Shield tunnel earthquake response simplified analysis method based on shell-spring model

Abstract

The invention relates to a shield tunnel seismic response simplified analysis method based on a shell-spring model. The method comprises the following steps: constructing a soil-shield tunnel calculation model considering bolt contact connection; establishing a seismic oscillation evolution power spectrum model and a variable dry function model, and generating a seismic oscillation time history curve; inputting the soil-shield tunnel model into a ground vibration time-history curve, performing three-dimensional dynamic time-history analysis, and determining a value of spring stiffness; on the basis of the determined value of the spring stiffness, constructing a shield tunnel refined model based on the shell-spring unit, and obtaining a shield tunnel earthquake response rule based on the shell-spring unit; through comparison with a simplified homogeneous tunnel model seismic response rule, determining a correction factor, and establishing a simplified analysis model based on a standard design method and the correction factor; and verifying the accuracy of the simplified analysis model through a vibration table test. According to the method, discontinuity and local rigidity reduction of bolt contact connection in the shield tunnel model are considered, and the accuracy of seismic response analysis is improved.

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 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. As a result, the seismic response of the tunnel structure obtained is quite different 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 is even less able to consider the spatial effect of shield tunnels.

[0003] The deficiencies of the existing technologies are mainly reflected in: 1) Defects of the uniform model: Most current 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 spring stiffness errors, the deviation of joint opening exceeds 20%, and the error of dislocation 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 seismic design is still carried out according to the traditional simplified homogeneous model, 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: S1. Construct a three-dimensional refined calculation model of soil-shield tunnel considering bolt contact connection; 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 seismic ground motion time history curves; S3. Input the soil-shield tunnel model in S1 into the seismic ground 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 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; 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; S6. Verify the accuracy of the simplified analysis model for the seismic response in S5 through a shaking table test.

[0007] Furthermore, the steps for constructing the three-dimensional refined calculation model of soil-shield tunnel considering bolt contact connection in S1 are as follows: S11. Determine the parameters of the shield tunnel of the solid element 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, and both the soil and the lining segments are discretized by 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, 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, adopt a lateral binding boundary to make the nodes at the same height of the model have the same horizontal displacement to simulate the shear deformation of the soil during an earthquake; S17. Set the damping, adopt the Rayleigh damping model to set the damping, and the Rayleigh damping coefficient is determined by calculating the system frequency; S18. Set the dynamic time step, and the set dynamic time step shall not be greater than 0.001 s; S19. Establish a three-dimensional refined calculation model of soil-shield tunnel considering bolt connection.

[0008] Further, the steps for obtaining the ground motion time history curve in S2 are as follows: S21. Establish a ground motion evolution power spectrum model considering the fault rupture process of the earthquake source. 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 shown as follows: 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 geometric parameters of the earthquake source, the kinematic parameters of the earthquake source, and the ground motion spectrum; S22. Establish a ground motion time-phase coherence function model with directionality. The time-phase coherence function model consists of three multiplications, specifically as follows: 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; S23. Based on the estimation formulas of the evolution power spectrum and the time-phase coherence function of the generalized harmonic wavelet, identify the parameters of the ground motion model, combine 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.

[0009] Further, the steps for determining the value of the equivalent spring stiffness in S3 are as follows: S31. Input the soil-shield tunnel model in S1 into the ground motion time history curve generated in S2; S32. Conduct three-dimensional dynamic time history analysis to obtain the analysis results of the bolt force; S33. Equivalent the bolt into springs in different directions, and determine the value of the spring stiffness in combination with the bolt force in S32.

[0010] Further, 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 force.

[0011] Furthermore, the evolution power spectrum identification formula of the synthetic ground motion in S23 is as follows: where and are the wavelet coefficients of different ground motions, is the wavelet bandwidth, and the evolution power spectrum is ; The time-varying coherence function:: After identifying the model parameters, the evolution power spectrum model and the time-varying coherence function model are combined into a time-varying cross-spectrum, and the ground motion is simulated by the spectral representation method. The formula of the spectral representation method is as follows: where is the random phase angle.

[0012] Furthermore, after the refined shield tunnel model based on shell-spring elements is completed in S4, the results obtained from the shell-spring element model are compared and analyzed with the contact elements and the shaking table test to verify the rationality of the refined shield tunnel model based on shell-spring elements.

[0013] Furthermore, the correction factors include a structural deformation correction factor and a structural internal force correction factor.

[0014] Furthermore, the main influencing factors include ground motion parameters, the shear wave velocity of the site soil, and tunnel parameters. The ground motion parameters include the ground motion amplitude and the ground motion type, and the tunnel parameters include the tunnel diameter, the lining thickness, the bolt parameters, and the burial depth.

[0015] Advantages of the present invention: 1) Considering the influence of longitudinal and radial bolts in the shield tunnel model and applying it 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; 2) It is proposed to simulate the segment with shell elements and the bolt connection with spring elements, and characterize the bending, shear, and slip behaviors of the segment joints through the shell-spring cooperative action, and construct a refined shield tunnel model based on shell-spring elements, 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; 3) A ground motion synthesis method considering the seismic 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

[0016] Figure 1 is the flow chart of a simplified analysis method for the seismic response of shield tunnels based on the shell-spring model; Figure 2 is a three-dimensional calculation model of soil-shield tunnel based on contact setting; Figure 3 is Figure 2 the detailed model of the shield tunnel and bolts in Figure 4 is the comparison schematic diagram of the measured seismic ground motion evolution power spectrum (a) and the identified modeling (b); Figure 5 is the schematic diagram of the identification of the coherence function at different positions; Figure 6 is the schematic diagram of the fitting effect of the time-varying coherence function at different positions; Figure 7 is the comparison schematic diagram of the measured time history (a) and the simulated time history (b); Figure 8 is the comparison schematic diagram of the model and the measured time-varying coherence function in the rising (a), steady (b), and decaying (c) stages of the seismic ground motion intensity; Figure 9 is the comparison schematic diagram of the time-varying coherence function model and the measured record at different times. Specific Embodiments

[0017] To further elaborate on the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific embodiments, structures, features, and effects according to the present invention as follows.

[0018] Referring to Figure 1-8 shown, the present invention provides a simplified analysis method for the seismic response of shield tunnels based on the shell-spring model, including the following steps: S1. Construct a three-dimensional refined calculation model of soil-shield tunnel considering bolt contact connection ( Figure 2 and Figure 3 shown).

[0019] 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: S11. Determine the shield tunnel parameters of the entity unit and the corresponding calculation range. The shield tunnel parameters include the tunnel diameter, tunnel burial depth, and tunnel lining thickness. The calculation range includes the 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 bedrock surface depth of the local stratum.

[0020] 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) to quickly realize the relative position relationship of different structures, so as to realize an efficient modeling method for the overall model.

[0021] global D_tunnel = 12.0 ; Tunnel diameter (m) global H_tunnel = 12.0 ; Tunnel burial depth (m) global T_tunnel = 0.50 ; Tunnel lining thickness (m) global W_model = 84.0 ; Calculation range width (m) global L_model = 100.0 ; Calculation range length (m) global HH_model = 70.0 ; Calculation range height (m) global E_tunnel = 35e9 ; Elastic modulus of shield tunnel lining (Pa) global Density_tunnel = 2500; Density of shield tunnel lining (kg / m 3 ) S13. Mesh generation. Perform tetrahedral mesh generation on the 3D calculation model of the shield tunnel in S12. Both the soil body and the lining segment are discretized using 10-node tetrahedral elements.

[0022] S14. Constitutive model. In the 3D calculation model of the shield tunnel in S13, the nonlinearity of the soil body adopts the Davidenkov equivalent linearization model, and the structure adopts the plastic damage model of concrete.

[0023] S15. Set contact conditions. Contact elements are set 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 adopts a hard connection, and the tangential friction adopts the Coulomb model (the shear coefficient is tentatively set to 0.5 and will be further corrected by fitting the shaking table test later).

[0024] S16. Set boundary conditions. The lateral binding boundary is adopted to make the nodes at the same height of the model have the same horizontal displacement to simulate the shear deformation of the soil during an earthquake.

[0025] 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.

[0026] 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 the 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.

[0027] S19. Establish a calculation model of the shield tunnel considering bolt contact connection, that is, a three-dimensional refined calculation model of the soil-shield tunnel considering bolt contact connection.

[0028] S2. Generate the ground motion time history curve.

[0029] 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-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 synthesize the multi-point ground motion (non-uniform ground motion) by the spectral representation method to generate the ground motion time history curve. The specific implementation steps are as follows: S21. Establish a ground motion evolving power spectrum model considering the earthquake source fault rupture process.

[0030] The ground motion evolving power spectrum model includes an envelope function and a seismic spectrum. 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 dislocations at various points 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 effects. In terms of the local site, the site filters the seismic waves.

[0031] The evolution power spectrum model of ground motion 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. The model parameters are obtained by fitting the geometric parameters of the earthquake source, the kinematic parameters of the source, and the ground motion spectrum.

[0032] S22. Establish a time-varying coherence function model of ground motion with directivity.

[0033] The time-varying coherence function model consists of three terms multiplied together, specifically as follows: 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, and 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.

[0034] S23. Based on the estimation formulas of the evolution power spectrum and the time-varying coherence function of the generalized harmonic wavelet, identify the parameters of the ground motion model, combine 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.

[0035] The generalized harmonic wavelet has the characteristic of non-overlapping frequency domain, and the evolution power spectrum and the time-varying coherence function can be explicitly expressed by the generalized harmonic wavelet coefficients. Using the generalized harmonic wavelet, the evolution power spectrum and the time-varying coherence function of the measured non-stationary ground motion are estimated to identify the model parameters. The evolution power spectrum identification formula: where 、 are the wavelet coefficients of different ground motions, is the wavelet bandwidth, and the evolution power spectrum is .

[0036] The time-varying coherence function identification formula: After identifying the model parameters, the evolution power spectrum model and the time-varying coherence function model are combined 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: , where is a random phase angle.

[0037] Referring to Figures 4-9 as shown, 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 the real record. Specifically, Figure 4 is the comparison of the evolving power spectrum of the real ground motion record and the identified and modeled evolving power spectrum. Figure 5 is the time-varying coherence function of the ground motion excitation 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 the real record and the simulated ground motion record. The simulated ground motion has the non-stationary characteristics of the measured record. Figure 9 is the comparison of the time-varying coherence function model and the measured record at different times. The agreement is good, indicating that the ground motion excitation synthesized by this method has the non-stationarity of the real record.

[0038] S3. Determine the value of the equivalent spring stiffness. The specific steps are as follows: S31. Input the soil-shield tunnel model in S1 into the ground motion time history curve generated in S2.

[0039] 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, and the general laws of the numerical parameters of the main influencing factors will be analyzed. Then, focus on analyzing the forces on the bolts, including axial tensile and compressive forces, lateral shear forces, and the bending moments received, etc., to obtain the analysis results of the bolt forces. Among them, the main influencing factors include ground motion parameters, site soil shear wave velocity, 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.

[0040] 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 verify the rationality of the numerical analysis by using a shaking table test to reduce the error rate of the spring stiffness.

[0041] S4. Determine the seismic response law of the shield tunnel based on the shell-spring element.

[0042] Based on S3 to determine the value of the spring stiffness, the shell element is used to simulate the segment of the shield tunnel, and the spring element is used to simulate the bolt, and a refined model of the shield tunnel based on the shell-spring element is constructed. Through the 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.

[0043] S5. Establish a simplified analysis model for the seismic response considering the influence of bolt connections in the shield tunnel.

[0044] 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; Table 1 Values of correction factors obtained from computational analyses under a large number of working conditions

[0045] S6. Verify the accuracy of the simplified model in S5 through the shaking table test.

[0046] 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. In the test, the axial force of the bolts can be directly measured through the axial force gauges, which can provide direct data support for the subsequent equivalent of the bolts as 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, and 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.

[0047] The above are only the preferred embodiments of the present invention, and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above with the preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to equivalent embodiments by using the above-disclosed technical content without departing from the technical solution of the present invention. However, as long as it does not depart from the technical solution content of the present invention, 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 seismic response of shield tunnels based on the shell-spring model is characterized by: Included steps as follows: S1. Construct a three-dimensional refined calculation model of soil-shield tunnel considering bolt contact connection; S2. Establish a seismic motion evolution power spectrum model and a time-varying coherence function model, identify 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 time history curve generated in S2, perform a three-dimensional dynamic time history analysis, and determine the value of the equivalent spring stiffness; S4. Based on S3, the value of the spring stiffness is determined. The structural unit uses shell elements to simulate the pipe segments and spring elements to simulate the bolts. A refined model of the shield tunnel based on the shell-spring element is constructed. The numerical parameter analysis is performed through the main influencing factors to determine the seismic response law of the shield tunnel based on the shell-spring element. S5. Compare the seismic response law of the shield tunnel based on the shell-spring unit 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 seismic response analysis model that considers the influence of the shield tunnel bolt connection; S6. Verify the accuracy of the simplified analysis model of seismic response in S5 through shaking table tests.

2. The simplified analysis method for seismic response of a shield tunnel based on a shell-spring model according to claim 1 is characterized by: The steps for constructing the three-dimensional refined calculation model of the soil-shield tunnel considering bolt contact connection in S1 are as follows: S11. Determine the shield tunnel parameters of the entity unit 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. Perform tetrahedral meshing on the three-dimensional calculation model of the shield tunnel in S12, and use 10-node tetrahedral units to discretize the soil and lining segments; S14. In the three-dimensional calculation model of the shield tunnel in S13, the Davidenkov equivalent linearization model is used for soil nonlinearity, and the plastic damage model of concrete is used for the structure; S15. Set the contact conditions, set contact units between the bolts and the lining segments, and between the lining segments and the surrounding soil, use hard connection for normal contact, and use the Coulomb model for tangential friction; S16. Set boundary conditions and use lateral binding boundaries so that nodes at the same height of the model have the same horizontal displacement to simulate the shear deformation of the soil during an earthquake; S17. Set the damping. Use the Rayleigh damping model to set the damping. The Rayleigh damping coefficient is determined by the system frequency calculation. S18. Set the power time step, which should not be greater than 0.001s; S19. Establish a three-dimensional refined calculation model of soil-shield tunnel considering bolt contact connection.

3. The simplified analysis method for seismic response of a shield tunnel based on a shell-spring model according to claim 1 is characterized by: The steps of obtaining the ground motion time history curve in S2 are as follows: S21. Establish a power spectrum model of earthquake motion evolution considering the fault dislocation process of the earthquake source. The power spectrum model of earthquake motion evolution includes envelope function and earthquake spectrum. The modeling takes into account the earthquake source, propagation path and local site effect. The power spectrum model of earthquake motion evolution is as follows: in is the strength coefficient, is the envelope function of source intensity variation, is the propagation path filter function, It is a local site filtering function, and the model parameters are obtained by fitting the earthquake source geometry parameters, source kinematic parameters and seismic motion spectrum; S22. Establish a time-varying coherence function model of directional ground motion. The time-varying coherence function model consists of three multiplications, as follows: The first term is the attenuation of the peak value of the coherence function with distance, the second term is the change of the coherence function with frequency in the direction parallel to the incident seismic wave, and the third term is the change of the coherence function with frequency in the direction perpendicular to the incident seismic wave; S23. Based on the estimation formula of the evolving power spectrum and time-varying coherence function of generalized harmonic wavelet, the parameters of the seismic motion model are identified, the two models are merged into a time-varying cross-spectrum, the seismic motion is simulated through the spectral expression method, the multi-point seismic excitation input is synthesized, and the seismic motion time history curve is generated.

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

5. The simplified analysis method for seismic response of a shield tunnel based on a shell-spring model according to claim 4 is characterized by: The three-dimensional dynamic time history analysis in S32 is to perform numerical parameter analysis based on the main influencing factors, change the parameter values ​​of the main influencing factors, analyze the general rules of the numerical parameters of the main influencing factors, and obtain the analysis results of the bolt force.

6. The simplified analysis method for seismic response of a shield tunnel based on a shell-spring model according to claim 3 is characterized by: The evolution power spectrum identification formula of the synthetic ground motion in S23 is as follows: in , 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 combined into a time-varying cross-spectrum, and the ground motion is simulated by the spectral expression method. The spectrum expression method formula is as follows: in is a random phase angle.

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

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

9. The simplified analysis method for seismic response of a shield tunnel based on a shell-spring model according to claim 5 is characterized by: The main influencing factors include seismic parameters, site soil shear wave velocity, and tunnel parameters. The seismic parameters include seismic amplitude and seismic type. The tunnel parameters include tunnel diameter, lining thickness, bolt parameters, and burial depth.

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