Seismic Response Analysis of a Shield Tunnel in a Coastal Nuclear Power Plant under a Complex Foundation

Abstract

As a transportation hub connecting sea and land, the seismic safety of an undersea tunnel is very important. Based on the structural and stress characteristics of a shield tunnel, a seismic response analysis of a coastal nuclear power plant under a complex foundation is carried out in this paper. Firstly, adopting the lateral and longitudinal response displacement methods, the authors study the variation and distribution features of the rate of diameter change and joint-stretching value of the shield tunnel segments. On this basis, a three-dimensional refined finite element model of a sinking tube–soil mass under a complex soil foundation is established. Finally, when the joints and segments of the shield tunnel are subjected to ground motion, the deformation and internal force distribution of its lining segments are studied. The findings show that under influence of SL-2-magnitude ground motion, the soft–hard stratum junction is the weak point of the shield tunnel structure’s longitudinal seismic resistance. When the silt layer at the position of the shield segment is thicker and the geological conditions are relatively poorer, the internal force, diameter deformation rate, and joint-stretching value will be larger. The research results can provide a reference for seismic research on shield tunnels in sea areas under complex foundations.

1. Introduction

An undersea tunnel has been planned and constructed on a large scale due to its obvious advantages of direct access, great convenience, large traffic volume, and small climate impact [1]. It is, however, located in a complex marine environment, leading to a huge investment cost and long-term construction period. Additionally, due to the complicated circumstances, the undersea tunnel’s seismic safety becomes a crucial problem that engineering designers should pay considerable attention to.

At present, seismic research on underground structures under land is relatively mature; however, there are few research studies on submarine tunnels, and they mainly focus on theoretical analyses, experimental research, and numerical simulations. Of these avenues, the response displacement method does not need to carry out a finite element time-history analysis of the structure of the continuous soil layer, which simplifies the analysis and research workload and has been widely used in the seismic codes of underground structures [2,3]. In addition, research involving subsea tunnel seismic response analyses mostly concentrates on numerical simulations with the increasing development of computer science and technology, which makes the analysis results more reasonable and reliable. Gong et al. [4] studied the seismic response of tunnel structures in complex foundations by changing the seismic peak. The influence of seismic force on the tunnel structures was obtained by studying the internal forces of the tunnel segments. Chen [5] synthesized the dynamic characteristics of structure, soil, and water and established a numerical analysis model of tunnel structure. By doing so, she concluded that the maximum internal force of a tunnel structure was directly proportional to the foundation modulus ratio, lining thickness, and water depth and that the softer the soil was, the more remarkable the structural inertia force would be. Peng et al. [6] constructed a fluid–solid coupling numerical model of a shield tunnel under the condition of the seepage flow of segment joints and analyzed the tunnel’s mechanical deformation mechanism and surface settlement rule in accordance with distinctive factors, including the seepage of different joints, seepage flow, joint stiffness, and waterproof performance. Chen et al. [7] built a finite element model of the dynamic interaction between seawater, the seabed, and a tunnel and studied the seismic response rule of a submarine tunnel with different ground motion inputs, seismic excitation directions, and overlaying water depths. Zhu [8] systematically researched the seismic response rule of underwater tunnels under different conditions through the use of analytical methods and revealed the dynamic fluid–solid coupling mechanism of the water–soil structure system during an earthquake. Zhang et al. [9] proposed a transient seismic structure–water–sediment–rock interaction model to evaluate the marine spatial seismic response of ocean structures experiencing oblique incidence earthquakes and studied the influence of sediment properties such as the thickness, porosity, and permeability of the sinking tube tunnel as well as the incident angle of the seismic wave on the dynamic response of structures. The marine geological environment which the subsea tunnel faces is complex. Compared with a land tunnel, apart from the differences in the physical and mechanical properties of the surrounding submarine rock–soil mass, there exists overlying sea water exerting an impact on the seabed and the structures within the seabed [10]. Therefore, the impact of the coupling effect of the overlying sea water and an earthquake on the response of an undersea tunnel should be taken into account when conducting seismic research on undersea tunnels. Through numerical examples, Chen et al. [11] studied the influence of seawater depth, the thickness of overlying rock strata, and the permeability coefficient on the seismic dynamic stability safety coefficient and plastic zone variation of a cross-sea tunnel structure experiencing seepage flow and bidirectional seismic action. According to the study by Zhao et al. [12], the continuous disturbance of sea waves and currents has a significant impact on the soil–structure interaction, such as the EPWP response, seabed liquefaction mode above the contact area, uplift of the sinking tube tunnel, and subsidence. Chen et al. [13] investigated the dynamic response of a submarine tunnel under the action of sea waves and an earthquake, considering the coupling effect of stress field and seepage field.

As a type of long, linear structure, the internal forces and deformations of a shield tunnel in both the transverse and longitudinal directions are closely related to the site conditions along the line. Therefore, the seismic analysis of a shield tunnel in a complex site has an important reference value for its seismic design. Nowadays, among the construction methods for establishing undersea tunnels, the shield method has gradually developed into the most widely adopted method thanks to its advantages, which include a fast speed, fine quality, high geological adaptability, safe construction, and sound working environment [14,15]. A shield tunnel is a tunnel structure composed of a large number of lining segments assembled by bolts and other connections. The rupture of a tunnel’s joints under the influence of a seismic force is mainly caused by the uneven settlement of the soil layer and the traveling wave effect of seismic waves. In some specifications, therefore, it is recommended to use the diameter deformation rate of the shield tunnel lining structure as the lateral seismic performance control index and use the longitudinal response displacement method to calculate the longitudinal stress and distortion experienced by the tunnel. Kiyomiya et al. [16] adopted the multi-mass-spring model while considering the influence of sinking tube tunnel joints to conduct a dynamic response analysis. Anastasopoulos et al. [17] utilized the mass-spring model to calculate the three-dimensional nonlinear seismic responses of 70-meter-deep submarine sinking tunnels. Yan et al. [18] carried out a study on the response displacement method for two different types of rings—a homogeneous ring and jointed ring—and calculated that the internal force value of the shield tunnel model with homogeneous rings was greater than that of the shield tunnel model with jointed rings. Liu et al. [19] used the response displacement method and ABAQUS software to establish a beam–spring finite element model, and the cross-sectional seismic analysis of a shield tunnel in a complex soft-soil site was carried out. The calculation was combined with the soft-soil shield tunnel of Tianjin Binhai Line Z2. Geng et al. [20] proposed a set of holistic to local numerical analysis processes to analyze the mechanical characteristics of the detailed structure of a longitudinal joint under the action of an earthquake. Mei [21] discussed the influence of bolt prestress, bolt strength, tunnel diameter, and other factors on the structural equivalent stiffness and used an iterative calculation to realize a longitudinal seismic calculation method for a shield tunnel that updated the structural stiffness. Wang et al. [22] calculated the longitudinal dynamic response of shield tunnels in heterogeneous strata under the action of an earthquake by using the stratum structure model and the tunnel’s longitudinal equivalent stiffness model. Cai et al. [23] established a longitudinal section finite element model via the viscoelastic artificial boundary method, combined the equivalent nodal force method for ground motion input, and used the soil equivalent linearization method to conduct a longitudinal seismic analysis of the Mawan cross-sea large-diameter shield tunnel by using the generalized response displacement method. Zhang Jing et al. [24] also applied the three-dimensional finite element method to analyze the longitudinal seismic response of a shield tunnel through the soft–hard stratum junction and compared the results with the results of shaking table tests. Chen et al. [25], considering the longitudinal bolted connection between pipe rings and other factors of a shield tunnel, proposed a generalized response displacement method for tunnel longitudinal seismic response based on submodel technology. He et al. [26] studied the advantages and disadvantages of common shield tunnel analysis methods and proposed applicability recommendations for lateral and longitudinal earthquake-resistant methods for tunnels.

Currently, little research exists on subsea shield tunnels in the field of nuclear power plant safety-level water-intake engineering. A tunnel’s seismic stability under the action of an ultimate earthquake motion is a vital technical difficulty and key issue to be solved in the water-intake engineering of a coastal nuclear power plant. Using the setting of the Sanmen Nuclear Power Project and taking into consideration the characteristics of the structure and stress of the shield tunnel, this paper carries out a lateral and longitudinal seismic analysis of the shield tunnel for water intake in the sea area of the nuclear power plant. In order to obtain more reliable results, the response displacement method and time-history analysis method are used to carry out a seismic analysis of a shield tunnel in the sea area of the nuclear power plant simulated by a lateral and longitudinal beam–spring model and a three-dimensional soil–structure interaction model, respectively. During the process, the deformation and stress distribution regularity of the lining segments under the ground motion is emphatically studied. Moreover, the variation and distribution features of the lining segment’s joint-stretching value are discussed, and the maximum stress, deformation position, and factors affecting their change are determined. In addition, the approach to the seismic response analysis of the shield tunnel put forward by this paper is intelligible, feasible, and effective. In conclusion, this analysis method can provide a reference for seismic research on shield tunnels in sea areas under complex foundations and can better enable readers to comprehend the seismic response rule of an actual submarine tunnel.

2. Methods and Principles

2.1. Response Deformation Method

The response displacement method can be used to analyze the lateral and longitudinal seismic behavior of an underground pipe culvert. This method introduces a foundation soil spring to simulate the surrounding soil. When the underground structure is supported on the foundation soil spring, the stiffness difference between the underground structure and the surrounding soil can be quantitatively revealed through the foundation soil spring. At the same time, the seismic load acts on the structure through the foundation soil spring.

2.1.1. Lateral Response Deformation Method

During the analysis, the correlation between the soil layer and the tunnel is approximately simulated by laying foundation soil springs around the lining segments. The beam–spring model can better achieve the splicing of the staggered joints of the shield tunnel’s lining segments and consider the influence of the joints on the internal forces of the tunnel. The above is shown in Figure 1.

In the calculation model, it is assumed that the calculated stratum is a single homogeneous layer (the laminate stratum can be simplified to a single layer via the weighted average method). The maximum response displacement of the stratum can then be obtained through the approximate treatment of Equation (1):

$$u_h\left(z\right)=\frac{2}{{\pi }^2}{S}_u{T}_s\cos \left(\frac{\pi z}{2H}\right)$$

(1)

In the above equation, $S_u$ represents the velocity response spectrum of the stratum bedrock surface; $T_s$ signifies the natural vibration period of the formation; $Z$ stands for the variable of the downward coordinate system with the origin at the surface; $H$ represents the soil layer thickness.

Equation (1) takes the derivative of $Z$ and multiplies the formation shear modulus to obtain the shear of the natural stratum corresponding to Equation (2):

$${\tau }_h\left(z\right)=\frac{G_d}{\pi H}{S}_u{T}_s\sin \left(\frac{\pi z}{2H}\right)$$

(2)

In the above equation, $G_{d }$ denotes the dynamic shear elastic modulus; $S_{u }$ represents the velocity response spectrum of the stratum bedrock surface; $T_s$ signifies the natural vibration period of the formation; $Z$ stands for the variable of the downward coordinate system with the origin at the surface; $H$ represents the soil layer thickness.

2.1.2. Longitudinal Response Deformation Method

The longitudinal response displacement method is based on the basic principle that the deformation of a tunnel structure is affected by the displacement of the surrounding soil. In this method, a foundation soil spring is often used to simulate the interaction between the shield tunnel and the surrounding soil. Specifically, normal and tangential springs are used to simulate the action in different directions. The above is demonstrated in Figure 2. In order to calculate the internal force and deformation of the shield tunnel, the maximum deformation of the surrounding soil under the action of an earthquake is added to the constraint end of the foundation soil spring at the response part of the analysis model via applying displacement.

Based on the longitudinal response displacement method, the beam–spring combination model is used to simulate the lining segments of the shield tunnel and the surrounding soil mass to study the joint-stretching value of every joint of the integrated shield tunnel. The beam unit is adopted as a model to simulate the main body of the sinking tube tunnel. In the model, the foundation soil springs along the axial and lateral directions of the tunnel are set at each node to simulate the effect of the subsoil layer on the integrated sinking tube tunnel. An analytical model of the shield tunnel–joint–foundation system is formed, as shown in Figure 3.

2.2. Equivalent Linear Dynamic Time-History Analysis Method

According to the Standard for Seismic Design of Nuclear Power Plants (GB50267-2019) [27] and ASCE 4-98 [28] of the United States, the use of the equivalent linearization method to describe the nonlinear characteristics of a non-lithologic foundation is suggested. By doing so, the nonlinear issue can be transformed into a linear one, which greatly improves computational efficiency; hence, it is widely used in the seismic analysis of nuclear power structures. Dong et al. [29] proposed a simplified general software parameter calculation method for a soil-constitutive model for a pile–soil–structure interaction system. The key to adopting the equivalent linearization method is to calculate the effective shear strain of the soil. Firstly, a linear analysis is carried out in accordance with the average value of the material characteristics, and then through the effective shear strain, the next analysis can be rectified. In this way, the iterative analysis is conducted step by step until it is close to the parameter characteristics of the soil. Afterwards, the change in the shear strain value γ for each stratum with respect to its time history is calculated, and the equivalent modulus and damping of the soil mass are obtained according to the G~γ and D~γ curves. The specific calculation process is shown in Figure 4. According to practical engineering experience, reliable convergence results can be obtained after 3–5 iterations.

2.2.1. Viscoelastic Artificial Boundary Method

Considering that the dynamic artificial boundary is the critical point for studying the seismic performance of an underwater shield tunnel [30], the basic principle of the viscoelastic artificial boundary method [27] is that a new physical element formed by a parallel viscous damper and a spring is imposed on the boundary of the foundation to simulate the infinite foundation during seismic analysis and calculation. Firstly, the seismic wave at the boundary of the model is converted into the equivalent load of each node of the boundary. With the scattered wave propagating to the boundary, which is produced by the calculation, part of the model is absorbed by the viscoelastic artificial boundary. At this time, the node corresponding to the boundary would generate free-field motion under the action of the seismic load. Therefore, the seismic wave input issue should be equivalently transformed into the free-field motion issue under the action of the nodes corresponding to the viscoelastic boundary through the viscoelastic artificial boundary, and these loads are finally applied to the foundation boundary of the model in the form of an equivalent nodal force. The boundary model is displayed in Figure 5. When calculating the model, the normal and tangential damping coefficients can be obtained by the following equations:

Normal damping coefficients:

$$C_t=\rho ·V_s·\Delta A_i$$

(3)

Tangential damping coefficients:

$$C_n=\rho ·V_p·\Delta A_i$$

(4)

2.2.2. Hydrodynamic Pressure

It is generally believed that the dynamic water pressure of a nuclear power intake culvert under the action of an earthquake has a great influence on the dynamic response of the structure and is an important dynamic load for the design of a water-intake tunnel. There are relevant provisions in the American standards (ASCE 4-98) [28]. In the analysis and calculation of a seismic response, it is necessary to consider the convection effect and pulse effect caused by the flow oscillation in the sinking tube klystron under the action of an earthquake, which could generate pressure on the wall of the sinking tube. In other words, the horizontal and vertical motion components of the fluid should be taken into account simultaneously. The Housner spring mass system for calculating hydrodynamic pressure is shown in Figure 6.

3. Engineering Example

3.1. Project Profile

The Zhejiang Sanmen Nuclear Power Plant is located in Sanmen County of Taizhou City, which is in the eastern part of Zhejiang Province. The water-intake structure consists of a circulating-water-intake tunnel and a water-intake head. The diversion tube of the circulating water-intake tunnel comprises two shield tunnels, each with an inner diameter of Φ5800 mm. The bottom elevation of the tunnel is from −17.5 m to −28.5 m. A natural foundation and shield construction are adopted, and tunnel top is covered with soil of a depth of about 10 m.

Precast reinforced concrete is selected for the shield tunnel lining segments, as shown in Figure 7. The inner diameter of the lining segments is 6.2 m, the thickness is 0.45 m, and the longitudinal width is 1.2 m. Each section is assembled with six segments (three standard segments, two adjacent segments, and one top sealing block), and the angles of the segments are 67.5° × 3, 67.5° × 2, and 22.5° × 1 (Figure 7a). The segments are connected via the splicing method with staggered joints (Figure 7b). The joints are mainly connected by straight bolts (Figure 7c).

3.1.1. Distribution in Soil Layers and Calculation Parameters

According to the Geotechnical Investigation (Detailed Survey) Report on Water intake and Drainage Structures during the Preliminary Design Stage of the First Phase of Sanmen Nuclear Power Plant, the quaternary system is widely distributed in the coastal plain and terrace, with different thickness mainly consisting of marine deposits and eluvium. The maximum thickness shown by this investigation is 43.6 m. The soil layer in the tunnel excavation area is divided into flowing soil, silt, clay, silty clay, silty clay mixed with gravel, moderately weathered rock, andesite basalt, etc. The engineering geological section is displayed in Figure 8, and the parameters of the soil layer and concrete are shown in

Table 1. Lining and soil layer parameters.

No.	Soil Layer	Density (kg/m3)	Static Modulus of Elasticity (E/Pa)	Static Poisson’s Ratio (μ)	Dynamic Modulus of Elasticity (Ed/Pa)	Dynamic Poisson’s Ratio (μd)
1	Concrete	2500	3.25 × 1010	0.20	4.225 × 1010	0.20
2	Silt	1610	1.00 × 107	0.30	1.95 × 107	0.45
3	Muddy clay	1750	1.30 × 107	0.30	2.91 × 107	0.45
4	Clay	1830	2.07 × 107	0.32	1.68 × 108	0.45
5	Silty clay	1950	2.61 × 107	0.30	1.49 × 108	0.45
6	Moderately weathered rock	2550	2.46 × 107	0.24	4.60 × 1010	0.21

. Equivalent linear parameters of the soil mass are shown in Figure 9.

3.1.2. Seismic Parameters

At seismic level SL-2, the horizontal peak acceleration of bedrock is 0.15 g and the vertical peak acceleration is 0.10 g according to the seismic safety evaluation of the engineering site at the Sanmen Nuclear Power Plant, which was provided by the entrusted organization. The response spectrum provided in the seismic safety evaluation report of the Sanmen Nuclear Power Plant project is used for a dynamic time-history analysis, as shown in Figure 10. The corresponding time history of ground motion is illustrated in Figure 11, for which the vibration duration is 28 s.

3.2. Seismic Response Analysis of Shield Tunnel Based on

3.2.1. Computational ModelResponse Displacement Method

(1)

Lateral Analysis Model

Figure 8 is selected as the typical section of shield tunnel, and a beam–spring combined model is adopted to simulate the lining segments and the surrounding soil mass of the shield tunnel. The analysis model is shown in Figure 12.

The locations and number of monitoring sites for the shield tunnel lining segments are shown in Figure 13, in which Figure 13a is the monitoring site for the rate of diameter change in the lining segments, and Figure 13b is the joint-stretching value monitoring point for the lining segments.

(2)

Longitudinal Analysis Model

The water-intake shield tunnel of the longitudinal analysis model is divided into 820 sections, with a total length of 984 m. There are six types of inter-ring springs which have different directions, and the stiffness coefficients are obtained from the actual bolt connection. The local model of the longitudinal response displacement method for shield tunnel is illustrated in Figure 14.

The free-field model of the area along the shield tunnel was established using the SuperFLUSH/2D of the Japan Institute of Seismic Engineering according to the soil layer distribution and the parameters in the site’s rock project reconnaissance report. Figure 15 shows the two-dimensional section model of the whole field of the shield tunnel.

A viscous boundary is applied to the bottom and to two boundaries of the finite element model, and the seismic input takes the equivalent nodal force. In order to simulate the nonlinear characteristics of the soil mass under ground motion and achieve the equivalent linearization of nonlinear material, the shear strain of the soil mass is calculated iteratively according to the correlation between the shear modulus ratio, damping ratio, and shear strain. The calculation process is as follows: firstly, the initial shear modulus and damping ratio are used for the initial calculation; next, the maximum shear strain and equivalent shear strain of each unit are calculated from the strain time-history curve of each unit; at last, according to the equivalent shear strain of each unit, the shear modulus and damping ratio of each unit are updated and re-calculated until the errors of the two successive calculations are in the allowable range. After the nonlinear seismic response analysis of the whole field of the shield tunnel is completed, the displacement time history of the soil layer with the same buried depth as the tunnel’s axis is extracted and applied to the foundation soil spring. The relative displacement of the soil layer in the whole field of the shield tunnel under an SL-2-magnitude ground motion is demonstrated in Figure 16.

3.2.2. Calculating Working Conditions

Combining the report of the water-intake engineering of the nuclear power plant with the fact that in most experiments, the horizontal bedrock peak acceleration at the SL-2 level is about 0.15 g in a coastal nuclear power plant, 0.15 g is therefore used for the SL-2-magnitude ground motion when studying the seismic performance of the submarine shield tunnel in this project. Based on the flexural mechanical model of the shield tunnel segment joint studied by Feng et al. [31,32], M30 bolts are used to connect the shield tunnel segment joints in this paper. The working condition is shown in

Table 2. Calculated working conditions of seismic performance for shield tunnel’s joints.

Seismic Peak	Bolt	Coefficient of Joint Stiffness				Working Condition
		Tensile Strength 106 (N/m3)	Shear Resistance 106 (N/m3)	Bending Stiffness1 106(N·m)/Rad	Bending Stiffness1 106 (N·m)/Rad
SL-2: 0.15 g	M30	300	125	25	40	1
				50	80	2
				75	100	3

:

3.2.3. Result Analysis

(1)

Lateral Analysis

Table 3. Rate of diameter change of lining segment (Response Displacement Method).

Working Condition	Rate of Diameter Change at the Positions at which Monitoring Sites are Located (‰)
	1–9	2–10	3–11	4–12	5–13	6–14	7–15	8–16
1	1.085	1.416	1.816	1.914	1.761	1.809	1.712	1.551
2	1.074	1.402	1.755	1.868	1.744	1.775	1.701	1.524
3	1.067	1.394	1.721	1.846	1.735	1.755	1.694	1.507

and

Table 4. Joint-stretching value of lining segment (Response Displacement Method).

Working Condition	Position of Joints
	1	2	3	4	5	6
1	0.032	0.976	0.428	0.676	1.159	0.759
2	0.028	0.648	0.206	0.505	0.858	0.559
3	0.022	0.494	0.123	0.402	0.680	0.442

and Figure 17 and Figure 18 manifest the rate of the diameter change and the joint-stretching values of the lining segment when the peak seismic acceleration at the SL-2 level is 0.15 g. It can be seen that when the joint stiffness is small, the rate of change of the diameter of the lining segment is 1.914‰, and the maximum joint-stretching value of the lining segment is 1.159 mm; when the joint stiffness is large, the lining segment’s rate of diameter change is 1.846‰, and the maximum joint-stretching value of the lining segment is 0.680 mm.

(2)

Longitudinal Analysis Results

Table 5. Deformation of longitudinal joints of lining segment.

Working Condition	Longitudinal Joint
	Opening Volume (mm)	Amount of Dislocation (mm)
1	6.274	0.999
2	5.536	0.919
3	5.093	0.836

demonstrates the deformation of the longitudinal joints of the shield tunnel when the seismic acceleration at the SL-2 level is 0.15 g. The longitudinal misalignment of the shield tunnel varies from 0.836 mm to 0.999 mm, and the inter-section joint-stretching value varies from 5.093 mm to 6.274 mm. The general regulation of deformation is that the greater the stiffness of the joint bolt is, the smaller the deformation is. Taking working condition 1 as an example, the change curve for the inter-section joint-stretching value and the misalignment of the longitudinal joint of the shield tunnel are shown in Figure 19. Firstly, the left side of the model is the interface between the land and sea areas of the tunnel; secondly, when the mileage is about 200 m, the thicknesses of the silt soft-soil layer and clay layer change obviously, and the stiffnesses of the soft and hard soil layers change obviously. Thirdly, under different structural excitation directions and seismic actions, the maximum of the longitudinal deformation always appears at the position at which the soft strata abruptly change to hard strata. Therefore, this is the weak position of the longitudinal seismic resistance of the shield tunnel structure and should be given priority in the design.

3.3. Seismic Response Analysis of Shield Tunnel Based on Time-History Analysis Method

3.3.1. Calculation Model

In order to further study the seismic response characteristics of the shield tunnel in the sea area of the nuclear power plant, a three-dimensional refined numerical model of a sinking tube–soil under a complex soil foundation is established based on the lateral and longitudinal response displacement method, taking into account the nonlinear characteristics of the soil mass, the structure–foundation infinite dynamic interaction, and the convection and pulse effects of flowing water inside the sinking tube. The equivalent linear unit and viscous elastic artificial boundary are created in the secondary development of ANSYS using UPFs; on this basis, the dynamic time-history analysis of the sinking tube tunnel under the action of ultimate ground motion is carried out as indicated in Figure 20, and the lining segment structure is indicated in Figure 21.

The grid of the foundation is as uniform as possible, with different colors representing different material properties. The soil layer model extends 45 m along the left and right sides of the tunnel, the tunnel is buried at the depth of 9.3 m, and the bottom of the soil model is 80 m away from the center of the tunnel. The soil materials and layer thicknesses are silt for 13.85 m, muddy clay for 4.55 m, clay for 12.68 m, silty clay for 11.5 m, and moderately weathered rock for 50 m from the top to the bottom.

3.3.2. Calculated Working Conditions

According to the characteristics of the model soil layer, three typical sections of lining segments in the calculated model were selected as the three working conditions for analysis. The upper part of the first section is located in the silt layer, and the lower part is located in the muddy clay layer. The second section is located at the junction of the silt, muddy clay, and clay soil layers. In the third section, the clay layer increases, and the silt layer becomes thin. The positions of the sections are shown in Figure 22.

3.3.3. Result Analysis

(1)

Internal Force Analysis

Table 6. Internal force distribution of lining segments under influence of ground motion.

Working Condition	Position	Tunnel Thickness (mm)	Axial Force (kN)		Shear (kN)		Bending Moment (kN·m)
			Max	Min	Max	Min	Max	Min
Section 1	Normal X	450	180.7	−3456.3	1361.6	−1021.7	222.5	−9.4
	Normal Z	450	616.2	−1270.9	89.3	−77.9	25.5	−24.3
Section 2	Normal X	450	47.5	−3368.2	1448.3	−1118.4	204.1	−1.6
	Normal Z	450	686.7	−1351.0	97.0	−55.1	40.2	−40.7
Section 3	Normal X	450	85.4	−3247.4	1259.7	−931.6	192.6	−4.8
	Normal Z	450	386.6	−1434.8	101.3	−108.6	25.1	−21.8

provides the internal force distribution and variation of different cross sections of the shield tunnel under the action of an SL-2-level ground motion via the dynamic time-history analysis method. It suggests that the maximum bending moment is 222.5 kN·m, the maximum shear is 1448.3 kN, and the maximum axial force is 3456.3 kN. The strength requirement of lining segment can be satisfied by proper reinforcement.

It can also be seen that consistent with the regulation of the response displacement method, the geological condition has a certain influence on the internal force of the lining segment. Section 1 is positioned at a thick silt layer with a relatively poor geological condition, so the calculated internal force is larger.

(2)

Analysis of the Rate of Diameter Change and Joint-Stretching value of Lining Segment

Table 7. Rate of diameter change of lining segment (Time-History Analysis Method).

Working Condition	Rate of Diameter Change at the Positions at which Monitoring Sites are Located (‰)
	1–9	2–10	3–11	4–12	5–13	6–14	7–15	8–16
Section 1	1.076	1.060	1.076	1.336	1.228	1.156	1.148	1.112
Section 2	1.008	1.204	1.244	1.300	1.200	1.080	1.044	0.984
Section 3	0.872	0.908	1.048	1.248	0.864	1.068	0.956	0.880

and Figure 23 show the rate of the lining segment’s diameter change at the cross section of the shield tunnel in which the maximum rate of diameter change for the shield tunnel under the action of an SL-2-level ground motion is 1.336‰.

Table 8. Joint stretching value of lining segment (Time-History Analysis Method).

Working Condition	Joint Position
	1	2	3	4	5	6
Section 1	0.312	0.482	0.391	0.386	0.529	0.393
Section 2	0.302	0.460	0.434	0.384	0.525	0.373
Section 3	0.261	0.411	0.359	0.298	0.473	0.348

and Figure 24 show the opening of a lining segment in the shield tunnel in which the maximum joint-stretching value of the lining segment under the action of an SL-2-level ground motion is 0.529 mm.

It can also be seen that the geological condition has some influence on the deformation of the lining segment. The silt layer at the Section 1 position is thick and the geological condition is relatively poor, so the calculated rate of diameter change and joint-stretching value are larger.

3.4. Results

(1) When the response displacement method is adopted and the peak acceleration of SL-2 is 0.15 g, during the lateral seismic analysis, the rate of the diameter change varies between 1.846‰ and 1.914‰, and the maximum joint-stretching value between sections varies between 0.680 and 1.159 mm; during the longitudinal seismic analysis, the longitudinal misalignment varies between 0.836~0.999 mm, and the joint-stretching value varies between 5.093 and 6.274 mm. Under different seismic actions, the maximum value of the longitudinal deformation of the structure always appears at the position at which the abrupt change from soft to hard strata occurs, proving that this is the weak position of the longitudinal seismic resistance of the shield tunnel structure; thus, it should be given priority in the design.

(2) The calculation results of the dynamic time-history analysis indicate that the maximum bending moment, maximum shear, and maximum axial force of the shield tunnel are 222.5 kN·m, 1448.3 kN, and 3456.3 kN, respectively. The strength requirement of the lining segment can be satisfied by proper reinforcement. Under the action of an SL-2-level ground motion, the maximum rate of diameter change for the shield tunnel is 1.336‰, and the maximum joint-stretching value is 0.529 mm. The geological condition has a certain influence on the internal force and deformation of lining segments. When the silt layer of the shield tunnel lining segments is thicker and the geological condition is relatively poor, the internal force, the rate of diameter change, and joint-stretching value of the joints are larger.

4. Conclusions

This paper carries out research on the seismic adaptability of a shield tunnel in a sea area under a complex foundation, supported by a shield tunnel water-intake project of a nuclear power plant in a sea area. The seismic analysis is carried out based on the response displacement method and the dynamic time-history method, and the following conclusions are drawn:

(1) The fracture of the tunnel’s joints under seismic force is mainly caused by the uneven settlement of the soil layer and the traveling wave effect of seismic waves. The rate of diameter change and the joint-stretching value of the lining structure in the shield tunnel can be used as control indexes of the lateral seismic performance. The inter-section joint-stretching value in the shield tunnel affects the water-tightness requirement inside the tunnel structure and can be used as an index of its longitudinal seismic performance.

(2) The opening amount generated by the same joint at different section positions shows a similar change.

(3) The rates of change of the diameter of lining segments at positions 4–12, where the vault and the bottom of the arch are relatively high, indicate that the tunnel is subjected to the lateral compression of the soil mass, resulting in a large deformation at the top and bottom of the lining segments. By comparing the two models, the rate of change of the joint model with consideration of the joint is greater than that of the model without consideration of the joint, so it should be taken as the control index for the analysis of the joint model with consideration.

(4) Compared with the time-history analysis method, the displacement, internal force, rate of diameter change, and opening volume of the tunnel segments calculated by the reaction displacement method are not so rigorous; however, the rules are the same. Therefore, in order to solve the seismic response problems caused by shield tunnels in practical engineering, we should adopt the practice of combining the two methods, with the time-history analysis method used as the main method and the response displacement method used as the auxiliary method, which can make the results more reasonable.

(5) Bolts link each segment in the shield tunnel, but they have nonlinear characteristics in practical engineering applications. In this paper, spring units are used to simulate the function of bolts in the processing of segment joints, which can only approximately reflect the deformation of the shield tunnel joints under the action of ground motion. Therefore, further research is needed in the simulation analysis of the joints.

(6) In this study, only a corresponding numerical simulation analysis was carried out for the shield tunnel, and a shaking table test was not carried out. If the two kinds of analyses are combined for a comparative analysis and the actual test results are referenced, the obtained results will be more perfect and more referential and can thus be taken as a direction for further research.