Method for mapping relationship between vertical displacement of ballast track line and bridge on high-speed long-span bridge

Abstract

The application provides a ballast track line-bridge vertical displacement mapping relationship analysis method on a long-span bridge, belongs to the technical field of high-speed railway engineering design, establishes track mechanics differential balance equations, obtains an analytical solution of a ballast track line structure submodel and a lower foundation structure mapping relationship, calculates a vertical displacement deformation curve of a bridge deck based on a long-span bridge finite element model, adopts an interpolation method to obtain a bridge deck vertical displacement corresponding to each sleeper position when the long-span bridge is divided into grids smaller than sleeper support spacing, obtains a rail vertical deformation curve and a fastener vertical force related result based on taking the bridge vertical displacement as a boundary condition, and obtains a line-bridge vertical deformation mapping relationship. The application has the advantages of simple operation, small calculation amount, high calculation precision and strong reusability, and can be widely applied to line-bridge space deformation mapping relationship research of long-span bridges.

Description

Technical Field

[0001] This invention relates to the field of high-speed railway engineering design technology, specifically to a method for analyzing the vertical displacement mapping relationship between ballast track and bridge on a long-span high-speed railway bridge. Background Technology

[0002] With the rapid construction and development of high-speed railways, the requirements for line smoothness are becoming increasingly stringent, and the proportion of bridges in the lines is gradually increasing. To ensure that high-speed railway lines can cross special sections such as deep valleys and large rivers, a large number of long-span bridge structures, such as cable-stayed and suspension bridges, have been applied and developed in high-speed railway projects.

[0003] Cable-stayed bridges, suspension bridges, and other long-span bridges, due to their large spans and flexible structures, undergo extremely complex spatial deformations under external loads such as temperature and wind. The smoothness of the track on these long-span bridges largely depends on the bridge's structural alignment, presenting a challenge in coordinating the track's deformation with the bridge's overall deformation. The track-bridge interaction is highly complex, and traditional single-factor analysis and simplified modeling are insufficient to address the deformation coordination issues of the bridge structure under the combined effects of the track and the complex environment. Studying the deformation characteristics of long-span bridges under multi-factor coupling and the mapping mechanism between track and bridge deformation are crucial scientific issues that must be addressed to improve the operational quality of high-speed trains.

[0004] In recent years, researchers both domestically and internationally have conducted extensive research on the line-bridge vertical deformation mapping relationship of medium- and small-span bridges, establishing numerous line-bridge vertical displacement coupling models and achieving fruitful results. However, with the rapid increase in the number of long-span bridges, the drawbacks of line-bridge displacement mapping coupling models—such as complex modeling, the need for separate models for each bridge, and low simulation efficiency—have become increasingly apparent. Therefore, there is an urgent need to propose a novel refined analysis method for the line-bridge vertical displacement mapping of ballast track bridges in long-span bridges to rapidly analyze the line-bridge vertical deformation mapping relationship and improve computational efficiency. Summary of the Invention

[0005] The purpose of this invention is to provide a method for analyzing the vertical displacement mapping relationship between ballast track and bridge on a long-span high-speed railway bridge, so as to quickly, efficiently, accurately and effectively analyze the spatial deformation mapping relationship between the track and bridge on a long-span bridge, thereby solving at least one of the technical problems existing in the background art.

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

[0007] On the one hand, the present invention provides a method for analyzing the vertical displacement mapping relationship between ballast track and bridge on a long-span high-speed railway bridge, including the following steps:

[0008] The method for analyzing the vertical displacement mapping relationship between ballasted track lines and bridges on long-span bridges differs from the traditional method. Based on assumptions, the analysis model for the vertical displacement mapping relationship between ballasted track lines and bridges is divided into a ballasted track line structure sub-model and a bridge structure sub-model.

[0009] Based on the mechanical properties of the track structure, a differential equilibrium equation for track mechanics was established, and an analytical solution was obtained to determine the mapping relationship between the sub-model of the ballasted track line structure and the substructure. A program for calculating the analytical solution was also developed.

[0010] Based on the finite element principle and the stress characteristics of bridge structural components, and combined with simulation software such as ABAQUS, ANSYS and MIDAS, a finite element model of a long-span bridge was established.

[0011] Based on the research and design requirements, and using the established finite element model of the long-span bridge, the vertical displacement deformation curve of the bridge deck under complex conditions such as complex temperature and pier settlement is calculated. When the grid of the long-span bridge is smaller than the sleeper support spacing, the interpolation method is used to calculate the vertical displacement of the bridge beam surface corresponding to each sleeper position.

[0012] By using the bridge's vertical displacement as a boundary condition and inputting it into the analytical solution calculation program, the program obtains relevant results such as the rail's vertical deformation curve and the fastener's vertical force, thereby revealing the mapping relationship between the line and the bridge's vertical deformation.

[0013] Furthermore, this analytical method requires the following assumptions:

[0014] (1) Compared with the structure of a long-span bridge, the vertical stiffness of the ballast track structure is much smaller than that of the structure of a long-span bridge. Therefore, the contribution of the vertical stiffness of the track structure is ignored when calculating the deformation of the bridge. (2) The thickness distribution of the ballast track bed in a long-span bridge is uneven. When calculating the vertical displacement of the bridge, the secondary dead load of the ballast track structure is considered as a non-uniformly distributed force or the unit weight of the bridge deck. (3) The vertical and lateral coupling effect is not considered when calculating the vertical deformation of the track structure. (4) The vertical stiffness of the sleepers is ignored when calculating, and only the vertical mass of the sleepers is considered.

[0015] The analysis model of the vertical displacement mapping relationship between the line and the bridge is divided into a ballast track sub-structure model and a bridge structure sub-model. The track structure sub-model is solved using the analytical method, while the bridge structure sub-model is established using the finite element method, thus realizing the joint simulation of the analytical method and the finite element method.

[0016] Furthermore, the ballasted track sub-model is considered as a layered structural system composed of beams, mass points, and springs. The rail is equivalent to an elastically supported continuous beam model that can account for its own weight. The vertical stiffness of the fasteners is simulated as spring supports, and the vertical stiffness of the track bed is simulated as spring units. Considering the continuous action characteristics of the track bed, the continuous track bed medium is discretized along the longitudinal direction of the track. The masses of the sleepers and track bed are combined and simulated as sleeper-track bed mass blocks considering only mass. Shear springs are added between the discrete sleeper-track bed mass blocks. The track structure model system, from top to bottom, includes rail beams, fastener springs, sleeper mass blocks, track bed springs, and a virtual bridge deck. Each fastener spring is connected to the rail beam at one end and the sleeper mass block at the other; each track bed spring is connected to the sleeper mass block at one end and the bridge deck foundation at the other; for the track bed shear springs, one end is connected to the track bed mass block, and the other end is connected to the adjacent track bed mass block. During calculations, parameters such as the vertical stiffness of the fasteners and the vertical stiffness of the track bed can be modified with reference to actual field measurements.

[0017] The mechanical equilibrium equations for the steel rail beam are as follows:

[0018] Gravitational equilibrium equations: Torque balance equation:

[0019] The mechanical equilibrium equations for the steel rail beam are as follows:

[0020]

[0021] The mechanical equilibrium equations for the sleeper track bed mass block are as follows:

[0022]

[0023] Combining the above two equations, we can obtain the following equations for solving the mass blocks of the rail and sleeper track bed.

[0024] K RB *u RB =F RB

[0025] Transfer matrix K RB Displacement matrix u RB and F RB Boundary conditions are expressed as follows.

[0026]

[0027] u R,B =[u r,1 ;u r,2 ;…;u r,j ;…;u r,N ;u r,N+1 ;u b,1 ;u b,2 ;…;ub,j ;…;u b,N ;u b,N+1 ]

[0028]

[0029] After deriving the mechanical equations of the track structure sub-model, a MATLAB program needs to be developed to solve the mechanical equations in order to determine the vertical displacement of the rail and the vertical force of the fastener.

[0030] Furthermore, a refined finite element model of a long-span bridge needs to be established separately. Long-span bridges mainly include special bridges such as cable-stayed bridges and suspension bridges. The construction method of the finite element model of a long-span bridge is introduced using long-span cable-stayed bridges and suspension bridges as examples.

[0031] The finite element model of a long-span cable-stayed bridge includes major components such as the steel truss main girder, bridge deck, stay cables, main tower, and auxiliary piers. The steel truss main girder consists of members such as the upper chord, lower chord, web members, and steel longitudinal beams, as well as an orthotropic bridge deck. The upper chord, lower chord, steel longitudinal beams, and web members are simulated using spatial beam element models, with rigid connections between adjacent members. The orthotropic plate is simulated using shell elements to consider its stress characteristics. The main tower and auxiliary piers mainly bear pressure and bending moment under symmetrical temperature action, and are simulated using spatial beam elements to consider their variable cross-section characteristics. Long-span bridges often adopt a semi-floating system, with longitudinal dampers connecting the main tower and main girder in the longitudinal direction. The longitudinal dampers are simulated using linear springs, and the bridge tower and main girder are coupled and constrained in the transverse and vertical directions. The stay cables are slender and flexible structures that cannot withstand pressure and bending moment, and are simulated using tension-only member elements. The stay cables are coupled and connected to the upper chord nodes of the main girder and the main tower nodes in the longitudinal, transverse, and vertical directions, respectively. The base of the main tower and the base of the auxiliary side piers are fully constrained.

[0032] The modeling objects of the finite element model of the long-span suspension bridge include the main components such as the steel truss main girder, bridge deck, suspenders, main cable, main tower, and auxiliary side piers. The modeling method of the steel truss main girder, main tower, and longitudinal damper is the same as that of the long-span cable-stayed bridge. The main cable and suspenders are considered to have tensile characteristics and are simulated using tension-only rod elements. The two sides of the main cable are connected to the nodes of the two main towers respectively. One end of the suspender node is connected to the main cable and the other end is connected to the upper chord of the main girder. One side of the back cable is connected to the node of the main tower, and the other side is connected to the ground by anchorage. The back cable is fully constrained. The bottom of the main tower and the bottom of the auxiliary side pier are also fully constrained.

[0033] The construction environment and procedures for long-span cable-stayed bridges and suspension bridges are complex, with numerous structural components. Construction deviations often occur during construction, leading to discrepancies between the completed bridge alignment and the design alignment. Furthermore, as the operating time increases, phenomena such as ballast breakage and pulverization occur, requiring timely ballast replenishment to ensure the smoothness of the track. Uneven track bed thickness and other issues cause changes in the secondary dead load on the bridge, resulting in changes in the bridge alignment. In such cases, when performing finite element modeling, the deformation of the bridge structure is calculated by changing the unit weight of the bridge deck or applying a uniformly distributed force.

[0034] Furthermore, the design values ​​for loads such as temperature, creep, and settlement need to be determined based on design and research requirements, and then input into the finite element model of the long-span bridge to obtain the vertical displacement of the bridge beam surface under complex loads. Since the finite element model of a long-span bridge is large, considering computational efficiency and accuracy, the mesh size of the bridge is generally large, while the sleeper support spacing is small. To ensure that the bridge deformation energy can be used as a boundary condition input into the track structure sub-model, a polynomial function fitting is performed on the bridge's vertical deformation curve. Then, the polynomial function is interpolated according to the sleeper support spacing to obtain the vertical displacement of the bridge deck under each sleeper.

[0035] Furthermore, the calculated vertical displacement deformation curve of the bridge is used as the boundary condition of the track substructure and input into the MATLAB program to obtain the vertical displacement deformation curve of the rail, thereby revealing the vertical displacement mapping relationship between the track and the bridge.

[0036] Furthermore, by establishing finite element sub-models for long-span bridges and ballasted tracks, it is easy to perform spatial displacement mapping relationship analysis between tracks and bridges without having to establish coupled finite element models of long-span bridges and ballasted tracks. Since the ballasted track sub-model is an independent module, when performing vertical deformation mapping relationship analysis between tracks and bridges for other bridges, only the bridge finite element model needs to be established, and the track structure sub-model can be universally applied, thus improving modeling efficiency.

[0037] Thirdly, the present invention provides a non-transitory computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, they implement the above-described method for analyzing the vertical displacement mapping relationship between ballast track lines and bridges on long-span high-speed railway bridges.

[0038] Fourthly, the present invention provides a computer device, including a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the above-described method for analyzing the vertical displacement mapping relationship between ballast track lines and bridges on high-speed railway long-span bridges.

[0039] Fifthly, the present invention provides an electronic device, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to execute instructions for implementing the above-described method for analyzing the vertical displacement mapping relationship between ballast track lines and bridges on high-speed railway long-span bridges.

[0040] The advantages of this invention are: simple operation, low computational load, high computational accuracy, strong reusability, and wide applicability to universities, research institutions, design institutes and other departments to carry out research on the spatial deformation mapping relationship of long-span bridge lines.

[0041] The advantages of additional aspects of the invention will be set forth more clearly in the following description or will be learned by practice of the invention. Attached Figure Description

[0042] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 This is a flowchart illustrating the analysis of the vertical displacement mapping relationship between the ballast track line on the bridge and the bridge, as described in an embodiment of the present invention.

[0044] Figure 2 This is a schematic diagram of a ballast track on a bridge according to an embodiment of the present invention.

[0045] Figure 3 This is a diagram of the ballast track-bridge displacement mapping model for a long-span bridge as described in an embodiment of the present invention.

[0046] Figure 4 This is a schematic diagram model of the rail micro-element as described in an embodiment of the present invention.

[0047] Figure 5 This is a model diagram of the rail point support beam according to an embodiment of the present invention.

[0048] Figure 6 This is a force diagram of the rail sleeper mass blocks at both ends of the rail according to an embodiment of the present invention.

[0049] Figure 7 This is a force diagram of the intermediate sleeper track bed mass block according to an embodiment of the present invention.

[0050] Figure 8 This is a schematic diagram of a suspension bridge sub-model according to an embodiment of the present invention.

[0051] Figure 9 This is a comparison diagram of the vertical displacement of the rails under the main beam cooling condition described in the embodiment of the present invention.

[0052] Figure 10 This is a magnified comparison of the vertical displacement of the rails in the section under the main beam cooling condition (470m-950m) described in an embodiment of the present invention.

[0053] Figure 11 This is a comparison diagram of the vertical displacement of the rail under the cooling condition of the suspension rod as described in the embodiment of the present invention.

[0054] Figure 12 This is a magnified comparison of the vertical displacement of the rail in the section (600m-850m) under the cooling condition of the suspension rod as described in the embodiment of the present invention.

[0055] Figure 13 This is a comparison diagram of the vertical displacement of the rail under the cooling of the main cable as described in an embodiment of the present invention.

[0056] Figure 14 This is a magnified view of the deformation within the 156-157m range of the main cable under cooling conditions, as described in an embodiment of the present invention.

[0057] Figure 15 This is a comparison diagram of the vertical displacement of the rails under the cable-stayed bridge cable cooling condition described in the embodiment of the present invention.

[0058] Figure 16 This is a magnified view of the deformation within the 390-391m range of the cable-stayed bridge cooling condition described in this embodiment of the invention. Detailed Implementation

[0059] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0060] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0061] It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as here.

[0062] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, and / or groups thereof.

[0063] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0064] To facilitate understanding of the present invention, the present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. However, the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0065] Those skilled in the art should understand that the accompanying drawings are merely schematic diagrams of embodiments, and the components in the drawings are not necessarily essential for implementing the present invention.

[0066] Example 1

[0067] In this embodiment 1, a system for analyzing the vertical displacement mapping relationship between ballasted track and bridge on a high-speed railway long-span bridge is first provided. This system includes: a construction module, used to establish differential equilibrium equations of track mechanics based on the mechanical properties of the track structure, and to obtain analytical solutions for the mapping relationship between the ballasted track line structure sub-model and the substructure; a finite element model of the long-span bridge is established based on the finite element principle and the stress characteristics of bridge structural components; a calculation module, used to calculate the vertical displacement deformation curve of the bridge deck based on the established finite element model of the long-span bridge. When the grid of the long-span bridge is smaller than the sleeper support spacing, interpolation is used to calculate the vertical displacement of the bridge beam surface corresponding to each sleeper position; and a mapping module, used to obtain the vertical deformation curve of the rails and the related results of the vertical force of the fasteners based on the bridge vertical displacement as a boundary condition, thus obtaining the vertical deformation mapping relationship between the track and the bridge.

[0068] In this embodiment 1, the above-described system is used to realize the method for analyzing the vertical displacement mapping relationship between ballasted track line and bridge on a high-speed railway long-span bridge. This includes: establishing differential equilibrium equations of track mechanics based on the mechanical properties of the track structure, and obtaining analytical solutions for the mapping relationship between the ballasted track line structure sub-model and the substructure; establishing a finite element model of the long-span bridge based on the finite element principle and the stress characteristics of bridge structural components; calculating the vertical displacement deformation curve of the bridge deck based on the established finite element model of the long-span bridge; when the grid of the long-span bridge is smaller than the sleeper support spacing, using interpolation to calculate the vertical displacement of the bridge beam surface corresponding to each sleeper position; and obtaining the vertical deformation curve of the rails and the related results of the vertical force of the fasteners by using the bridge vertical displacement as a boundary condition, thus obtaining the vertical deformation mapping relationship between the line and the bridge.

[0069] The contribution of the vertical stiffness of the track structure is ignored when calculating bridge deformation; the ballast track thickness distribution is uneven on long-span bridges, so the secondary dead load of the ballast track structure is considered as a non-uniformly distributed force or the unit weight of the bridge deck when calculating the vertical displacement of the bridge; the vertical and lateral coupling effects are not considered when calculating the vertical deformation of the track structure; the vertical stiffness of the sleepers is ignored in the calculation, and only the vertical mass of the sleepers is considered; the line-bridge vertical displacement mapping relationship analysis model is divided into a ballast track sub-structure model and a bridge structure sub-model. The line structure sub-model is solved analytically, and the bridge structure sub-model is established using the finite element method.

[0070] The mechanical equilibrium equations for the steel rail beam are as follows:

[0071] Gravitational equilibrium equations:

[0072] Torque balance equation:

[0073] The mechanical equilibrium equations for the steel rail beam are as follows:

[0074]

[0075] The mechanical equilibrium equations for the sleeper track bed mass block are as follows:

[0076]

[0077] Combining the above two equations, we can obtain the following equations for solving the mass block of the rail and sleeper track bed:

[0078] K RB *u RB =F RB

[0079] Transfer matrix K RB Displacement matrix u RB and F RB Boundary conditions are expressed as follows:

[0080]

[0081] u R,B =[u r,1 ;u r,2 ;…;u r,j ;…;u r,N ;u r,N+1 ;u b,1 ;u b,2 ;…;u b,j ;…;u b,N ;u b,N+1 ]

[0082]

[0083] After deriving the mechanical equations of the track structure sub-model, the equations are solved to obtain the vertical displacement of the rails and the vertical force of the fasteners.

[0084] The finite element model of the long-span cable-stayed bridge includes the steel truss main girder, bridge deck, stay cables, main tower, and auxiliary piers. The steel truss main girder consists of upper chords, lower chords, web members, steel longitudinal beams, and orthotropic bridge deck. The upper chords, lower chords, steel longitudinal beams, and web members are simulated using spatial beam element models, with rigid connections between adjacent members. The orthotropic plates are simulated using shell elements to consider their stress characteristics. The main tower and auxiliary piers mainly bear pressure and bending moment under symmetrical temperature action, and their variable cross-section characteristics are considered, so they are simulated using spatial beam elements. The long-span bridge adopts a semi-floating system. The main tower and main girder are connected longitudinally by longitudinal dampers, which are simulated using linear springs. The bridge tower and main girder are coupled and constrained laterally and vertically. The stay cables are slender and flexible structures, simulated using tension-only member elements. The stay cables are coupled and connected longitudinally, laterally, and vertically to the upper chord nodes of the main girder and the nodes of the main tower, respectively. The bases of the main tower and auxiliary piers are fully constrained.

[0085] The modeling objects of the finite element model of the long-span suspension bridge include the steel truss main girder, bridge deck, suspenders, main cable, main tower, and auxiliary side piers. The modeling method of the steel truss main girder, main tower, and longitudinal dampers is the same as that of the long-span cable-stayed bridge. The main cable and suspenders are considered to have tensile characteristics and are simulated using tension-only rod elements. The two sides of the main cable are connected to the nodes of the two main towers respectively. One end of the suspender node is connected to the main cable, and the other end is connected to the upper chord of the main girder. One side of the back cable is connected to the node of the main tower, and the other side is connected to the ground by anchorage. The back cable is fully constrained. The bottom of the main tower and the bottom of the auxiliary side pier are also fully constrained.

[0086] The calculated vertical displacement deformation curve of the bridge is used as the boundary condition of the track substructure. The vertical displacement deformation curve of the rail is then obtained, thus obtaining the vertical displacement mapping relationship between the track and the bridge.

[0087] Example 2

[0088] Given the increasing prominence of drawbacks in long-span bridge line-bridge displacement mapping coupling models, such as complex modeling, the need for separate bridge-to-bridge vertical coupling models, and low simulation efficiency, this embodiment 2 provides a method for analyzing the vertical displacement mapping relationship between ballasted track lines and bridges on high-speed railway long-span bridges. This method aims to quickly, efficiently, accurately, and effectively analyze the spatial deformation mapping relationship between lines and bridges on long-span bridges. To achieve the above objectives, the present invention adopts the following technical solution.

[0089] The method for analyzing the vertical displacement mapping relationship between ballasted track lines and bridges on long-span bridges differs from the traditional method. Based on assumptions, the analysis model for the vertical displacement mapping relationship between ballasted track lines and bridges is divided into a ballasted track line structure sub-model and a bridge structure sub-model.

[0090] Based on the mechanical properties of the track structure, a differential equilibrium equation for track mechanics was established, and an analytical solution was obtained to determine the mapping relationship between the sub-model of the ballasted track line structure and the substructure. A program for calculating the analytical solution was also developed.

[0091] Based on the finite element principle and the stress characteristics of bridge structural components, and combined with simulation software such as ABAQUS, ANSYS and MIDAS, a finite element model of a long-span bridge was established.

[0092] Based on the research and design requirements, and using the established finite element model of the long-span bridge, the vertical displacement deformation curve of the bridge deck under complex conditions such as complex temperature and pier settlement is calculated. When the grid of the long-span bridge is smaller than the sleeper support spacing, the interpolation method is used to calculate the vertical displacement of the bridge beam surface corresponding to each sleeper position.

[0093] By using the bridge's vertical displacement as a boundary condition and inputting it into the analytical solution calculation program, the program obtains relevant results such as the rail's vertical deformation curve and the fastener's vertical force, thereby revealing the mapping relationship between the line and the bridge's vertical deformation.

[0094] In this embodiment, to ensure the feasibility of the model, the following assumptions are required when establishing the model, including: the basic assumptions for calculation are as follows: (1) Compared with the large-span bridge structure, the vertical stiffness of the ballast track structure is much smaller than that of the large-span bridge structure, so the contribution of the vertical stiffness of the track structure is ignored when calculating the bridge deformation; (2) The thickness distribution of the ballast track bed in the large-span bridge is uneven, so the secondary dead load of the ballast track structure is considered as a non-uniformly distributed force or the unit weight of the bridge deck when calculating the vertical displacement of the bridge; (3) The vertical and lateral coupling effect is not considered when calculating the vertical deformation of the track structure; (4) The vertical stiffness of the sleepers is ignored when calculating, and only the vertical mass of the sleepers is considered.

[0095] In this embodiment, the ballasted track sub-model adopts the mechanical equilibrium analytical method. The ballasted track sub-model is regarded as a layered structural system composed of beams, mass points, and springs. The rail is equivalent to an elastic point-supported continuous beam model that can take into account its own weight. The vertical stiffness of the fasteners is simulated as spring supports, and the vertical stiffness of the track bed is simulated as spring units. Considering the continuous action characteristics of the track bed, the continuous track bed medium is discrete along the longitudinal direction of the track. The mass of the sleepers and track bed is combined and simulated as a sleeper-track bed mass block considering only the mass. Shear springs are added between the discrete sleeper-track bed mass blocks. The track structure model system from top to bottom includes rail beams, fastener springs, sleeper mass blocks, track bed springs, and virtual bridge decks. Each fastener spring is connected to the rail beam at one end and the sleeper mass block at the other end; each track bed spring is connected to the sleeper mass block at one end and the bridge deck foundation at the other end; for the track bed shear springs, one end is connected to the track bed mass block and the other end is connected to the adjacent track bed mass block. During calculations, parameters such as the vertical stiffness of the fasteners and the vertical stiffness of the track bed can be modified by referring to the actual measurement results on site. The method is based on the principle of mechanical equilibrium, and the mechanical equations of the track structure sub-model are derived in detail. A related MATLAB program is compiled to solve the mechanical equations. This program can easily calculate the vertical displacement of the rails and the vertical force of the fasteners.

[0096] This method employs the finite element method to simulate long-span bridge models and presents methods for constructing long-span suspension and cable-stayed bridge models. Design values ​​for loads such as temperature, creep, and settlement need to be determined based on design and research requirements, and these values ​​are input into the long-span bridge finite element model to obtain the vertical displacement of the bridge beam surface under complex loads. Since the finite element model of a long-span bridge is relatively large, considering computational efficiency and accuracy, the mesh size for the bridge is generally large, while the sleeper support spacing is small. To ensure that the bridge deformation energy can be used as a boundary condition input into the track structure sub-model, a polynomial function fitting is performed on the bridge's vertical deformation curve. Then, the polynomial function is interpolated according to the sleeper support spacing to obtain the vertical displacement of the bridge deck under each sleeper.

[0097] In this embodiment, the vertical displacement deformation curve of the bridge calculated by the finite element model is used as the boundary condition of the line substructure and input into the MATLAB calculation program of the line substructure to obtain the vertical displacement deformation curve of the rail, thereby revealing the vertical displacement mapping relationship between the line and the bridge.

[0098] By establishing finite element models of long-span bridges and sub-models of ballasted tracks, it is convenient to perform spatial displacement mapping relationship analysis between tracks and bridges without having to establish coupled finite element models of long-span bridges and ballasted tracks. Furthermore, since the ballasted track sub-model is an independent module, when performing vertical deformation mapping relationship analysis between tracks and bridges for other bridges, only the bridge finite element model needs to be established, and the track structure sub-model can be universally applied, thus improving modeling efficiency.

[0099] Example 3

[0100] Figure 1 This embodiment provides a flowchart for analyzing the mapping relationship between the ballast track line on the bridge and the vertical displacement of the bridge. Figure 2 A schematic diagram of a ballast track on a bridge, for reference. Figure 1 The core idea of ​​the analysis method for the vertical displacement mapping relationship between the ballasted track line and the bridge described in this embodiment 3 is as follows: the analysis model of the vertical displacement mapping relationship between the line and the bridge is divided into a ballasted track line sub-structure model and a bridge structure sub-model. The track structure sub-model is solved by analytical method, and the bridge structure sub-model is established by finite element method, thus realizing the joint simulation of analytical method and finite element method.

[0101] Reference Figure 1 and Figure 2 When analyzing the mechanical model of the ballast track on the bridge as an equivalent linear-bridge vertical deformation mapping, some computational assumptions need to be made. Specifically:

[0102] (1) Compared with the structure of long-span bridges, the vertical stiffness of the ballast track structure is much smaller than that of the structure of long-span bridges. The contribution of the vertical stiffness of the track structure is ignored when calculating the deformation of the bridge. (2) The thickness distribution of the ballast track bed in long-span bridges is uneven. When calculating the vertical displacement of the bridge, the secondary dead load of the ballast track structure is considered as a non-uniformly distributed force or the unit weight of the bridge deck. (3) The vertical and lateral coupling effect is not considered when calculating the vertical deformation of the track structure. (4) The vertical stiffness of the sleepers is ignored when calculating. Only the vertical mass of the sleepers is considered.

[0103] Figure 3 This embodiment provides a schematic diagram of the displacement mapping model of a long-span bridge with ballasted track. The diagram includes the rail beam, fastener springs, sleeper track mass blocks, and track springs. The rail can be simulated as an Euler beam model considering the elastic support of the fasteners. Figure 4 The rail beam micro-element shown is analyzed. Under the action of complex forces, the rail micro-element is in force equilibrium. The force equilibrium equation of the rail micro-element is as follows.

[0104] ∑F Y =0 Q+w(x)*dx-(Q+dQ)=0 (1)

[0105]

[0106] Higher-order differentials are omitted in equation (2) We can obtain:

[0107]

[0108]

[0109] Where: E is the elastic modulus of the rail, Irz Let be the vertical section moment of inertia of the rail; the shear force Q is constant between the two fasteners. Equations (4) and (5) are typical non-homogeneous linear differential equations with constant coefficients. It is assumed that the shape function of the vertical displacement of the rail beam satisfies the polynomial:

[0110] z = ax 3 +bx 2 +cx+d (5)

[0111] Using the method of variation of constants, a system of conditional equations for the particular solution can be written, and by differentiating the displacement function, the rotation angle of the rail beam can be calculated. Bending moment M(x) and shear force Q(x)

[0112]

[0113] M(x) = -EI rz z”=-EI rz (6ax+2b) (7)

[0114] Q(x) = -EI rz z”'=-6aEI rz (8)

[0115] Assuming initial boundary conditions (when x = 0), the vertical displacement, rotation angle, bending moment, and shear force are z0, ... Substituting M0 and Q0 into (4)-(7), we get:

[0116]

[0117] The deformation function of the rail is:

[0118] When the rail beam model is sufficiently long, the boundary conditions at both ends of the side rail have little impact on the rail's study area. Therefore, the boundary conditions of the rail can be taken as a simply supported beam, i.e., M0 = 0, z0 = 0. Let the total length of the rail be L0, and when the concentrated force F... fj Acting on l j At this point, it can be seen from the structural equilibrium equations and the structural mechanics graphical method that:

[0119]

[0120]

[0121] The displacement function at x is:

[0122]

[0123] When a uniformly distributed load w(x) is applied to the entire beam, the displacement function at point x is:

[0124]

[0125] The formula for calculating the vertical deformation of the rails above can be written as z j =F fi *R i,j .

[0126] Where R j,i F represents the compliance coefficient of rail deformation. i This refers to the concentrated vertical force on the rail.

[0127] Figure 5 This is a model of a rail point-supported beam. The stress and deformation of the rail beam are positively considered downwards. The fastener support spacing is set to l. f There are a total of N+1 fasteners. As can be seen from the figure, the rail bears the force of its own weight and the constraint force of the fasteners. Under the combined force of the two, the rail is in force balance.

[0128]

[0129]

[0130] Where F f,i Let be the fastener constraint force of the j-th fastener.

[0131] By combining equations (15) and (16), we can see that:

[0132]

[0133] Considering the fastener stiffness as k f Then the magnitude of the fastener constraint force is: F f,j =k f *(u b,j -u r,j u b,j u is the vertical displacement of the track sleeper mass block. r,j Let be the vertical displacement of the rail directly above the sleeper mass block. The expressions for the vertical displacement at both ends of the rail are shown in equations (19) and (20).

[0134]

[0135]

[0136] Solving equations (19) and (20) reveals that:

[0137]

[0138] The expression for the vertical displacement of the rail is shown in equation (23).

[0139]

[0140] In the formula R j,i R is the compliance coefficient of the rail under concentrated load. i R Let be the compliance coefficient of the rail under uniformly distributed load. Equation (23) can be transformed into:

[0141]

[0142] The force diagram of the sleeper track bed block is as follows: Figure 6 and Figure 7 As shown, the mechanical equilibrium equation is given by equation (25).

[0143]

[0144] In the formula, F b,i For the vertical constraint force of the track bed; F f,i For the vertical constraint force of the fastener; and The constraint force provided by the vertical shear springs of the track bed, M b *g represents the mass of the sleeper track bed. The equations for the four constraint forces are as follows:

[0145]

[0146] Substituting equation (26) into equation (25), the mechanical equilibrium equation of equation (24) can be written in the following form.

[0147]

[0148] Combining equations (24) and (27), we can rearrange them into matrix form K. RB *u RB =F RB The coefficient matrix (hereinafter referred to as the "transfer matrix") is K. RB u RB Let F be the displacement matrix of the rail and sleeper track mass blocks. RB Let K be the boundary condition matrix, where the transfer matrix is ​​K. RB Displacement matrix u RB and F RB The boundary condition matrix is ​​in the form of equations (28)-(30).

[0149]

[0150] u R,B =[u r,1 ;u r,2 ;…;u r,j ;…;u r,N ;u r,N+1 ;ub,1 ;u b,2 ;…;u b,j ;…;u b,N ;u b,N+1 (29)

[0151]

[0152] By solving equation K RB *u RB =F RB The vertical displacement of the rail and sleeper track mass block can be obtained; after obtaining the displacement of the rail and sleeper track mass block, the vertical force of the fastener can be calculated by formula (26).

[0153] Figure 8 This is a schematic diagram of the finite element model of the long-span suspension bridge provided in this embodiment. The diagram shows in detail the connection methods of the various components of the long-span suspension bridge. The long-span suspension bridge is a double-tower, five-span suspension bridge with a span arrangement of (84+84+1092+84+84)m, and a main span of 1092m. The modeling objects of the finite element model include the main steel truss girder, bridge deck, suspenders, main cables, main towers, and auxiliary side piers.

[0154] The main steel truss girder consists of members such as the top chord, bottom chord, web members, and steel longitudinal beams, as well as an orthotropic bridge deck. The top chord, bottom chord, steel longitudinal beams, and web members are simulated using spatial beam element models, with rigid connections between adjacent members. The orthotropic plate is simulated using shell elements to consider its stress characteristics. The main tower and auxiliary abutments mainly bear pressure and bending moment under symmetrical temperature action, and are simulated using spatial beam elements to consider their variable cross-section characteristics. Long-span suspension bridges often adopt a semi-floating system, with longitudinal dampers connecting the main tower and main girder in the longitudinal direction. The longitudinal dampers are simulated using linear springs, and the bridge tower and main girder are coupled and constrained in the lateral and vertical directions.

[0155] Considering the tensile characteristics of the main cable and suspenders, a tension-only rod element is used for simulation. The two sides of the main cable are connected to the nodes of the two main towers respectively. One end of the suspender node is connected to the main cable, and the other end is connected to the upper chord of the main beam. One side of the back cable is connected to the node of the main tower, and the other side is connected to the ground by an anchor. The back cable is fully constrained. The bottom of the main tower and the bottom of the auxiliary side pier are fully constrained.

[0156] In this embodiment, the correctness of the line-bridge spatial deformation mapping relationship analysis method was verified. Based on equations (24) and (27), and combined with equations (28), (29) and (30), a MATLAB program for the ballasted track sub-model was developed. At the same time, the finite element model of the double-tower five-span large-span suspension bridge and the line-bridge spatial coupling model of the line-large-span suspension bridge described in Embodiment 3 were established respectively. When establishing the line-bridge spatial coupling model of the line-large-span suspension bridge, the relevant parameters of the track components (rail elastic modulus, moment of inertia, fastener vertical stiffness, sleeper track bed mass block, ballasted track bed vertical stiffness, and track bed shear spring stiffness) were completely consistent with the parameter values ​​of the ballasted track sub-model proposed in this invention.

[0157] Figure 9 This diagram shows the vertical displacement and deformation of the rails under cooling conditions on the main girder of a suspension bridge. Figure 10 This is a magnified view of the vertical displacement of the rails (470-950m) under main girder cooling. The main girder is expected to be cooled by 25℃. Figure 9 The solid lines in the diagram represent the vertical deformation of the rails calculated using the spatial coupling model of the railway line, the long-span suspension bridge, and the bridge. Figure 9 The dashed line in the figure represents the vertical deformation of the rail calculated by the method of this invention. From Figure 9 As can be seen, under the same conditions, the vertical deformation curves of the rail calculated by the two methods basically overlap, indicating the accuracy of the calculation in this invention. From Figure 10 It can be seen that the vertical displacement curve of the rail calculated by the method of the present invention is smoother. The line-bridge coupled spatial model divides the rail into multiple units, and there are differences in the displacement between adjacent rail nodes and between nodes. Therefore, the line shape is not as smooth as the curve calculated by the method of the present invention.

[0158] Figure 11 Diagram showing the vertical displacement and deformation of the rails under cooling conditions for suspension bridge suspenders. Figure 12 A localized magnified comparison of the vertical displacement of the rails in a section (600m-850m) under the condition of gantry cooling. The calculations show a gantry cooling of 25℃. Figure 11 and Figure 12 As can be seen, the vertical displacement profile of the rail calculated by the coupled model and the method of this invention are basically the same, and the difference between the two is extremely small and can be ignored.

[0159] Figure 13 Diagram showing the vertical displacement and deformation of the rails under cooling conditions for the main cable of a suspension bridge. Figure 14 A local magnified comparison of the vertical displacement of the rails in the section from 156m to 157.5m under the main cable cooling condition. The calculations show a main cable cooling of 25℃. Figure 13 and Figure 14 As can be seen, the vertical displacement curves of the rail calculated by the coupled model and the method in this embodiment are basically the same, and the difference between the two is extremely small and can be ignored.

[0160] In summary, the vertical displacement mapping analysis method for the line-bridge proposed in this invention and the calculation results of the vertical deformation of the rails in the line-bridge spatial coupling model are basically consistent, demonstrating the correctness of the method. It is worth noting that this invention only requires the establishment of a long-span suspension bridge model. In the embodiment, the total number of elements in the long-span suspension bridge model is 21,500, while the total number of elements in the line-bridge spatial coupling model is 85,640. The total number of elements in the model is reduced by half, greatly saving computational space.

[0161] In this embodiment 5, the universality and portability of the line-bridge spatial deformation mapping relationship analysis method were also verified. The method and its developed program in this embodiment are applicable not only to suspension bridges but also to cable-stayed bridges. In this verification, a large-span cable-stayed bridge model and a large-span cable-stayed bridge-line spatial coupling model were established. The cable-stayed bridge is a three-tower concrete cable-stayed bridge with a span arrangement of (48+118+2×228+118+48) m. Considering a 10℃ temperature drop in the cable-stayed bridge's stay cables, the results calculated by the invented method and the line-bridge coupling model are as follows: Figure 15 and Figure 16 As shown.

[0162] Figure 15 The diagram shows the vertical displacement and deformation of the rails under the cooling condition of the stay cables of a cable-stayed bridge. Figure 16 A magnified comparison of the vertical displacement of the rails in the 390m-391m section under cable-stayed bridge cooling conditions. Figure 15 and Figure 16 It can be seen that the vertical displacement profile of the rail calculated by the coupled model and the method of this invention is basically consistent, and the difference between the two is extremely small and can be ignored. Therefore, this method is also applicable to the analysis of the line-bridge spatial displacement mapping relationship of cable-stayed bridges, demonstrating good versatility.

[0163] Example 4

[0164] This embodiment 4 provides a non-transitory computer-readable storage medium for storing computer instructions. When these computer instructions are executed by a processor, they implement the above-described method for analyzing the vertical displacement mapping relationship between ballasted track lines and bridges on long-span high-speed railway bridges. This method includes: establishing differential equilibrium equations for track mechanics based on the mechanical properties of the track structure, and obtaining analytical solutions for the mapping relationship between the ballasted track line structure sub-model and the substructure; establishing a finite element model of the long-span bridge based on the finite element principle and the stress characteristics of bridge structural components; calculating the vertical displacement deformation curve of the bridge deck based on the established finite element model of the long-span bridge; when the grid of the long-span bridge is smaller than the sleeper support spacing, using interpolation to calculate the vertical displacement of the bridge beam surface corresponding to each sleeper position; and obtaining the vertical deformation curve of the rails and the related results of the vertical force of the fasteners based on the bridge vertical displacement as a boundary condition, thus obtaining the vertical deformation mapping relationship between the track and the bridge.

[0165] Example 5

[0166] This embodiment 5 provides a computer device, including a memory and a processor. The processor and the memory communicate with each other. The memory stores program instructions that can be executed by the processor. The processor calls the program instructions to execute a method for analyzing the vertical displacement mapping relationship between ballasted track lines and bridges on high-speed railway long-span bridges. The method includes: establishing differential equilibrium equations of track mechanics based on the mechanical properties of the track structure, and obtaining analytical solutions for the mapping relationship between the ballasted track line structure sub-model and the substructure structure; establishing a finite element model of the long-span bridge based on the finite element principle and the stress characteristics of bridge structural components; calculating the vertical displacement deformation curve of the bridge deck based on the established finite element model of the long-span bridge; when the grid of the long-span bridge is smaller than the sleeper support spacing, using interpolation to calculate the vertical displacement of the bridge beam surface corresponding to each sleeper position; and obtaining the vertical deformation curve of the rails and the related results of the vertical force of the fasteners based on the vertical displacement of the bridge as a boundary condition, thus obtaining the vertical deformation mapping relationship between the line and the bridge.

[0167] Example 6

[0168] This embodiment 6 provides an electronic device, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to execute instructions to implement the above-described method for analyzing the vertical displacement mapping relationship between ballasted track lines and bridges on high-speed railway long-span bridges. The method includes: establishing differential equilibrium equations of track mechanics based on the mechanical properties of the track structure, and obtaining analytical solutions for the mapping relationship between the ballasted track line structure sub-model and the substructure structure; establishing a finite element model of the long-span bridge based on the finite element principle and the stress characteristics of bridge structural components; calculating the vertical displacement deformation curve of the bridge deck based on the established finite element model of the long-span bridge; when the grid of the long-span bridge is smaller than the sleeper support spacing, using interpolation to obtain the vertical displacement of the bridge beam surface corresponding to each sleeper position; and obtaining the vertical deformation curve of the rails and the related results of the vertical force of the fasteners based on the vertical displacement of the bridge as a boundary condition, thus obtaining the vertical deformation mapping relationship between the line and the bridge.

[0169] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0170] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0171] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0172] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 Figure 1 The steps of the function specified in one or more boxes.

[0173] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solutions disclosed in the present invention, various modifications or variations that can be made by those skilled in the art without creative effort should be included within the scope of protection of the present invention.

Claims

1. A method for analyzing the mapping relationship between ballast track lines and vertical displacement of a high-speed railway long-span bridge, characterized in that, include: Based on the mechanical properties of the track structure, a differential equilibrium equation for track mechanics is established, and an analytical solution is obtained to determine the mapping relationship between the sub-model of the ballast track line structure and the substructure. Based on the finite element principle and the stress characteristics of bridge structural components, a finite element model of a long-span bridge is established. Based on the established finite element model of the long-span bridge, the vertical displacement deformation curve of the bridge deck is calculated. When the mesh of the long-span bridge is smaller than the sleeper support spacing, the interpolation method is used to find the vertical displacement of the bridge beam surface corresponding to the position of each sleeper. The calculated vertical displacement deformation curve of the bridge is used as the boundary condition of the ballast track line structure sub-model. The vertical displacement deformation curve of the rail is then obtained, and the vertical displacement mapping relationship between the line and the bridge is derived.

2. The method for analyzing the vertical displacement mapping relationship between ballast track and bridge on a high-speed railway long-span bridge according to claim 1, characterized in that, The contribution of the vertical stiffness of the track structure is ignored when calculating bridge deformation; The ballast track thickness distribution on the long-span bridge is uneven. When calculating the vertical displacement of the bridge, the secondary dead load of the ballast track structure is considered as a non-uniformly distributed force or the unit weight of the bridge deck. When calculating the vertical deformation of the track structure, the vertical and lateral coupling effects are not considered. The vertical stiffness of the sleepers is ignored in the calculation, and only the vertical mass of the sleepers is considered. The analysis model of the vertical displacement mapping relationship between the line and the bridge is divided into a ballast track sub-structure model and a bridge sub-model. The track sub-model is solved analytically, while the bridge sub-model is established using the finite element method.

3. The method for analyzing the vertical displacement mapping relationship between ballast track and bridge on a high-speed railway long-span bridge according to claim 1, characterized in that, A ballasted track model was established using analytical methods, and the mechanical equilibrium equations of the rail beam are as follows: Gravitational equilibrium equations: Torque balance equation: The mechanical equilibrium equations for the steel rail beam are as follows: The mechanical equilibrium equations for the sleeper track bed mass block are as follows: Combining the above two equations, we can obtain the following equations for solving the mass block of the rail and sleeper track bed: Among them, the transfer matrix Displacement matrix and Boundary conditions are expressed as follows: After deriving the mechanical equations of the track structure sub-model, the equations are solved to obtain the vertical displacement of the rails and the vertical force of the fasteners.

4. The method for analyzing the vertical displacement mapping relationship between ballasted track lines and bridges on high-speed railway long-span bridges according to claim 1, characterized in that, The finite element model of the long-span cable-stayed bridge includes the steel truss main girder, bridge deck, stay cables, main tower, and auxiliary piers. The steel truss main girder consists of upper chords, lower chords, web members, steel longitudinal beams, and orthotropic bridge deck. The upper chords, lower chords, steel longitudinal beams, and web members are simulated using spatial beam element models, with rigid connections between adjacent members. The orthotropic plates are simulated using shell elements to consider their stress characteristics. The main tower and auxiliary piers mainly bear pressure and bending moment under symmetrical temperature action, and their variable cross-section characteristics are considered, so they are simulated using spatial beam elements. The long-span bridge adopts a semi-floating system. The main tower and main girder are connected longitudinally by longitudinal dampers, which are simulated using linear springs. The bridge tower and main girder are coupled and constrained laterally and vertically. The stay cables are slender and flexible structures, simulated using tension-only member elements. The stay cables are coupled and connected longitudinally, laterally, and vertically to the upper chord nodes of the main girder and the nodes of the main tower, respectively. The bases of the main tower and auxiliary piers are fully constrained.

5. The method for analyzing the vertical displacement mapping relationship between ballasted track lines and bridges on high-speed railway long-span bridges according to claim 1, characterized in that, The modeling objects of the finite element model of the long-span suspension bridge include the steel truss main girder, bridge deck, suspenders, main cable, main tower, and auxiliary side piers. The modeling method of the steel truss main girder, main tower, and longitudinal dampers is the same as that of the long-span cable-stayed bridge. The main cable and suspenders are considered to have tensile characteristics and are simulated using tension-only rod elements. The two sides of the main cable are connected to the nodes of the two main towers respectively. One end of the suspender node is connected to the main cable, and the other end is connected to the upper chord of the main girder. One side of the back cable is connected to the node of the main tower, and the other side is connected to the ground by anchorage. The back cable is fully constrained. The bottom of the main tower and the bottom of the auxiliary side pier are also fully constrained.

6. A system for analyzing the mapping relationship between ballasted track lines and vertical displacement of a high-speed railway long-span bridge, characterized in that, include: The module is used to establish differential equilibrium equations of track mechanics based on the mechanical properties of the track structure, and to obtain analytical solutions for the mapping relationship between the sub-model of the ballast track line structure and the substructure. Based on the finite element principle and the stress characteristics of bridge structural components, a finite element model of a long-span bridge is established. The calculation module is used to calculate the vertical displacement deformation curve of the bridge deck based on the established finite element model of the long-span bridge. When the mesh of the long-span bridge is smaller than the sleeper support spacing, the interpolation method is used to find the vertical displacement of the bridge beam surface corresponding to the position of each sleeper. The mapping module is used to calculate the vertical displacement deformation curve of the bridge as the boundary condition of the ballast track line structure sub-model, to obtain the vertical displacement deformation curve of the rail, and to obtain the vertical displacement mapping relationship between the line and the bridge.

7. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement the method for analyzing the vertical displacement mapping relationship between ballast track lines and bridges on high-speed railway long-span bridges as described in any one of claims 1-5.

8. A computer device, characterized in that, The system includes a memory and a processor, which communicate with each other. The memory stores program instructions that can be executed by the processor. The processor calls the program instructions to execute the method for analyzing the vertical displacement mapping relationship between ballast track lines and bridges on high-speed railway long-span bridges as described in any one of claims 1-5.

9. An electronic device, characterized in that, include: The device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to execute instructions for implementing the method for analyzing the vertical displacement mapping relationship between ballast track lines and bridges on high-speed railway long-span bridges as described in any one of claims 1-5.

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