Bridge pier and abutment rigidity calculation method based on railway continuous welded rail design

Abstract

This invention discloses a method for calculating the stiffness of bridge piers and abutments based on seamless railway track design, comprising: S1, constructing a spatial model of pier-beam-track bed-rail; S2, calculating the mechanical properties of the track and bridge under temperature effects; S3, calculating the mechanical properties of the track and bridge under train loads; S4, determining constraint limits based on the calculation results; S5, optimizing the range of each index in S4 and determining the stiffness of the bridge piers and abutments; if no adjustment is needed, proceed to S7; if adjustment is needed, proceed to S6; S6, adjusting the stiffness of the bridge piers and abutments in the model in S1, and executing S2, S3, and S4 until the indexes are within the optimized range; S7, outputting the bridge pier and abutment stiffness dataset; S2 and S3 are parallel steps. This invention establishes a mechanical analysis model of seamless track-bridge under various bridge types, derives reasonable bridge pier and abutment stiffness based on seamless railway tracks, and provides theoretical support for railway bridge structural design.

Description

Technical Field

[0001] This invention relates to the field of railway engineering structural design, specifically to a method and computer equipment for calculating the stiffness of bridge piers and abutments based on seamless railway track design. Background Technology

[0002] Seamless track eliminates rail joints through welding or freezing techniques, achieving a seamless track surface. This improves train stability, reduces noise, and decreases maintenance workload. In the design of the substructure bridge, the stiffness of the bridge piers is a core parameter for controlling the coordinated deformation of the beam and rail, and ensuring the safe operation of the line.

[0003] Under the influence of train traction and braking loads, temperature changes, and other factors, seamless railway tracks will undergo longitudinal deformation. When the deformation of the seamless railway track and the bridge cannot be coordinated, there is a risk that the longitudinal stress of the seamless railway track will exceed the limit, leading to rail breakage or rail bulging. The rationality of the stiffness values ​​of bridge piers and abutments must be determined through data calculation and verification.

[0004] In actual engineering design, each bridge pier along the route has independent stiffness parameter samples, covering different pier heights, foundation types, and geological conditions, forming a massive dataset of bridge pier stiffness data. Traditional experience-based verification methods cannot meet the needs of large-scale and precise design. When the stiffness value of the bridge pier is too high, it significantly increases project investment. At the same time, the stiffness value of the bridge pier should not be too low to avoid excessive additional forces and displacements on the rails, which could lead to damage, affecting structural safety and passenger comfort.

[0005] Therefore, it is urgent to develop a method for calculating the stiffness of bridge piers and abutments based on seamless railway track design. By reasonably optimizing the longitudinal stiffness of the piers and abutments, the project construction investment can be effectively controlled while ensuring the safe operation of the seamless track, thereby achieving a synergistic improvement in technical reliability and economic benefits. Summary of the Invention

[0006] This invention addresses at least one technical problem in the prior art by disclosing a method for calculating the stiffness of bridge piers based on seamless railway track design. By constructing a finite element model of the space between the pier, beam, track bed, and rail, this invention takes into account both the temperature changes of the seamless track and the dual working conditions of train load. The stress deformation of the seamless track and the stiffness calculation of the piers conform to the law of beam-rail coordinated deformation, solving the problems of incoordination between the deformation of the seamless track and the sub-bridge and unreasonable pier design, and avoiding the resource waste caused by structural design redundancy.

[0007] This invention is achieved through the following technical solution:

[0008] This invention first provides a method for calculating the stiffness of bridge piers and abutments based on seamless railway track design, including the following steps:

[0009] S1. Construct a finite element model of the space between the pier, the beam, the track bed, and the rail;

[0010] S2. Obtain the rail stress, horizontal displacement of the bridge pier top, and rail fracture under temperature changes using a finite element model.

[0011] S3. Obtain the tensile stress at the bottom of the rail under the vertical load of the train, and obtain the rail stress, relative displacement of the beam and rail, and horizontal displacement of the bridge pier top under the finite element model under the traction and braking load of the train.

[0012] S4. Calculate the total stress of the rail. The total stress of the rail = the rail stress under temperature change + the tensile stress on the rail base under the vertical load of the train + the rail stress under the traction and braking load of the train. Set the constraints on the total stress of the rail, the rail joint, the relative displacement between the beam and the rail, and the horizontal displacement of the bridge pier top to meet the actual needs of the project.

[0013] S5. Optimize the constraint limit range of the total stress of the rail, the rail joint, the relative displacement of the beam and rail, and the horizontal displacement of the bridge pier top, and determine whether the stiffness of the bridge pier needs to be adjusted based on the optimized limit range. If no adjustment is needed, proceed directly to S7; if adjustment is needed, proceed to S6.

[0014] S6. Adjust the stiffness of the bridge piers in the S1 model, and perform calculations S2, S3, and S4 until the total stress of the rail, the rail joint, the relative displacement of the beam and rail, and the horizontal displacement of the bridge pier top are within the optimized limit range. S7. Output the optimized bridge pier stiffness;

[0015] Steps S2 and S3 are parallel steps.

[0016] This application establishes a finite element model of the pier-beam-track bed-rail space, taking into account both temperature variations and train loads on the seamless track. The stress deformation and pier stiffness calculations for the seamless track conform to the beam-rail coordinated deformation law. Simultaneously, multi-index constraint control is employed, and index limits are defined to ensure railway operational safety. By iteratively correcting pier stiffness parameters and repeatedly recalculating and verifying, reasonable stiffness parameters are selected, effectively reducing the blindness of manual calculations for pier stiffness in long-span, multi-span bridges and significantly shortening the pier stiffness design verification cycle. This application controls pier stiffness from the source of coupled forces between the track and the bridge, effectively controlling issues such as total rail stress, rail gaps, relative beam-rail displacement, and excessive bridge pier top displacement. By rationally optimizing the longitudinal stiffness of the piers, while ensuring the safe operation of the seamless track, engineering construction investment is effectively controlled, achieving a synergistic improvement in technical reliability and economic benefits.

[0017] As a further option, the track bed includes ballast track bed and ballastless track bed.

[0018] As a further solution, S1 includes the following method:

[0019] S11. Obtain the database, which includes the actual dimensions, material characteristic values, and cross-sectional characteristic values ​​of the bridge and track structures, as well as the bridge span arrangement and the stiffness of each bridge pier.

[0020] S12. Input the material characteristic values ​​and cross-sectional characteristic values ​​of the bridge, track bed, and rail into the finite element software respectively;

[0021] S13. Based on the spatial relationship between the rails, track bed, beams, bridge piers and abutments and the roadbed surface, set up the nodes corresponding to each structure;

[0022] S14. Connect the corresponding nodes of the rail, track bed and beam in sequence to generate rail, track bed and beam elements. Select beam element as the element type.

[0023] S15. Add boundary conditions to constrain the nodes mentioned in S13.

[0024] This method accurately recreates the mechanical properties of rails and bridges by inputting key material and cross-sectional parameters item by item, eliminating simulation calculation errors caused by coarse parameter values ​​and improving the baseline reliability of the finite element model. It divides nodes according to the actual spatial topology and uses beam elements to simulate the structure, closely matching the coordinated stress structure of rails, track bed, beams, and piers, accurately reflecting the linkage deformation characteristics of each component. It recreates the actual support conditions of piers and roadbeds, avoiding boundary distortion problems, making the finite element simulation close to the actual on-site engineering, and providing a reliable model basis for subsequent simulations of temperature effects and train loads.

[0025] As a further solution, the method for constraining the node in S15 includes:

[0026] S151. Add general supports at the bridge pier nodes, without restricting the longitudinal displacement of the bridge pier nodes along the line, and without restricting the rotation of the bridge pier nodes along the horizontal axis perpendicular to the line.

[0027] S152. Add general supports at the roadbed surface nodes to fully constrain the roadbed surface nodes;

[0028] S153. Add elastic supports at the bridge pier nodes to constrain the bridge pier nodes along the longitudinal direction of the line. The stiffness of the elastic supports is the stiffness of the bridge pier. When the bridge is a T-shaped rigid frame beam or a continuous rigid frame beam, rotational constraints about the horizontal axis perpendicular to the line should be added to the bridge pier nodes.

[0029] S154. Add elastic connections between bridge pier nodes and beam nodes to fix displacement and rotation in all directions;

[0030] S155. Add elastic connections between beam nodes and track bed nodes to fix displacement and rotation in all directions;

[0031] S156. Add an elastic connection between the track bed node and the rail node to fix lateral and vertical displacement and rotation in all directions;

[0032] S157. Establish the deformation-internal force function, define the nonlinear spring stiffness to simulate the longitudinal resistance of the track, add elastic connections between the track bed nodes and rail nodes, and input the nonlinear spring stiffness into the longitudinal direction of the track.

[0033] S158. Add general supports at the rail nodes corresponding to the end point of the roadbed surface to fully constrain the rail nodes.

[0034] This method employs unrestricted lateral rotation and partial translation of the piers, along with full consolidation of the roadbed. By using longitudinal elastic supports to represent the actual stiffness of the piers, it recreates the actual deformation characteristics of the piers. The pier stiffness values ​​and iterative verification are based on sound evidence, better reflecting engineering realities. Specifically, by rigidly connecting the piers and beams and imposing lateral and vertical constraints on the rails, it distinguishes the relationship between the bridge's consolidation and the track's flexible coupling, accurately transmitting lateral and vertical loads and avoiding simulation distortion caused by excessive or insufficient displacement constraints. These constraints rely on a custom deformation internal force function to simulate the nonlinear characteristics of track resistance, accurately simulating beam-rail interaction and improving the accuracy of track-bridge coupled force calculations under temperature changes and train load conditions. In particular, the full constraint of the rails at the end of the line fully considers the impact of boundary effects, ensuring the overall reliability of the finite element calculation convergence.

[0035] As a further embodiment, S2 includes:

[0036] S21. Calculate the temperature change of the rail;

[0037] S22. Calculate the temperature change of the bridge;

[0038] S23. Input the temperature changes obtained in S21 and S22 into the finite element model of S1. The finite element model outputs the horizontal displacement of the bridge pier top under rail stress and temperature changes.

[0039] S24. Set the positions of each bridge pier in the finite element model as broken rails, and input the temperature changes in S21 and S22 to calculate the rail gap.

[0040] This method applies temperature-varying loads independently to both the rails and the bridge, fully considering the differences in temperature deformation of different structural materials. This effectively avoids calculation errors caused by uniform temperature loading and accurately obtains data on rail stress and pier top horizontal displacement under temperature conditions. Simultaneously, by setting a rail breakage condition at the pier location and applying temperature loads concurrently, the rail breakage value can be accurately calculated, effectively verifying the risk of low-temperature rail breakage on seamless tracks. This step reuses a unified finite element model to complete calculations for both conventional temperature-varying and extreme rail breakage conditions, ensuring a unified benchmark and realistic simulation, thus improving the comprehensiveness and accuracy of the calculations. This method simultaneously considers the coupled effects of multiple conditions, including train vertical loads, traction loads, and braking loads, covering the main stress forms during train operation and avoiding omissions caused by single-load calculations. By uniformly solving for indicators such as rail stress, beam-rail relative displacement, and pier top horizontal displacement using a finite element model, the coupled stress and deformation characteristics of the rail-bridge under train loads can be comprehensively reflected, effectively improving the engineering applicability of pier stiffness calculations.

[0041] As a further solution, the method for optimizing the constraint limit range of the total rail stress, the rail breakage, the relative displacement of the beam and rail, and the horizontal displacement of the bridge pier top in S5 is as follows: the constraint conditions of the total rail stress, the rail breakage, the relative displacement of the beam and rail, and the horizontal displacement of the bridge pier top are each multiplied by a coefficient less than 1.

[0042] This method superimposes multiple stress sources, including temperature, vertical stress, and traction / braking stress, to obtain the total stress of the rail. It closely matches the actual composite stress state of the line and sequentially sets limit constraints for the total stress of the rail, joint fracture, relative displacement between beam and rail, and displacement at the pier top. This achieves coordinated control of multiple indicators, avoids design oversights caused by controlling a single indicator, and provides a complete and reliable basis for iterative optimization of pier stiffness.

[0043] As a further solution, the method for adjusting the stiffness of bridge piers and abutments in the finite element model in S6 includes:

[0044] S61. Based on the initial stiffness dataset of each bridge pier, if the total stress of the rail, the rail joint, the relative displacement of the beam and rail, and the horizontal displacement of the bridge pier top at the i-th bridge pier position are outside the constraints in S4, increase the stiffness of the i-th bridge pier until all the above parameters satisfy the constraints in S4.

[0045] S62. Based on S61, if the total stress of the rail, the rail joint, the relative displacement of the beam and rail, and the horizontal displacement of the bridge pier top at the i-th bridge pier position do not meet the optimized range in S5, reduce the stiffness of the i-th bridge pier to form the first adjusted stiffness dataset of each bridge pier.

[0046] S63. Substitute the adjusted stiffness dataset of each bridge pier into the finite element model and execute calculations S2, S3, and S4 to obtain a set of data including the total stress of the rails. 调1 Rail joint 调1 Relative displacement between beam and rail 调1 and horizontal displacement of bridge pier top 调1 The new dataset was used to generate the second adjusted stiffness dataset for each bridge pier using a data fitting method.

[0047] S64. Continuously adjust the stiffness dataset of each bridge pier until a certain index value of the total stress of the rail, the rail joint, the relative displacement of the beam and rail, and the horizontal displacement of the bridge pier top at each bridge pier position meets the optimized range in S5 and the constraint conditions in S4.

[0048] This step iteratively adjusts the stiffness parameters of bridge piers and abutments, and repeatedly recalculates various control indicators under temperature and train load conditions to achieve closed-loop optimization design of pier stiffness. Through continuous iterative correction, the rail stress, joint fracture, relative displacement between beam and rail, and pier top displacement all meet the specification limits, avoiding the problems of conservative indicators or insufficient safety reserves in traditional fixed-value design, and effectively improving the rationality, safety, and economy of pier stiffness design.

[0049] The features and beneficial effects of this invention are as follows:

[0050] (1) This invention constructs a mechanical analysis model of seamless track-bridge structure under various bridge types. The stress on the rail, the relative displacement between the beam and the rail, the rail joint and the horizontal displacement of the bridge pier top are used as control indicators. The calculation and analysis are carried out in combination with the dual working conditions of temperature change and train load. The obtained pier stiffness value conforms to the law of beam-rail cooperative deformation, which provides theoretical support for the structural design of railway bridge piers.

[0051] (2) In view of the fact that the amount of sample data of bridge pier stiffness in actual engineering is large and traditional experience verification is difficult to meet the requirements of large-scale and precise design, the present invention has formed an iterative calculation method for bridge pier stiffness, which can reasonably control the value of bridge pier stiffness, ensuring the safe operation of seamless lines and effectively controlling the investment in engineering construction, thereby achieving a synergistic improvement in technical reliability and economic benefits. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. 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.

[0053] Figure 1This is a flowchart of the method for calculating the stiffness of bridge piers and abutments based on seamless railway track design, as described in an embodiment of the present invention.

[0054] Figure 2 This is a schematic diagram of the spatial finite element model of pier-beam-track bed-rail described in an embodiment of the present invention;

[0055] Figure 3 This is a schematic diagram of the spatial finite element model of pier-beam-track bed-rail when the beam body is a simply supported beam according to an embodiment of the present invention;

[0056] Figure 4 This is a schematic diagram of the ZK load according to an embodiment of the present invention. Detailed Implementation

[0057] To facilitate understanding of the present invention, a more comprehensive description of the present invention will be given below, and embodiments of the present invention will be provided, but this does not limit the scope of the present invention.

[0058] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0059] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0060] Definitions:

[0061] ZK: Z represents the load code of China's dedicated railway trains, and K represents high-speed passenger transport (passenger dedicated line / high-speed rail).

[0062] General support: This refers to the common preset boundary conditions used in finite element analysis software in this field. Its mechanical essence is a six-degree-of-freedom fully constrained fixed support. Those skilled in the art can clearly understand its constraint range, and it is not a vague technical feature.

[0063] A method for calculating the stiffness of bridge piers and abutments based on seamless railway track design, such as Figures 1 to 4 As shown, it includes the following steps:

[0064] S1. A spatial finite element model of the pier-beam-track bed-rail is constructed using finite element software, such as... Figure 2 As shown, △ represents a fixed support and ○ represents a movable support.

[0065] In some embodiments, the finite element software used is Midas Civil software.

[0066] The track bed includes ballast track bed and ballastless track bed.

[0067] The ballast bed is an important component of the track and forms the foundation of the track frame. It typically refers to the ballast layer or reinforced concrete layer laid on top of the substructure such as roadbed, bridge, or tunnel, beneath the rails. This structure bears the load of the upper track and distributes it evenly to the lower foundation, maintaining the good geometry of the rails.

[0068] Methods for constructing finite element models using Midas Civil software include:

[0069] S11. Obtain the database, which includes the actual dimensions, material characteristic values, and cross-sectional characteristic values ​​of the bridge and track structures, as well as the bridge span arrangement and the stiffness of each bridge pier.

[0070] The track structure includes rails, fasteners, sleepers, and ballast; the ballast is divided into two categories: ballasted (crushed stone ballast) and ballastless (concrete monolithic ballast).

[0071] The material characteristic values ​​include elastic modulus, Poisson's ratio, and coefficient of linear expansion; the cross-sectional characteristic values ​​include cross-sectional area and moment of inertia.

[0072] S12. Input the material characteristic values ​​and cross-sectional characteristic values ​​of the bridge, track bed, and rail into the finite element software respectively;

[0073] S13. Establish nodes: Based on the spatial relationship between the rails, track bed, beams, bridge piers and the roadbed surface, set up the nodes corresponding to each structure.

[0074] S14. Create elements: Connect the corresponding nodes of the rail, track bed, and beam in sequence to generate rail, track bed, and beam elements. Select beam element as the element type.

[0075] S15. Add boundary conditions to constrain the nodes mentioned in S13.

[0076] The methods for constraining the nodes include:

[0077] S151. Add general supports at the bridge pier nodes, without restricting the longitudinal displacement of the bridge pier nodes along the line, and without restricting the rotation of the bridge pier nodes along the horizontal axis perpendicular to the line.

[0078] S152. Add general supports at the roadbed surface nodes to fully constrain the roadbed surface nodes.

[0079] S153. Add elastic supports at the bridge pier nodes to constrain the bridge pier nodes along the longitudinal direction of the line. The stiffness of the elastic supports is the stiffness of the bridge pier.

[0080] S154. Add elastic connections between bridge pier nodes and beam nodes to fix displacement and rotation in all directions.

[0081] In practical applications, the material types of beams include concrete beams and steel beams.

[0082] The structural forms of beams include simply supported beams, continuous beams, T-shaped rigid frame beams, and continuous rigid frame beams.

[0083] For simply supported beams and continuous beams, the elastic support constraints added to the bridge pier nodes are simulated according to S151 and S153. For T-shaped rigid frame beams and continuous rigid frame beams, the elastic support added to the bridge pier nodes at the rigid frame pier positions should be based on the simulation of S151 and S153, and rotation constraints about the horizontal axis perpendicular to the line should be added to the bridge pier nodes.

[0084] The initial bridge pier stiffness is reflected in the elastic supports of the nodes and can be expressed by Equation 1:

[0085] (1);

[0086] in, This represents the initial dataset of stiffness for each bridge pier and abutment. represents the stiffness of the i-th bridge pier; k represents the total number of bridge piers.

[0087] S155. Add elastic connections between beam nodes and track bed nodes to fix lateral and vertical displacements and rotations in all directions.

[0088] S156. Add elastic connections between the track bed nodes and rail nodes to fix lateral and vertical displacements and rotations in all directions.

[0089] S157. Establish the deformation-internal force function and define the nonlinear spring stiffness to simulate the longitudinal resistance of the track. Add an elastic connection between the track bed node and the rail node, and input the nonlinear spring stiffness into the longitudinal direction of the track.

[0090] S158. Add general supports at the rail nodes corresponding to the end point of the roadbed surface to fully constrain the rail nodes.

[0091] S2. Calculate the mechanical properties of the track and bridge under temperature changes;

[0092] S21. Calculate the temperature change of the rail;

[0093] The temperature variation of the rails is determined based on geological data along the route, using the local historical extreme maximum and minimum rail temperatures. The temperature change of the rail is expressed as:

[0094] (2);

[0095] Among them, t r This indicates the temperature change of the rail, expressed in °C. Indicates the design lock-in rail temperature. This represents the design locking rail temperature correction value, ranging from 0 to 5℃; This indicates the local lowest orbital temperature, in °C.

[0096] S22. Calculate the temperature change of the bridge: Based on geological data and the type of bridge materials, determine the values ​​of the overall uniform temperature rise and fall of the structure and the vertical temperature gradient in accordance with current specifications.

[0097] S23. Input the temperature changes obtained from S21 and S22 into the finite element model of S1. The finite element model outputs the rail stress under the temperature change. Horizontal displacement of bridge pier top under temperature changes .

[0098] (3);

[0099] in, This represents a dataset of rail stress under temperature variations at various bridge pier locations. This represents the rail stress at the i-th bridge pier location under temperature changes.

[0100] (4);

[0101] in, This dataset represents the horizontal displacement of the bridge pier top under temperature changes at various bridge pier locations. This represents the horizontal displacement of the top of the bridge pier due to temperature changes at the location of the i-th bridge pier.

[0102] S24. Set the locations of each bridge pier in the finite element model of S1 as rail breaks, and input the temperature changes in S21 and S22 to calculate the rail fracture. .

[0103] (5);

[0104] in, This represents the rail breakage calculated at the location of the i-th bridge pier.

[0105] S3. Calculate the mechanical properties of the track and bridge under train load;

[0106] Train loads include vertical train loads and train traction and braking loads (along the longitudinal direction of the track).

[0107] S31. Obtain the tensile stress at the bottom of the rail under the vertical load of the train.

[0108] (6);

[0109] in, Data set representing the tensile stress at the bottom of the rails under vertical train loads at each bridge pier location; This represents the rail stress under the vertical load of the train at the i-th bridge pier location.

[0110] S32. Calculate the train traction and braking loads, simulating the static effects of the train on the track infrastructure using railway train load diagrams. For high-speed railways, intercity railways, passenger-freight mixed lines, and heavy-haul railways, ZK, ZC, ZKH, and ZH load diagrams are used respectively. By using traction load coefficients and braking load coefficients, the railway train load diagrams are transformed from vertical loads into longitudinal loads along the track.

[0111] The train traction load is expressed as:

[0112] F q =F t ×a q (7);

[0113] Among them, F q Indicates the train traction load; F t Represents railway load diagrams; a q This indicates the traction load factor.

[0114] Train braking load is expressed as:

[0115] F z =F t ×a z (8);

[0116] Among them, F zIndicates the train braking load; F t Represents railway load diagrams; a z This indicates the braking load coefficient.

[0117] S33, the train traction load F in S32 q and train braking load F z In the finite element model input S1, the finite element model outputs the rail stress under train traction and braking. Relative displacement between beam and rail and horizontal displacement of bridge pier top The following are respectively represented:

[0118] (9);

[0119] in, This dataset represents the maximum values ​​of rail stress under traction and braking loads at various bridge pier locations. This represents the rail stress dataset under traction load at the i-th bridge pier location. This represents the rail stress dataset under braking load at the i-th bridge pier position.

[0120] (10);

[0121] in, This dataset represents the largest relative displacement values ​​between the beam and rail under traction and braking loads at each bridge pier location. This represents the relative displacement of the beam and rail under the traction load at the position of the i-th bridge pier; This represents the relative displacement of the beam and rail under braking load at the position of the i-th bridge pier.

[0122] (11);

[0123] in, This indicates the maximum horizontal displacement of the bridge pier top under traction and braking loads at each bridge pier location. This represents the horizontal displacement of the top of the bridge pier under the traction load at the position of the i-th bridge pier. This represents the horizontal displacement of the top of the bridge pier under the braking load at the i-th bridge pier position.

[0124] S4. Constraints are given to the calculated index results to meet actual needs. The index results include total rail stress, rail fracture, relative displacement between beam and rail, and horizontal displacement of bridge pier top.

[0125] S41. Calculate the total stress of the rail and set constraints. Total stress of the rail The rail stress calculated by S2 under temperature changes, the rail stress calculated by S3 under vertical train load, and the rail stress calculated by S3 under train traction and braking must meet the following requirements:

[0126] (12);

[0127] This indicates the stress limit of the rail. The stress limit varies depending on the rail material. When the rail is U71Mn or U71MnG, the stress limit is 351.5 MPa; when the rail is U75V or U75VG, the stress limit is 363 MPa.

[0128] S42. Set constraint conditions for rail joint breaks;

[0129] The rail gap is calculated using S2 and must meet the following requirements:

[0130] (13);

[0131] in, This indicates the limit for rail breakage. To ensure that vehicles can pass safely and normally after a rail breakage, the limit for breakage is 70mm.

[0132] S43. Set the constraint conditions for the relative displacement of the beam and rail;

[0133] The relative displacement between the beam and the rail is calculated as S3, and must satisfy the following:

[0134] (14);

[0135] in, This represents the relative displacement limit between the beam and the rail. To ensure track stability, a value of 4mm is used.

[0136] S44. Set constraints on the horizontal displacement of the bridge pier top;

[0137] The horizontal displacements at the top of the bridge piers, S2 and S3, are calculated as follows:

[0138] (15);

[0139] (16);

[0140] in, This indicates the maximum horizontal displacement of the bridge pier top under temperature changes, traction, and braking loads. The value represents the horizontal displacement limit at the top of the bridge pier; L is the calculated span of the bridge: when the actual span is less than 24m, the calculated value is uniformly taken as 24m; when the bridge has an unequal span arrangement, the smaller span between two adjacent spans is selected as the calculated span L.

[0141] S5. In order to improve the accuracy of the model, the range of the values ​​of each index in S4 is optimized, and the stiffness of the bridge piers is determined based on the optimized results.

[0142] S51. When all parameters in S4 meet the requirements, it indicates that the stiffness values ​​of all bridge piers and abutments meet the structural safety requirements. However, excessive stiffness of bridge piers and abutments may lead to poor engineering economics. Therefore, each parameter is optimized, as follows:

[0143] Total stress of rail :

[0144] (17);

[0145] in, This represents the rail stress limit factor. ;

[0146] Rail gap :

[0147] (18);

[0148] in, This represents the limit coefficient for rail fracture. ;

[0149] relative displacement between beam and rail :

[0150] (19);

[0151] in, This represents the limit coefficient for the relative displacement between the beam and the rail. ;

[0152] Horizontal displacement of bridge pier top :

[0153] (20);

[0154] in, This represents the limit coefficient for horizontal displacement at the top of the bridge pier. .

[0155] S52. Determine whether the optimized parameter requirements in S51 are met based on the results of S4.

[0156] When the total stress of the rail Rail joint Relative displacement between beam and rail Horizontal displacement of bridge pier top If any of the index values ​​exceeds the limits of formulas (12), (13), (14) and (16), it indicates that the stiffness of some bridge piers is too small. At this time, increase the stiffness of the bridge pier at that location, adjust the stiffness of the bridge pier in model S1, and perform calculations S2, S3, and S4 until all index values ​​are within the limits of formulas (12), (13), (14) and (16).

[0157] When the total stress of the rail Rail joint Relative displacement between beam and rail Horizontal displacement of bridge pier top When all values ​​are within the limits of formulas (12), (13), (14) and (16), it is then determined whether the value of a certain index at each bridge pier position meets the requirements of formulas (17), (18), (19) and (20). If the requirements are not met, S6 is executed to adjust the stiffness of the bridge pier. If the requirements are met, S7 is executed directly to output the stiffness of the bridge pier.

[0158] S6. Adjust the stiffness of the bridge piers in the finite element model, and perform calculations S2, S3, and S4 until each index is within the optimized limit range.

[0159] The method for adjusting the stiffness of bridge piers and abutments is as follows:

[0160] S61. In the initial stiffness dataset of each bridge pier... Based on this, if the total stress of the rail at the i-th bridge pier position... Rail joint Relative displacement between beam and rail Horizontal displacement of bridge pier top Outside the range of formulas (12), (13), (14) and (16), increase the stiffness of the i-th bridge pier until all the above parameters satisfy formulas (12), (13), (14) and (16).

[0161] S62, If the total stress of the rail at the i-th bridge pier position... Rail joint Relative displacement between beam and rail Horizontal displacement of bridge pier top Outside the range of formulas (17), (18), (19), and (20), the stiffness of the i-th bridge pier needs to be reduced to form the first adjusted stiffness dataset of each bridge pier. .

[0162] (twenty one);

[0163] in, This represents the stiffness of the i-th bridge pier after the first adjustment.

[0164] S63. The adjusted stiffness dataset for each bridge pier / abutment after the first adjustment. Substituting into model S1, calculations S2, S3, and S4 are performed to obtain a new dataset of total rail stress, rail fracture, relative beam-rail displacement, and horizontal displacement at the top of bridge piers. A second set of adjusted stiffness datasets for each bridge pier is then generated using a data fitting method. Data fitting methods include linear fitting, exponential fitting, logarithmic fitting, and polynomial fitting.

[0165] S64. Continuously adjust the stiffness dataset of each bridge pier until the calculated total stress of the rail, the rail joint, the relative displacement of the beam and rail and the horizontal displacement of the bridge pier top at each bridge pier position satisfy the formulas (17), (18), (19) and (20), and at the same time, the values ​​of each indicator at each bridge pier position satisfy the formulas (12), (13), (14) and (16).

[0166] S7. Output the optimized bridge pier stiffness.

[0167] Example

[0168] The parameters of the finite element model of the pier-beam-track-rail space of the high-speed railway double-track simply supported beam bridge are shown in Table 1 below.

[0169] Table 1

[0170]

[0171] Based on empirical values ​​for bridge pier and abutment stiffness, for the above structure, the abutment stiffness is taken as 3000 kN / cm, and the bridge pier and abutment stiffness is taken as 350 kN / cm. The specific calculation process is as follows:

[0172] A1, such as Figure 3 As shown, △ represents a fixed support and ○ represents a movable support. In this embodiment, there are 6 bridge piers. A spatial finite element model of pier-beam-track bed-rail is established for calculation.

[0173] The initial stiffness dataset for each bridge pier is obtained according to formula (1):

[0174] .

[0175] A2. Calculate the mechanical properties of the track and bridge under temperature changes;

[0176] Calculate the temperature change of the rail: local minimum rail temperature The temperature is -27.4℃, and the designed locking rail temperature is 23±5℃. The rail temperature change is determined according to formula (2): .

[0177] Calculation of bridge temperature changes: Based on geological data and bridge material type, the overall temperature rise and fall range of the bridge is 15℃.

[0178] Inputting the aforementioned temperature changes into the model S1 outputs the rail stress. Horizontal displacement of bridge pier top According to formulas (3) and (4), we get:

[0179] ;

[0180] ;

[0181] Set the locations of each bridge pier in the S1 model as rail breaks, input the above temperature changes, calculate the rail breakage, and obtain the result from formula (5):

[0182] ;

[0183] A3. Under the vertical load of the train, the tensile stress at the bottom of the rail is obtained from formula (6): High-speed railways use the ZK load.

[0184] ;

[0185] ZK load as Figure 4 As shown, combined with Figure 4 Perform the following calculations:

[0186] The train traction load (where a is the load length range) is obtained from formula (7):

[0187] ;

[0188] The train braking load (where a is the load length range) is obtained from formula (8):

[0189] ;

[0190] The traction load F of the above-mentioned train q and train braking load F z In the model input S1, the output rail stress, relative displacement between beam and rail, and horizontal displacement at the top of bridge pier are obtained from formulas (9), (10), and (11):

[0191] ;

[0192] ;

[0193] ;

[0194] When U71MnG rail is used, the rail stress limit is... It is 351.5 MPa.

[0195] According to formula (12):

[0196] ;

[0197] Breakage limit It is 70mm.

[0198] The rail gap is calculated according to formula (7). ;

[0199] Beam-rail relative displacement limit It is 4mm.

[0200] The relative displacement between the beam and the rail is obtained according to formula (14):

[0201] ;

[0202] The horizontal displacement limit of the bridge pier top is obtained according to formulas (15) and (16). Horizontal displacement of bridge pier top ;

[0203] Calculations show that the total stress in the rail is... Rail joint Relative displacement between beam and rail Horizontal displacement of bridge pier top All control index values ​​meet the restriction requirements of formulas (12), (13), (14) and (16);

[0204] This indicates that under the empirically selected values ​​of bridge pier stiffness used in this study, the structural stress and deformation both meet the control standards, verifying the applicability and rationality of the S1 model modeling assumptions and the S2~S4 calculation algorithms under this working condition. According to the above results, the bridge pier stiffness is too large, resulting in poor engineering economy. Next, the stiffness values ​​of each bridge pier are appropriately reduced, the bridge pier stiffness in the S1 model is adjusted, and the S2, S3, and S4 calculations are performed until a certain index value at each bridge pier location satisfies formulas (17), (18), (19), and (20), while all index values ​​at each bridge pier location satisfy formulas (12), (13), (14), and (16).

[0205] Based on experience, the stress limit coefficient of the rail is taken as follows. Rail breakage limit coefficient Beam-rail relative displacement limit coefficient Horizontal displacement limit coefficient of bridge pier top . It is 291.7 MPa. It is 61.6mm. It is 2.8mm. It is 22.6mm.

[0206] A4. In the initial stiffness dataset of each bridge pier and abutment Based on this, the values ​​of various indicators at each bridge pier location all satisfy formulas (12), (13), (14) and (16). At the same time, the total stress of the rails at bridge pier locations 2, 3, 5 and 6 is... The requirements of formula (17) are met. The stiffness of bridge piers 1 and 4 is reduced, and according to formula (21), the stiffness dataset of each bridge pier after the first adjustment is formed. .

[0207] ;

[0208] The stiffness dataset of each bridge pier after the first adjustment Substituting into the S1 model, performing calculations S2, S3, and S4, and according to formulas (12), (5), (10), and (15), the datasets of the total rail stress, rail fracture, relative displacement between beam and rail, and horizontal displacement at the top of the bridge pier after the first adjustment are obtained, respectively:

[0209] ;

[0210] ;

[0211] ;

[0212] ;

[0213] The stiffness dataset of each bridge pier after the first adjustment Based on this, the values ​​of various indicators at each bridge pier location all satisfy formulas (12), (13), (14), and (16). Simultaneously, the total stress of the rails at bridge pier locations 2, 3, 4, 5, and 6 satisfies the requirement of formula (17). A linear fitting method is used to reduce the stiffness of bridge pier 1, forming a second adjusted stiffness dataset for each bridge pier. .

[0214] Linear fitting of the stiffness of bridge abutment No. 1:

[0215] ;

[0216] ;

[0217] Where, m 21 This indicates the stiffness of the first bridge pier after the second adjustment.

[0218] The second adjusted dataset of bridge pier stiffness Substituting into the S1 model, and performing calculations S2, S3, and S4, according to formulas (12), (5), (10), and (15), a new set of datasets for the total rail stress, rail joint fracture, relative displacement between beam and rail, and horizontal displacement at the top of bridge piers after the second adjustment are obtained, which are expressed as follows:

[0219] ;

[0220] ;

[0221] ;

[0222] At this point, the total stress of the rails at each bridge pier location satisfies formula (17), and the values ​​of various indicators at each bridge pier location satisfy formulas (12), (13), (14), and (16). That is, under this bridge span arrangement, the final output is the optimized bridge pier stiffness:

[0223] .

[0224] This embodiment also provides a computer device applicable to a method for calculating the stiffness of bridge piers and abutments based on seamless railway track design, including a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to realize the method for calculating the stiffness of bridge piers and abutments based on seamless railway track design as proposed in the above embodiment.

[0225] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements a method for calculating the stiffness of bridge piers and abutments based on seamless railway track design as proposed in the above embodiment.

[0226] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0227] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0228] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0229] More specific examples (a non-exhaustive list) of computer-readable media include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which programs can be printed, because programs can be obtained electronically, for example, by optically scanning the paper or other media, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0230] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0231] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A bridge pier stiffness calculation method based on railway seamless line design, characterized by: Includes the following steps: S1. Construct a finite element model of the space between the pier, the beam, the track bed, and the rail; S2. Obtain the rail stress, horizontal displacement of the bridge pier top, and rail fracture under temperature changes using a finite element model. S3. Obtain the tensile stress at the bottom of the rail under the vertical load of the train, and obtain the rail stress, relative displacement of the beam and rail, and horizontal displacement of the bridge pier top under the finite element model under the traction and braking load of the train. S4. Calculate the total stress of the rail. The total stress of the rail = the rail stress under temperature change + the tensile stress on the rail base under the vertical load of the train + the rail stress under the traction and braking load of the train. Set the constraints on the total stress of the rail, the rail joint, the relative displacement between the beam and the rail, and the horizontal displacement of the bridge pier top to meet the actual needs of the project. S5. Optimize the constraint limit range of the total stress of the rail, the rail joint, the relative displacement of the beam and rail, and the horizontal displacement of the bridge pier top, and determine whether the stiffness of the bridge pier needs to be adjusted based on the optimized limit range. If no adjustment is needed, proceed directly to S7; if adjustment is needed, proceed to S6. S6. Adjust the stiffness of the bridge piers in the S1 model, and perform calculations S2, S3, and S4 until the total stress of the rail, the rail joint, the relative displacement of the beam and rail, and the horizontal displacement of the bridge pier top are within the optimized limit range. S7. Output the optimized bridge pier stiffness; Steps S2 and S3 are parallel steps.

2. The method for calculating the stiffness of bridge piers and abutments based on seamless railway track design according to claim 1, characterized in that: The track bed includes ballast track bed and ballastless track bed.

3. The method for calculating the stiffness of bridge piers and abutments based on seamless railway track design according to claim 1, characterized in that: S1 includes the following method: S11. Obtain the database, which includes the actual dimensions, material characteristic values, and cross-sectional characteristic values ​​of the bridge and track structures, as well as the bridge span arrangement and the stiffness of each bridge pier. S12. Input the material characteristic values ​​and cross-sectional characteristic values ​​of the bridge, track bed, and rail into the finite element software respectively; S13. Based on the spatial relationship between the rails, track bed, beams, bridge piers and abutments and the roadbed surface, set up the nodes corresponding to each structure; S14. Connect the corresponding nodes of the rail, track bed and beam in sequence to generate rail, track bed and beam elements. Select beam element as the element type. S15. Add boundary conditions to constrain the nodes mentioned in S13.

4. The method for calculating the stiffness of bridge piers and abutments based on seamless railway track design according to claim 3, characterized in that: The method for constraining the node in S15 includes: S151. Add general supports at the bridge pier nodes, without restricting the longitudinal displacement of the bridge pier nodes along the line, and without restricting the rotation of the bridge pier nodes along the horizontal axis perpendicular to the line. S152. Add general supports at the roadbed surface nodes to fully constrain the roadbed surface nodes; S153. Add elastic supports at the bridge pier nodes to constrain the bridge pier nodes along the longitudinal direction of the line. The stiffness of the elastic supports is the stiffness of the bridge pier. When the bridge is a T-shaped rigid frame beam or a continuous rigid frame beam, rotational constraints about the horizontal axis perpendicular to the line should be added to the bridge pier nodes. S154. Add elastic connections between bridge pier nodes and beam nodes to fix displacement and rotation in all directions; S155. Add elastic connections between beam nodes and track bed nodes to fix displacement and rotation in all directions; S156. Add an elastic connection between the track bed node and the rail node to fix lateral and vertical displacement and rotation in all directions; S157. Establish the deformation-internal force function, define the nonlinear spring stiffness to simulate the longitudinal resistance of the track, add elastic connections between the track bed nodes and rail nodes, and input the nonlinear spring stiffness into the longitudinal direction of the track. S158. Add general supports at the rail nodes corresponding to the end point of the roadbed surface to fully constrain the rail nodes.

5. The method for calculating the stiffness of bridge piers and abutments based on seamless railway track design according to claim 1, characterized in that: S2 includes: S21. Calculate the temperature change of the rail; S22. Calculate the temperature change of the bridge; S23. Input the temperature changes obtained in S21 and S22 into the finite element model of S1. The finite element model outputs the horizontal displacement of the bridge pier top under rail stress and temperature changes. S24. Set the positions of each bridge pier in the finite element model as broken rails, and input the temperature changes in S21 and S22 to calculate the rail gap.

6. The method for calculating the stiffness of bridge piers and abutments based on seamless railway track design according to claim 1, characterized in that: The method for optimizing the constraint limit range of the total rail stress, the rail breakage, the relative displacement of the beam and rail, and the horizontal displacement of the bridge pier top in S5 is as follows: multiply the constraint conditions of the total rail stress, the rail breakage, the relative displacement of the beam and rail, and the horizontal displacement of the bridge pier top by a coefficient less than 1.

7. The method for calculating the stiffness of bridge piers and abutments based on seamless railway track design according to claim 6, characterized in that: The method for adjusting the stiffness of bridge piers and abutments in the finite element model in S6 includes: S61. Based on the initial stiffness dataset of each bridge pier, if the total stress of the rail, the rail joint, the relative displacement of the beam and rail, and the horizontal displacement of the bridge pier top at the i-th bridge pier position are outside the constraints in S4, increase the stiffness of the i-th bridge pier until all parameters satisfy the constraints in S4. S62. Based on S61, if the total stress of the rail, the rail joint, the relative displacement of the beam and rail, and the horizontal displacement of the bridge pier top at the i-th bridge pier position do not meet the optimized range in S5, reduce the stiffness of the i-th bridge pier to form the first adjusted stiffness dataset of each bridge pier. S63, the first adjusted each bridge pier stiffness dataset is substituted into the finite element model, S2, S3, S4 calculation is executed, a new dataset including steel rail total stress 调1 , steel rail broken joint 调1 , beam rail relative displacement 调1 and bridge pier top horizontal displacement 调1 is obtained, and a second adjusted each bridge pier stiffness dataset is generated by using a data fitting method; S64. Continuously adjust the stiffness dataset of each bridge pier until a certain index value of the total stress of the rail, the rail joint, the relative displacement of the beam and rail, and the horizontal displacement of the bridge pier top at each bridge pier position meets the optimized range in S5 and the constraint conditions in S4.

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