A method and system for safety evaluation of a bridge under train load and fire

Abstract

The present application relates to the technical field of civil engineering structure safety and reliability evaluation, in particular to a kind of train load under the fire bridge safety evaluation method and system.Method includes: establishing the reference finite element model of bridge not under fire;Obtain the three-dimensional temperature field of structure by fire inversion simulation, establish damage degradation function in combination with material high-temperature performance;Damage parameters are mapped to finite element model, stiffness matrix is corrected, and post-fire degradation model is formed;Vehicle track bridge coupling dynamic equation is established on this model and time history is solved, and train over-bridge dynamic response is obtained;Key response parameters are extracted, safety evaluation index and comprehensive safety parameter are calculated, and finally safety grade and operation suggestion are output.The present application realizes the whole process analysis from quantitative identification to coupling dynamic response of fire damage, significantly improves the accuracy and engineering applicability of evaluation.

Description

Technical Field

[0001] This invention relates to the field of civil engineering structural safety and reliability assessment technology, and in particular to a method and system for assessing the safety of a bridge subjected to fire under train load. Background Technology

[0002] As a critical load-bearing structure in the train operation system, the dynamic performance of railway bridges directly affects the safety and comfort of train operation. With increasing train speeds and traffic density, the dynamic response of bridges during service has received increasing attention. Existing research typically assesses the dynamic characteristics of bridges under train loads using methods such as finite element analysis or monitoring data inversion, and evaluates bridge operational performance using indexing methods. Related research has established a relatively mature technical system in areas such as vehicle dynamics models, track structure mechanical properties, and prediction of bridge beam dynamic response, providing a theoretical foundation for the operational safety assessment of railway bridges.

[0003] When a bridge is subjected to fire, the mechanical properties of its components, such as strength, stiffness, and ductility, will degrade to varying degrees. The effective load-bearing capacity of the cross-section and the overall stiffness of the components decrease with changes in temperature rise time and the range of high temperature exposure. This type of damage not only manifests as a reduction in static load-bearing capacity but also alters the structural dynamic characteristics, thereby affecting the coupling and transmission mechanism of the vehicle-bridge system during train operation. In cases where there are spatial differences in the degree of degradation or localized concentrated damage, the overall dynamic boundary conditions and mode shape characteristics of the bridge may differ significantly from those in its healthy state at room temperature.

[0004] Although some studies have focused on the impact of fire on bridge materials and cross-sectional properties, existing assessment methods still have the following shortcomings:

[0005] (i) The focus is mainly on judging the residual bearing capacity and static performance after the fire, and an analysis and transmission mechanism from "quantification of fire damage" to "changes in train operation dynamic response" has not yet been established.

[0006] (ii) Existing vehicle-track-bridge coupled dynamic models typically still use healthy structural parameters as input, lacking dynamic characteristic corrections for degraded structural states, and thus failing to reflect the impact of post-fire damage on train operation safety. Therefore, in the operational safety assessment after a fire, there is still a lack of an analytical approach that can unify fire damage, dynamic response, and operational criteria. Summary of the Invention

[0007] This invention aims to at least improve one of the technical problems existing in the prior art. To this end, this invention proposes a method and system for safety assessment of bridges exposed to fire under train load.

[0008] The technical solution of the present invention is as follows:

[0009] A method for safety assessment of a bridge under fire under train load, comprising:

[0010] S1: Establish a healthy benchmark finite element model of the railway bridge, determine the component elements to be tested, input material parameters to the component elements to be tested, and form the benchmark stiffness and dynamic characteristics of the healthy structure;

[0011] S2: Perform fire inversion simulation on the finite element model of the railway bridge to obtain a three-dimensional temperature field, and obtain the temperature field distribution and deformation of the fire-damaged parts based on the three-dimensional temperature field.

[0012] S3: Construct a damage degradation function, input the temperature field of the fire-damaged component into the damage degradation function to output degradation parameters, and map the degradation parameters into the finite element software to form a distributed degradation parameter field;

[0013] S4: Based on the distributed degradation parameter field, the stiffness matrix of the railway bridge finite element model of the health benchmark is corrected to form a degradation structure model after fire.

[0014] S5: Establish the dynamic equations of the coupled system of vehicle, track, and bridge on the degraded structural model and solve for the time history to obtain the dynamic response time history;

[0015] S6: Extract the parameter indicators of the train crossing the bridge based on the dynamic response time history, and calculate the safety evaluation index based on the parameter indicators;

[0016] S7: Based on safety evaluation indicators, calculate comprehensive safety parameters, and output a report on the post-fire operational safety level and operational recommendations of the bridge based on the comprehensive safety parameters.

[0017] In one possible technical solution, S2 is further defined as follows:

[0018] Using standard temperature rise curves or measured fire curves, and based on the flame radiation heat transfer equation, the temperature field distribution of fire-damaged components is obtained through finite element heat conduction analysis. An annealing effect correction during the cooling phase is then introduced after the fire.

[0019]

[0020] In the formula: For material density ( c is the specific heat capacity ( ), It is the temperature field (K or °C). For time (s), Thermal conductivity ( ), It is the Laplace operator of the temperature field ( ), Indicates the heat source intensity per unit volume ( ).

[0021] In one possible technical solution, further, in S4, the stiffness matrix... The corrected expression is:

[0022]

[0023] In the formula The element strain matrix, The elastic modulus at room temperature, Here, V represents the elastic modulus reduction factor at different temperatures, and V is the element geometric volume. This represents the temperature at the corresponding node in the spatial coordinate system, i.e., the spatial temperature field.

[0024] In one possible technical solution, further, in S5, the dynamic equations of the vehicle-track-bridge coupled system are solved using a numerical integration method, and the contact force is iteratively updated at each time step to ensure numerical stability and energy conservation. The dynamic equations of the coupled system are:

[0025]

[0026] In the formula , , These are the mass, damping, and degradation stiffness matrices, respectively. For moving load vectors, For acceleration vectors, For velocity vector, This is the displacement vector.

[0027] In one possible technical solution, S6 is further defined as follows:

[0028] Based on the dynamic response time history, the vertical dynamic deflection and vertical acceleration at the mid-span of the bridge, and the vertical acceleration of the train and the vertical force between the wheel and rail are extracted when the train crosses the bridge.

[0029] The maximum dynamic deflection and maximum vertical vibration acceleration of the bridge at mid-span are calculated based on the extracted vertical dynamic deflection and vertical acceleration at mid-span of the bridge.

[0030] The vehicle wheel load reduction rate is calculated based on the extracted vertical acceleration of the train and the vertical force between the wheel and rail.

[0031] In one possible technical solution, S7 further includes:

[0032] By wheel load reduction rate Sperling index, mid-span vertical acceleration As a safety evaluation indicator, the comprehensive safety index is calculated. :

[0033]

[0034] in These are the weighting coefficients. , The Sperling Index;

[0035] Based on the comprehensive safety index The values ​​are used to classify operational safety into five levels: Level I, Level II, Level III, Level IV, and Level V, and output a report on the operational safety level and operational recommendations after a bridge fire.

[0036] In one possible technical solution, further, based on the comprehensive safety index... The values ​​categorize operational safety into five levels: Level I, Level II, Level III, Level IV, and Level V, and output a report on the operational safety level and recommendations after a bridge fire, specifically including:

[0037] If the overall safety factor is Ks≥1.2 and the safety level is Level I, the output recommendation report is "The structure is intact, the operation is safe and stable, and normal operating speed can be restored";

[0038] If the overall safety factor is 1.00≤Ks<1.20, the safety level is Level II, and the recommended report output is "Operational safety is acceptable, regular monitoring required";

[0039] If the overall safety factor is 0.80≤Ks<1.00 and the safety level is Level III, the recommended report output is "Immediately shut down the operation, carry out temporary reinforcement, and reassess after reinforcement";

[0040] If the overall safety factor is 0.60≤Ks<0.80, the safety level is IV, and the output recommendation report is "speed-limited operation";

[0041] If the overall safety factor Ks < 0.60 and the safety level is V, the output recommendation report will be "Immediate repair or shutdown".

[0042] A safety assessment system for bridges under fire conditions under train load, comprising:

[0043] The first construction module is used to establish a healthy benchmark finite element model of a railway bridge, determine the component elements to be tested, input material parameters to the component elements to be tested, and form the benchmark stiffness and dynamic characteristics of the healthy structure.

[0044] The fire damage calculation module is used to perform fire inversion simulation on the finite element model of the railway bridge to obtain a three-dimensional temperature field, and to obtain the temperature field distribution and deformation of the fire-damaged components based on the three-dimensional temperature field.

[0045] The second construction module is used to construct a damage degradation function, input the temperature field of the fire-damaged component into the damage degradation function to output degradation parameters, and map the degradation parameters into the finite element software to form a distributed degradation parameter field.

[0046] Correction module: used to correct the stiffness matrix of the railway bridge finite element model based on the health benchmark according to the distributed degradation parameter field, so as to form a degraded structural model after fire.

[0047] The coupled dynamics solution module is used to establish the dynamic equations of the coupled system of vehicle, track, and bridge on the degraded structural model and to solve the time history to obtain the dynamic response time history.

[0048] The response analysis module is used to extract the parameter indicators of the train when crossing the bridge based on the dynamic response time history, and to calculate the safety evaluation index based on the parameter indicators.

[0049] The safety assessment and reporting module calculates comprehensive safety parameters based on safety evaluation indicators and outputs a report on the operational safety level and operational recommendations after a bridge fire based on these comprehensive safety parameters.

[0050] The method and system for safety assessment of bridges under fire load according to the present invention have the following beneficial effects:

[0051] 1. By introducing fire damage parameter mapping on the basis of the healthy bridge model, the unified coupling of fire damage and structural dynamic model is realized, avoiding the defect of the separation of damage information and dynamic analysis in traditional methods.

[0052] 2. By obtaining bridge fire damage parameters through fire inversion analysis, post-disaster stiffness degradation functions for different parts of the bridge structure can be constructed, which can accurately reflect the impact of fire on the overall stiffness and dynamic characteristics of the bridge and improve the physical consistency of the assessment results.

[0053] 3. Based on the degraded structure model, the coupled dynamic equations of vehicle-track-bridge are established, and the safety level is determined by system response extraction and criterion comparison, so that the operation assessment is quantitative and repeatable.

[0054] 4. The evaluation system constructed by this invention has modular and scalable features, and can realize the automation of data acquisition, modeling analysis and safe output, and has good engineering application and promotion value.

[0055] A computer device, characterized in that it includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to perform the safety assessment of a fire-affected bridge under train load as described above.

[0056] A computer storage medium, characterized in that the computer storage medium stores instructions, which, when executed on a computer, cause the computer to perform the aforementioned safety assessment of a fire-affected bridge under train load.

[0057] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0058] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments 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.

[0059] Figure 1 This is a diagram of the vehicle-track-bridge coupled vibration model in the safety assessment method for fire-affected bridges under train load according to an embodiment of the present invention.

[0060] Figure 2 This is a flowchart of a method for safety assessment of a bridge under fire under train load according to an embodiment of the present invention;

[0061] Figure 3 It is a temperature rise curve according to ISO-834 standard;

[0062] Figure 4 This is a diagram of the fire damage area;

[0063] Figure 5 This is a temperature isopleth diagram of the entire bridge.

[0064] Figure 6 This is a cross-sectional temperature isopleth map;

[0065] Figure 7 Time history diagram of temperature at cross-sectional measuring points under fire conditions in the entire area under the bridge;

[0066] Figure 8 A diagram showing a train passing over a fire-damaged bridge and the bridge's damage.

[0067] Figure 9 Damage diagram of model elements;

[0068] Figure 10 A diagram showing the wheel load reduction rate of the locomotive and carriages when the train crosses the bridge;

[0069] Figure 11 Vertical acceleration response diagrams of train locomotives at different mileages;

[0070] Figure 12 Vertical acceleration response diagrams for train carriages at different mileages;

[0071] Figure 13 The maximum vertical acceleration response of the train head at different fire exposure times is shown in the diagram.

[0072] Figure 14 Response diagram of maximum vertical acceleration of train carriages at different fire durations

[0073] Figure 15 Sperling coefficient diagram for trains exposed to fire for different durations;

[0074] Figure 16 A standard chart for early warning of wheel load reduction rate for different fire exposure times. Detailed Implementation

[0075] The embodiments of the present invention are described in detail below. The embodiments described with reference to the accompanying drawings are exemplary. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit this application.

[0076] It should be noted that when a component is said to be "fixed to" another component, it can be directly attached to the other component or there may be an intervening component. When a component is said to be "connected to" another component, it can be directly connected to the other component or there may be an intervening component.

[0077] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0078] The terms "first," "second," "third," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish different objects and not to describe a particular order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, it may include a series of steps or units, or optionally, steps or units not listed, or other steps or units inherent to these processes, methods, products, or devices.

[0079] The accompanying drawings show only the portions relevant to this application, not all of them. Before discussing exemplary embodiments in more detail, it should be noted that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe operations (or steps) as sequential processes, many of these operations may be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the operations may be rearranged. The process may be terminated when its operation is completed, but may also have additional steps not included in the drawings. The process may correspond to a method, function, procedure, subroutine, subprogram, etc.

[0080] The terms “component,” “module,” “system,” “unit,” etc., used in this specification are used to refer to computer-related entities, hardware, firmware, combinations of hardware and software, software, or software in execution. For example, a unit can be, but is not limited to, a process running on a processor, a processor, an object, an executable file, a thread of execution, a program, and / or distributed between two or more computers. Furthermore, these units can be executed from various computer-readable media on which various data structures are stored. Units can communicate, for example, via local and / or remote processes based on signals having one or more data packets (e.g., data from a second unit interacting with another unit between a local system, a distributed system, and / or a network; for example, the Internet interacting with other systems via signals).

[0081] Example 1

[0082] like Figure 2 As shown, this embodiment provides a method for safety assessment of a bridge under fire under train load, which includes:

[0083] S1: Establish a healthy benchmark finite element model of the railway bridge, determine the component elements to be tested, input material parameters to the component elements to be tested, and form the benchmark stiffness and dynamic characteristics of the healthy structure;

[0084] It should be noted that, specifically, the finite element model of the railway bridge under healthy conditions is established in a fire-free state. The components to be tested include the main beam, piers, supports, rails, sleepers, and track bed. Spatial solid elements (such as SOLID185) are used to simulate the main beam, piers, and sleepers to accurately simulate the temperature gradient distribution and local buckling effect under fire conditions. Spring-constrained elements are used to simulate the support conditions of the beam end supports, beam elements (such as BEAM188) are used to simulate the rails, and linear spring and damping elements are used to define the track bed. In the finite element model of the railway bridge under healthy conditions, ideal elastoplastic constitutive models of concrete and steel are defined, and their initial elastic modulus, Poisson's ratio, yield strength, and density are input to realize the structural division and parameterization definition of the vehicle-track-bridge system.

[0085] S2: Perform fire inversion simulation on the finite element model of the railway bridge to obtain a three-dimensional temperature field, and obtain the temperature field distribution and deformation of the fire-damaged parts based on the three-dimensional temperature field.

[0086] It should be noted that, based on on-site fire traces (such as changes in concrete color, cracking and spalling, and carbonization of paint film on steel components), the type of combustibles and loads, as well as possible surveillance videos, a fire inversion simulation was performed on the finite element model of the railway bridge using a standard temperature rise curve. Through sequential coupling analysis of thermal structure, the three-dimensional non-uniform temperature field of the tested component unit structure was calculated during the entire fire process. The time-temperature history curve of each tested component unit was output, and combined with the high-temperature residual performance curves of concrete and steel reinforcement, the degree of performance degradation of each tested component unit material was determined.

[0087] S3: Construct a damage degradation function. Input the temperature field of the fire-damaged component into the damage degradation function to output degradation parameters. Map the degradation parameters into the finite element software to form a distributed degradation parameter field. The damage degradation function includes a concrete elastic modulus reduction function and a peak stress reduction function. and steel yield strength reduction function ;

[0088] It should be noted that the damage degradation function is constructed based on the "Code for Fire Resistance Design of Building Structures", establishing a reduction function for the elastic modulus of concrete. Peak stress reduction function and peak strain growth function ;

[0089] The elastic modulus reduction function for steel is established according to the relevant specifications. Steel yield strength reduction function and ultimate strength reduction function ;

[0090] When mapping degradation parameters to the finite element software, the highest temperature Tmax experienced by each test component element obtained from S2 is used as input. The damage degradation function is called to calculate the new material parameters of the test component element. The material degradation coefficient in the finite element software is then calculated by writing an APDL script. Assign elements to the component under test to generate a spatially variable material parameter field.

[0091] S4: Based on the distributed degradation parameter field, the stiffness matrix of the railway bridge finite element model of the health benchmark is corrected to form a degradation structure model after fire.

[0092] It should be noted that the material degradation coefficient obtained from S3 Stiffness matrix of a finite element model of a railway bridge based on a healthy benchmark After correction, the degenerate stiffness matrix is ​​obtained. A dynamic model of a degraded bridge after fire is formed. This treatment realizes the spatial non-uniform coupling of fire damage, so that the model can reflect the overall dynamic performance degradation caused by local fire.

[0093] During the establishment of the degraded structural model, the element stiffness matrix is ​​automatically calculated based on the degraded material parameters corresponding to the integration point of each component element under test. The stiffness matrices of all component elements under test are then integrated to obtain the overall degraded stiffness matrix considering fire damage. The degraded structure model, in terms of visualization, can intuitively display the degree of stiffness reduction caused by fire in different areas of the tested component unit through different colors or cloud maps, clearly reflecting the spatial distribution of damage.

[0094] S5: Establish the dynamic equations of the coupled system of vehicle, track, and bridge on the degraded structural model and solve for the time history to obtain the dynamic response time history;

[0095] It should be noted that, based on the degenerate structural model established in S4, the vehicle subsystem and track subsystem are integrated to establish a complete dynamic equation for the vehicle-track-bridge coupled system. This equation is then solved using numerical integration methods to determine the time-history response of the vehicle-track-bridge coupled system when a train passes. Specifically, this includes:

[0096] The vehicle system is modeled using multibody dynamics theory, simulating the vehicle as a system composed of rigid bodies such as the car body, bogie, and wheelsets. The rigid bodies are connected by primary and secondary spring-damping elements. The train system is simulated using a 14-DOF model. The rails, sleepers, track bed, and their connecting parts in the track subsystem are simulated using beam elements (BEAM188 elements), solid elements (SOLID65 elements), and spring-damping elements.

[0097] Based on d'Alembert's principle and Lagrange's equations, the differential equations of motion for three subsystems—vehicle, track, and degraded bridge—are established. Simulations are then performed using Hertzian contact theory, considering track irregularities and their excitation through wheel-rail contact forces. The three are combined as coupling terms to form the coupled dynamic equations of the system. The dynamic equations of the coupled system are solved by numerical integration method (Newmark-β method) to obtain the dynamic response time history of each part of the entire system when the train passes through the fire-damaged bridge at a specific speed.

[0098] S6: Extract the parameter indicators of the train crossing the bridge based on the dynamic response time history, and calculate the safety evaluation index based on the parameter indicators;

[0099] It should be noted that, from the dynamic response time history of the coupled system obtained by solving S5, the vertical dynamic deflection and vertical acceleration at the mid-span of the bridge, the vertical acceleration of the train and the vertical force between the wheel and rail are extracted when the train crosses the bridge.

[0100] The maximum dynamic deflection and maximum vertical vibration acceleration of the bridge at mid-span are calculated based on the extracted vertical dynamic deflection and vertical acceleration at mid-span of the bridge.

[0101] The vehicle wheel load reduction rate is calculated based on the extracted vertical acceleration of the train and the vertical force between the wheel and rail.

[0102] S7: Based on safety evaluation indicators, calculate comprehensive safety parameters, and output a report on the post-fire operational safety level and operational recommendations of the bridge based on the comprehensive safety parameters.

[0103] It should be noted that the wheel load reduction rate is used. Sperling index, mid-span vertical acceleration As a safety evaluation indicator, the comprehensive safety index is calculated. :

[0104]

[0105] in These are the weighting coefficients. , The Sperling Index;

[0106] Based on the comprehensive safety index The values ​​categorize operational safety into five levels: Level I, Level II, Level III, Level IV, and Level V, and output a report on the operational safety level and recommendations after a bridge fire, specifically including:

[0107] If the overall safety factor is Ks≥1.2 and the safety level is Level I (corresponding to the safe operation level), the output recommendation report is "The structure is intact, the operation is safe and stable, and normal operating speed can be restored";

[0108] If the overall safety factor is 1.00≤Ks<1.20, the safety level is Level II (corresponding to the basic safety level), and the output recommendation report is "Operational safety is acceptable, regular monitoring is required";

[0109] If the overall safety factor is 0.80≤Ks<1.00 and the safety level is Level III (corresponding to the temporarily unsafe level), the output recommendation report is "Immediately shut down the operation, carry out temporary reinforcement, and reassess after reinforcement";

[0110] If the overall safety factor is 0.60≤Ks<0.80, the safety level is Level IV (corresponding to the speed-limited operation level), and the output recommendation report is "speed-limited operation";

[0111] If the overall safety factor is Ks < 0.60 and the safety level is V (corresponding to the hazard level), the output recommendation report is "Immediate repair or shutdown".

[0112] It is worth mentioning that, as the optimal option in this embodiment, the threshold for the operational safety judgment indicator is set as follows: ≤0.6, ≤2.5, ≤3.5m / s²; at the same time, a comprehensive safety index Ks≤0.6 is judged as dangerous, and Ks≥1.2 is judged as safe.

[0113] It should be noted that, in this embodiment, S2 specifically refers to:

[0114] Using standard temperature rise curves or measured fire curves, and based on the flame radiation heat transfer equation, the temperature field distribution of fire-damaged components is obtained through finite element heat conduction analysis. An annealing effect correction during the cooling phase is then introduced after the fire.

[0115]

[0116] In the formula: For material density ( c is the specific heat capacity ( ), It is the temperature field (K or °C). For time (s), Thermal conductivity ( ), It is the Laplace operator of the temperature field ( ), Indicates the heat source intensity per unit volume ( ).

[0117] It should be noted that, in this embodiment, in S3, the concrete elastic modulus degradation function Determined by experimental regression; Degradation function of steel bar yield strength Determined according to GB50010-2010 and Eurocode2 standards. The function is defined as follows:

[0118]

[0119]

[0120] In the formula, The initial elastic modulus, For the temperature field, The initial yield strength of the steel reinforcement is given, and the function is applicable from 20°C to 800°C. The degradation coefficient of each element is obtained by spatially superimposing the temperature field and the degradation function. .

[0121]

[0122] in Let be the stiffness degradation rate of the i-th component element under test; numerical calculation software including but not limited to MATLAB or ORIGIN is used, according to... The spatial distribution of damage is automatically used to generate a damage visualization map.

[0123] It should be noted that in this embodiment, in S4, the stiffness matrix... The corrected expression is:

[0124]

[0125] In the formula The element strain matrix, The elastic modulus at room temperature, Here, V represents the elastic modulus reduction factor at different temperatures, and V is the element geometric volume. This represents the temperature at the corresponding node in the spatial coordinate system, i.e., the spatial temperature field.

[0126] It should be noted that in this embodiment, in S5, the dynamic equations of the vehicle-track-bridge coupled system are solved using a numerical integration method, and the contact force is iteratively updated at each time step to ensure numerical stability and energy conservation. The dynamic equations of the coupled system are as follows:

[0127]

[0128] In the formula , , These are the mass, damping, and degradation stiffness matrices, respectively. For moving load vectors, For acceleration vectors, For velocity vector, The displacement vector is used. The vehicle adopts a 14-degree-of-freedom model, and the wheel-rail interaction is expressed through a nonlinear contact spring. The Newmark-β integral method (β=0.25, γ=0.5) is used to solve the time history integral, realizing the dynamic response simulation of the train crossing the bridge.

[0129] It should be noted that, in this embodiment, the vertical acceleration of the train in S5 and the vertical force between the wheel and rail (i.e., the wheel-rail force) are uniformly represented by the contact geometry relationship:

[0130]

[0131] in For equivalent wheel-rail contact stiffness, , These represent the vertical displacement responses of the wheelset and the rail, respectively. By iteratively updating the contact force step by step, the impact of the non-uniform stiffness degradation of the beam caused by fire on the vehicle's operational stability can be explicitly demonstrated.

[0132] This embodiment provides the following specific implementation case, taking the operational safety assessment of a single-track ballasted railway simply supported beam bridge after a fire as an example:

[0133] Step 1: Establish a healthy bridge model before the fire.

[0134] (1) Establishment of thermal analysis model

[0135] This embodiment first establishes a healthy finite element model of the simply supported beam railway bridge before the fire, such as... Figure 1 As shown, this model serves as the baseline state for the fire damage model. The model is constructed following a layered modeling logic of "material layer—section layer—component / unit layer—overall system layer."

[0136] Material layer modeling: The main beam and bridge deck adopt a C55 concrete material model, and the material constitutive parameters are taken from the test data under room temperature conditions, including elastic modulus, Poisson's ratio, and compressive strength; the reinforcement is simulated using embedded steel bar elements. The rail adopts an elastoplastic material model, and the track bed and sleepers are simulated as a spring-damping combination to simulate their contact flexibility.

[0137] Section layer modeling: Based on the actual structural form of railway simply supported beam bridges, T-shaped sections are adopted. The different stress characteristics of the material stiffness in the upper compression zone and the lower tension zone are considered to ensure that the bending stiffness and moment of inertia of the section can accurately reflect the actual service performance.

[0138] Unit-level modeling: The beam, sleepers, and rails are all modeled using SOLID70 temperature elements, differentiated by modifying material parameters. All connections are simulated using COMBIN14 linear elastic spring-damper elements, with parallel springs used between the beam and sleepers to simulate ballast action. The spring stiffness K1 of the rail fastener is set to... Damping C1 is taken The spring stiffness K2 of the sleeper under the fastener is taken as follows: Damping C2 is taken .

[0139] System-level modeling and boundary conditions: A three-dimensional finite element model was established using the Mechanical APDL module in ANSYS finite element software. Nodal constraints were applied to simulate pier support and motion restrictions. The mesh size was controlled based on the high-frequency modal sensitivity in dynamic analysis to ensure the model's accuracy in the mid-to-low-order modal frequency bands. The model outputs the initial natural frequencies, the overall stiffness reference matrix, and the mid-span static deflection, providing a reference benchmark for dynamic degradation after fire damage.

[0140] (2) Construction of fire damage field

[0141] A fire under a bridge occurs in a semi-open space, where heat diffuses outwards. Under these conditions, a bridge fire can be described as a special fire scenario where the fire source is located in a partially enclosed area and is covered by a bridge structure. The fire field was inverted using finite element thermal analysis, combined with the ISO-834 standard temperature rise curve (see [reference]). Figure 3 As shown in the figure, by considering the combined effects of thermal radiation, thermal convection, and thermal conduction, a heat input boundary under time is established. Two fire-affected models are set up: the entire area of ​​the lower part of the left and right beams under the bridge and the L / 4 area of ​​the lower part of the left and right beams under the bridge. Fire load and self-weight load are applied simultaneously, and the fire time is 180 minutes. The fire conditions are as follows. Figure 4 As shown, where Figure 4 (a) in the diagram shows the fire exposure of the entire area under the bridge along the longitudinal direction. Figure 4 (b) in the diagram shows a partial fire exposure at the mid-span of the bridge along the longitudinal direction. Figure 4 (c) in the diagram shows the fire exposure from the transverse bridge to the area below the bridge.

[0142] (3) Establishment of structural analysis model

[0143] After the thermal analysis is completed, the structural analysis is carried out. The temperature elements of the beam, sleeper and rail are converted into structural elements SOLID185. The bridge model is divided using a mapped mesh with a mesh size of 0.15m. Under the same modeling method and mesh division as the thermal analysis, the nodal temperature corresponding to the fire time of the standard heating curve in the previous thermal analysis is applied as the nodal external load to the structural analysis for thermo-mechanical coupling analysis.

[0144] Step 2: Obtain fire damage parameters and temperature field distribution

[0145] Temperature contour maps and temperature time history curves: Under fire conditions in the entire area under the bridge, the temperature time history curves of the beam and rail over the period of 20 min to 180 min are as follows. Figure 7 As shown, the highest temperature on the fire-facing surface was 1096.7℃ at 180 minutes, while the temperatures of the rails and sleepers remained constant. When the entire area under the T-beam bridge was exposed to fire, the temperature distribution of the T-beam cross-section resembled an inverted wine glass centered on the beam ribs. The temperature isopleths of the entire bridge are shown in the figure below. Figure 5 and Figure 6 As shown, where Figure 5 and Figure 6 In the figure, A to I represent the temperature values ​​at different depths of the cross section, with the temperature increasing sequentially from A to I.

[0146] Step 3: Construct a material property degradation model and establish a degradation parameter field

[0147] (1) Material degradation stiffness matrix

[0148] When the substructure of a bridge is exposed to fire from one or more sides, the concrete will inevitably deteriorate in the high-temperature field. The elastic modulus of the concrete decreases with temperature. Based on the principle of virtual layer burn depth and the stiffness characteristics of the material itself, each layer contributes to the stiffness of the cross section. The sum of the stiffness of several layers is the total stiffness of the cross section. The formula is as follows:

[0149]

[0150] In the formula, The number of layers to divide the cross-section virtual layer; Let i be the elastic modulus of the i-th virtual layer; Let i be the cross-sectional area of ​​the i-th virtual layer; Let be the area moment of inertia of layer i; Let be the distance from the center of each layer on the cross section to the neutral axis. When the i-th virtual layer... When the value is 0, it means that the concrete at that location contributes 0 to the total stiffness of the cross section.

[0151] (2) Elastic modulus reduction factor

[0152] Based on the temperature distribution of different parts at various times obtained above, and referring to the stiffness degradation coefficient of concrete at different temperatures in existing studies, i.e., the elastic modulus reduction coefficient,... :

[0153]

[0154]

[0155]

[0156] in: Represents the time of exposure to fire. This represents the temperature at the corresponding fire exposure time. The i-th layer of concrete at temperature The elastic modulus below; Elastic modulus of concrete at room temperature; Stiffness degradation coefficient. Original thickness; Effective thickness after fire; The equivalent "burn-off" depth is equivalent to the thickness of a completely failed concrete layer. This represents the thickness of the virtual layer.

[0157] (3) Calculation of equivalent burn depth

[0158] The equivalent burn depth of the bridge structure under the most unfavorable fire conditions was calculated for the entire area under the bridge. Since the fire originated under the bridge, the T-beam section was divided into three parts: the horseshoe section, the web, and the top plate for equivalent analysis. Based on the temperature cloud map extracted earlier, the virtual layer at the horseshoe and top plate was set to 4cm, and at the web, it was set to 2cm. To simplify the calculation, the effects of concrete spalling and cross-sectional area loss were ignored; only the reduction in the elastic modulus of concrete at fire temperature was considered to cause stiffness loss in the beam.

[0159] Based on the cumulative equivalent burn depth of the concrete in the three parts of the horseshoe, web, and top slab of a simply supported T-beam railway bridge under fire with the entire area exposed to fire according to the standard temperature rise curve, the material degradation function was fitted using Origin software:

[0160] Horse hoof:

[0161] Web:

[0162] roof: .

[0163] Step 4: Create a post-fire degraded bridge structure model based on the degradation parameter field.

[0164] According to structural dynamics theory, during the service life of a simply supported railway beam bridge, its geometric state and boundary conditions remain unchanged. Assuming that the bridge's cross-section, length, and mass also remain constant, the change in the bridge's modal frequencies can be characterized by the change in its elastic modulus. The appearance of breakage indicates that the bridge is damaged. Based on the formula for the cumulative equivalent burn depth of concrete at different locations, calculations are performed as follows... Figure 8 The cumulative burn depth corresponding to different fire exposure times under the full-area fire exposure condition of the lower part of the left and right beams at L / 4 of the span shown. Thus, the elastic modulus reduction factor is obtained. , generate as Figure 9 The element degradation coefficients shown are mapped to the stiffness matrix of the finite element model to form the degraded structural dynamic model.

[0165] Step 5: Establish a coupled dynamic model of vehicle-track-bridge and perform dynamic time history analysis.

[0166] The train system adopts a 14-DOF model, connecting the wheels, bogies and car body through primary and secondary suspension systems. It consists of eight passenger cars, including one locomotive, and the train travels across the bridge at a speed of 45 km / h.

[0167] The displacement contact method is used to simulate the train operation process. The train system and the track system form contact pairs through the combination of contact elements and target elements, realizing the bidirectional transfer of load and displacement. The track and bridge are connected by nodal degree-of-freedom coupling equations to ensure the effective transfer of load and displacement.

[0168] The numerical solution uses the Newmark-β method (where β=0.25, γ=0.5) to ensure stability and energy conservation.

[0169] Step Six: Extract dynamic response and construct operational status observation indicators

[0170] Considering the three dimensions of train operation mechanical contact reliability, structural stability, and running comfort, the wheel load reduction rate of the train when traveling across the bridge after different fire exposure times is extracted. (See also) Figure 10 ), Index (see also) Figure 15 ) and mid-span vertical acceleration (See also) Figures 11 to 14 These three indicators were analyzed using a combined statistical method of root mean square and peak values ​​to improve their stability. The results showed that after 40 minutes of fire exposure on the bridge, the maximum wheel load reduction rate of the train locomotive was 0.622. The index is 2.18, and the maximum vertical acceleration at mid-span is... It is 0.23.

[0171] Step 7: Comprehensive Safety Assessment

[0172] (1) Security level determination

[0173] Calculate the overall safety factor:

[0174] ,

[0175] in, The wheel load reduction rate is 0.40. This is the Sperling exponent, which equals 0.40. The maximum vertical acceleration at mid-span is 0.20. The value is 1.1668.

[0176] (2) Early warning and decision support

[0177] System-generated report: Key Indicators The coefficients are within the permissible limits, but some indicators (maximum wheel load reduction rate) exceed the limits (see [reference]). Figure 16 The recommended output report is: limit weight operations and strengthen regular monitoring.

[0178] Example 2

[0179] This embodiment provides a safety assessment system for bridges under fire during train loads, comprising:

[0180] The first construction module is used to establish a healthy benchmark finite element model of a railway bridge, determine the component elements to be tested, input material parameters to the component elements to be tested, and form the benchmark stiffness and dynamic characteristics of the healthy structure.

[0181] The fire damage calculation module is used to perform fire inversion simulation on the finite element model of the railway bridge to obtain a three-dimensional temperature field, and to obtain the temperature field distribution and deformation of the fire-damaged components based on the three-dimensional temperature field.

[0182] The second construction module is used to construct a damage degradation function, input the temperature field of the fire-damaged component into the damage degradation function to output degradation parameters, and map the degradation parameters into the finite element software to form a distributed degradation parameter field.

[0183] Correction module: used to correct the stiffness matrix of the railway bridge finite element model based on the health benchmark according to the distributed degradation parameter field, so as to form a degraded structural model after fire.

[0184] The coupled dynamics solution module is used to establish the dynamic equations of the coupled system of vehicle, track, and bridge on the degraded structural model and to solve the time history to obtain the dynamic response time history.

[0185] The response analysis module is used to extract the parameter indicators of the train when crossing the bridge based on the dynamic response time history, and to calculate the safety evaluation index based on the parameter indicators.

[0186] The safety assessment and reporting module calculates comprehensive safety parameters based on safety evaluation indicators and outputs a report on the operational safety level and operational recommendations after a bridge fire based on these comprehensive safety parameters.

[0187] The safety assessment system for a bridge under fire under train load in this application embodiment can be a device, or a component, integrated circuit, or chip in a terminal. The device can be a mobile electronic device or a non-mobile electronic device. For example, mobile electronic devices can be mobile phones, tablets, laptops, PDAs, ultra-mobile personal computers (UMPCs), netbooks, or personal digital assistants (PDAs), etc., while non-mobile electronic devices can be servers, network-attached storage (NAS), personal computers (PCs), etc. This application embodiment does not specifically limit the scope of the system.

[0188] The safety assessment system for a bridge under fire under train load in this application embodiment can be a device with an operating system. This operating system can be Android, iOS, or other possible operating systems; this application embodiment does not specifically limit it.

[0189] This application provides a safety assessment system for bridges under fire during train loads, which can achieve... Figure 1 The various processes involved in implementing a method for safety assessment of a bridge under fire under train load are described in the following embodiments. To avoid repetition, they will not be repeated here.

[0190] The present invention relates to a method and system for safety assessment of bridges under train loads subjected to fire. By introducing fire damage parameter mapping based on a healthy bridge model, it achieves unified coupling between fire damage and structural dynamic models, avoiding the shortcomings of traditional methods that separate damage information from dynamic analysis. Through fire inversion analysis, the obtained bridge fire damage parameters are used to construct post-disaster stiffness degradation functions for different parts of the bridge structure, accurately reflecting the impact of fire on the overall stiffness and dynamic characteristics of the bridge, and improving the physical consistency of the assessment results. The present invention establishes coupled dynamic equations for vehicle-track bridges based on a degraded structural model, and achieves safety level determination through system response extraction and criterion comparison, making the operational assessment quantitative and repeatable. The assessment system constructed by the present invention has modular and scalable characteristics, enabling automation of data acquisition, modeling analysis, and safety output, and has good engineering application and promotion value.

[0191] Optionally, this application also provides an electronic device, including a processor, a memory, and a program or instructions stored in the memory and executable on the processor. When the program or instructions are executed by the processor, they implement the various processes of the above-described embodiment of the method for safety assessment of a fire-damaged bridge under train load and achieve the same technical effect. To avoid repetition, they will not be described again here.

[0192] This application also provides a readable storage medium storing a program or instructions. When the program or instructions are executed by a processor, they implement the various processes of the above-described embodiment of the method for safety assessment of a fire-damaged bridge under train load, and achieve the same technical effect. To avoid repetition, they will not be described again here.

[0193] The processor is the processor in the electronic device described in the above embodiments. The readable storage medium includes computer-readable storage media, such as computer read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk.

[0194] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this 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. Therefore, they should not be construed as limitations on the invention.

[0195] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example.

[0196] Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. The reference to "embodiment" herein means that a specific feature, structure, or characteristic described in connection with an embodiment can be included in at least one embodiment of this application. The appearance of this phrase in various places in the specification does not necessarily indicate the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0197] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for safety assessment of a bridge under fire under train load, characterized in that, include: S1: Establish a finite element model of a railway bridge with a healthy baseline, determine the element to be tested, and input material parameters into the element to be tested; S2: Perform fire inversion simulation on the finite element model of the railway bridge to obtain a three-dimensional temperature field, and obtain the temperature field distribution and deformation of the fire-damaged parts based on the three-dimensional temperature field. S3: Construct a damage degradation function, input the temperature field of the fire-damaged component into the damage degradation function to output degradation parameters, and map the degradation parameters into the finite element software to form a distributed degradation parameter field; S4: Based on the distributed degradation parameter field, the stiffness matrix of the railway bridge finite element model with the health benchmark is corrected to form a degraded structural model after fire, wherein the stiffness matrix... The corrected expression is: In the formula The element strain matrix, The elastic modulus at room temperature, Here, V represents the elastic modulus reduction factor at different temperatures, and V is the element geometric volume. This refers to the temperature at the corresponding node in the spatial coordinate system, i.e., the spatial temperature field. S5: Establish the dynamic equations of the coupled system of vehicle, track, and bridge on the degraded structural model and solve for the time history to obtain the dynamic response time history; S6: Extract parameter indicators for the train crossing the bridge based on the dynamic response time history, and calculate safety evaluation indicators based on the parameter indicators, specifically including: Based on the dynamic response time history, the vertical dynamic deflection and vertical acceleration at the mid-span of the bridge, and the vertical acceleration of the train and the vertical force between the wheel and rail are extracted when the train crosses the bridge. The maximum dynamic deflection and maximum vertical vibration acceleration of the bridge at mid-span are calculated based on the extracted vertical dynamic deflection and vertical acceleration at mid-span of the bridge. The vehicle wheel load reduction rate is calculated based on the extracted vertical acceleration of the train and the vertical force between the wheel and rail. S7: Based on safety evaluation indicators, calculate comprehensive safety parameters, and output a report on the post-fire operational safety level and operational recommendations for the bridge based on these parameters. Specifically, this includes: By wheel load reduction rate The Sperling index and mid-span vertical acceleration are used as safety evaluation indicators to calculate the comprehensive safety index. : in These are the weighting coefficients. , For the Sperling Index, The vertical acceleration at mid-span; Based on the comprehensive safety index The values ​​are used to classify operational safety into five levels: Level I, Level II, Level III, Level IV, and Level V, and output a report on the operational safety level and operational recommendations after a bridge fire.

2. The method for safety assessment of bridges under fire under train load according to claim 1, characterized in that, S2 specifically refers to: Using standard temperature rise curves or measured fire curves, and based on the flame radiation heat transfer equation, the temperature field distribution of fire-damaged components is obtained through finite element heat conduction analysis. An annealing effect correction during the cooling phase is then introduced after the fire. In the formula: Where c is the material density and c is the specific heat capacity. It is a temperature field. For time, Thermal conductivity, It is the Laplace operator of the temperature field. This indicates the intensity of the heat source per unit volume.

3. The method for safety assessment of a bridge under fire under train load according to claim 1, characterized in that, In S5, the dynamic equations of the vehicle-track-bridge coupled system are solved using numerical integration, with contact force iteratively updated at each time step to ensure numerical stability and energy conservation. The dynamic equations of the coupled system are as follows: In the formula , , These are the mass, damping, and degradation stiffness matrices, respectively. For moving load vectors, For acceleration vectors, For velocity vector, This is the displacement vector.

4. The method for safety assessment of a bridge under fire under train load according to claim 1, characterized in that, Based on the comprehensive safety index The values ​​categorize operational safety into five levels: Level I, Level II, Level III, Level IV, and Level V, and output a report on the operational safety level and recommendations after a bridge fire, specifically including: If the overall safety factor is Ks≥1.2 and the safety level is Level I, the output recommendation report is "The structure is intact, the operation is safe and stable, and normal operating speed can be restored"; If the overall safety factor is 1.00≤Ks<1.20, the safety level is Level II, and the recommended report output is "Operational safety is acceptable, regular monitoring required"; If the overall safety factor is 0.80≤Ks<1.00 and the safety level is Level III, the recommended report output is "Immediately shut down the operation, carry out temporary reinforcement, and reassess after reinforcement"; If the overall safety factor is 0.60≤Ks<0.80, the safety level is IV, and the output recommendation report is "speed-limited operation"; If the overall safety factor is Ks < 0.60 and the safety level is V, the output recommendation report is "Immediate repair or shutdown".

5. A safety assessment system for bridges exposed to fire under train load, characterized in that, The method for implementing the safety assessment of a fire-affected bridge under train load as described in any one of claims 1 to 4 includes: The first construction module is used to establish a healthy benchmark finite element model of a railway bridge, determine the component elements to be tested, input material parameters to the component elements to be tested, and form the benchmark stiffness and dynamic characteristics of the healthy structure. The fire damage calculation module is used to perform fire inversion simulation on the finite element model of the railway bridge to obtain a three-dimensional temperature field, and to obtain the temperature field distribution and deformation of the fire-damaged components based on the three-dimensional temperature field. The second construction module is used to construct a damage degradation function, input the temperature field of the fire-damaged component into the damage degradation function to output degradation parameters, and map the degradation parameters into the finite element software to form a distributed degradation parameter field. Correction module: Used to correct the stiffness matrix of the railway bridge finite element model based on the healthy benchmark according to the distributed degradation parameter field, forming a degraded structural model after fire action, wherein the stiffness matrix... The corrected expression is: In the formula The element strain matrix, The elastic modulus at room temperature, Here, V represents the elastic modulus reduction factor at different temperatures, and V is the element geometric volume. This refers to the temperature at the corresponding node in the spatial coordinate system, i.e., the spatial temperature field. The coupled dynamics solution module is used to establish the dynamic equations of the coupled system of vehicle, track, and bridge on the degraded structural model and to solve the time history to obtain the dynamic response time history. The response analysis module is used to extract parameter indicators when the train crosses the bridge based on the dynamic response time history, and to calculate safety evaluation indicators based on the parameter indicators, specifically including: Based on the dynamic response time history, the vertical dynamic deflection and vertical acceleration at the mid-span of the bridge, and the vertical acceleration of the train and the vertical force between the wheel and rail are extracted when the train crosses the bridge. The maximum dynamic deflection and maximum vertical vibration acceleration of the bridge at mid-span are calculated based on the extracted vertical dynamic deflection and vertical acceleration at mid-span of the bridge. The vehicle wheel load reduction rate is calculated based on the extracted vertical acceleration of the train and the vertical force between the wheel and rail. The safety assessment and reporting module calculates comprehensive safety parameters based on safety evaluation indicators, and outputs a report on the post-fire operational safety level and operational recommendations for the bridge based on these parameters. Specifically, this includes: By wheel load reduction rate The Sperling index and mid-span vertical acceleration are used as safety evaluation indicators to calculate the comprehensive safety index. : in These are the weighting coefficients. , For the Sperling Index, The vertical acceleration at mid-span; Based on the comprehensive safety index The values ​​are used to classify operational safety into five levels: Level I, Level II, Level III, Level IV, and Level V, and output a report on the operational safety level and operational recommendations after a bridge fire.

6. A computer device, characterized in that, It includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method for safety assessment of a fire-affected bridge under train load as described in any one of claims 1 to 4.

7. A computer storage medium, characterized in that, The computer storage medium stores instructions that, when executed on the computer, cause the computer to perform the safety assessment method for a fire-affected bridge under train load as described in any one of claims 1 to 4.

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