A layered site shield tunnel seismic response analysis method

Abstract

The present application relates to a kind of layered site shield tunnel earthquake response analysis method, it is related to shield tunnel aseismatic numerical simulation technical field.The method includes the following steps: S1, intercepting the calculation area in line with the requirement of aseismic specification, the numerical model of shield tunnel and layered stratum is established;S2, the viscoelastic boundary parameter of each layer stratum, amplitude variation coefficient and time delay are calculated;S3, selected incident seismic wave, obtains the free field motion of layered site, calculates the equivalent node load of model viscoelastic boundary;S4, to model, applies viscoelastic boundary and equivalent node load, calculates the seismic response of shield tunnel.The present application adopts the seismic motion input method of equivalent load of viscoelastic boundary, can according to the travel effect of seismic wave and its transmission and reflection characteristics in different layered medium, provides effective support for the safety analysis of layered site shield tunnel under earthquake action.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology for seismic resistance of shield tunnels, and specifically to a method for analyzing the seismic response of shield tunnels in layered sites. Background Technology

[0002] Shield tunneling, with its advantages of rapid construction, good technical and economic efficiency, and minimal susceptibility to external environmental influences, is widely used in tunnel construction. As a crucial infrastructure, the safety and stability of urban shield tunnels during construction and service are paramount, with the impact of seismic forces being particularly significant. Seismic response analysis of shield tunnels involves issues such as seismic input and soil-structure dynamic interaction; therefore, analytical and experimental methods have significant limitations in studying the seismic performance of shield tunnels. Numerical methods, on the other hand, offer greater versatility and reliability, and can consider a wider range of factors, effectively addressing the seismic response issues of shield tunnels in practical engineering projects.

[0003] Currently, scholars have conducted some useful studies on the seismic effects of P-waves and S-waves on shield tunnels. However, most of these studies are based on the assumption that the shield tunnel site is a homogeneous stratum. In actual engineering projects, the strata of the site often exhibit a complex layered distribution. The propagation of seismic waves in layered sites is much more complex than in homogeneous sites. It is necessary to consider not only the absorption and elastic recovery capabilities of scattered waves in semi-infinite space, but also the transmission and reflection effects between different layers.

[0004] Therefore, current research methods that treat shield tunnel sites as a single homogeneous soil layer for seismic response analysis differ significantly from actual engineering practices. Summary of the Invention

[0005] To address the technical problems existing in the prior art, the purpose of this invention is to provide a seismic response analysis method for shield tunnels in layered sites, thereby solving the problem that current research methods treat shield tunnel sites as a single homogeneous soil layer when conducting seismic response analysis, resulting in significant differences.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for seismic response analysis of shield tunnels in layered sites includes the following steps:

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

[0009] S2. Calculate the viscoelastic boundary parameters, amplitude variation coefficient, and time delay for each stratum;

[0010] S3. Select the incident seismic wave, obtain the free field motion of the layered site, and calculate the equivalent nodal load of the viscoelastic boundary of the model.

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

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

[0013] The seismic design code requires that the distance between the bottom boundary and the side boundary of the numerical model and the shield tunnel should not be less than 3 times the diameter of the shield tunnel.

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

[0015] A pressure load of 1 Pa is applied to the bottom and side boundaries of the numerical model, and the normal displacements of the bottom and side boundaries are constrained. The nodal reactions at the bottom and side boundaries of the numerical model are extracted, and the values ​​of the nodal reactions are the equivalent areas of the corresponding boundary nodes.

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

[0017] Equivalent area Substitute into the viscoelastic boundary coefficient calculation formula:

[0018] Normal direction:

[0019] Tangential:

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

[0021] The amplitude variation coefficient for each stratum is calculated as follows:

[0022] When f > 1

[0023]

[0024] When f = 1

[0025]

[0026] In the formula, and These are the amplitude variation coefficients of the transmitted S-wave and the reflected S-wave in the f-th layer, respectively. and These are the amplitude variation coefficients for the transmitted P-wave and the reflected P-wave at the f-th layer, respectively; ρ j It is the density of the j-th soil layer; and These are the wave velocities of the P-wave and S-wave in the j-th layer, respectively.

[0027] The time delay for each formation is calculated as follows:

[0028] When f > 1

[0029]

[0030] When f = 1

[0031]

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

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

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

[0035] According to the seismic design code, actual recorded seismic waves and artificially simulated seismic waves should be selected, with the number of actual recorded seismic waves not less than 2 / 3 of the total.

[0036] The selected actual recorded seismic waves will be amplitude-modulated according to the amplitude specified in the seismic design code.

[0037] Taking the time when the seismic wave reaches the bottom of the numerical model as zero, and combining the amplitude variation coefficient and time delay calculated in step S2, the displacement time histories of the bottom boundary node and the side boundary node under the action of incident seismic wave, transmitted wave and reflected wave are obtained. The free field displacement time histories of the bottom boundary and the side boundary node can be obtained by superimposing the three.

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

[0039] Substitute the viscoelastic boundary parameters, free field velocity time history, and free field stress obtained in step S2 into the formula for calculating the equivalent nodal load of the viscoelastic boundary:

[0040]

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

[0042] The equivalent nodal load of the viscoelastic boundary is calculated.

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

[0044] Combining the spring stiffness and damping coefficient obtained in step S2 and the equivalent nodal load obtained in step S3, export the command stream format file for creating a new viscoelastic boundary and applying the equivalent nodal load according to the numerical software command stream format.

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

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

[0047] This invention, based on the propagation characteristics of seismic waves in layered sites, employs a simplified seismic motion input method combining viscoelastic boundaries and equivalent loads to simulate the seismic response of shield tunnels in layered sites. This solves the problem of significant differences in seismic response when existing methods treat the shield tunnel site as a single homogeneous soil layer. This 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. It considers the first reflection process at the interface between different media, ignoring subsequent reflection and transmission propagation processes, thus reducing the use of parameters on subsequent transmission and reflection propagation paths and enabling rapid acquisition of amplitude variation coefficients and time delays for each stratum. This method limits the computational domain to the near-field local area of ​​the shield tunnel and its surrounding site, without needing to consider far-field sources and seismic wave propagation information. This facilitates implementation in numerical simulation software, effectively improving computational efficiency and rapidly obtaining the seismic response of shield tunnels in layered sites, making it highly practical.

[0048] In the aforementioned seismic response analysis method for shield tunnels in layered sites, the shield tunnel parameters and stratum parameters can be modified according to engineering or research needs, such as the shield tunnel's geometric dimensions, burial depth, stratum thickness, and degree of weakness. Summarizing the seismic response patterns of shield tunnels in layered sites provides effective support for the safety analysis of shield tunnels in layered sites under seismic loading, and offers a certain reference for the seismic safety evaluation and seismic mitigation measures research of shield tunnels in layered sites. Attached Figure Description

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

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

[0051] Figure 3 This is a schematic diagram of the incident, reflection, and transmission of P-waves and S-waves. Detailed Implementation

[0052] The present invention will now be described in further detail with reference to specific embodiments.

[0053] like Figures 1-3 As shown in the figure, this embodiment provides a method for seismic response analysis of shield tunnels in layered sites, which includes the following steps:

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

[0055] S2. Calculate the viscoelastic boundary parameters, amplitude variation coefficient, and time delay for each stratum;

[0056] S3. Select the incident seismic wave, obtain the free field motion of the layered site, and calculate the equivalent nodal load of the viscoelastic boundary of the model.

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

[0058] Application examples:

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

[0060] (I) Establishing a finite element model of shield tunnel-layered site based on actual engineering conditions;

[0061] 1. Establish such Figure 1 The ABAQUS finite element model shown is provided. The bottom and side boundaries of the numerical model are at least three times the diameter of the shield tunnel.

[0062] 2. The model mesh size is determined according to the required analysis accuracy. The mesh density for the shield tunnel section should be refined, and the maximum mesh size in the model should not exceed 1 / 8 of the minimum wavelength. Four-node plane strain solid elements are used for both the shield tunnel and the site strata.

[0063] 3. Select an 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 a Tie contact, assuming that the displacement of the two contact interfaces is the same.

[0065] (ii) Obtain model boundary node information and calculate 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 1 Pa to the bottom boundary and side boundary of the numerical model respectively, and constrain the normal displacement of the corresponding boundary.

[0067] 2. Extract the nodal reactions at the bottom and side boundaries of the numerical model. The values ​​of the nodal reactions are the equivalent areas of the corresponding bottom and side boundary nodes. The node information, including node numbers and corresponding coordinates, of the bottom and side boundaries of the numerical model is exported.

[0068] 3. Based on the exported node information, calculate the viscoelastic boundary spring stiffness, damping coefficient, amplitude variation coefficient, and time delay for each stratum.

[0069] The viscoelastic boundary coefficients, spring stiffness, and damping coefficients are calculated as follows:

[0070] Normal direction:

[0071] Tangential:

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

[0073] Depend on Figure 3 It is known that incident P-waves and S-waves will generate transmitted and reflected waves at the interfaces of different layered media. The amplitude variation coefficient of each stratum is calculated by the following formula:

[0074] When f > 1

[0075]

[0076] When f = 1

[0077]

[0078] In the formula, and These are the amplitude variation coefficients of the transmitted S-wave and the reflected S-wave in the f-th layer, respectively. and These are the amplitude variation coefficients for the transmitted P-wave and the reflected P-wave at the f-th layer, respectively; ρ j It is the density of the j-th soil layer; and These are the wave velocities of the P-wave and S-wave at the j-th layer, respectively.

[0079] The time delay for each formation is calculated as follows:

[0080] When f > 1

[0081]

[0082] When f = 1

[0083]

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

[0085] (iii) Obtain the free wave field of the bottom boundary node and the side boundary node, and calculate the seismic equivalent nodal load;

[0086] 1. Based on the engineering site, 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 reaches the bottom of the numerical model as the zero time, after obtaining the amplitude variation coefficient and time delay of each stratum, the displacement time histories of the bottom boundary node and the side boundary node under the action of incident seismic wave, transmitted wave and reflected wave can be obtained. The three are superimposed to obtain the free field displacement time histories of the bottom boundary node and the side boundary node.

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

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

[0090]

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

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

[0093] 1. Combining the spring stiffness and damping coefficient obtained in step (II) and the equivalent nodal load obtained in step (III), export the inp file for adding grounding Springs / dashpots and the inp file for applying equivalent nodal loads according to the inp file format of ABAQUS software.

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

[0095] 3. Using the Include keyword, reference the .p files exported in the above steps that add grounding Springs / dashpots and apply equivalent nodal loads in the output implicit dynamic analysis .p files. Apply viscoelastic boundaries and equivalent nodal loads to the bottom and side boundaries of the numerical model in batches, and calculate the seismic response of the shield tunnel.

[0096] This invention provides a method for seismic response analysis of shield tunnels in layered sites, converting the seismic motion input of the layered site into equivalent nodal loads based on viscoelastic boundaries. This 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. It provides effective support for the safety analysis of shield tunnels in layered sites under seismic loading and offers a certain reference for the seismic safety evaluation and seismic mitigation measures research of shield tunnels in layered sites.

[0097] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for seismic response analysis of shield tunnels in layered sites, characterized in that, Includes the following steps: S1. Extract the calculation area that meets the requirements of the seismic code and establish a numerical model of the shield tunnel and layered strata; In step S1, a numerical model of the shield tunnel and layered strata is established using numerical simulation software; The seismic design code requires that the distance between the bottom boundary and the side boundary of the numerical model and the shield tunnel should not be less than 3 times the diameter of the shield tunnel. S2. Calculate the viscoelastic boundary parameters, amplitude variation coefficient, and time delay for each stratum; S3. Select the incident seismic wave, obtain the free field motion of the layered site, and calculate the equivalent nodal load of the viscoelastic boundary of the model. Step S3 specifically includes: According to the requirements of the seismic design code, actual recorded seismic waves and artificially simulated seismic waves shall be selected, with the number of actual recorded seismic waves not less than 2 / 3 of the total. The actual recorded seismic waves selected will be amplitude-modulated according to the amplitude specified in the seismic design code. Taking the time when the seismic wave reaches the bottom of the numerical model as zero, and combining the amplitude variation coefficient and time delay calculated in step S2, the displacement time histories of the bottom boundary node and the side boundary node under the action of incident seismic wave, transmitted wave and reflected wave are obtained. The free field displacement time histories of the bottom boundary and the side boundary node can be obtained by superimposing the three. The free field velocity time history of the boundary nodes can be obtained by differentiating the free field displacement time history of the boundary nodes. According to the theory of elasticity, the free field stress of the bottom boundary node and the side boundary node can be obtained. Substitute the viscoelastic boundary parameters, free field velocity time history, and free field stress obtained in step S2 into the formula for calculating the equivalent nodal load of the viscoelastic boundary: In the formula: F l (t) represents the equivalent nodal load at the viscoelastic boundary node l; K l and C l These are the spring stiffness and damping coefficient at node l, respectively; u l (x l ,z l ,t) and These are the displacement and velocity at node l, respectively; σ l (x l ,z l ,t) represents the free field stress at node l; x l and z l These are the coordinates of node l; The equivalent nodal loads of the viscoelastic boundary are calculated. S4. Apply viscoelastic boundary conditions and equivalent nodal loads to the model and calculate the seismic response of the shield tunnel.

2. The seismic response analysis method for shield tunnels in layered sites according to claim 1, characterized in that, Step S2 specifically includes: A pressure load of 1 Pa is applied to the bottom and side boundaries of the numerical model, and the normal displacements of the bottom and side boundaries are constrained. The nodal reactions at the bottom and side boundaries of the numerical model are extracted, and the values ​​of the nodal reactions are the equivalent areas of the corresponding boundary nodes. The numerical model discretizes the computational domain into several grids. The points connecting the grids are called nodes, and the points connecting the boundary grids are called boundary nodes. Equivalent area Substitute into the viscoelastic boundary coefficient calculation formula: Normal direction: Tangential: In the formula, and These are the normal spring stiffness and tangential spring stiffness of the f-th layer, respectively; and These are the normal damping coefficient and tangential damping coefficient of the f-th layer, respectively; α N and α T These are the normal and tangential correction factors for the viscoelastic boundary, α. N It is 1, α T It is 0.5; G f and ρ f These are the shear modulus and density of the f-th soil layer, respectively. and , respectively, are the wave velocities of the P-wave and S-wave in the f-th layer; R is the distance from the scattering source to the bottom boundary node and the side boundary node, and R is set to a constant value; The amplitude variation coefficient for each stratum is calculated as follows: When f > 1 When f = 1 In the formula, and These are the amplitude variation coefficients of the transmitted S-wave and the reflected S-wave in the f-th layer, respectively. and These are the amplitude variation coefficients for the transmitted P-wave and the reflected P-wave at the f-th layer, respectively; ρ j It is the density of the j-th soil layer; and These are the wave velocities of the P-wave and S-wave at the j-th layer, respectively. The time delay for each formation is calculated as follows: When f > 1 When f = 1 In the formula, and These are the times when the incident S-wave and the reflected S-wave arrive at node l, respectively; and These are the times when the incident P-wave and the reflected P-wave arrive at node l, respectively; d f h is the distance from node l to the bottom of layer f; f h is the thickness of the f-th layer; j Let j be the thickness of the j-th layer; The spring stiffness, damping coefficient, amplitude variation coefficient, and time delay of each stratum were calculated.

3. The seismic response analysis method for shield tunnels in layered sites according to claim 2, characterized in that, Step S3 specifically includes: Combining the spring stiffness and damping coefficient obtained in step S2 and the equivalent nodal load obtained in step S3, export the command stream format file for creating a new viscoelastic boundary and applying the equivalent nodal load according to the numerical software command stream format. The command stream format file exported through the above steps is used to apply viscoelastic boundary and equivalent nodal loads to the bottom and side boundaries of the numerical model in batches, and the seismic response of the shield tunnel is calculated.

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