Simplified Analysis Method for Seismic Response of Shield Tunnels Based on Shell-Spring Model

Abstract

The present invention relates to a simplified analysis method for the seismic response of shield tunnels based on a shell-spring model, and the steps are as follows: constructing a soil-shield tunnel calculation model considering bolt contact connection; establishing a seismic ground motion evolution power spectrum model and a phase coherence function model to generate seismic ground motion time history curves; inputting the soil-shield tunnel model into the seismic ground motion time history curves for three-dimensional dynamic time history analysis to determine the value of spring stiffness; based on the determined value of spring stiffness, constructing a refined model of the shield tunnel based on shell-spring elements to obtain the seismic response law of the shield tunnel based on shell-spring elements; determining a correction factor by comparing with the seismic response law of a simplified homogeneous tunnel model, and establishing a simplified analysis model based on the code design method and the correction factor; verifying the accuracy of the simplified analysis model through a shaking table test. This method takes into account the discontinuity and local stiffness reduction of bolt contact connection in the shield tunnel model, and improves the accuracy of seismic response analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic analysis of underground engineering structures, and particularly to a simplified analysis method for seismic response of shield tunnels based on a shell-spring model. Background Art

[0002] A shield tunnel is a slender and flexible underground structure formed by segment linings connected by bolts. However, most of the current tunnel seismic analyses simplify it into a uniform model, ignoring the influence of details such as bolt connections, resulting in an overestimated overall stiffness of the tunnel structure. Thus, the seismic response of the tunnel structure obtained is far from the actual situation. For example, the current national code "Code for Seismic Design of Urban Rail Transit Structures" recommends the response displacement method based on a plane model, etc., which cannot consider the spatial effect of shield tunnels either.

[0003] The deficiencies of the existing technologies are mainly reflected in: 1) Defects of the uniform model: Most of the existing seismic analyses of shield tunnels simplify the structure into a homogeneous continuum (such as a beam-spring model or an equivalent stiffness model), ignoring the discontinuity of bolt connections and local stiffness reduction, resulting in an overestimated overall stiffness (existing research shows that the maximum error can reach 20% - 40%); 2) Unclear basis for spring stiffness value: The bolt stiffness value mostly depends on empirical values and lacks experimental verification, and the reliability of the model is insufficient (existing research shows that due to the spring stiffness error, the deviation of the joint opening amount exceeds 20%, and the error of the dislocation amount exceeds 30%); 3) Limitations of solid elements: Some studies use solid elements to model bolts and segment linings, and complex contact pairs need to be set (such as the contact between the bolt head and the hole wall of the segment lining), resulting in difficulties in nonlinear solution convergence; 4) Distortion of seismic wave propagation: Shield tunnels are slender structures, and the spatial effect of seismic waves, especially the traveling wave effect, is significant (existing research shows that the traveling wave effect can cause a relative deformation error of the structure up to 30%); 5) The current two-dimensional analysis method based on a plane model recommended by the code cannot consider the spatial characteristics of precast shield tunnels.

[0004] The construction of urban rail transit in China is still in full swing. If the traditional simplified homogeneous model is still used for seismic design, it will surely cause great potential safety hazards. Therefore, a reasonable and efficient refined model of shield tunnels has important theoretical significance and engineering application value for the seismic design of shield tunnels. Summary of the Invention

[0005] In view of the deficiencies in the background art, the technical problem to be solved by the present invention is to provide a simplified analysis method for seismic response of shield tunnels based on a shell-spring model. This method considers the discontinuity of bolt contact connections and local stiffness reduction in the shield tunnel model, and improves the accuracy of seismic response analysis.

[0006] The present invention is achieved by adopting the following technical solutions: A simplified analysis method for the seismic response of shield tunnels based on a shell-spring model, including the following steps:

[0007] S1. Construct a three-dimensional refined calculation model of soil-shield tunnel considering bolt contact connection;

[0008] S2. Establish a seismic ground motion evolution power spectrum model and a time-phase coherence function model, identify model parameters, synthesize multi-point seismic ground motion, and generate a seismic ground motion time history curve;

[0009] S3. Input the soil-shield tunnel model in S1 into the seismic ground motion time history curve generated in S2, conduct three-dimensional dynamic time history analysis, and determine the value of the equivalent spring stiffness;

[0010] S4. Based on the value of the spring stiffness determined in S3, use shell elements to simulate the segments and spring elements to simulate the bolts for the structural units, construct a refined model of the shield tunnel based on shell-spring elements, conduct numerical parameter analysis through the main influencing factors, and determine the seismic response law of the shield tunnel based on shell-spring elements;

[0011] S5. Compare the seismic response law of the shield tunnel based on shell-spring elements in S4 with the results of the traditional homogeneous model, determine the correction factor, multiply the results of the traditional homogeneous model by the determined correction factor, and establish a simplified analysis model for the seismic response considering the influence of bolt connection of the shield tunnel;

[0012] S6. Verify the accuracy of the simplified analysis model for the seismic response in S5 through a shaking table test.

[0013] Further, the steps for constructing the three-dimensional refined calculation model of soil-shield tunnel considering bolt contact connection in S1 are as follows:

[0014] S11. Determine the shield tunnel parameters of the solid element and the corresponding calculation range;

[0015] S12. Input the shield tunnel parameters and calculation range determined in S11 into the three-dimensional model to construct a three-dimensional calculation model of the shield tunnel;

[0016] S13. Conduct tetrahedral mesh division on the three-dimensional calculation model of the shield tunnel in S12, and both the soil and the lining segments are discretized using 10-node tetrahedral elements;

[0017] S14. In the three-dimensional calculation model of the shield tunnel in S13, the soil nonlinearity adopts the Davidenkov equivalent linearization model, and the structure adopts the plastic damage model of concrete;

[0018] S15. Set the contact conditions. Contact elements are set between the bolts and the lining segments, and between the lining segments and the surrounding soil. The normal contact is set as hard contact, and the Coulomb model is adopted for the tangential friction.

[0019] S16. Set the boundary conditions. The lateral binding boundary is adopted to make the nodes at the same height in the model have the same horizontal displacement, so as to simulate the shear deformation of the soil during an earthquake.

[0020] S17. Set the damping. The Rayleigh damping model is adopted to set the damping, and the Rayleigh damping coefficient is determined by calculating the system frequency.

[0021] S18. Set the dynamic time step. The dynamic time step is set to be no greater than 0.001 s.

[0022] S19. Establish a three-dimensional refined calculation model of the soil-shield tunnel considering the bolt contact connection.

[0023] Furthermore, the steps to obtain the ground motion time history curve in S2 are as follows:

[0024] S21. Establish a ground motion evolution power spectrum model considering the earthquake source fault rupture process.

[0025] The ground motion evolution power spectrum model includes an envelope function and a seismic spectrum. Modeling considers the earthquake source - propagation path - local site effect. The ground motion evolution power spectrum model is as follows:

[0026]

[0027] Where is the intensity coefficient, is the envelope function of the earthquake source intensity change, is the propagation path filtering function, is the local site filtering function. The model parameters are obtained by fitting the earthquake source geometric parameters, earthquake source kinematic parameters and ground motion spectrum.

[0028] S22. Establish a ground motion time-phase coherence function model with directivity.

[0029] The time-phase coherence function model consists of the multiplication of three terms, specifically as follows:

[0030]

[0031] The first term is the attenuation of the coherence function peak with distance, the second term is the change of the coherence function with frequency in the direction parallel to the incident direction of the seismic wave, and the third term is the change of the coherence function with frequency in the direction perpendicular to the incident direction of the seismic wave.

[0032] S23. Estimate the parameters of the ground motion model based on the evolution power spectrum and time-varying coherence function estimation formulas of the generalized harmonic wavelet, merge the two models into a time-varying cross-spectrum, simulate the ground motion through the spectral expression method, synthesize the multi-point seismic excitation input, and generate the ground motion time history curve.

[0033] Further, the steps to determine the value of the equivalent spring stiffness in S3 are as follows:

[0034] S31. Input the soil-shield tunnel model in S1 into the ground motion time history curve generated in S2;

[0035] S32. Conduct three-dimensional dynamic time history analysis to obtain the analysis results of the bolt forces;

[0036] S33. Equivalent the bolts into springs in different directions, and determine the value of the spring stiffness in combination with the bolt forces in S32.

[0037] Further, the three-dimensional dynamic time history analysis in S32 is to conduct numerical parameter analysis based on the main influencing factors, change the parameter values of the main influencing factors, analyze the general laws of the numerical parameters of the main influencing factors, and obtain the analysis results of the bolt forces.

[0038] Further, the evolution power spectrum identification formula for synthesizing ground motion in S23 is as follows:

[0039]

[0040] where 、 are the wavelet coefficients of different ground motions, is the wavelet bandwidth, and the evolution power spectrum is ;

[0041] The time-varying coherence function::

[0042]

[0043] After identifying the model parameters, the evolution power spectrum model and the time-varying coherence function model are merged into a time-varying cross-spectrum, and the ground motion is simulated through the spectral expression method,

[0044] The formula of the spectral expression method is as follows:

[0045]

[0046] where is the random phase angle.

[0047] Further, after the refined shield tunnel model based on the shell-spring element is completed in S4, the results obtained from the shell-spring element model are compared and analyzed with the contact element and the shaking table test to verify the rationality of the refined shield tunnel model based on the shell-spring element.

[0048] Further, the correction factors include the structural deformation correction factor and the structural internal force correction factor.

[0049] Further, the main influencing factors include ground motion parameters, shear wave velocity of site soil, and tunnel parameters. The ground motion parameters include ground motion amplitude and ground motion type, and the tunnel parameters include tunnel diameter, lining thickness, bolt parameters, and burial depth.

[0050] Beneficial effects of the present invention:

[0051] 1) The influence of longitudinal and radial bolts is considered in the shield tunnel model and applied to its seismic analysis. Compared with the traditional mean model, the seismic response analysis results obtained by this model are closer to the actual situation;

[0052] 2) It is proposed to simulate the segment with shell elements and the bolt connection with spring elements. The bending, shear, and slip behaviors of the segment joint are characterized by the shell-spring synergy, and a refined shield tunnel model based on the shell-spring element is constructed, effectively overcoming the deficiencies of low calculation efficiency and difficult convergence caused by the contact setting of the traditional solid model, and improving the calculation efficiency;

[0053] 3) A ground motion synthesis method considering the earthquake source mechanism and propagation path is proposed to consider the spatial effect of ground motion, and a corresponding traveling wave input method is established. Compared with the solid element model, the calculation efficiency of the present invention is increased by more than 50%, and the convergence stability is significantly improved, and the stress prediction error at the bolt connection is less than 12%. Description of the Drawings

[0054] Figure 1 It is a flow chart of the simplified analysis method for the seismic response of the shield tunnel based on the shell-spring model;

[0055] Figure 2 It is a three-dimensional calculation model of soil-shield tunnel based on contact setting;

[0056] Figure 3 For Figure 2 The detailed model of the shield tunnel and bolts in

[0057] Figure 4 It is a comparison schematic diagram of the measured ground motion evolution power spectrum (a) and the identification modeling (b);

[0058] Figure 5 It is a schematic diagram of the coherence function identification at different positions;

[0059] Figure 6 Schematic diagram of the fitting effect of the time-varying coherence function at different positions;

[0060] Figure 7 Schematic diagram for comparing the measured time history (a) and the simulated time history (b);

[0061] Figure 8 Schematic diagram for comparing the model with the measured time-varying coherence function during the ascending (a), steady (b), and decaying (c) stages of ground motion intensity;

[0062] Figure 9 Schematic diagram for comparing the time-varying coherence function model with the measured records at different times. Specific implementation manner

[0063] To further elaborate on the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following will, in conjunction with the accompanying drawings and preferred embodiments, elaborate in detail on the specific implementation manner, structure, features, and effects of the present invention as follows.

[0064] Refer to Figure 1-8 As shown, the present invention provides a simplified analysis method for the seismic response of shield tunnels based on a shell-spring model, including the following steps:

[0065] S1. Construct a three-dimensional refined calculation model of soil-shield tunnel considering bolt contact connection ( Figure 2 and Figure 3 as shown).

[0066] Based on the parameters of the shield tunnel with solid elements, construct a three-dimensional calculation model of the shield tunnel, set bolt contact, boundary conditions, damping, and dynamic time steps in the three-dimensional calculation model of the shield tunnel, and construct a calculation model of soil-shield tunnel considering bolt contact connection. The specific steps are as follows:

[0067] S11. Determine the parameters of the shield tunnel with solid elements and the corresponding calculation range. The parameters of the shield tunnel include tunnel diameter, tunnel burial depth, and tunnel lining thickness, and the calculation range includes calculation range width, calculation range length, and calculation range height. The corresponding calculation range can be determined according to the "Code for Seismic Design of Urban Rail Structure" and the shield tunnel diameter D. Generally, the transverse calculation width is taken as 7 times the tunnel diameter, the longitudinal calculation length is equal to the length of the shield tunnel, and the vertical calculation depth depends on the depth of the bedrock surface of the formation where it is located.

[0068] S12. Element type. Input the shield tunnel parameters and calculation range determined in S11 into the 3D model to construct a 3D calculation model of the shield tunnel. Specifically, the 3D model can use the parametric design language of BIM or other software to write the corresponding code program (example below), quickly realize different relative position relationships of structures, and thus realize an efficient modeling method for the overall model.

[0069] global D_tunnel = 12.0 ; Tunnel diameter (m)

[0070] global H_tunnel = 12.0 ; Tunnel burial depth (m)

[0071] global T_tunnel = 0.50 ; Tunnel lining thickness (m)

[0072] global W_model = 84.0 ; Calculation range width (m)

[0073] global L_model = 100.0 ; Calculation range length (m)

[0074] global HH_model = 70.0 ; Calculation range height (m)

[0075] global E_tunnel = 35e9 ; Elastic modulus of shield tunnel lining (Pa)

[0076] global Density_tunnel = 2500; Density of shield tunnel lining (kg / m 3 )

[0077] S13. Mesh generation. Perform tetrahedral mesh generation on the 3D calculation model of the shield tunnel in S12. Both the soil and the lining segments are discretized using 10-node tetrahedral elements.

[0078] S14. Constitutive model. In the 3D calculation model of the shield tunnel in S13, the Davidenkov equivalent linearization model is used for the nonlinearity of the soil, and the plastic damage model of concrete is used for the structure.

[0079] S15. Set contact conditions. Set contact elements between the bolts and the lining segments, and between the lining segments and the surrounding soil to consider the interaction. Among them, the normal contact uses hard contact, and the tangential friction uses the Coulomb model (the shear coefficient is tentatively set to 0.5 and will be further corrected by fitting the shaking table test later).

[0080] S16. Set boundary conditions. Lateral binding boundaries are adopted to make the nodes at the same height of the model have the same horizontal displacement, so as to simulate the shear deformation of the soil mass during an earthquake.

[0081] S17. Set damping. The Rayleigh damping model is used to set the damping, and the Rayleigh damping coefficient is determined by calculating the system frequency.

[0082] S18. Set the dynamic time step, and the dynamic time step is set not to be greater than 0.001 s. To ensure the effective response to the propagation of ground motion, there are at least 10 calculation steps within the time interval of the ground motion record (such as 0.02 s). Therefore, the dynamic time step can be set to 0.001 s or a smaller time step generated by the system. The calculation efficiency should be considered to seek a balance between accuracy and efficiency.

[0083] S19. Establish a calculation model of the shield tunnel considering bolt contact connection, that is, a three-dimensional refined calculation model of soil-shield tunnel considering bolt contact connection.

[0084] S2. Generate the ground motion time history curve.

[0085] The non-uniform ground motion (multi-point ground motion) is synthesized by the spectral representation method, and the spectral representation method needs to use the time-varying cross-spectrum of the ground motion. Among them, the time-varying cross-spectrum is a complex function, the amplitude is the evolving power spectrum, and the phase is the time-dependent coherence function. Therefore, first establish a ground motion evolving power spectrum model and a phase coherence function model, identify the model parameters using the measured records, combine the two models into a time-varying cross-spectrum, and use the spectral representation method to synthesize the multi-point ground motion (non-uniform ground motion) to generate the ground motion time history curve. The specific implementation steps are as follows:

[0086] S21. Establish a ground motion evolving power spectrum model considering the fault rupture process of the earthquake source.

[0087] The ground motion evolving power spectrum model includes an envelope function and a seismic spectrum, and the modeling considers the earthquake source - propagation path - local site effect. Specifically, in terms of the earthquake source, the time non-stationarity of the ground motion is mainly determined by the earthquake fault rupture process. The rectangular fault model is adopted, and the fault rupture propagates along the diagonal of the rectangular fault. The rupture process is described by the dislocation function. Integrate the seismic waves generated by the dislocation at each point on the rectangular fault to obtain the expression of the ground motion envelope curve. In terms of the propagation path, the seismic wave propagation medium is a homogeneous and isotropic elastic body with dispersion effect. In terms of the local site, the site filters the seismic waves.

[0088] The ground motion evolving power spectrum model is as follows:

[0089]

[0090] Among them is the intensity coefficient, is the envelope function of the source strength change, is the propagation path filtering function, is the local site filtering function. The model parameters are obtained by fitting the seismic source geometric parameters, source kinematic parameters and ground motion spectrum.

[0091] S22. Establish a time-varying coherence function model of ground motion with directivity.

[0092] The time-varying coherence function model is composed of the product of three terms, specifically as follows:

[0093]

[0094] The first term is the attenuation of the coherence function peak with distance, the second term is the variation of the coherence function with frequency in the direction parallel to the incident direction of the seismic wave, and the third term is the variation of the coherence function with frequency in the direction perpendicular to the incident direction of the seismic wave. The coherence function in the direction parallel to the incident direction of the seismic wave decays exponentially with frequency and distance. The form of the coherence function in the direction perpendicular to the incident direction of the seismic wave can be obtained by solving the stochastic wave equation. The non-stationarity of the coherence function is described by time-varying parameters, and the parameters have a piecewise constant form. The ground motion time history is divided into three segments: intensity rising, stable and decaying, and the model parameters are constant in each segment.

[0095] S23. Based on the estimation formulas of the evolving power spectrum and time-varying coherence function of the generalized harmonic wavelet, identify the parameters of the ground motion model, merge the two models into a time-varying cross-spectrum, simulate the ground motion by the spectral expression method, synthesize the multi-point seismic excitation input, and generate the ground motion time history curve.

[0096] The generalized harmonic wavelet has the characteristic of non-overlapping frequency domain, and the evolving power spectrum and time-varying coherence function can be explicitly expressed by the generalized harmonic wavelet coefficients. Using the generalized harmonic wavelet, the evolving power spectrum and time-varying coherence function of the measured non-stationary ground motion are estimated to identify the model parameters. The evolving power spectrum identification formula:

[0097]

[0098] where 、 are the wavelet coefficients of different ground motions, is the wavelet bandwidth, and the evolving power spectrum is .

[0099] The time-varying coherence function identification formula:

[0100]

[0101] After identifying the model parameters, the evolving power spectrum model and the time-varying coherence function model are merged into a time-varying cross-spectrum, and the ground motion is simulated by the spectral expression method. The formula of the spectral expression method is:

[0102] , where is a random phase angle.

[0103] Referring to Figures 4-9 shown in the figure, comparing the synthetic ground motion excitation method synthesized above with the real data, the agreement is good. It can be seen that the synthetic ground motion excitation above has the non-stationarity of real records. Specifically, Figure 4 is the comparison of the evolving power spectrum of real ground motion records and the identified and modeled evolving power spectrum. Figure 5 is the time-varying coherence function of ground motion excitations at different positions. Figure 6 is the fitting result of the time-varying coherence function at different positions. Figure 7 . (a) Measured time history and (b) simulated time history comparison diagram. Figure 8 is the comparison diagram of real records and simulated ground motion records. The simulated ground motion has the non-stationary characteristics of measured records. Figure 9 is the comparison of the time-varying coherence function model and measured records at different times. The agreement is good, indicating that the ground motion excitation synthesized by this method has the non-stationarity of real records.

[0104] S3. Determine the value of the equivalent spring stiffness. The specific steps are as follows:

[0105] S31. Input the soil-shield tunnel model in S1 into the ground motion time history curve generated in S2.

[0106] S32. Conduct three-dimensional dynamic time history analysis to obtain the analysis results of the bolt forces. Specifically, the three-dimensional dynamic time history analysis is based on the main influencing factors for numerical parameter analysis. The parameter values of the main influencing factors will be changed to analyze the general laws of the numerical parameters of the main influencing factors. Then, focus on analyzing the forces on the bolts, including axial tensile and compressive forces, transverse shear forces, and the bending moments received, to obtain the analysis results of the bolt forces. Among them, the main influencing factors include ground motion parameters, shear wave velocity of site soil, and tunnel parameters. The ground motion parameters include ground motion amplitude and ground motion type. The tunnel parameters include tunnel diameter, lining thickness, bolt parameters, and burial depth.

[0107] S33. Equivalent the bolts into springs in different directions, and combine the analysis results of the bolt forces to determine the value of the spring stiffness. Among them, the value of the spring stiffness can use the shaking table test to verify the rationality of the numerical analysis and reduce the error rate of the spring stiffness.

[0108] S4. Determine the seismic response law of shield tunnels based on shell-spring elements.

[0109] Based on S3 to determine the value of the spring stiffness, the shell element is used to simulate the segment in the structural unit, and the spring element is used to simulate the bolt, so as to construct a refined model of the shield tunnel based on the shell-spring element. Through numerical parameter analysis of the main influencing factors, the seismic response law of the shield tunnel based on the shell-spring element is determined. Among them, after the refined model of the shield tunnel based on the shell-spring element is completed, the results obtained from the shell-spring element model are compared and analyzed with the contact element and the shaking table test to verify the rationality of the refined model of the shield tunnel based on the shell-spring element.

[0110] S5. Establish a simplified analysis model for the seismic response considering the influence of bolt connections in the shield tunnel.

[0111] Compare the seismic response law of the shield tunnel based on the shell-spring element in S4 with the results of the traditional homogeneous model to determine the correction factors. The correction factors include the structural deformation correction factor and the structural internal force correction factor. Multiply the results of the traditional homogeneous model by the correction factors determined in S5 to establish a simplified analysis model for the seismic response considering the influence of bolt connections in the shield tunnel, that is, a simplified analysis model for the seismic response based on the shell-spring element, the design method based on the code, and the correction factors. Based on a large number of existing computational analyses, the correction factors shown in Table 1 can be statistically obtained;

[0112] Table 1 Values of correction factors obtained from computational analysis of a large number of working conditions

[0113]

[0114] S6. Verify the accuracy of the simplified sub-model in S5 through the shaking table test.

[0115] In the existing shaking table test of the shield tunnel, the segment joints of the shield tunnel lining are connected by bolts. The bolts and the axial force gauges are combined into one. During the test, the bolt axial force can be directly measured through the axial force gauges, which can provide direct data support for the subsequent equivalence of the bolts to springs. Place the shield tunnel on the shaking table, and the shaking table simulates the earthquake to obtain the seismic response law considering the influence of bolt connections. Compare it with the seismic response law considering the influence of bolt connections obtained from the simplified analysis model for the seismic response considering the influence of bolt connections in the shield tunnel in S5 to verify its rationality. Among them, the shaking table test of the shield tunnel is an existing technology, so it will not be described in detail.

[0116] The above are only the preferred embodiments of the present invention and do not impose any formal restrictions on the present invention. Although the present invention has been disclosed above in its preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to the above-disclosed technical content to obtain equivalent embodiments with equivalent changes within the scope of the technical solution of the present invention. However, as long as the content of the technical solution of the present invention is not departed from, any brief modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A simplified analysis method for the seismic response of shield tunnels based on a shell-spring model, characterized in that: Including the steps as follows: S1. Construct a three-dimensional refined calculation model of soil-shield tunnel considering bolted contact connections; S2. Establish a seismic motion evolution power spectrum model and a time-phase coherence function model, identify the model parameters, synthesize multi-point seismic motions, and generate seismic motion time history curves; S3. Input the soil-shield tunnel model in S1 into the seismic motion time history curves generated in S2, conduct three-dimensional dynamic time history analysis, and determine the value of the equivalent spring stiffness; S4. Based on the value of the spring stiffness determined in S3, use shell elements to simulate the segment lining and spring elements to simulate the bolts for the structural units, construct a refined model of the shield tunnel based on shell-spring elements, conduct numerical parameter analysis through the main influencing factors, and determine the seismic response law of the shield tunnel based on shell-spring elements. The main influencing factors include seismic motion parameters, shear wave velocity of the site soil, and tunnel parameters; S5. Compare the seismic response law of the shield tunnel based on shell-spring elements in S4 with the results of the traditional homogeneous model, determine the correction factor, multiply the results of the traditional homogeneous model by the determined correction factor, and establish a simplified analysis model of seismic response considering the influence of bolted connections in the shield tunnel; S6. Verify the accuracy of the simplified analysis model of seismic response in S5 through a shaking table test.

2. The simplified analysis method for seismic response of shield tunnels based on the shell-spring model according to claim 1, wherein: The steps for constructing the three-dimensional refined calculation model of soil-shield tunnel considering bolted contact connections in S1 are as follows: S11. Determine the shield tunnel parameters of the solid elements and the corresponding calculation range; S12. Input the shield tunnel parameters and calculation range determined in S11 into the three-dimensional model to construct a three-dimensional calculation model of the shield tunnel; S13. Conduct tetrahedral mesh division on the three-dimensional calculation model of the shield tunnel in S12. Both the soil and the lining segments are discretized using 10-node tetrahedral elements; S14. In the three-dimensional calculation model of the shield tunnel in S13, the soil nonlinearity adopts the Davidenkov equivalent linearization model, and the structure adopts the plastic damage model of concrete; S15. Set the contact conditions, and set contact elements between the bolts and the lining segments, and between the lining segments and the surrounding soil. The normal contact adopts a hard connection, and the tangential friction adopts the Coulomb model; S16. Set the boundary conditions, and adopt a lateral binding boundary to make the nodes at the same height in the model have the same horizontal displacement to simulate the shear deformation of the soil during an earthquake; S17. Set the damping, and adopt the Rayleigh damping model to set the damping. The Rayleigh damping coefficient is determined by calculating the system frequency; S18. Set the dynamic time step, and the dynamic time step is set to be no greater than 0.001 s; S19. Establish a three-dimensional refined calculation model of soil-shield tunnel considering bolted contact connections.

3. The simplified analysis method for the seismic response of a shield tunnel based on the shell-spring model according to claim 1, characterized in that: The steps for obtaining the seismic motion time history curves in S2 are as follows: S21. Establish a seismic motion evolution power spectrum model considering the fault rupture process of the earthquake source, The seismic motion evolution power spectrum model includes an envelope function and a seismic spectrum. The modeling considers the earthquake source - propagation path - local site effect. The seismic motion evolution power spectrum model is as follows: where is the intensity coefficient, is the envelope function of the source intensity variation, is the propagation path filtering function, is the local site filtering function, and the model parameters are obtained through the geometric parameters of the earthquake source, the kinematic parameters of the source, and the ground motion spectrum fitting; S22. Establish a directional seismic motion time-phase coherence function model, The time-phase coherence function model consists of three terms multiplied together, specifically as follows: The first term is the decay of the coherence function peak with distance, the second term is the variation of the coherence function with frequency in the direction of parallel seismic wave incidence, and the third term is the variation of the coherence function with frequency in the direction perpendicular to the seismic wave incidence direction; S23. Based on the estimation formulas of the evolving power spectrum and time-varying coherence function of the generalized harmonic wavelet, identify the parameters of the ground motion model, merge the two models into a time-varying cross-spectrum, simulate the ground motion through the spectral expression method, synthesize the multi-point seismic excitation input, and generate the ground motion time history curve.

4. The simplified analysis method for seismic response of shield tunnels based on the shell-spring model according to claim 1, characterized in that: S3 The steps for determining the value of the equivalent spring stiffness are as follows: S31. Input the soil-shield tunnel model in S1 into the ground motion time history curve generated in S2; S32. Conduct a three-dimensional dynamic time history analysis to obtain the analysis results of the bolt forces; S33. Equivalent the bolts into springs in different directions, and combine the bolt forces in S32 to determine the value of the spring stiffness.

5. The simplified analysis method for seismic response of shield tunnels based on the shell-spring model according to claim 4, characterized in that: The three-dimensional dynamic time history analysis in S32 is based on the main influencing factors for numerical parameter analysis. Change the parameter values of the main influencing factors, analyze the general laws of the numerical parameters of the main influencing factors, and obtain the analysis results of the bolt forces.

6. The simplified analysis method for seismic response of shield tunnel based on shell-spring model according to claim 3, characterized in that: The identification formula for the evolving power spectrum of the synthesized ground motion in S23 is as follows: Among them and are the wavelet coefficients of different ground motions, is the wavelet bandwidth, and the evolving power spectrum is ; The time-varying coherence function: After identifying the model parameters, the evolving power spectrum model and the time-varying coherence function model are merged into a time-varying cross-spectrum, and the ground motion is simulated through the spectral expression method, The formula of the spectral expression method is as follows: wherein is a random phase angle.

7. The simplified analysis method for the seismic response of a shield tunnel based on the shell-spring model according to claim 1, characterized in that: After the refined shield tunnel model based on the shell-spring element in S4 is completed, compare and analyze the results obtained from the shell-spring element model with the contact element and the shaking table test to verify the rationality of the refined shield tunnel model based on the shell-spring element.

8. The simplified analysis method for the seismic response of a shield tunnel based on the shell-spring model according to claim 1, characterized in that: The correction factors include the structural deformation correction factor and the structural internal force correction factor.

9. The simplified analysis method for seismic response of shield tunnels based on the shell-spring model according to claim 5, characterized in that: The ground motion parameters include the ground motion amplitude and the ground motion type, and the tunnel parameters include the tunnel diameter, lining thickness, bolt parameters, and burial depth.

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