Earthquake response analysis method for stratified site shield tunnel

Abstract

The invention relates to a stratified site shield tunnel earthquake response analysis method, and relates to the technical field of shield tunnel earthquake resistance numerical simulation. The method comprises the following steps: S1, intercepting a calculation area meeting an anti-seismic specification requirement, and establishing a numerical model of a shield tunnel and a stratified stratum; s2, calculating viscoelastic boundary parameters, amplitude change coefficients and time delay of each stratum; s3, selecting an incident seismic wave, obtaining free field motion of a layered field, and calculating an equivalent node load of a viscoelastic boundary of the model; and S4, applying viscoelastic boundary and equivalent node load to the model, and calculating the seismic response of the shield tunnel. The seismic oscillation input method combining the viscoelastic boundary with the equivalent load is adopted, and effective support can be provided for safety analysis of the stratified site shield tunnel under the earthquake action according to the traveling wave effect of seismic waves and the transmission and reflection characteristics of the seismic waves in different stratified media.

Description

Technical Field

[0001] The invention relates to the technical field of shield tunnel seismic numerical simulation, and in particular to a layered site shield tunnel seismic response analysis method. Background Art

[0002] The shield method has the characteristics of fast construction, good technical and economic efficiency, and little impact from the external environment. It is currently widely used in tunnel construction. As an important infrastructure, the safety and stability of urban shield tunnels during construction and service are crucial. Among them, the impact of earthquakes on shield tunnels cannot be ignored. The seismic response analysis of shield tunnels involves issues such as ground motion input and soil-structure dynamic interaction. Therefore, analytical and experimental methods have great limitations in studying the seismic performance of shield tunnels. Numerical methods have strong versatility and reliability, and the factors that can be considered are relatively comprehensive, which can effectively solve the seismic response problem of shield tunnels in actual projects.

[0003] At present, relevant scholars have conducted some useful research on the seismic effects of shield tunnels under the incidence of P waves and S waves, but most of these studies are based on the situation that the shield tunnel site is a homogeneous stratum. In actual engineering, the site strata often present a complex layered distribution. The propagation of seismic waves in layered sites is much more complicated than that in homogeneous sites. It is necessary to consider not only the absorption and elastic recovery capacity of scattered waves in semi-infinite space, but also the transreflection effect between different layers.

[0004] Therefore, the current research method, which treats the shield tunnel site as a single homogeneous soil layer for seismic response analysis, is quite different from engineering practice. Summary of the invention

[0005] In view of the technical problems existing in the prior art, the purpose of the present invention is to provide a method for analyzing the seismic response of a shield tunnel in a layered site, so as to solve the problem that the current research method regards the shield tunnel site as a single homogeneous soil layer and produces large differences when conducting seismic responses.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A method for analyzing seismic response of a shield tunnel in a layered site comprises the following steps:

[0008] S1. Intercept the calculation area that meets the requirements of the seismic code and establish the numerical model of the shield tunnel and layered strata;

[0009] S2, calculating the viscoelastic boundary parameters, amplitude variation coefficient and time delay of each layer;

[0010] S3, select the incident seismic wave, obtain the free field motion of the layered site, and calculate the equivalent nodal loads of the viscoelastic boundaries of the model;

[0011] S4. Apply viscoelastic boundary and equivalent nodal loads to the model and calculate the seismic response of the shield tunnel.

[0012] As a preferred embodiment, in step S1, a numerical model of the shield tunnel and the layered strata is established by numerical simulation software;

[0013] The seismic code requires that the bottom boundary and side boundary of the numerical model should be no less than 3 times the diameter of the shield tunnel.

[0014] As a preferred embodiment, step S2 specifically includes:

[0015] A pressure load of 1Pa is applied to the bottom and side boundaries of the numerical model, and the normal displacement of the bottom and side boundaries is constrained. The node reaction force of the bottom and side boundaries of the numerical model is extracted. The value of the node reaction force is the equivalent area of ​​the corresponding boundary node.

[0016] The numerical model discretizes the calculation area into several grids. The points connecting the grids are called nodes, and the points connecting the boundary grids are called boundary nodes.

[0017] The equivalent area Substitute into the calculation formula of viscoelastic boundary coefficient:

[0018] Normal:

[0019] Tangential:

[0020] In the formula, and are the normal spring stiffness and tangential spring stiffness of the fth layer respectively; and are the normal damping coefficient and tangential damping coefficient of the fth layer respectively; α N and α T are the normal correction coefficient and tangential correction coefficient of the viscoelastic boundary, α N The recommended value is 1, T The recommended value is 0.5; G f and ρ f are the shear modulus and density of the f-th layer of soil medium respectively; and are the wave velocities of the P wave and S wave of the fth layer respectively; R is the distance from the scattered wave source to the bottom boundary node and the side boundary node, let R be a constant;

[0021] Calculate the amplitude variation coefficient for each layer as follows:

[0022] When f>1,

[0023]

[0024] When f = 1,

[0025]

[0026] In the formula, and are the amplitude variation coefficients of the transmitted S-wave and reflected S-wave of the f-th layer respectively; and are the amplitude variation coefficients of the transmitted P wave and reflected P wave of the fth layer respectively; ρ j is the density of the j-th layer of soil medium; and are the wave velocities of the P wave and S wave at the jth layer, respectively;

[0027] Calculate the time delay for each layer as follows:

[0028] When f>1,

[0029]

[0030] When f = 1,

[0031]

[0032] In the formula, and are the arrival times of the incident S-wave and the reflected S-wave at node l, respectively; and are the time when the incident P wave and the reflected P wave arrive at node l respectively; d f is the distance from node l to the bottom of layer f; h f is the thickness of the fth layer; h j is the thickness of the jth layer;

[0033] The spring stiffness, damping coefficient, amplitude variation coefficient and time delay of each layer are calculated.

[0034] As a preferred embodiment, step S3 specifically includes:

[0035] According to the seismic code, actual recorded seismic waves and artificial simulated seismic waves are selected, and the number of actual recorded seismic waves should not be less than 2 / 3 of the total number;

[0036] The selected actual recorded seismic waves are amplitude modulated according to the amplitude specified in the seismic code;

[0037] Taking the time when the seismic wave propagates to the bottom of the numerical model as time zero, combined with the amplitude variation coefficient and time delay calculated in step S2, the displacement time history of the bottom boundary node and the side boundary node under the action of the incident seismic wave, the transmitted wave and the reflected wave is obtained, and the free field displacement time history of the bottom boundary node and the side boundary node can be obtained by superimposing the three;

[0038] The free field velocity time history of the boundary node can be obtained by differentiating the free field displacement time history of the boundary node. According to the theory of elastic mechanics, the free field stress of the bottom boundary node and the side boundary node can be obtained.

[0039] Substitute the viscoelastic boundary parameters obtained in step S2 and the free field velocity time history and free field stress of the boundary nodes into the calculation formula of the viscoelastic boundary equivalent node load:

[0040]

[0041] Where: F l (t) is the equivalent nodal load at the viscoelastic boundary node l; K l and C l are the spring stiffness and damping coefficient at node l; u l (x l ,z l ,t) and are the displacement and velocity at node l respectively; σ l (x l ,z l ,t) is the free field stress at node l; x l and z l are the coordinates of node l;

[0042] The equivalent nodal loads of the viscoelastic boundaries are calculated.

[0043] As a preferred embodiment, step S3 specifically includes:

[0044] Combined with the spring stiffness and damping coefficient obtained in step S2 and the equivalent node load obtained in step S3, a command stream format file for generating a new viscoelastic boundary and applying an equivalent node load is exported according to the command stream format of the numerical software;

[0045] The command stream format file exported through the above steps is used to batch apply viscoelastic boundary and equivalent node loads to the bottom and side boundaries of the numerical model, and the seismic response of the shield tunnel is calculated.

[0046] In general, the present invention has the following advantages:

[0047] Based on the propagation law of seismic waves in layered sites, the present invention adopts a simplified seismic input method combining viscoelastic boundaries with equivalent loads to simulate the seismic response of shield tunnels in layered sites, solving the problem that the existing method produces large differences when treating the shield tunnel site as a single homogeneous soil layer for seismic response. The method is applicable to two-dimensional plane problems, can simulate the traveling wave effect of seismic waves and their transmission and reflection characteristics in different layered media, considers the first reflection process of the incident wave at the interface of different media, ignores the subsequent reflection and transmission propagation process, reduces the use of parameters on the subsequent transmission and reflection propagation path, and quickly obtains the amplitude variation coefficient and time delay of each layer of stratum. The method can limit the calculation area to the near-field local area of ​​the shield tunnel and its surrounding sites, without paying attention to the far-field source and seismic wave propagation information, is easy to implement in numerical simulation software, can effectively improve the calculation efficiency, and quickly obtain the seismic response of the shield tunnel in the layered site, which has strong practicality.

[0048] In the above-mentioned analysis method of seismic response of shield tunnel in layered site, the parameters of shield tunnel and stratum can be changed according to engineering requirements or research requirements, such as geometric dimensions, burial depth, thickness and softness of stratum of shield tunnel. The seismic response law of shield tunnel in layered site is summarized, which provides effective support for the safety analysis of shield tunnel in layered site under earthquake action, and provides a certain reference basis for the seismic safety evaluation and anti-seismic reduction measures research of shield tunnel in layered site. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a schematic diagram of the seismic wave incident shield tunnel-layered site model.

[0050] Figure 2 is a schematic diagram of a viscoelastic boundary.

[0051] Figure 3 It is a schematic diagram of the incidence, reflection and transmission of P waves and S waves. DETAILED DESCRIPTION

[0052] The present invention will be further described in detail below in conjunction with specific implementation methods.

[0053] like Figure 1-Figure 3 As shown, this embodiment provides a method for analyzing seismic response of a shield tunnel in a layered site, comprising the following steps:

[0054] S1. Intercept the calculation area that meets the requirements of the seismic code and establish the numerical model of the shield tunnel and layered strata;

[0055] S2, calculating the viscoelastic boundary parameters, amplitude variation coefficient and time delay of each layer;

[0056] S3, select the incident seismic wave, obtain the free field motion of the layered site, and calculate the equivalent nodal loads of the viscoelastic boundaries of the model;

[0057] S4. Apply viscoelastic boundary and equivalent nodal loads to the model and calculate the seismic response of the shield tunnel.

[0058] Application examples:

[0059] This embodiment provides a method for analyzing seismic response of a shield tunnel in a layered site. Taking the large-scale commercial finite element software ABAQUS as an example, the specific analysis process is mainly as follows:

[0060] (1) Establish a finite element model of shield tunnel-layered site based on engineering practice;

[0061] 1. Establish Figure 1 The ABAQUS finite element model is shown. The distance between the bottom boundary and the side boundary of the numerical model and the shield tunnel is not less than 3 times the diameter of the shield tunnel.

[0062] 2. The model grid size is divided according to the analysis accuracy requirements. The grid size density of the shield tunnel part should be set more densely. The maximum grid size in the model should not be greater than 1 / 8 of the minimum wavelength. Four-node plane strain solid units are used for both the shield tunnel and the site strata.

[0063] 3. Select the elastic constitutive model and assign values ​​to the formation parameters and tunnel parameters.

[0064] 4. Set the contact interface between the shield tunnel and the soil as Tie contact, assuming that the displacement of the contact interface between the two is consistent.

[0065] (ii) obtaining the model boundary node information and calculating the viscoelastic boundary parameters, amplitude variation coefficient and time delay of each stratum;

[0066] 1. Establish a static general analysis step, apply a pressure load of 1Pa to the bottom and side boundaries of the numerical model, and constrain the normal displacement of the corresponding boundaries.

[0067] 2. Extract the node reaction forces of the bottom and side boundaries of the numerical model. The value of the node reaction force is the equivalent area of ​​the corresponding bottom and side boundary nodes. And export the node information such as the node number and corresponding coordinates of the bottom boundary and side boundary of the numerical model.

[0068] 3. Based on the derived node information, the viscoelastic boundary spring stiffness, damping coefficient, amplitude variation coefficient and time delay of each layer are calculated.

[0069] Calculate the viscoelastic boundary coefficients, spring stiffness, and damping coefficients as follows:

[0070] Normal:

[0071] Tangential:

[0072] In the formula, and are the normal spring stiffness and tangential spring stiffness of the fth layer respectively; and are the normal damping coefficient and tangential damping coefficient of the fth layer respectively; α N and α T are the normal correction coefficient and tangential correction coefficient of the viscoelastic boundary, α N The recommended value is 1, T The recommended value is 0.5; G f and ρ f are the shear modulus and density of the f-th layer of soil medium respectively; and are the wave velocities of the P wave and S wave of the fth layer respectively; R is the distance from the scattered wave source to the bottom boundary node and the side boundary node, and R is set to be a constant.

[0073] Depend on Figure 3 It can be seen that the incident P wave and S wave will generate transmission waves and reflection waves at the interface of different layered media. The amplitude variation coefficient of each layer is calculated by the following formula:

[0074] When f>1,

[0075]

[0076] When f = 1,

[0077]

[0078] In the formula, and are the amplitude variation coefficients of the transmitted S-wave and reflected S-wave of the f-th layer respectively; and are the amplitude variation coefficients of the transmitted P wave and reflected P wave of the fth layer respectively; ρ j is the density of the j-th layer of soil medium; and are the speeds of P-wave and S-wave in the jth layer respectively.

[0079] Calculate the time delay for each layer as follows:

[0080] When f>1,

[0081]

[0082] When f = 1,

[0083]

[0084] In the formula, and are the arrival times of the incident S-wave and the reflected S-wave at node l, respectively; and are the time when the incident P wave and the reflected P wave arrive at node l respectively; d f is the distance from node l to the bottom of layer f; h f is the thickness of the fth layer; h j is the thickness of the jth layer.

[0085] (iii) Obtain the free wave fields of the bottom boundary nodes and side boundary nodes and calculate the earthquake equivalent node loads;

[0086] 1. Based on the project site, the Kobe wave is selected as the incident seismic wave, and the Kobe wave is filtered and amplitude modulated according to the seismic fortification level.

[0087] 2. Taking the time when the seismic wave propagates to the bottom of the numerical model as time zero, after obtaining the amplitude change coefficient and time delay of each layer, the displacement time history of the bottom boundary node and the side boundary node under the action of the incident seismic wave, the transmitted wave and the reflected wave can be obtained, and the three are superimposed to obtain the free field displacement time history of the bottom boundary node and the side boundary node.

[0088] 3. The free field velocity time history of the bottom boundary node and the side boundary node can be obtained by differentiating the free field displacement time history of the bottom boundary node and the side boundary node. According to the theory of elastic mechanics, the free field stress of the bottom boundary node and the side boundary node can be obtained.

[0089] 3. Substitute the equivalent node area, viscoelastic boundary parameters, node displacement, node velocity and node stress obtained in the above steps into the following formula to calculate the seismic equivalent node load of the boundary;

[0090]

[0091] Where: F l (t) is the equivalent nodal load at the viscoelastic boundary node l; K l and C l are the spring stiffness and damping coefficient at node l; u l (x l ,z l ,t) and are the displacement and velocity at node l respectively; σ l (x l ,z l ,t) is the free field stress at node l; x l and z l are the coordinates of node l.

[0092] (iv) Apply viscoelastic boundary and equivalent nodal loads to calculate the seismic response of the shield tunnel;

[0093] 1. Combine the spring stiffness and damping coefficient obtained in step (ii) and the equivalent node load obtained in step (iii), and export the inp file for adding grounded springs / dashpots and the inp file for applying equivalent node loads according to the inp file format of ABAQUS software.

[0094] 2. Establish an implicit dynamic analysis step, set the output results and frequency in advance, remove the boundary conditions and loads in the original model, and output the implicit dynamic analysis inp file at this time.

[0095] 3. Use the Include keyword to reference the inp file for adding grounding springs / dashpots and the inp file for applying equivalent node loads exported in the above steps in the output implicit dynamic analysis inp file, apply viscoelastic boundaries and equivalent node loads to the bottom and side boundaries of the numerical model in batches, and calculate the seismic response of the shield tunnel.

[0096] The present invention provides a method for analyzing the seismic response of a shield tunnel in a layered site, which converts the seismic input of the layered site into an equivalent node load based on a viscoelastic boundary. The method is applicable to two-dimensional plane problems, and can simulate the traveling wave effect of seismic waves and their transmission and reflection characteristics in different layered media, providing effective support for the safety analysis of shield tunnels in layered sites under earthquakes, and providing a certain reference basis for the seismic safety evaluation of shield tunnels in layered sites and the study of anti-seismic measures.

[0097] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A method for analyzing seismic response of a shield tunnel in a layered site, characterized in that: The following steps are involved: S1. Intercept the calculation area that meets the requirements of the seismic code and establish the numerical model of the shield tunnel and layered strata; S2, calculating the viscoelastic boundary parameters, amplitude variation coefficient and time delay of each layer; S3, select the incident seismic wave, obtain the free field motion of the layered site, and calculate the equivalent nodal loads of the viscoelastic boundaries of the model; S4. Apply viscoelastic boundary and equivalent nodal loads to the model and calculate the seismic response of the shield tunnel.

2. A method for analyzing seismic response of a shield tunnel in a layered site according to claim 1, characterized in that: In step S1, a numerical model of the shield tunnel and the layered strata is established by numerical simulation software; The seismic code requires that the bottom boundary and side boundary of the numerical model should be no less than 3 times the diameter of the shield tunnel.

3. A method for analyzing seismic response of a shield tunnel in a layered site according to claim 1, characterized in that: Step S2 specifically includes: A pressure load of 1Pa is applied to the bottom and side boundaries of the numerical model, and the normal displacement of the bottom and side boundaries is constrained. The node reaction force of the bottom and side boundaries of the numerical model is extracted. The value of the node reaction force is the equivalent area of ​​the corresponding boundary node. The numerical model discretizes the calculation area into several grids. The points connecting the grids are called nodes, and the points connecting the boundary grids are called boundary nodes. The equivalent area Substitute into the calculation formula of viscoelastic boundary coefficient: Normal: Tangential: In the formula, and are the normal spring stiffness and tangential spring stiffness of the fth layer respectively; and are the normal damping coefficient and tangential damping coefficient of the fth layer respectively; α N and α T are the normal correction coefficient and tangential correction coefficient of the viscoelastic boundary, α N The recommended value is 1, T The recommended value is 0.5; G f and ρ f are the shear modulus and density of the f-th layer of soil medium respectively; and are the wave velocities of the P wave and S wave of the fth layer respectively; R is the distance from the scattered wave source to the bottom boundary node and the side boundary node, let R be a constant; Calculate the amplitude variation coefficient for each layer as follows: When f>1, When f = 1, In the formula, and are the amplitude variation coefficients of the transmitted S-wave and reflected S-wave of the f-th layer respectively; and are the amplitude variation coefficients of the transmitted P wave and reflected P wave of the fth layer respectively; ρ j is the density of the j-th layer of soil medium; and are the wave velocities of the P wave and S wave at the jth layer, respectively; Calculate the time delay for each layer as follows: When f>1, When f = 1, In the formula, and are the arrival times of the incident S-wave and the reflected S-wave at node l, respectively; and are the time when the incident P wave and the reflected P wave arrive at node l respectively; d f is the distance from node l to the bottom of layer f; h f is the thickness of the fth layer; h j is the thickness of the jth layer; The spring stiffness, damping coefficient, amplitude variation coefficient and time delay of each layer are calculated.

4. A method for analyzing seismic response of a shield tunnel in a layered site according to claim 3, characterized in that: Step S3 specifically includes: According to the seismic code, actual recorded seismic waves and artificial simulated seismic waves are selected, and the number of actual recorded seismic waves should not be less than 2 / 3 of the total number; The selected actual recorded seismic waves are amplitude modulated according to the amplitude specified in the seismic code; Taking the time when the seismic wave propagates to the bottom of the numerical model as time zero, combined with the amplitude variation coefficient and time delay calculated in step S2, the displacement time history of the bottom boundary node and the side boundary node under the action of the incident seismic wave, the transmitted wave and the reflected wave is obtained, and the free field displacement time history of the bottom boundary node and the side boundary node can be obtained by superimposing the three; The free field velocity time history of the boundary node can be obtained by differentiating the free field displacement time history of the boundary node. According to the theory of elastic mechanics, the free field stress of the bottom boundary node and the side boundary node can be obtained. Substitute the viscoelastic boundary parameters obtained in step S2 and the free field velocity time history and free field stress of the boundary nodes into the calculation formula of the viscoelastic boundary equivalent node load: Where: F l (t) is the equivalent nodal load at the viscoelastic boundary node l; K l and C l are the spring stiffness and damping coefficient at node l; u l (x l ,z l ,t) and are the displacement and velocity at node l respectively; σ l (x l ,z l ,t) is the free field stress at node l; x l and z l are the coordinates of node l; The equivalent nodal loads of the viscoelastic boundaries are calculated.

5. A method for analyzing seismic response of a shield tunnel in a layered site according to claim 3, characterized in that: Step S3 specifically includes: Combined with the spring stiffness and damping coefficient obtained in step S2 and the equivalent node load obtained in step S3, a command stream format file for generating a new viscoelastic boundary and applying an equivalent node load is exported according to the command stream format of the numerical software; The command stream format file exported through the above steps is used to batch apply viscoelastic boundary and equivalent node loads to the bottom and side boundaries of the numerical model, and the seismic response of the shield tunnel is calculated.

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