A method for obtaining the performance of the joints of a immersed tube tunnel considering formation changes under the action of traveling waves

Abstract

The present invention provides a method for obtaining the performance of a submerged tunnel joint considering formation changes under the action of traveling waves, including establishing a first semi-infinite elastic foundation beam and a second semi-infinite elastic foundation beam. The first semi-infinite elastic foundation beam is located in soil layer I, and the second semi-infinite elastic foundation beam is located in soil layer II; ignoring the deformation of the cross-section of the submerged tunnel, regarding the pipe segment as an Euler beam model and the foundation as a Pasternak foundation model, introducing a displacement phase angle to simulate the traveling wave effect of the earthquake, considering the influence of the traveling wave action on the non-uniform excitation of the pipe segment, with the submerged tunnel joint located at the interface of the changing formation, obtaining the bending control equation of the submerged tunnel at the interface of the changing formation; using a flexural spring and a shear spring to simulate the bending and shearing of the joint, considering the transfer effect of the joint on the vertical displacement difference, rotation angle, bending moment and shear force, analyzing the change of the peak value of the joint force and the influence range of the joint mutation section, and the present invention can accurately obtain the response law of the joint deformation and force.

Description

Technical Field

[0001] The present invention belongs to the technical field of underground engineering, and particularly relates to a method for obtaining the performance of a submerged tunnel joint considering formation changes under the action of traveling waves. Background Technique

[0002] In recent years, with the rapid development of urban rail transit, the longitudinal length of cross-sea submerged tunnels has been continuously increasing. Inevitably, they have to cross formations of different properties. The sudden change of the formation causes large deformations of the submerged tunnel under seismic action. The pipe segments above the interface between different formations are subject to sudden changes in force and deformation, and the sealing performance near the interface between different formations must be strictly ensured. Therefore, it is necessary to establish pipe segment joints at the formation change positions so that the overall structure of the submerged tunnel can relieve and adapt to the sudden changes in force and deformation of the pipe segments above the interface caused by the formation changes. In order to explore the influence law of seismic loads on the force and deformation of pipe segment joints and prevent leakage at the joints, the present invention establishes a calculation model and method for pipe segment joints of a submerged tunnel considering formation changes under the action of traveling waves.

[0003] At present, in the structural design of submerged tunnels at home and abroad, the responses of joints under seismic loads are mostly numerically simulated and experimentally studied. There is less theoretical calculation on the performance of pipe segment joints crossing changing formations. In the existing force calculation of submerged tunnel structures, the foundation model is mostly regarded as the Winkler foundation model, without considering the continuity of the foundation, and at the same time ignoring the continuity conditions of the force and deformation of the joints. Summary of the Invention

[0004] In view of the deficiencies of the prior art, the purpose of the present invention is to provide a method for obtaining the performance of a submerged tunnel joint considering formation changes under the action of traveling waves. The pipe segment is regarded as an Euler beam model, the foundation is regarded as a Pasternak foundation model, the displacement phase angle is introduced to simulate the traveling wave effect of the earthquake, the influence of the traveling wave action on the non-uniform excitation of the pipe segment is considered, and the continuity conditions of the force and deformation of the joint are considered to obtain the change of the peak force of the joint and the influence range of the joint mutation section.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0006] A method for obtaining the performance of a submerged tunnel joint considering formation changes under the action of traveling waves, comprising the following steps:

[0007] Step 1: In the finite element software, establish a first semi-infinite elastic foundation beam and a second semi-infinite elastic foundation beam. The first semi-infinite elastic foundation beam is located in soil layer I, and the second semi-infinite elastic foundation beam is located in soil layer II;

[0008] Step 2: Ignoring the deformation of the cross-section of the immersed tunnel, regarding the pipe segment as an Euler beam model and the foundation as a Pasternak foundation model, introducing the displacement phase angle to simulate the traveling wave effect of the earthquake, considering the influence of the traveling wave action on the non-uniform excitation of the pipe segment, with the immersed tunnel joint located at the changing stratum interface between Soil Layer I and Soil Layer II, and obtaining the bending control equation of the immersed tunnel for the changing stratum interface related to the flexural stiffness of the pipe segment;

[0009] Step 3: Using flexural springs and shear springs to simulate the bending and shearing of the joint, considering the transfer effects of the flexural stiffness and shear stiffness at the joint on the vertical displacement difference, rotation angle, bending moment, and shear force, and analyzing the change of the peak force at the joint and the influence range of the joint mutation section.

[0010] Furthermore, in Step 2, the free-field displacement functions acting on Soil Layer I and Soil Layer II are as follows:

[0011]

[0012] where: u(z)1 and u(z)2 are respectively the peak values of the free-field displacements of Soil Layer I and Soil Layer II at a distance of z meters from the ground surface; and λ are respectively the incident angle of the seismic wave and the wavelength of the seismic wave, with the units of rad and m respectively; S1 and S2 are respectively the free-field vertical displacements received by Soil Layer I and Soil Layer II, with the unit of m; θ0 is the displacement phase angle of the seismic wave, with the unit of rad; x is the different positions of the immersed tunnel along the longitudinal direction of the structure, with the unit of m;

[0013] The bending control equation of the immersed tunnel can be expressed as:

[0014]

[0015] where: EI is the flexural stiffness of the pipe segment, with the unit of N·m 2 , P is the interaction force between the immersed tunnel and the stratum, with the unit of N, b is the width of the pipe segment of the immersed tunnel, with the unit of m; w is the deformation of the immersed tunnel, with the unit of m;

[0016] Simplifying the interaction between the soil layer and the immersed tunnel into the reaction force of the foundation compression layer and the shear force of the foundation shear layer, in this case, the interaction force between the soil layer and the immersed tunnel can be expressed as:

[0017]

[0018] where: S is the free-field vertical displacement, with the unit of m; K h is the foundation elastic resistance coefficient, with the unit of Pa;

[0019] The calculation of the foundation elastic resistance coefficient can be expressed as:

[0020]

[0021] In the formula: ρ s and v are the density and Poisson's ratio of the foundation soil respectively, with the density unit being kg / m 3 , H is the height of the immersed tube tunnel, with the unit being m; λ is the wavelength of the seismic wave, with the unit being m; V s is the shear wave velocity of soil layer Ⅰ and soil layer Ⅱ, with the unit being m / s;

[0022] Introducing the displacement phase angle, the bending control equations of the immersed tube tunnel in the areas of soil layer Ⅰ and soil layer Ⅱ are as follows:

[0023]

[0024] In the formula: K h1 and K h2 are the foundation soil elastic resistance coefficients of soil layer Ⅰ and soil layer Ⅱ respectively, with the unit being Pa; G1 and G2 are the foundation soil shear coefficients of soil layer Ⅰ and soil layer Ⅱ respectively, with the unit being Pa.

[0025] Furthermore, using the generalized reaction displacement method to analyze the force and deformation of the immersed tube tunnel joints, the angular displacement and vertical displacement difference at the immersed tube tunnel joints can be expressed as:

[0026] Δψ = M Ⅰ / k w (6)

[0027] Δw = Q Ⅰ / k j (7)

[0028] In the formula: k w and k j are the flexural stiffness and shear stiffness at the joint respectively, M Ⅰ and Q Ⅰ are the bending moment and shear force of the previous pipe segment near the joint respectively;

[0029] Define the position of the joint at the interface of the varying strata as the coordinate origin, the longitudinal direction of the pipe segment as the x-axis, and the vertical direction along the strata as the y-axis. The continuity conditions of the force and deformation at the joint are:

[0030]

[0031] Through the matrix transfer principle, the vertical displacement difference, angular displacement, bending moment, and shear force at the joints of the immersed tube tunnel in different strata sections can be calculated.

[0032] Furthermore, according to the vertical displacement difference, angular displacement, bending moment, and shear force at the joints of the immersed tube tunnel in different strata sections, the optimal solutions of deformation and force are selected.

[0033] Furthermore, in step 1, the finite element software is ABAQUS.

[0034] Further, for Step 2 and Step 3, a program is written using Matlab software to endow reasonable characteristic parameters to Soil Layer Ⅰ, Soil Layer Ⅱ, pipe segments and joints, and earthquakes.

[0035] Further, for pipe segments and joints, the smaller the force within the allowable range is, the better, and the deformation is within the allowable range. Appropriate flexural stiffness of pipe segments, flexural stiffness of joints, and shear stiffness of joints are selected.

[0036] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0037] In existing references, the research on the deformation of immersed tube tunnels under seismic loads focuses on numerical simulations and experiments. There is less research on the change in the peak force of pipe segments near the interface of different strata and the influence range of the force and deformation of pipe segments caused by stratum changes. In theoretical calculations, the establishment of joints near the interface of different strata is not considered, and the deformation and force transfer effects under earthquakes are not analyzed. The theoretical basis of the present invention is solid. Two semi-infinite elastic foundation beams are established, the sine wave load is used to simulate earthquakes, and the displacement phase angle is introduced to simulate the traveling wave effect of earthquakes. The influence of the traveling wave effect on the non-uniform excitation of pipe segments is considered. The joints of the immersed tube tunnel are located at the changing interface, and flexural springs and shear springs are used to simulate the bending and shearing of the joints. The transfer effects of the joints on the vertical displacement difference, rotation angle, bending moment, and shear force are considered, and the change in the peak force of the joints and the influence range of the joint mutation section are analyzed. In actual calculations, a program can be written using Matlab software to endow reasonable characteristic parameters to Soil Layer Ⅰ, Soil Layer Ⅱ, pipe segments and joints, and earthquakes, and the computing power of the computer is used to improve the calculation accuracy and speed.

[0038] Using the calculation model and theoretical method of pipe segment joints under seismic loads proposed by the present invention, the seismic response of immersed tube tunnels under traveling wave effects can be calculated, so as to study the response laws of joint deformation and force. In addition, by controlling a single variable, changing the values of relevant parameters such as joint stiffness and pipe segment stiffness, calculating the joint dynamic response results under different working conditions and conducting comparative analysis, the influence of single factors on the performance of pipe segment joints can be discussed. Description of the Drawings

[0039] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0040] Figure 1 is the flowchart of the implementation process of the present invention;

[0041] Figure 2 is the schematic longitudinal section of the immersed tube tunnel of the present invention;

[0042] Figure 3 Schematic diagram of the Pasternak foundation beam model of the present invention;

[0043] Figure 4 Schematic diagram of seismic wave-displacement of the present invention;

[0044] Figure 5 Schematic diagram of force transmission of joint deformation of the present invention;

[0045] Figure 6(a) is a comparison diagram of the theoretical calculation results of shear force of joints with different flexural rigidities of the present invention;

[0046] Figure 6(b) is a comparison diagram of the theoretical calculation results of bending moment of joints with different flexural rigidities of the present invention;

[0047] Figure 6(c) is a comparison diagram of the theoretical calculation results of the vertical displacement values of joints with different flexural rigidities of the present invention;

[0048] Figure 6(d) is a comparison diagram of the rotation angle results of joints with different flexural rigidities of the present invention;

[0049] Figure 7(a) is a comparison diagram of the theoretical calculation results of shear force of joints with different shear rigidities of the present invention;

[0050] Figure 7(b) is a comparison diagram of the theoretical calculation results of bending moment of joints with different shear rigidities of the present invention;

[0051] Figure 7(c) is a comparison diagram of the theoretical calculation results of different shear rigidities of joints of the present invention and the vertical displacement values;

[0052] Figure 7(d) is a comparison diagram of the theoretical calculation results of different shear rigidities of joints of the present invention and the rotation angle;

[0053] Figure 8(a) is a comparison diagram of the theoretical calculation results of the shear force of joints affected by different pipe section bending rigidities of the present invention;

[0054] Figure 8(b) is a comparison diagram of the theoretical calculation results of the bending moment of joints affected by different pipe section bending rigidities of the present invention;

[0055] Figure 8(c) is a comparison diagram of the theoretical calculation results of the vertical displacement values of joints affected by different pipe section bending rigidities of the present invention;

[0056] Figure 8(d) is a comparison diagram of the theoretical calculation results of the rotation angle of joints affected by different pipe section bending rigidities of the present invention. Detailed implementation manners

[0057] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention.

[0058] The present invention provides a method for obtaining the performance of a submerged tunnel joint considering formation changes under the action of traveling waves, as Figures 1-5 shown, which includes the following steps:

[0059] Step 1: In the finite element software, establish the first semi-infinite elastic foundation beam and the second semi-infinite elastic foundation beam. The first semi-infinite elastic foundation beam is located in soil layer I, and the second semi-infinite elastic foundation beam is located in soil layer II;

[0060] Step 2: Ignore the deformation of the cross-section of the submerged tunnel, regard the pipe segment as an Euler beam model, regard the foundation as a Pasternak foundation model, introduce the displacement phase angle to simulate the traveling wave effect of the earthquake, consider the influence of the traveling wave action on the non-uniform excitation of the pipe segment, and the submerged tunnel joint is located at the changing formation interface between soil layer I and soil layer II, and obtain the bending control equation of the submerged tunnel at the changing formation interface related to the flexural stiffness of the pipe segment;

[0061] Step 3: Use a flexural spring and a shear spring to simulate the bending and shearing of the joint, consider the transfer effects of the flexural stiffness and shear stiffness at the joint on the vertical displacement difference, rotation angle, bending moment and shear force, and analyze the change of the peak force of the joint and the influence range of the joint mutation section.

[0062] In existing references, the research on the deformation of submerged tunnels under seismic loads focuses on numerical simulations and experiments. There is less research on the change of the peak force of the pipe segments of submerged tunnels near different formation interfaces and the influence range of the deformation and force of the pipe segments caused by formation changes. In terms of theoretical calculations, the establishment of joints near different formation interfaces is not considered, and the transfer effect of their deformation and force under earthquakes is not analyzed.

[0063] The method for obtaining the performance of a submerged tunnel joint considering formation changes under the action of traveling waves provided by the present invention has a solid theoretical basis. Two semi-infinite elastic foundation beams are established, a sine wave load is used to simulate the earthquake, the displacement phase angle is introduced to simulate the traveling wave effect of the earthquake, and the influence of the traveling wave action on the non-uniform excitation of the pipe segment is considered. The submerged tunnel joint is located at the changing interface. A flexural spring and a shear spring are used to simulate the bending and shearing of the joint, the transfer effects of the joint on the vertical displacement difference, rotation angle, bending moment and shear force are considered, and the change of the peak force of the joint and the influence range of the joint mutation section are analyzed. In actual calculations, a program can be written using Matlab software, reasonable characteristic parameters are given to soil layer I and soil layer II, the pipe segment and the joint, and the earthquake, and the computing power of the computer is used to improve the calculation accuracy and speed.

[0064] Since submerged tunnels are getting longer and longer, seismic waves do not reach different positions simultaneously. The present invention has better simplifications in the calculation, reflecting the non-uniformity (non-uniform excitation) of seismic wave propagation.

[0065] The present invention believes that the joint of the immersed tube tunnel is located at the interface of the changing strata between soil layer I and soil layer II. By ignoring the influence of boundary conditions, the calculation results of the joint are more in line with the deformation and stress in actual engineering.

[0066] The present invention mainly adopts a flexible joint of the immersed tube tunnel at the strata junction, which can better adapt to the deformation of the pipe segment caused by the changing strata.

[0067] In the present invention, the pipe segment is regarded as an Euler beam model, and the foundation is regarded as a Pasternak foundation model. In recent years, the immersed tube tunnels built are getting longer and have a large slenderness ratio, so they can be regarded as Euler beams, ignoring the shear force on the cross-section.

[0068] The present invention regards the foundation as a Pasternak foundation, not a Winkler foundation, because the Winkler foundation only considers the compressibility of the strata and does not consider the continuity between soil spring elements. The Pasternak foundation improves this phenomenon and is more in line with the characteristics of actual engineering.

[0069] The present invention uses a bending spring and a shear spring to simulate the bending and shearing of the joint, mainly to reflect the transfer characteristics of the joint, which can transfer the force and deformation between the front and rear pipe segments. The bending spring can transfer the bending moment and then transfer the rotation angle, and the shear spring can transfer the shear force and then transfer the vertical displacement difference.

[0070] In the present invention, in step 2, by obtaining the free-field displacement functions acting on soil layer I and soil layer II, it is convenient to establish the pipe-soil interaction method, and analyze the deformation of the pipe segment through the formation deformation. The free-field displacement functions acting on soil layer I and soil layer II are:

[0071]

[0072] In the formula: u(z)1 and u(z)2 are the peak values of the free-field displacements of soil layer I and soil layer II at a distance of z meters from the ground surface respectively; and λ are the incident angle of the seismic wave and the wavelength of the seismic wave respectively, with the units of rad and m; S1 and S2 are the free-field vertical displacements received by soil layer I and soil layer II respectively, with the unit of m; θ0 is the displacement phase angle of the seismic wave, with the unit of rad; x is the different positions of the immersed tube tunnel along the longitudinal direction of the structure, with the unit of m. Taking the formation mutation point as the origin, the pipe segment above the soil layer in the left area is where x < 0, and the pipe segment above the soil layer in the right area is where x > 0.

[0073] Figures 1-4 All illustrate this point;

[0074] The bending control equation of the immersed tube tunnel can be expressed as:

[0075]

[0076] Where: EI is the flexural stiffness of the pipe segment, with the unit of N·m 2 , P is the interaction force between the immersed tunnel and the stratum, with the unit of N, b is the width of the pipe segment of the immersed tunnel, with the unit of m; w is the deformation of the immersed tunnel, with the unit of m;

[0077] The interaction between the soil layer and the immersed tunnel is simplified as the reaction force of the foundation compression layer and the shear force of the foundation shear layer. In this case, the interaction force between the soil layer and the immersed tunnel can be expressed as:

[0078]

[0079] Where: S is the vertical displacement of the free field, with the unit of m; K h is the coefficient of subgrade elastic resistance, with the unit of Pa;

[0080] The calculation of the coefficient of subgrade elastic resistance can be expressed as:

[0081]

[0082] Where: ρ s and v are the density and Poisson's ratio of the foundation respectively. The density unit is kg / m 3 , H is the height of the immersed tunnel, with the unit of m; λ is the wavelength of the seismic wave, with the unit of m; V s is the shear wave velocity of soil layer I and soil layer II, with the unit of m / s;

[0083] Introducing the displacement phase angle, the bending control equation of the immersed tunnel in the areas of soil layer I and soil layer II is:

[0084]

[0085] Where: K h1 and K h2 are the coefficients of subgrade elastic resistance of soil layer I and soil layer II respectively, with the unit of Pa; G1 and G2 are the subgrade shear coefficients of soil layer I and soil layer II respectively, with the unit of Pa.

[0086] In the present invention, in step 3, the generalized response displacement method is used to analyze the forces and deformations of the immersed tunnel joints. The rotation angle and vertical displacement difference at the immersed tunnel joints can be expressed as:

[0087] Δψ = M Ⅰ / k w (5)

[0088] Δw = Q Ⅰ / k j (6)

[0089] Where: k w and k jare the flexural stiffness and shear stiffness at the joint, respectively, and M Ⅰ and Q Ⅰ are the bending moment and shear force of the previous pipe section near the joint, respectively;

[0090] Define the joint position at the interface of the varying strata as the coordinate origin, the longitudinal direction of the pipe section as the x-axis, and the vertical direction along the strata as the y-axis. The continuity conditions for the forces and deformations at the joint are:

[0091]

[0092] Through the matrix transfer principle, the vertical displacement difference, rotation angle, bending moment, and shear force at the joints of the immersed tunnel in different strata can be calculated.

[0093] In an embodiment of the present invention, as Figures 1-5 shown, the present invention takes a certain immersed tunnel project as the background. In the calculation, the flexural stiffness of the pipe section EI = 1.464×10 11 N·m 2 , the flexural stiffness of the joint k w = 2.44×10 8 N·m 2 , the shear stiffness of the joint kj = 1.1×10 9 N / m. The standard shear wave velocities of soil layer Ⅰ and soil layer Ⅱ are 200 m / s (V s1 ) and 100 m / s (V s2 ), respectively. The peak values of the free-field displacements of soil layer Ⅰ and soil layer Ⅱ are 0.1 m and 0.12 m, respectively. Using Matlab to write a program, according to a method for obtaining the performance of the joints of an immersed tunnel considering stratum variation under the action of traveling waves provided by the present invention, the performance of the joints of the immersed tunnel considering varying strata under the action of traveling waves is solved, and the results are shown in Figures 6 - 8.

[0094] Figures 6(a)-6(d) The results show that the smaller the flexural stiffness of the joint, the larger the joint bending moment and the larger the joint rotation angle, without affecting the joint shear force and vertical displacement difference.

[0095] Figures 7(a)-7(d) The results show that due to the introduction of the shear stiffness of the joint, the joint forces are buffered, the forces (shear force and bending moment) are weakened, and the smaller the shear stiffness, the smaller the forces (shear force and bending moment), and the greater the allowable vertical deformation capacity. The rotation angle and bending moment show the same trend.

[0096] Figures 8(a)-8(d) The results show that when the bending stiffness of the pipe section increases, under the action of seismic loads, the forces generated along the longitudinal direction of the pipe section cannot dissipate and accumulate at the ends of the pipe section, resulting in an increase in the joint shear force and bending moment and an increase in the joint deformation.

[0097] In the present invention, for the pipe segments and joints, the smaller the force within the allowable range, the better, and the deformation is within the allowable range. Appropriate flexural stiffness of the pipe segments, flexural stiffness of the joints, and shear stiffness of the joints are selected.

[0098] When the deformation of the joint is too large, water leakage may occur. Therefore, the calculation results of the present invention can be used to predict the deformation of the immersed tunnel joints under the action of traveling waves, predict the stress positions where water leakage may occur, and conduct key monitoring and prevention on them.

[0099] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these changes and modifications.

[0100] The above examples are illustrative of the present invention, not restrictive. Any solution obtained by simply transforming the present invention belongs to the protection scope of the present invention.

Claims

1. A method for obtaining the performance of a joint of a immersed tube tunnel considering formation changes under the action of traveling waves, characterized in that, It includes the following steps: Step 1: In the finite element software, establish the first semi-infinite long elastic foundation beam and the second semi-infinite long elastic foundation beam. The first semi-infinite long elastic foundation beam is located in soil layer I, and the second semi-infinite long elastic foundation beam is located in soil layer II; Step 2: Ignore the deformation of the cross-section of the immersed tunnel, regard the pipe joint as an Euler beam model, regard the foundation as a Pasternak foundation model, introduce the displacement phase angle to simulate the traveling wave effect of the earthquake, consider the influence of the traveling wave action on the non-uniform excitation of the pipe joint. The immersed tunnel joint is located at the variable formation interface between soil layer I and soil layer II, and obtain the bending control equation of the immersed tunnel at the variable formation interface related to the flexural stiffness of the pipe joint; Step 3: Use the flexural spring and shear spring to simulate the bending and shearing of the joint, consider the transfer effects of the flexural stiffness and shear stiffness at the joint on the vertical displacement difference, rotation angle, bending moment and shear force, and analyze the change of the peak force of the joint and the influence range of the joint mutation section.

2. The method for obtaining the performance of the immersed tunnel joint considering the formation change under the action of traveling wave according to claim 1, wherein: In step 2, the free field displacement functions acting on soil layer I and soil layer II are: In the formula: \(u(z)_1\) and \(u(z)_2\) are the peak values of the free-field displacements of soil layer Ⅰ and soil layer Ⅱ at a depth of \(z\) meters from the ground surface, respectively; \(\theta\) and \(\lambda\) are the incident angle of the seismic wave and the wavelength of the seismic wave, with the units of rad and m respectively; \(S_1\) and \(S_2\) are the free-field vertical displacements received by soil layer Ⅰ and soil layer Ⅱ, with the unit of m; θ0 is the displacement phase angle of the seismic wave, with the unit of rad; x is the different positions of the immersed tunnel along the longitudinal direction of the structure, with the unit of m; The bending control equation of the immersed tunnel can be expressed as: Where: EI is the flexural stiffness of the pipe joint, with the unit of N·m 2 , P is the interaction force between the immersed tunnel and the formation, with the unit of N, and b is the width of the pipe joint of the immersed tunnel, with the unit of m; w is the deformation of the immersed tunnel, with the unit of m; Simplify the interaction between the soil layer and the immersed tunnel into the reaction force of the foundation compression layer and the shear force of the foundation shear layer. In this case, the interaction force between the soil layer and the immersed tunnel can be expressed as: Where: S is the vertical displacement of the free field, with the unit of m; K h is the coefficient of subgrade elastic resistance, with the unit of Pa; The calculation of the foundation elastic resistance coefficient can be expressed as: Where: ρ s and v are the density and Poisson's ratio of the foundation respectively, and the unit of density is kg / m 3 , and H is the height of the immersed tunnel, with the unit of m; λ is the wavelength of seismic waves, with the unit of m; V s is the shear wave velocity of soil layer Ⅰ and soil layer Ⅱ, with the unit of m / s; Introduce the displacement phase angle, and the bending control equations of the immersed tunnel in the areas of soil layer I and soil layer II are: where: K h1 and K h2 are the foundation elastic resistance coefficients of soil layer Ⅰ and soil layer Ⅱ respectively, with the unit of Pa; G1 and G2 are the foundation shear coefficients of soil layer Ⅰ and soil layer Ⅱ respectively, with the unit of Pa.

3. The method for obtaining the performance of the immersed tunnel joint considering the formation change under the action of traveling wave according to claim 1, wherein: Use the generalized reaction displacement method to analyze the force and deformation of the immersed tunnel joint. The rotation angle and vertical displacement difference at the immersed tunnel joint can be expressed as: Δψ = M Ⅰ / k w (6) Δw = Q Ⅰ / k j (7) where: k w and k j are the flexural stiffness and shear stiffness at the joint respectively, M Ⅰ and Q Ⅰ are the bending moment and shear force of the previous pipe segment near the joint respectively; Define the position of the joint at the variable formation interface as the coordinate origin, the longitudinal direction of the pipe joint as the x-axis, and the vertical direction along the formation as the y-axis. The continuity conditions of the force and deformation at the joint are: Through the matrix transfer principle, the vertical displacement difference, rotation angle, bending moment and shear force at the immersed tunnel joint in different formation sections can be calculated.

4. The method for obtaining the performance of the immersed tunnel joint considering the formation change under the action of traveling wave according to claim 3, wherein: Select the optimal deformation and force solutions according to the vertical displacement difference, rotation angle, bending moment and shear force at the immersed tunnel joint in different formation sections.

5. The method for obtaining the performance of the immersed tunnel joint considering the formation change under the action of traveling wave according to claim 1, wherein: In step 1, the finite element software is ABAQUS.

6. The method for obtaining the performance of the immersed tunnel joint considering the formation change under the action of traveling wave according to claim 1, wherein: In step 2 and step 3, use Matlab software to write a program and assign reasonable characteristic parameters to soil layer I and soil layer II, the pipe joint and the joint, and the earthquake.

7. The method for obtaining the performance of the immersed tunnel joint considering the formation change under the action of traveling waves according to claim 1, wherein: For the pipe segment and the joint, the smaller the force within the allowable range is, the better, and the deformation is within the allowable range, and appropriate flexural stiffness of the pipe segment, flexural stiffness of the joint and shear stiffness of the joint are selected.

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