A Modeling and Analysis Method for Dynamic Response of Shield Tunneling Bridges Under High-Speed ​​Railway Lines Based on Co-simulation

Abstract

This invention provides a method for modeling and analyzing the dynamic response of a shield tunneling tunnel under a high-speed railway overpass based on co-simulation. The method includes the following steps: S1, establishing a lower shield excavation sub-model and an upper dynamic coupling sub-model; S2, co-simulation calculation: at different excavation steps of the lower shield, calculating the matrix information of displacement, mass, stiffness, damping, and load of each node in the lower shield excavation sub-model at different excavation steps and importing it into the upper dynamic coupling sub-model; then, jointly solving the vibration acceleration, velocity, and displacement of the train system and track system based on the dynamic equations of motion of the train-track system; S3, dynamic performance evaluation and analysis. Using this method, the vibration response state and train dynamic performance of structures such as existing high-speed railway overpasses during shield tunneling can be accurately and quickly analyzed and evaluated, providing a reference for risk research in shield tunneling construction and the safe operation of existing railways.

Description

Technical Field

[0001] This invention belongs to the field of finite element simulation and calculation technology, specifically involving a method for modeling and analyzing the dynamic response of a shield tunneling overpass for high-speed railways based on co-simulation. Background Technology

[0002] With the development of urban rail transit, shield tunnels are increasingly passing under existing high-speed railway overpasses. When shield tunnels pass under existing railway overpasses, they cause a certain degree of ground settlement, leading to deformation of the overpass and track irregularities. This exacerbates the dynamic response problem between the train and the track, reduces the service life of the structure, affects the comfort and stability of train operation, and in severe cases, jeopardizes train safety and endangers passenger lives. Therefore, it is necessary to study the dynamic response characteristics between the train and the track system when shield tunnels pass under existing high-speed railway overpasses, providing a theoretical basis for ensuring the safe and stable operation of trains and the safe construction of shield tunnels.

[0003] Numerical simulation methods are widely used in the study of the impact of tunnel boring machine (TBM) construction. They take into account various factors in the modeling process and can accurately reflect the actual construction situation. However, in the dynamic response simulation of a TBM passing under a high-speed railway overpass, most finite element modeling software often has limitations. They can only consider the upper track-vehicle coupling effect or the lower TBM excavation effect, and cannot comprehensively consider the interaction between TBM construction and train operation. Summary of the Invention

[0004] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a method for modeling and analyzing the dynamic response of shield tunnels passing under high-speed railway overpasses based on co-simulation. This method considers the influence of environmental factors and shield tunneling parameters during shield construction, and also integrates the interaction between the operation of the upper train and the lower shield construction. Using this method, the vibration response status and train dynamic performance of existing high-speed railway overpasses and other structures can be accurately and quickly analyzed and evaluated during the shield tunneling process. This can provide a reference for the risk research of shield tunneling construction and the safe operation of existing railways.

[0005] The present invention is achieved through the following technical solution.

[0006] A method for modeling and analyzing the dynamic response of a shield tunneling bridge under a high-speed railway overpass based on co-simulation is characterized by the following steps:

[0007] S1. Establish the lower shield excavation sub-model and the upper dynamic coupling sub-model: Based on the engineering design data, the lower shield excavation sub-model of the shield tunnel passing under the high-speed railway overpass is established using ABAQUS finite element software; the upper dynamic coupling sub-model of the train-track is established using programming language in MATLAB numerical analysis software.

[0008] S2, Joint simulation calculation: When the lower shield tunneling is excavated to different excavation steps, the displacement, mass, stiffness, damping and load matrix information of each node of the lower shield tunneling sub-model at different excavation steps are calculated and imported into the upper dynamic coupling sub-model. Then, the vibration acceleration, velocity and displacement of the train system and the track system are jointly solved based on the dynamic motion equation of the vehicle-track system.

[0009] S3, Dynamic Performance Evaluation and Analysis: Based on the joint solution results of step S2, evaluate and analyze the train's operational safety and stability as well as its structural dynamic response.

[0010] As a specific technical solution, step S1, establishing the lower shield excavation sub-model includes the following steps: establishing a geometric model, assigning material properties, adding loads and boundary conditions, simulating shield excavation, and meshing the model.

[0011] As a specific technical solution, step S1, establishing the lower shield excavation sub-model, includes the following steps:

[0012] S11, Establish a geometric model: Determine the size of the lower shield excavation sub-model based on the engineering design data and the influence range of shield construction. The lower shield excavation sub-model includes the high-speed railway overpass, the stratum and the shield tunnel from top to bottom. The shield tunnel includes the segments, shield shell and grouting layer from the inside to the outside.

[0013] S12, assigning material properties: the Mohr-Coulomb constitutive model is used for the stratum material, and the linear elastic constitutive model is used for the high-speed railway overpass and shield tunnel material.

[0014] S13, Add loads and boundary conditions: Apply gravity loads to the model, constrain its horizontal displacement around the model, constrain its vertical displacement at the bottom, and apply a uniformly distributed load on the upper surface of the piers that is equivalent to the weight of the superstructure of the high-speed railway overpass.

[0015] S14, Shield excavation simulation: The shield excavation simulation is implemented using the birth and death element method in ABAQUS software;

[0016] S15, Model Mesh Generation: The shield shell uses S4R shell element type, while the high-speed railway overpass, strata, segments and grouting layer use C3D8R hexahedral linear elements.

[0017] As a specific technical solution, in step S14, the simulation of shield excavation is achieved through the birth and death element method in ABAQUS software. Before excavation, the ground stress balance is performed. During the simulation, the width of the four-ring segment is taken as one excavation step. Each excavation step includes tunnel soil excavation, shield activation, segment and grouting layer generation, as well as the simulation of grouting pressure and support pressure. At the same time, the method of changing field variables is used to set two properties for the grouting layer: initial setting and final setting, so as to realize the change of elastic modulus of the grouting layer in different excavation steps.

[0018] As a specific technical solution, in step S1, the upper dynamic coupling sub-model includes a train vehicle model, a track structure model, and a wheel-rail contact model.

[0019] As a specific technical solution, the train vehicle model adopts a complete vehicle with a secondary suspension, and the train vehicle model includes a car body, bogies and wheelsets; the track structure model adopts ballastless track, and the track structure model includes rails and track slabs from top to bottom, and different units of the track structure model are connected by linear spring-damping units; the wheel-rail contact model is constructed based on the wheel-rail spatial dynamic coupling relationship and the principle of energy variational method, and the wheel-rail spatial dynamic coupling matrix is ​​derived from the nonlinear normal elastic force and tangential creep force of the wheel and rail.

[0020] As a specific technical solution, the joint simulation calculation in step S2 is as follows: when the lower shield tunneling reaches different excavation steps, the matrix information of displacement, mass, stiffness, damping, and load of each node in the lower shield tunneling sub-model at different excavation steps is calculated and imported into the upper dynamic coupling sub-model. Then, based on the dynamic motion equation of the vehicle-track system, the vibration acceleration, velocity, and displacement of the train system and the track system are jointly solved according to the following formula:

[0021]

[0022] in,

[0023] In the formula, the subscripts V and T represent the train system and track system, respectively; M VV M TT C represents the mass matrix of the train system and the track system, respectively; VV C VT C TV C TT K represents the interaction damping matrices of the train system, the train system to the track system, the track system to the train system, and the track system, respectively; VV K VT K TV K TT F represents the interaction stiffness matrix of the train system, the interaction between the train system and the track system, the interaction between the track system and the train system, and the interaction between the track system and the train system, respectively;V and F T These represent the load arrays for the train system and the track system, respectively. These represent the vibration acceleration, velocity, and displacement vectors of the train system, respectively. W represents the vibration acceleration, velocity, and displacement vectors of the track system, respectively. i,k The axle load is denoted by ; the subscripts i and k represent the i-th car and the k-th wheelset of the i-th car, respectively; the superscript D indicates transpose.

[0024] As a specific technical solution, in step S3, the evaluation and analysis of train operation safety and stability are carried out by using wheel-rail force, derailment coefficient and wheel load reduction rate to evaluate train operation safety, and by using car body vibration acceleration to evaluate train operation stability.

[0025] As a specific technical solution, in step S3, the dynamic response of the structure is evaluated and analyzed by the dynamic displacement and dynamic acceleration of the rail, track slab, and high-speed railway overpass from top to bottom.

[0026] Compared with existing technologies, the present invention has the following beneficial effects: By conducting joint simulation analysis of shield tunneling under high-speed railway overpasses in different software, the present invention considers not only the influence of environmental factors and shield tunneling parameters during shield construction, but also the interaction between the operation of the upper train and the lower shield construction. This enables accurate and rapid analysis and evaluation of the vibration response status and train dynamic performance of existing high-speed railway overpasses and other structures during the shield tunneling process. Thus, it can provide a reference for the risk research of shield tunneling construction and the safe operation of existing railways, so as to prevent and reduce the safety risks of shield construction and train operation in actual engineering projects. Attached Figure Description

[0027] Figure 1 This is a flowchart of the method of the present invention;

[0028] Figure 2 A flowchart simulating shield tunneling;

[0029] Figure 3 This is a schematic diagram of shield tunneling.

[0030] Figure 4 This is a schematic diagram of the mesh generation for the lower shield tunneling excavation sub-model.

[0031] Figure 5 This is a schematic diagram of the train model in the upper dynamic coupling sub-model;

[0032] Figure 6 This is a schematic diagram of the track model in the upper dynamic coupling sub-model;

[0033] Figure 7 Time history curves of wheel load reduction rate and derailment coefficient;

[0034] Figure 8 The time history curve of vehicle body vibration acceleration;

[0035] Figure 9 This is the time history curve of the dynamic displacement of the rail;

[0036] Figure 10 This is the time history curve of the dynamic acceleration of the rail. Detailed Implementation

[0037] The present invention will be further described below with reference to specific embodiments. It should be noted that the following embodiments are merely illustrative examples of the present invention, and all equivalent substitutions made by those skilled in the art in accordance with the spirit of the present invention fall within the protection scope of the present invention.

[0038] Example

[0039] The method for dynamic response modeling and analysis of shield tunneling under high-speed railway overpasses based on co-simulation includes the following steps:

[0040] S1, establish the lower shield excavation sub-model and the upper dynamic coupling sub-model:

[0041] Establishing the lower shield tunneling excavation sub-model: Based on the engineering design data, the ABAQUS finite element software was used to establish the lower shield tunneling excavation sub-model for the shield tunnel passing under the high-speed railway overpass; the specific method for modeling the lower shield tunneling excavation sub-model is as follows:

[0042] S11, Establish the geometric model: The dimensions of the lower shield excavation sub-model are selected based on the engineering design data and the influence range of shield construction; In this embodiment, the lower shield excavation sub-model mainly includes the high-speed railway overpass, the stratum, and the shield tunnel from top to bottom, wherein the shield tunnel includes the segments, the shield shell, and the grouting layer from the inside out.

[0043] S12, Assigning material properties: The Mohr-Coulomb constitutive model is used for the strata materials. Different soil material information is assigned to the strata layers according to the design data. The linear elastic constitutive model is used for other materials such as high-speed railway overpasses and shield tunnels.

[0044] S13, Add loads and boundary conditions: Apply gravity loads to the model, constrain its horizontal displacement around the model, constrain its vertical displacement at the bottom, and apply a uniformly distributed load on the upper surface of the piers that is equivalent to the weight of the superstructure of the high-speed railway overpass.

[0045] S14, Shield Excavation Simulation: The shield excavation simulation was implemented using the birth and death element method in ABAQUS software. Before excavation, ground stress balance was performed. The simulation used a four-ring segment width (6m) as one excavation step. Each excavation step mainly included: tunnel soil excavation, shield activation, grout layer generation, and simulation of grouting pressure and support pressure. To simulate the hardening process of the grouting material, the grout layer was given two properties: initial setting and final setting, by changing field variables to realize the change in the elastic modulus of the grout layer in different excavation steps. For details, please refer to [link to relevant documentation]. Figure 2 and Figure 3 The shield tunneling simulation process includes: first, removing the soil in one excavation step, then activating the shield unit at the corresponding location, applying support pressure on the excavation face, then activating the grouting layer unit (initial setting) and applying circumferential grouting pressure, then proceeding to the next excavation step (removing the soil in the next excavation step), deactivating the shield unit, support pressure and grouting pressure of the previous step, replacing the grouting layer unit (initial setting) with the grouting layer unit (final setting), and repeating the above steps until the double-track tunnel excavation is completed;

[0046] S15, Model mesh generation: (e.g.) Figure 4 As shown, the model mesh is denser the closer it is to the shield tunneling area. The shield shell uses S4R shell element type, while the high-speed railway overpass, stratum, tunnel segments, grouting layer, etc. use C3D8R hexahedral linear elements. The model is divided into a total of 400,166 nodes and 324,032 elements.

[0047] Establishing the superstructure dynamic coupling sub-model: A train-track superstructure dynamic coupling sub-model is established using the programming language in MATLAB numerical analysis software. The superstructure dynamic coupling sub-model includes a train vehicle model, a track structure model, and a wheel-rail contact model. The train vehicle is a complete vehicle with secondary suspension, and the train vehicle model includes the car body, bogies, and wheelsets, such as... Figure 5 As shown; the car body and bogies have 5 degrees of freedom in spatial vibration: roll, yaw, pitch, yaw, and heave. Each wheelset considers 2 degrees of freedom for yaw and heave, for a total of 23 degrees of freedom in the vehicle system during spatial vibration; the track structure model uses ballastless track, such as... Figure 6 As shown, the track structure model consists of rails and track slabs from top to bottom, with different units connected by linear spring-damping units; the wheel-rail contact model is constructed based on the wheel-rail spatial dynamic coupling relationship and the principle of energy variational method, deriving the wheel-rail spatial dynamic coupling matrix from the nonlinear normal elastic force and tangential creep force of the wheel-rail.

[0048] S2, Joint Simulation Calculation: When the lower shield tunneling reaches different excavation steps, the matrix information of displacement, mass, stiffness, damping, and load of each node in the lower shield tunneling sub-model at different excavation steps is calculated and imported into the upper dynamic coupling sub-model. Then, based on the dynamic motion equations of the vehicle-track system, the vibration acceleration, velocity, and displacement of the train system and track system are jointly solved according to the following formula:

[0049]

[0050] in,

[0051] In the formula, the subscripts V and T represent the train system and track system, respectively; M VV M TT C represents the mass matrix of the train system and the track system, respectively; VV C VT C TV C TT K represents the interaction damping matrices of the train system, the train system to the track system, the track system to the train system, and the track system, respectively; VV K VT K TV K TT F represents the interaction stiffness matrix of the train system, the interaction between the train system and the track system, the interaction between the track system and the train system, and the interaction between the track system and the train system, respectively; V and F T These represent the load arrays for the train system and the track system, respectively. These represent the vibration acceleration, velocity, and displacement vectors of the train system, respectively. W represents the vibration acceleration, velocity, and displacement vectors of the track system, respectively. i,k The axle load is the weight of the train; the subscripts i and k represent the i-th car and the k-th wheelset of the i-th car, respectively; the superscript D indicates transpose.

[0052] S3, Dynamic performance evaluation and analysis: Based on the joint solution results of step S2, evaluate and analyze the train's driving safety and stability and structural dynamic response.

[0053] For the analysis of train operation safety and stability: wheel-rail force, derailment coefficient, and wheel load reduction rate are used to evaluate train operation safety, while car body vibration acceleration is used to evaluate train operation stability. In this invention, the car body vibration acceleration can be obtained according to step S2, the wheel-rail force (lateral force and vertical force) can be obtained through the wheel-rail contact model in step S1, and the derailment coefficient and wheel load reduction rate can be obtained based on the wheel-rail force. The derailment coefficient is the ratio of the lateral force exerted by the wheel on the rail to its vertical force at a certain moment, used to assess whether the wheel flange will climb onto the rail head and derail under the action of lateral force. The wheel load reduction rate is the ratio of the wheel load reduction amount to the average static wheel weight of the axle, used to assess another derailment safety indicator caused by excessive wheel load reduction. Under normal circumstances, to ensure train operation safety, the wheel load reduction rate should be less than the specified limit (0.65 for speeds ≤160km / h and 0.8 for speeds >160km / h), and the derailment coefficient should meet the specification requirement of less than 0.8. Car body vibration acceleration is used to evaluate the train's running quality, i.e., stability; both the lateral and vertical vibration accelerations of the car body should be less than the specification requirement of 2.5 m / s². 2 The limit. In a specific implementation scheme, such as Figure 7 and Figure 8 As shown, by using the method of this invention for modeling and analysis based on co-simulation, the time history curves of wheel load reduction rate and derailment coefficient, as well as the time history curve of car body vibration acceleration, can be obtained when the shield tunnel passes under a high-speed railway overpass. This allows us to understand the changes in derailment coefficient, wheel load reduction rate, and car body vibration acceleration during train operation, thus enabling the evaluation and analysis of train operation safety and stability. Furthermore, from... Figure 7 and Figure 8 It is known that shield tunneling will have additional impacts on train operation. The vibration acceleration of the train body and the wheel-rail force are positively correlated with the operating speed. The vibration acceleration and dynamic displacement of the track structure are affected by shield tunneling and show a significant increase when passing over overpasses. Therefore, targeted measures such as reducing train speed or reinforcing the ground can be taken to reduce the impact of shield tunneling on train operation.

[0054] For the structural dynamic response analysis, based on the existing high-speed railway structure, the dynamic displacement and acceleration indices of the rails, track slabs, and high-speed railway overpasses are used sequentially from top to bottom to evaluate and analyze the structural dynamic response. In a specific implementation plan, such as... Figure 9 and Figure 10 As shown, by using the method of this invention to perform modeling and analysis based on co-simulation, the time history curves of rail dynamic displacement and rail dynamic acceleration can be obtained when the shield tunnel passes under a high-speed railway overpass. This allows us to know the changes in rail dynamic displacement and rail dynamic acceleration during train operation, so as to evaluate and analyze the structural dynamic response.

Claims

1. A method for modeling and analyzing the dynamic response of a shield tunneling overpass under a high-speed railway line based on co-simulation, characterized in that... Includes the following steps: S1. Establish the lower shield excavation sub-model and the upper dynamic coupling sub-model: Based on the engineering design data, the lower shield excavation sub-model of the shield tunnel passing under the high-speed railway overpass is established using ABAQUS finite element software; the upper dynamic coupling sub-model of the train-track is established using programming language in MATLAB numerical analysis software. The establishment of the sub-model for the lower shield tunneling excavation includes the following steps: S11, Establish a geometric model: Determine the size of the lower shield excavation sub-model based on the engineering design data and the influence range of shield construction. The lower shield excavation sub-model includes the high-speed railway overpass, the stratum and the shield tunnel from top to bottom. The shield tunnel includes the segments, shield shell and grouting layer from the inside to the outside. S12, assigning material properties: the Mohr-Coulomb constitutive model is used for the stratum material, and the linear elastic constitutive model is used for the high-speed railway overpass and shield tunnel material. S13, Add loads and boundary conditions: Apply gravity loads to the model, constrain its horizontal displacement around the model, constrain its vertical displacement at the bottom, and apply a uniformly distributed load on the upper surface of the piers that is equivalent to the weight of the superstructure of the high-speed railway overpass. S14, Shield excavation simulation: The shield excavation simulation is implemented using the birth and death element method in ABAQUS software; S15, Model mesh generation: The shield shell adopts the S4R shell element type, and the high-speed railway overpass, stratum, segment and grouting layer adopt C3D8R hexahedral linear elements; S2, Joint Simulation Calculation: When the lower shield tunneling reaches different excavation steps, the matrix information of displacement, mass, stiffness, damping, and load of each node in the lower shield tunneling sub-model at different excavation steps is calculated and imported into the upper dynamic coupling sub-model. Then, based on the dynamic motion equations of the vehicle-track system, the vibration acceleration, velocity, and displacement of the train system and the track system are jointly solved: ； in, ; In the formula, the subscript V and T They represent the train system and the track system, respectively. M VV , M TT These represent the mass matrices of the train system and the track system, respectively. C VV , C VT , C TV , C TT These represent the interaction damping matrices of the train system, the train system to the track system, the track system to the train system, and the track system, respectively. K VV , K VT , K TV , K TT These represent the interaction stiffness matrices of the train system, the train system to the track system, the track system to the train system, and the track system, respectively. F V and F T These represent the load arrays for the train system and the track system, respectively. , , These represent the vibration acceleration, velocity, and displacement vectors of the train system, respectively. , , These represent the vibration acceleration, velocity, and displacement vectors of the track system, respectively. W i,k Train axle load; subscript i and k They represent the first i Section of vehicles and the first i The first section of vehicles k Position wheel pair; superscript D Indicates transpose; S3, Dynamic Performance Evaluation and Analysis: Based on the joint solution results of step S2, evaluate and analyze the train's operational safety and stability as well as its structural dynamic response.

2. The method for dynamic response modeling and analysis of shield tunneling under high-speed railway overpasses based on co-simulation as described in claim 1, characterized in that, In step S14, the simulation of shield excavation is achieved using the birth and death element method in ABAQUS software. Before excavation, the ground stress balance is performed. During the simulation, the width of the four-ring segment is taken as one excavation step. Each excavation step includes tunnel soil excavation, shield activation, segment and grouting layer generation, as well as the simulation of grouting pressure and support pressure. At the same time, the method of changing field variables is used to set two properties for the grouting layer: initial setting and final setting, so as to realize the change of elastic modulus of the grouting layer in different excavation steps.

3. The method for dynamic response modeling and analysis of shield tunneling under high-speed railway overpasses based on co-simulation as described in claim 1, characterized in that, In step S1, the upper dynamic coupling sub-model includes a train vehicle model, a track structure model, and a wheel-rail contact model.

4. The method for dynamic response modeling and analysis of shield tunneling under high-speed railway overpasses based on co-simulation as described in claim 3, characterized in that: The train vehicle model is a complete vehicle with a secondary suspension. The train vehicle model includes a car body, bogies, and wheelsets. The track structure model adopts a ballastless track. The track structure model includes rails and track slabs from top to bottom. Different units of the track structure model are connected by linear spring-damping units. The wheel-rail contact model is constructed based on the wheel-rail spatial dynamic coupling relationship and the principle of energy variational method. The wheel-rail spatial dynamic coupling matrix is ​​derived from the nonlinear normal elastic force and tangential creep force of the wheel and rail.

5. The method for dynamic response modeling and analysis of shield tunneling under high-speed railway overpasses based on co-simulation as described in claim 1, characterized in that, In step S3, the evaluation and analysis of train operation safety and stability are carried out by using wheel-rail force, derailment coefficient and wheel load reduction rate to evaluate train operation safety, and using car body vibration acceleration to evaluate train operation stability.

6. The method for dynamic response modeling and analysis of shield tunneling under high-speed railway overpasses based on co-simulation as described in claim 1, characterized in that, In step S3, the dynamic response of the structure is evaluated and analyzed by the dynamic displacement and dynamic acceleration of the rail, track slab, and high-speed railway overpass from top to bottom.

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