Railway girder bridge post-earthquake track irregularity analysis method and system

Abstract

This invention discloses a method and system for analyzing post-earthquake track irregularities in railway beam bridges, relating to the field of seismic resistance, disaster prevention, and mitigation technology for bridge engineering structures. It solves the problems of complex, repetitive, and time-consuming modeling in existing integrated bridge-track analysis models. The invention includes simplifying the railway beam bridge analysis model into a bridge model without a track structure and a beam-track model. Step 1 establishes a bridge model without a track structure for nonlinear seismic analysis to obtain the seismic response of the main beam. Based on the seismic response of the main beam obtained in Step 1, it is applied as a displacement load to the beam-track model to obtain rail deformation. Based on the rail deformation in Step 2, the post-earthquake track irregularities of the railway bridge are calculated. Based on the characteristics of track damage under seismic loading on railway beam bridges, and addressing the shortcomings of existing integrated bridge-track analysis models, this invention proposes a reasonable simplified calculation method for track irregularities, enabling rapid analysis of post-earthquake irregularities in railway beam bridges.

Description

Technical Field

[0001] This invention belongs to the field of earthquake resistance, disaster prevention and mitigation technology for bridge engineering structures, specifically relating to a method and system for analyzing track irregularities after an earthquake in railway beam bridges. Background Technology

[0002] Currently, seismic design for railway engineering in my country primarily focuses on structural safety, lacking systematic research on the performance of track structures under earthquakes, which directly impact train traffic safety. Track irregularities are a significant source of vibration and a static control indicator for high-speed trains. Therefore, rapidly obtaining the deformation behavior of tracks under earthquakes is crucial for assessing the operational status of railway bridges.

[0003] The "Code for Seismic Design of Railway Engineering" (GB 50111-2006 (2009 edition)) uses simplified calculations for railway bridge track systems, neglecting track structures and making it impossible to directly analyze the seismic response of track structures under earthquakes. Furthermore, existing integrated bridge-track analysis methods require the creation of complex track models, and each bridge necessitates repeated modeling of the track structure, resulting in complex and repetitive modeling, high computational time costs, and making them unsuitable for widespread application in practical engineering. Summary of the Invention

[0004] In view of this, the present invention provides a method and system for analyzing track irregularities after earthquakes in railway beam bridges, in order to solve the problems in the existing integrated bridge-track analysis method, which requires the establishment of complex track models and repeated modeling of track structures for each bridge, resulting in complex and repetitive modeling, high computation time costs, and other issues that make it unsuitable for widespread application in actual engineering.

[0005] The technical solution adopted in this invention is as follows:

[0006] A method for analyzing track irregularities after an earthquake in railway beam bridges, comprising:

[0007] Step 1: Establish a nonlinear finite element analysis model of the trackless bridge, and obtain the seismic response of the main beam based on the nonlinear finite element analysis model of the trackless bridge;

[0008] Step 1 specifically includes:

[0009] Step 1.1: Considering the nonlinearity of the supports and piers, establish a nonlinear finite element analysis model for the trackless bridge;

[0010] Step 1.2: Input seismic waves into the nonlinear finite element analysis model of the trackless bridge and conduct nonlinear time history analysis to obtain the seismic response of the main beam.

[0011] The seismic response of the main beam includes the relative peak displacement and residual displacement of the adjacent ends of the main beam at each expansion joint.

[0012] Step 2: Establish a beam-rail nonlinear finite element model, which is based on the seismic response of the main beam obtained in Step 1 to obtain the rail deformation;

[0013] Step 2 includes:

[0014] Step 2.1: Establish a beam-track nonlinear finite element model based on the established rules;

[0015] In step 2.1, the rules for establishing rules include:

[0016] The beam-track nonlinear finite element model includes the main beam and track structure. A certain span needs to be considered to ensure the constraint force of the track on the main beam under seismic action. The span of a single main beam is ≥5m.

[0017] The main beam is equipped with a fixed side and a displacement loading side to simulate the seismic displacement behavior at the expansion joint of the main beam. The fixed side constrains the translation and rotation of the main beam, while the loading side of the main beam is not constrained.

[0018] The main beam is modeled using beam elements, the track structure needs to consider the nonlinear mechanical characteristics of fasteners and rails, and other components are simulated using elastic elements.

[0019] Step 2.2: Input the relative peak displacement and residual displacement obtained in Step 1.2 as loads into the beam-rail nonlinear finite element model and apply them to the main beam on the loading side. After the displacement loading is completed, unload the displacement of the main beam on the loading side to the magnitude of the residual displacement and record the displacement of the rail after unloading.

[0020] Step 3: Based on the rail deformation calculation in Step 2, the track irregularity of the railway bridge after the earthquake is obtained.

[0021] Step 3 includes:

[0022] Based on the rail deformation obtained in step 2, the track irregularity value is calculated using the chord measurement method (10m), as shown in equation (1).

[0023] V i ≈V i ′=H i -(H i-a +H i+a ) / twenty one)

[0024] In the formula: V i V i ′ represents the track irregularity value; H i-a H i H i+a These represent the distances from the original displacement at the starting point, midpoint, and ending point of the rail chord measurement.

[0025] A post-earthquake track irregularity analysis system for railway beam bridges includes:

[0026] Trackless bridge model building module: Establish a nonlinear finite element analysis model of the trackless bridge, and obtain the seismic response of the main beam based on the nonlinear finite element analysis model of the trackless bridge;

[0027] Beam-rail model establishment module: Establishes a beam-rail nonlinear finite element model, which obtains the rail deformation based on the seismic response of the main beam obtained in step 1;

[0028] Calculation module: Based on the rail deformation calculation in step 2, the track irregularity value of the railway bridge after the earthquake is obtained.

[0029] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0030] This invention proposes a reasonable method for analyzing track irregularities after earthquakes in railway beam bridges. It simplifies the integrated bridge-track system into a trackless bridge model and a beam-track model. The beam-track model can be applied to the analysis of track irregularities in similar railway beam bridges, avoiding repeated modeling of track structures during the analysis process, saving modeling and calculation analysis time, effectively improving analysis efficiency, and facilitating use by bridge design engineers. Attached Figure Description

[0031] The present invention will be described by way of example and with reference to the accompanying drawings, wherein:

[0032] Figure 1 This is the nonlinear finite element analysis model of the trackless bridge involved in Example 1;

[0033] Figure 2 This refers to the nonlinear time-history analysis seismic wave involved in Example 1;

[0034] Figure 3 This is a time history diagram of the relative displacement of the main beam end at the expansion joint in the finite element model of Example 1;

[0035] Figure 4 This refers to the beam-rail nonlinear finite element model involved in Example 1;

[0036] Figure 5 The nonlinear finite element model of the beam-rail system involved in Example 1 shows the rail displacement after unloading.

[0037] Figure 6 This is a schematic diagram illustrating the calculation of track irregularities using the chord measurement method described in Example 1.

[0038] Figure 7 This is a schematic diagram of the process structure of the present invention. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0040] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0041] It should be noted that, unless otherwise specified, the embodiments and features described in this invention can be combined with each other.

[0042] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0043] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0044] It should be noted that, unless otherwise specified, the embodiments and features described in this invention can be combined with each other.

[0045] Example 1

[0046] like Figures 1-6 As shown, in this embodiment of the invention, step 1 is disclosed: establishing a nonlinear finite element analysis model of the trackless bridge, and obtaining the seismic response of the main beam based on the nonlinear finite element analysis model of the trackless bridge;

[0047] Step 1 specifically includes:

[0048] Step 1.1: Considering the nonlinearity of the supports and piers, establish a nonlinear finite element analysis model for the trackless bridge;

[0049] During model building, elastic beam-column elements were used for simulation; for reinforced concrete piers that may experience plastic failure, nonlinear fiber beam-column elements were used. The steel reinforcement was modeled using Steel02 material, and the concrete using Kent-Part material. The support exhibits bilinear mechanical behavior in the sliding direction. In the fixed direction, the difference in mechanical properties of the support before and after the failure of the shear studs is considered. Therefore, a linear elastic constitutive model is used for the support before failure, and a bilinear constitutive model is used after failure, consistent with the sliding direction. Detailed information on the nonlinear finite element analysis model and material constitutive model of the trackless bridge can be found in [link to relevant documentation]. Figure 1 .

[0050] Step 1.2: Input seismic waves into the nonlinear finite element analysis model of the track bridge and conduct nonlinear time history analysis to obtain the seismic response of the main beam.

[0051] The seismic response of the main beam includes the relative peak displacement and residual displacement of the adjacent ends of the main beam at each expansion joint.

[0052] A naturally recorded seismic wave was selected from the Pacific Earthquake Engineering Research (PEER) data, and the seismic wave time history curve is shown below. Figure 2 As shown, the time history of the relative displacement at the ends of the main beam at the expansion joints of the finite element model is extracted by inputting the data along the transverse direction of the bridge into the bridge's refined model for nonlinear time history analysis. Figure 3 As shown in Table 1, the relative peak displacements of the main beams at the six beam joints are #0 to #5. The results show that the relative peak displacements and residual displacements of the main beams at the beam joints of abutments #0 and #5 are relatively large, while the relative peak displacements and residual displacements of the main beams at the beam joints of piers #1 to #4 are relatively small. The relative peak displacements and residual displacements of the main beams are shown in Table 1.

[0053] Table 1. Relative peak values ​​and residual displacements of the main beam at the beam joint.

[0054]

[0055] Step 2: Establish a beam-rail nonlinear finite element model, which is based on the seismic response of the main beam obtained in Step 1 to obtain the rail deformation;

[0056] Step 2 includes:

[0057] Step 2.1: Establish a beam-track nonlinear finite element model based on the established rules;

[0058] The base plate, track slab, sleepers, and main beam of the track structure are not considered for nonlinearity and are simulated using beam elements. Fasteners and rails are considered vulnerable components and are given elastoplastic constitutive materials (actual bridge earthquake damage shows that fasteners and rails are the most easily damaged components of the track structure; therefore, the nonlinear characteristics need to be considered in the refined analysis model to reflect the nonlinear mechanical behavior of the track structure under seismic loading, which has a significant impact on the analysis results). The main beam on one side is 12.98m long with a gap of 0.1m. The horizontal and rotational degrees of freedom are constrained at the bottom of the fixed-side main beam, while the sliding-side degrees of freedom are not constrained. The beam-track model is as follows: Figure 4 As shown.

[0059] In step 2.1, the rules for establishing rules include:

[0060] The beam-track nonlinear finite element model includes the main beam and track structure. A certain span needs to be considered to ensure the constraint force of the track on the main beam under seismic action. The span of a single main beam is ≥5m.

[0061] The main beam is equipped with a fixed side and a displacement loading side to simulate the seismic displacement behavior at the expansion joint of the main beam. The fixed side constrains the translation and rotation of the main beam, while the loading side of the main beam is not constrained.

[0062] The main beam is modeled using beam elements, the track structure needs to consider the nonlinear mechanical characteristics of fasteners and rails, and other components are simulated using elastic elements.

[0063] Step 2.2: Apply the peak displacements of the main beam obtained in Step 1 (12cm, 4cm, 6cm, 4cm, 3cm, 12cm) to the loading side main beam respectively. After the displacement loading is completed, unload the main beam displacement on the loading side to the residual displacements (9cm, 1cm, 2cm, 3cm, 0cm, 8cm) respectively, and record the rail displacement after unloading. The results are as follows. Figure 5 As shown.

[0064] Step 3: Based on the rail deformation calculation in Step 2, the track irregularity of the railway bridge after the earthquake is obtained.

[0065] Step 3 includes:

[0066] Based on the rail deformation obtained in step 2, and referring to the requirements for static track irregularity indices in the "Rules for Repairing Conventional Speed ​​Railway Lines" (TG-GW102-2019), the track irregularity values ​​under seismic loading are obtained. Track irregularity is generally analyzed and calculated using the chordal survey method (L=10m). The chordal survey method is as follows... Figure 6 As shown:

[0067] Calculate the reference formula (1).

[0068] V i ≈V i ′=H i-(H i-a +H i+a ) / twenty one)

[0069] In the formula: V i V i ′ represents the track irregularity value; H i-a H i H i+a These represent the distances from the original displacement at the starting point, midpoint, and ending point of the rail chord measurement.

[0070] The track irregularity values ​​for expansion joints #0 to #5 of the beam under seismic wave action are shown in Table 2. The post-earthquake track irregularity value for the railway beam bridge is 44 mm. The analysis of the specific embodiment has now been completed.

[0071] Table 2. Unevenness values ​​of beam joints

[0072]

[0073] Example 2

[0074] This embodiment proposes a post-earthquake track irregularity analysis system for railway beam bridges, including:

[0075] Trackless bridge model building module: Establish a nonlinear finite element analysis model of the trackless bridge, and obtain the seismic response of the main beam based on the nonlinear finite element analysis model of the trackless bridge;

[0076] Beam-rail model establishment module: Establishes a beam-rail nonlinear finite element model, which obtains the rail deformation based on the seismic response of the main beam obtained in step 1;

[0077] Calculation module: Based on the rail deformation calculation in step 2, the post-earthquake track irregularities of the railway bridge are obtained.

[0078] The circuits, electronic components, and modules involved are all existing technologies, which can be fully implemented by those skilled in the art, and need not be elaborated upon. The scope of protection of this invention does not involve any improvement to the software and methods.

[0079] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0080] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for analyzing track irregularities after an earthquake in railway beam bridges, characterized in that, include: Step 1: Establish a nonlinear finite element analysis model of the trackless bridge, and obtain the seismic response of the main beam based on the nonlinear finite element analysis model of the trackless bridge; Step 2: Establish a beam-rail nonlinear finite element model, which is based on the seismic response of the main beam obtained in Step 1 to obtain the rail deformation; Step 3: Based on the rail deformation calculation in Step 2, obtain the post-earthquake track irregularity value of the railway bridge; Step 1 specifically includes: Step 1.1: Considering the nonlinearity of the supports and piers, establish a nonlinear finite element analysis model for the trackless bridge; Step 1.2: Input seismic waves into the nonlinear finite element analysis model of the trackless bridge and conduct nonlinear time history analysis to obtain the seismic response of the main beam; The seismic response of the main beam includes the relative peak displacement and residual displacement of the adjacent ends of the main beam at each expansion joint. Step 2 includes: Step 2.1: Establish a beam-track nonlinear finite element model based on the established rules; Step 2.2: Input the relative peak displacement obtained in Step 1.2 as a load into the beam-rail nonlinear finite element model and apply it to the main beam on the loading side. After the displacement loading is completed, unload the displacement of the main beam on the loading side to the residual displacement and record the displacement of the rail after unloading. In step 2.1, the rules for establishing rules include: The beam-track nonlinear finite element model includes the main beam and track structure. The span needs to be considered to ensure the constraint force of the track on the main beam under seismic action. The span of a single main beam is ≥5m. The main beam is equipped with a fixed side and a displacement loading side to simulate the seismic displacement behavior at the expansion joint of the main beam. The fixed side constrains the translation and rotation of the main beam, while the loading side of the main beam is not constrained. The main beam is modeled using beam elements, the track structure needs to consider the nonlinear mechanical characteristics of fasteners and rails, and other components are simulated using elastic elements.

2. The method for analyzing track irregularities after an earthquake in a railway beam bridge according to claim 1, characterized in that, Step 3 includes: Based on the rail deformation obtained in step 2, the track irregularity value is calculated using the chord measurement method, as shown in equation (1): (1)； In the formula: This represents the track irregularity value. This is an approximation of the track irregularity value; , , These represent the distances from the original displacement at the starting point, midpoint, and ending point of the rail chord measurement.

3. A system for analyzing track irregularities after an earthquake in railway beam bridges, used to implement the method for analyzing track irregularities after an earthquake in railway beam bridges as described in any one of claims 1-2, characterized in that, include: Trackless bridge model building module: Establish a nonlinear finite element analysis model of the trackless bridge, and obtain the seismic response of the main beam based on the nonlinear finite element analysis model of the trackless bridge; Beam-rail model establishment module: Establishes a beam-rail nonlinear finite element model, which obtains the rail deformation based on the seismic response of the main beam obtained in step 1; Calculation module: Based on the rail deformation calculation in step 2, the track irregularity value of the railway bridge after the earthquake is obtained.

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