·Sρ−1/2	0.141
Poisson’s ratio	/	1
Internal friction angle	/	1
Time	St = Sl·SGd−1/2·Sρ1/2	0.141
Frequency	Sω = SGd1/2·Sl−1·Sρ−1/2	7.071
Stress	Sσ = SGd	1/50
Acceleration	Sa = SGd·Sl−1·Sρ−1	1
Cohesion	Sc = SGd	1/50

.

2.4. Test Model

2.4.1. Test Model Materials

In the model test, the selection of similar materials was very important, which will affect the reliability, rationality and validity of the test results. Similar materials were usually prepared from aggregates, cementitious materials and auxiliary materials. The aggregates mainly included quartz sand, barite powder, soft wood chips and mica powder. The cementitious materials mainly included gypsum, lime, cement, paraffin and resin. The auxiliary materials mainly included water, engine oil and vaseline. The physical and mechanical parameters of the materials are shown in

Table 3. Physical and mechanical parameters of the test materials.

Type		Density $\mathit{\gamma }$ (kN/m3)	Modulus of Deformation E (GPa)	Poisson’s Ratio $\mathit{u}$	Internal Friction Angle $\mathit{\phi }$ (°)	Cohesion C (MPa)	Axial Compressive Strength ${\mathit{f}}_{\mathit{c}\mathit{k}}/\mathbf{N}/{\mathbf{mm}}^2$
Grade IV surrounding rock	Model	20–23	1.3–6	0.3–0.35	27–39	0.2–0.7	-
	Prototype	20–23	1.3/50–6/50	0.3–0.35	27–39	0.2/50–0.7/50	-
C25 concrete	Model	25	28	0.2	-	-	16.7
	Prototype	25	28/50	0.2	-	-	-
Fault fracture zone	Model	17–20	1–2	0.35–0.45	20–27	0.05–0.2	-
	Prototype	17–20	-	0.35–0.45	20–27	-	-

.

Surrounding Rock and Fault Fracture Zone

In order to accurately simulate the mechanical properties of surrounding rock, a ratio range of cement content to quartz sand content was selected. Considering that the cement sand ratio and water content have a greater impact on the mechanical properties of the model, eight groups of model material ratios were proposed, as shown in

Table 4. Test proportioning table.

Type	Group Number	Cement Sand Ratio	Gypsum:Lime	Sawdust	Water
Grade IV surrounding rock	1	1:3	7:3	-	10%
	2	1:3	8:2	-	10%
	3	1:2	7:3	-	10%
	4	1:2	8:2	-	10%
	5	1:1	7:3	-	10%
	6	1:1	8:2	-	10%
Fault fracture zone	7	1:4	7:3	30%	10%
	8	1:4	7:3	10%	10%

.

The physical and mechanical parameters of the above eight groups of model materials with different proportions were measured and calculated by material mechanics tests. From the test results, it can be seen that the physical and mechanical parameters of the fourth group of model materials were most similar to those of Grade IV surrounding rock, and the eighth group of fault fracture zone was more appropriate as the model material, as shown in

Table 5. Model physical and mechanical parameters data table.

Type	Density (kN/m3)	Modulus of Deformation (GPa)	Internal Friction Angle (°)	Cohesion C (MPa)
Grade IV surrounding rock	21	0.07	34	0.014
Fault fracture zone	11	6.51 × 10−3	23	1.175 × 10−3

.

C25 Concrete

Gypsum has been used as lining material for more than 40 years. Its mechanical parameters in the elastic range have many similarities with concrete, such as brittle materials, compression and non-tension, and Poisson’s ratio of 0.2. Additionally, it has the advantages of easy processing and convenient molding and can better simulate the plastic work and test model conditions of concrete structures. Firstly, vaseline was painted on the inner side of the mold to facilitate demolding, then a certain amount of gypsum powder and water for manual mixing were poured into the mold. Secondly, the sample was formed and began to demold, cure and dry. Thirdly, the mechanical parameters were measured, and three different water gypsum ratios (water:gypsum = 1:0.9, water:gypsum = 1:1, water:gypsum = 1:1.1) were determined. The results were compared with the mechanical parameters of the prototype, and the gypsum model with a water gypsum ratio of 1:1.1 was selected as the lining model material.

2.4.2. Model Making

In this shaking table test, the design speed of 60 km/h for a single tunnel with two standard-section lanes was adopted as the tunnel prototype section to study the characteristics of near-fault tunnel seismic damage. The test simulated the vibration of the tunnel crossing the fault in a model box. The blockboard, wooden strip, roller, steel plate and rubber plastic sponge were used to simulate the active fault. The surrounding rock above the fault-sliding device can slide, and the rubber plastic sponge rebounded to realize the fault dislocation.

Design and Pouring of Surrounding Rock and Fault Fracture Zones

An appropriate amount of surrounding rock and fault fracture zone materials were prepared based on the above test results. The width of the middle fault fracture zone was set as 10 cm, the dip angle was 90° and both sides were Grade IV surrounding rock. The installation of the model structure and the compatibility between the lining structure and surrounding rock materials should be considered. Each layer shall be leveled and compacted as far as possible. The poured sample should be cured for 7 days to form, as shown in Figure 3A. The surrounding rock contained gypsum and water. After each pouring, it should be tightly covered with plastic film to ensure the stability of the water content of the filler.

Design and Fabrication of Lining

The safety performance of the tunnel lining structure is mainly controlled by bending stiffness. Therefore, the model’s similarity should be based on the bending stiffness. Considering its bending capacity and bending strain, the lining shell is regarded as a thin plate structure according to the similarity criteria. The lining model was considered as a plane strain model, with a longitudinal dimension of 70.3 cm, a thickness of 10 mm, a tunnel gap of 20.6 cm and a tunnel height of 19.35 cm. Fine wire mesh with a diameter of 0.2 mm was used in the lining to simulate reinforcement.

The lining model was made of customized mold and cast in situ gypsum, and the manufacturing process was shown in Figure 3B. According to the section of the tunnel model, two acrylic plate rings were customized at a ratio of 1:1. The two aluminum sheets were closely attached to the inner and outer sides of the acrylic plate ring. A layer of mold release agent was applied to the aluminum sheet. The middle of the inner aluminum sheet was filled with fine sand to better fix the mold. The outer aluminum sheet was fixed with wire mesh. Then, the gypsum solution was injected into the mold to fill the space. At last, the poured model was place in a certain temperature environment for curing for several days, and the mold was removed after the gypsum-hardening molding. The inside and outside of the formed lining model was brushed by a certain of clear paint to prevent moisture.

2.4.3. Layout and Sensor Installation

The model test aimed at collecting the acceleration of the tunnel structure and surrounding rock and the strain of the tunnel lining. The data-acquiring equipment used in the test included: the low-frequency piezoelectric acceleration sensor with a range of ±5 g and an axial sensitivity of 1000 mV/g; 120-5AA welding free strain gauge with a sensitivity of 2.0 mV/V. The main instruments were dynamic data-acquisition instruments and a vibration table.

The layout of the monitoring points was mainly determined based on the survey of the earthquake damage and the research results on the seismic response of near-fault tunnels. As shown in Figure 4A, in the portal section, the monitoring points A2, A3 and A4 were respectively arranged at the arch foot, arch shoulder and arch crown of the lining, and monitoring points A5, A6 and A1 were arranged at a horizontal distance of 30 cm, which were used to measure the acceleration time history of the table top of the vibration table. The acceleration sensors in the fault zone section were arranged as A10 at the top of the surrounding rock and A9 at a vertical elevation of 20 cm, which will be compared with A8 and A7 at a horizontal distance of 30 cm at the same elevation. It is worth noting that A is the abbreviation of the acceleration sensor, and S is the abbreviation of the strain sensor.

The layout of strain monitoring was arranged on the inner and outer sides of the lining, which were perpendicular to each other. There were two sections selected for monitoring, namely section 1-1 (referred to as the portal section) and section 2-2 (referred to as the fault zone section). Each monitoring point was pasted with a strain gauge inside and outside the lining. The monitoring points at the portal section were left arch foot S1 and S2, S3 and S4 of left spandrel, and S5 and S6 of left vault. The monitoring points of the fault zone section were left arch foot M1 and M2, left arch waist M3 and M4, left arch shoulder M5 and M6, and left arch crown M7 and M8. The location of the monitoring points is shown in Figure 4B. M is the abbreviation of monitoring point.

2.4.4. Seismic Wave Loading

In comprehensive consideration of the amplitude, spectrum characteristics, duration of the seismic wave and the near-field seismic wave records of the Taiwan Chi Chi earthquake and the California Northridge earthquake were used in this paper. The seismic wave characteristics and specific parameters are shown in

Table 6. Near-fault ground motion parameter table.

Ground Motion Characteristics	Station Component	Number	PGV/ cm/s	PGA/ g	PGD/ cm	PGV/PGA	Tp/s	Rjb/ km
Forward directivity effect pulse	CHY101-FN	1244	85.60	0.340	57.491	0.252	4.80	9.94
No pulse	Canyon Country-W Lost Cany-FN	960	53.12	0.404	10.651	0.132	-	11.39

. The “FN” in the component column in the table referred to the seismic records in the normal direction of the fault.

The two kinds of ground motion were input into different peak accelerations for research. Their acceleration time history curves were as follows: the maximum acceleration and corresponding time of “1244” ground motion were Max = 0.333 g and T = 37.42 s, and the minimum acceleration and corresponding time were Min = −0.340 g and T = 36.97 s, as shown in Figure 5A [13]. The maximum acceleration and corresponding time of “960” ground motion were Max = 0.404 g and T = 4.69 s, and the minimum acceleration and corresponding time are Min = −0.267 g and T = 5.64 s, s shown in Figure 5B. The detailed loading process is shown in

Table 7. Shaking table model test loading conditions.

Number	Type of Seismic Wave	Peak Acceleration
1	1244	0.03 g
2	960	0.03 g
3	1244	0.07 g
4	960	0.07 g
5	1244	0.10 g
6	960	0.10 g
7	1244	0.15 g
8	960	0.15 g
9	1244	0.20 g
10	960	0.20 g

Note: 0.03 g white noise sweep was input before each input of one seismic wave working condition.

.

3. Results and Analysis

Due to human operability, site conditions, equipment performance and other factors, some (data of A2 and A5 were not collected) of the final collected data were missing. However, the overall dynamic response of the near-fault tunnel and surrounding rock based on the premise of striving for the optimal test results was analyzed.

3.1. Acceleration Response of Portal Section

Monitoring points A3 and A4 were respectively arranged at the arch shoulder and arch crown of the lining in the portal section, and monitoring point A6 was arranged at a horizontal distance of 30 cm. A1 was used to measure the platform acceleration. This section mainly analyzed the acceleration time history data collected through the shaking table test. The input peak ground motion acceleration of 0.15 g was taken as an example. The acceleration response of the four monitoring points tended to zero under the action of one-way acceleration excitation, in which the acceleration response of monitoring point A3 near the tunnel arch shoulder was the largest, and the acceleration response of monitoring point A4 near the tunnel arch crown was similar with that of monitoring point A6 at the same elevation.

3.1.1. Spectrum Curve Analysis

The acceleration Fourier spectrums under unidirectional excitation are shown in Figure 6. The spectral amplitude of A1 at the “1244” platform monitoring point was 0.0317, and the spectral amplitudes of A3, A4 and A6 at the monitoring points were 0.0304, 0.0283 and 0.0301, respectively. The amplitude of the acceleration spectrum at the A1 monitoring point of the “960” worktop was 0.1336, and the amplitudes of acceleration spectrums at the A3, A4 and A6 monitoring points were 0.1238, 0.1252 and 0.1266, respectively. Under the action of forward-directional pulse ground motion, the spatial distribution of acceleration spectrum amplitude at the tunnel portal section showed that the arch shoulder amplitude had the characteristics of an outstanding response, and the amplitude of the spectrum under the action of non-pulse ground motion was larger than that under the action of forward-directional pulse ground motion.

Under the influence of near-fault ground motion, the predominant frequencies of worktops were concentrated in two frequency bands of 1–20 Hz and 50–70 Hz, and those of monitoring points A3, A4 and A6 were concentrated in two frequency bands of 1–10 Hz and 10–30 Hz, and the spectral values of arch shoulders were greater than those of arch roofs. It showed that the frequency spectrum value of the seismic wave input from the platform changed after the coupling of the surrounding rock and the tunnel structure, and the frequency did not change significantly. This was due to the fact that the damping effect of the surrounding rock material absorbed part of the seismic wave energy, and the tunnel lining also absorbed or reflected part of the seismic wave energy. It can be seen that the surrounding rock had a filtering effect on the high-frequency band of the seismic wave, and the tunnel structure was relatively safe, and the low frequency (<30 Hz) seismic wave had obvious influence on tunnel structure.

3.1.2. Analysis of Acceleration Response Spectrum Curves

On the basis of the above analysis of the acceleration time history diagram and frequency spectrum curve, the response spectrum characteristics of monitoring points at the portal section at damping ratios of 5%, 10%, 15%, 20%, 30%, 35%, 40% and 50% were analyzed, as shown in Figure 7 (the monitoring points A3 and A4 were taken as examples).

It can be seen from Figure 7 that the response spectrum curves of different damping ratios at the two monitoring points were different with a significant increase and decrease, which showed that the acceleration response decreased with the increase in the damping ratio. The maximum predominant frequency of the arch shoulder acceleration response was in the frequency bands of 1–10 Hz and 10–30 Hz, which was consistent with the aforementioned acceleration response predominant frequency. The maximum predominant frequency of the arch crown acceleration response no longer increased or decreased significantly after 1–5 Hz, which was mainly due to the influence of seismic wave fundamental frequency and damping, and the trend of the response spectrum curve tended to be stable and consistent after the damping ratio exceeded 20%. Therefore, it is suggested that the damping ratio should not be less than 20% in structural design.

3.1.3. Acceleration Amplification Factor

In order to better study the damage and acceleration distribution law of surrounding rock at the structure, the acceleration amplification factor was investigated in this paper. As shown in Figure 8, when the peak acceleration of the input ground motion was the same, the amplification factor was between 0.4–1.1, and there was a maximum value at the structure vault. The acceleration amplification factor of each monitoring point of the forward-directional pulse ground motion was greater than that of the non pulse ground motion, which indicated that the near-fault pulse ground motion had greater impact on the tunnel structure than that from the non-pulse ground motion. Under the condition of inputting different peak accelerations (forward-directional impulse ground motion was taken as an example), the structure vault changed most obviously, and the acceleration amplification factor of other measuring points changed less. This showed that under the action of different peak acceleration ground motions, the amplification factor of the horizontal acceleration of tunnel lining structure was less affected by the type and peak value of the seismic wave. It had a greater relationship with the location of the measuring point and had no obvious amplification effect on the excitation peak value.

3.2. Internal Force Analysis of the Portal Section

The internal force analysis of the lining structure in the portal section in the shaking table test was mainly investigated by the strain measuring. The monitoring points of the strain gauges were the corresponding pastes inside and outside the arch foot, arch waist and arch shoulder of the tunnel lining. The measured strain data can be calculated to obtain its axial force and bending moment as follows:

$$N=\frac{1}{2}({\sigma }_1+{\sigma }_2)A=\frac{1}{2}EA({\epsilon }_1+{\epsilon }_2)=\frac{1}{2}Ebh({\epsilon }_1+{\epsilon }_2)$$

(4)

$$M=\frac{1}{2}W({\sigma }_1-{\sigma }_2)=\frac{1}{2}EW({\epsilon }_1-{\epsilon }_2)=\frac{1}{12}Eb{h}^2({\epsilon }_1-{\epsilon }_2)$$

(5)

where, ${\sigma }_1$ and ${\sigma }_2$ are stresses of internal and external monitoring points, respectively; ${\epsilon }_1$ and ${\epsilon }_2$ are strains of internal and external monitoring points, respectively. $A$, $E$, $W$, $b$, $h$ are section area, lining elastic modulus, section bending moment resistance, section width and lining thickness, respectively.

The time history diagram of the axial force and bending moment at the portal section under various working conditions can be calculated by Equations (4) and (5). We can find from Figure 9 that the axial force of the structure of the tunnel lining was under the action of both tension and pressure, and the bending moment was a cyclic load in the positive and negative directions under the action of horizontal one-way earthquakes. The axial forces based on two selected seismic actions were almost the same, and the bending moment under the forward-directional impulse ground motion was larger than that under the non-impulse ground motion.

It can be seen from Figure 9 that the axial force and bending moment under the action of forward-directional ground motion gradually reduced in 0–40 s and gradually increased in 40–90 s, in which the axial force value of the arch shoulder was larger, the bending moment of the arch foot was larger and the arch waist was the smallest. It can be seen from Figure 9 that the axial force and bending moment under the action of non-pulse ground motion were balanced and consistent as a whole. The values of the axial force and bending moment from large to small were arch shoulder, arch foot and arch waist. This showed that the stress response at the arch shoulder and arch foot of the tunnel portal section under earthquakes was more severe than that at the arch waist, and the damage was likely to occur.

3.3. Acceleration Response of the Fault Zone

The acceleration sensors in the fault zone were arranged at A10 on the top of the surrounding rock and A9 with a vertical elevation of 20 cm, which will be compared with A8 and A7 with a horizontal distance of 30 cm at the same elevation. The acceleration time history data collected in the shaking table test were analyzed. The input peak ground motion acceleration of 0.15 g was taken as an example. The acceleration responses of the four monitoring points tended to zero under the action of one-way acceleration excitation. The acceleration responses of monitoring points A9 and A10 located on the fault zone were significantly greater than that of A7 and A8 located in the non-fault zone. The acceleration responses of monitoring points A8 and A10 located on the top of surrounding rock were significantly greater than that of A7 and A9 located at an elevation of 20 cm. This showed that the tunnel structure in the fault zone was more affected than that in the non-fault zone, and the acceleration response of the surrounding rock was related to the elevation.

3.3.1. Spectrum Curve Analysis

The acceleration Fourier spectrum under unidirectional excitation is shown in Figure 10. The acceleration spectral values of A9 and A10 of the surrounding rock monitoring points on the “1244” fault zone were 0.03 and 0.0307, respectively; and the acceleration spectral values of A7 and A8 of the surrounding rock monitoring points on the non-fault zone were 0.026 and 0.0285, respectively. The acceleration spectral values of A9 and A10 of the surrounding rock monitoring points on the “960” fault zone were 0.0918 and 0.0874, respectively, and the acceleration spectral values of A7 and he A8 of surrounding rock monitoring points on the non-fault zone were 0.0814 and 0.0882, respectively. It can be seen that the spectrum amplitude under the action of a forward-directional pulse was smaller than that under the action of no pulse, the spectrum amplitude of monitoring points on the fault zone was larger than that on the non fault zone and the spectrum amplitude of monitoring points on the top of surrounding rock was larger than that of monitoring points at an elevation of 20 cm. This showed that the acceleration response of the surrounding rock under earthquake action was related to the elevation and surrounding rock type.

3.3.2. Analysis of Acceleration Response Spectrum Curves

On the basis of the above analysis of the acceleration time history diagram and frequency spectrum curve, the response spectrum characteristics of monitoring points at the portal section at damping ratios of 5%, 10%, 15%, 20%, 30%, 35%, 40% and 50% were analyzed, as shown in Figure 11.

It can be seen from Figure 11 that the acceleration values of the monitoring points A9 and A10 of the fault zone were larger than that of monitoring points A7 and A8 at the same elevation, which indicated that the absorptive capacity of the fault zone to seismic waves was weaker than that of the surrounding rock. Therefore, the response of the fault zone to the ground motion acceleration was larger, and the structure crossing the fault zone suffered more obvious damage. However, the comparative analysis of two points at different elevations showed that the monitoring point A8 had a greater acceleration response than A7, and the monitoring point A10 had a greater acceleration response than A9, which indicated that the acceleration response tended to rise with the increase in the surrounding rocks’ elevation. The trend convergence of the response spectrum curve of forward-directional impulse ground motion was weak, and the trend of the response spectrum curve of non-impulse ground motion tended to be stable and consistent, which indicated that the influence of the surrounding rock on the fundamental frequency and damping of seismic waves under the action of non=impulse ground motion was more obvious than that of forward-directional impulse ground motion.

3.3.3. Acceleration Amplification Factor

The acceleration monitoring of the surrounding rock at the fault zone was analyzed, as shown in Figure 12. We can see that under the action of non-pulse ground motion, the difference in the acceleration amplification factors of monitoring points A7 and A8 was 7.124%, and the difference in the acceleration amplification factors of A9 and A10 was 3.627%. The difference in the acceleration amplification factors of monitoring points A7 and A8 under the action of forward-directional pulse ground motion was 6.152%, and the difference in the acceleration amplification factors of A9 and A10 was 7.439%. The experimental results showed that two kinds of ground motions had a significant influence on the surrounding rock at higher places. With the action of one-way excitation of ground motion, the four monitoring points all showed a weak downward trend when the PGA ranged from 0.03 g to 0.07 g, which indicated that the surrounding rock was now in a linear or weak nonlinear stage. When the PGA is in the range of 0.07 g to 0.15 g, this downward trend was significant. Therefore, the rock and soil mass may be damaged, and there was plastic deformation. The law of the acceleration amplification factors of the four monitoring points can be seen as follows: the acceleration amplification factors of A9 and A10 were greater than those of A7 and A8, respectively, which indicated that the acceleration response of the fault zone was stronger than that of the surrounding rock.

3.4. Internal Force Analysis of the Fault Zone

The internal force analysis of the lining structure in the fault zone section was also analyzed by the strain measuring. The monitoring points of strain gauges were the corresponding pastes inside and outside the arch foot, arch waist, arch shoulder and arch crown of the tunnel lining. The time history diagram of the axial force and bending moment at the portal section under various working conditions can be calculated by Equations (4) and (5). We can see from Figure 13 and Figure 14 that the tunnel lining was subjected to both tension and pressure under the action of horizontal one-way ground motion, and the bending moment was a cyclic load in the positive and negative directions. The axial force action of the structure under the two seismic actions was almost the same, and the bending moment under the forward-directivity effect pulse ground motion was greater than that under the action of no pulse ground motion. Additionally, under the action of near-fault ground motion, the axial force and bending moment of arch crown, arch shoulder, arch waist and arch foot of the tunnel in the fault zone were basically the same. The specified law was that the stress at the arch waist was relatively large, while the stress at the arch crown was relatively small, which indicated that under the action of earthquakes, the acceleration response at the arch waist of the tunnel in the fault zone was relatively intense and was prone to deformation and damage.

4. Conclusions

In this paper, the damage evolution and seismic response analysis of the lining and surrounding rock of the special tunnel section under the action of non-pulse and forward-directional pulse ground motions were studied based on the actual earthquake damage phenomenon of the special tunnel section by the shaking table model test. The following conclusions are drawn:

High frequency seismic waves will be filtered out by surrounding rock, and the low frequency (<30 Hz) seismic wave had obvious influence on the tunnel structure. The acceleration response of the structure decreased with the increase in the damping ratio, and it tended to be stable and consistent when the damping ratio exceeded 20%. The acceleration amplification factors were gradually decreasing with a fluctuation range of 0.4–1.1.

The peak internal force and bending moment of the tunnel portal lining appeared at the arch foot and the arch waist, respectively, which was more prone to plastic damage under the action of near-fault ground motion. Additionally, the acceleration response and frequency spectrum of the fault zone were more obvious than those of the other tunnel section, and this trend increased with the elevation. With the larger seismic acceleration response of the fault zone, the more obvious the damage to the structure crossing the fault zone.

The arch foot, arch waist, arch shoulder and arch crown of the tunnel portal and fault zone were vulnerable to damage, and the tensile failure arear first appeared at the arch foot crossing the fault zone. The compression failure first occurred at the junction of the surrounding rock, and the compression degree at the arch waist was prominent.

The stochasticity found in the spectrum curves should be explained here, which may be due to the following reasons. Firstly, the noise existing in the surrounding environment, the equipment itself and the acquisition process caused some fluctuations. Secondly, the selection of seismic wave does not match the adaptability of the tunnel model. Thirdly, the sampling frequency is too high, resulting in data overlap. Additionally, the safety factor of the lining structure was not calculated. Therefore, the following work will solve the two problems, and obtain better spectrum data and solve the reliability and failure probability of the tunnel.