A transverse bridge-direction post-earthquake traffic safety analysis method considering the seismic damage state of the longitudinal ballastless track-continuous beam bridge system

Abstract

The present invention discloses a transverse bridge direction post-earthquake driving safety analysis method considering the seismic damage state of a longitudinally connected ballastless track-continuous beam bridge system, establishes a vehicle-track-bridge coupling dynamic model considering the seismic damage state, analyzes the post-earthquake damage law of the longitudinally connected ballastless track-continuous beam bridge system, so as to clarify the seismic damage state of key inter-layer components, and conducts a post-earthquake operation safety performance evaluation of the train considering the seismic damage state. It is clarified that the over-limit of the train safety index is significantly stronger when the seismic damage state is considered than when the seismic damage state is not considered. If the seismic damage state is not considered, the judgment of post-earthquake driving safety will be underestimated. It is also clarified that the over-limit risk of the train safety index at different earthquake intensities when the seismic damage state is considered and not considered provides more sufficient protection to avoid the risk of post-disaster driving, which has important practical value.

Description

Technical Field

[0001] The invention relates to a post-earthquake driving safety analysis method in the transverse direction of the bridge, which takes into account the earthquake damage state of a longitudinally connected ballastless track-continuous beam bridge system. Background Art

[0002] The suddenness and destructive nature of earthquakes pose a significant threat to high-speed rail safety, endangering not only operating trains and passengers but also potentially causing prolonged disruptions, severely impacting the normal operation of the railway system. As vital engineering lines, high-speed railways are crucial for post-earthquake disaster relief and rescue efforts. After an earthquake, key components of the track-bridge system will inevitably experience varying degrees of damage, including stiffness and residual deformation. Whether these damage patterns can ensure continued operation, how to continue operation, and what types of vehicles should be used are crucial to post-earthquake disaster relief and rescue efforts.

[0003] In recent years, researchers have studied the driving behavior of high-speed railway ballastless track-bridge systems under earthquake-induced damage. For example, one study reported a seismic analysis of a track-bridge system subjected to near-field random earthquakes. Seismic track irregularities significantly affect the derailment coefficient and lateral acceleration of high-speed trains, increasing with increasing train speed. Seismic track irregularities have little impact on the vertical dynamic performance of high-speed trains. Another study, by refining train operating index values ​​to define track structure damage levels (intact, minor, moderate, severe, and completely damaged), investigated the impact of track lateral displacement amplitude and train speed on train safety and stability, and proposed using track lateral displacement as a measure of track structure damage. Another study conducted shaking table tests of trains traveling on high-speed railway bridges using a four-array shaking table and a 1:10 scale train-track-bridge model. The study analyzed the impact of near-fault vertical seismic effects on train derailment on the bridge. The results showed that vertical seismic excitation reduces the minimum wheel-rail vertical force and increases the likelihood of bouncing derailments. However, most existing post-earthquake driving safety analyses of ballastless track-bridge systems only consider the residual deformation of the rail mapping in the ballastless track-bridge system, but do not consider earthquake damage states such as the stiffness defects of key interlayer components of the ballastless track-bridge system.

[0004] Therefore, the extent of damage to key interlayer components of the ballastless track-bridge system during an earthquake and whether it will affect the judgment of post-earthquake driving safety remain unknown and are issues that need to be urgently addressed. Summary of the Invention

[0005] In view of the above-mentioned existing post-earthquake driving safety analysis of ballastless track-bridge systems, most of them only consider the residual deformation of the rail mapping in the ballastless track-bridge system, but do not consider the seismic damage status of the key components between the layers of the ballastless track-bridge system, such as the seismic defects of the stiffness. The present invention provides a transverse bridge-direction post-earthquake driving safety analysis method that considers the seismic damage status of the longitudinal ballastless track-continuous beam bridge system, establishes a vehicle-track-bridge coupling dynamic model that considers the seismic damage status, analyzes the post-earthquake damage law of the longitudinal ballastless track-continuous beam bridge system, and clarifies the seismic damage status of the key components between the layers. It also conducts a post-earthquake train operation safety performance assessment that considers the seismic damage status, providing further improved reference and suggestions for the safe operation of trains after an earthquake. The specific technical solutions are as follows:

[0006] A post-earthquake traffic safety analysis method for a longitudinally connected ballastless track-continuous beam bridge system, taking into account the seismic damage state of the system, comprises the following steps:

[0007] 1) Construct a coupled dynamic model of the train-longitudinal ballastless track-continuous beam bridge system considering earthquake damage;

[0008] 2) Conduct post-earthquake traffic safety analysis of the longitudinal ballastless track-continuous beam bridge system in the transverse direction taking into account the earthquake damage status.

[0009] In the aforementioned post-seismic traffic safety analysis method for the transverse bridge direction considering the seismic damage state of the longitudinally connected ballastless track-continuous beam bridge system, in step 1), constructing a coupled dynamic model of the train-longitudinal ballastless track-continuous beam bridge system considering the seismic damage state includes the following sub-steps:

[0010] 1-1) Establish a high-speed railway longitudinal ballastless track-continuous beam bridge system model with the CRTS II ballastless track, continuous beam bridge, simply supported beam approach bridge, and roadbed as the research objects;

[0011] 1-2) Selecting appropriate earthquake motions, conducting post-earthquake damage analysis, and defining damage indicators for key interlayer components of the high-speed railway longitudinal ballastless track-continuous beam bridge system model;

[0012] 1-3) Based on the wheel-rail contact relationship and the dynamic equations of the various subsystem models of the high-speed railway longitudinal ballastless track-continuous beam bridge system, the dynamic equations of the vehicle-track-continuous beam bridge coupled vibration system are established, and a train-ballastless track-continuous beam bridge coupled vibration model is obtained that takes into account the seismic damage state;

[0013] 1-4) Using Ansys-Matlab co-simulation methods to calculate dynamic responses, the impact of post-earthquake damage to key inter-layer components on train safety performance was analyzed, and a train safety threshold diagram considering post-earthquake damage to key inter-layer components was established, providing some reference and suggestions for the safe operation of trains after the earthquake.

[0014] 1-5) Verify the accuracy of the established coupled dynamic model of the train-longitudinal ballastless track-continuous beam bridge system considering the seismic damage state, in preparation for the transverse post-seismic traffic safety analysis of the longitudinal ballastless track-continuous beam bridge system considering the seismic damage state.

[0015] As a preferred technical solution, in the aforementioned transverse bridge post-earthquake traffic safety analysis method considering the earthquake damage state of the longitudinal ballastless track-continuous beam bridge system, in step 1-1), the high-speed railway longitudinal ballastless track-continuous beam bridge system model is specifically as follows:

[0016] The main bridge is a 32m+48m+32m double-track single-box single-chamber variable-height continuous box girder bridge. The approach bridges on both sides of the main bridge are 32m concrete simply supported box girder bridges with a single-box single-chamber section. The roadbed section is 200m long. Six springs at the pier bottom are used to simulate pile-soil interaction, and the spring stiffness is calculated using the m method.

[0017] As a preferred technical solution, the aforementioned transverse bridge post-earthquake traffic safety analysis method considering the seismic damage state of the longitudinal ballastless track-continuous beam bridge system, the dynamic equation of the high-speed railway longitudinal ballastless track-continuous beam bridge system model is expressed as:

[0018]

[0019] Where: M B represents the overall mass matrix of the longitudinal ballastless track-continuous beam bridge system; C B represents the overall damping matrix of the longitudinal ballastless track-continuous beam bridge system; K B represents the overall stiffness matrix of the longitudinal ballastless track-continuous beam bridge system; Q B represents the total nodal load matrix of the longitudinal ballastless track-continuous beam bridge system; x B represents the displacement vector of the longitudinal ballastless track-continuous beam bridge system; represents the velocity vector of the longitudinal ballastless track-continuous beam bridge system; represents the acceleration vector of the longitudinal ballastless track-continuous beam bridge system; B represents the longitudinal ballastless track-continuous beam bridge system.

[0020] As a preferred technical solution, the aforementioned transverse bridge post-earthquake traffic safety analysis method considering the seismic damage state of the longitudinal ballastless track-continuous beam bridge system is characterized in that the vehicle model in the high-speed railway longitudinal ballastless track-continuous beam bridge system model is a four-axle vehicle model, and its entire carriage contains 31 degrees of freedom; the dynamic equation of the vehicle model is expressed in matrix form as follows:

[0021]

[0022] Where Mc represents the mass matrix of the high-speed train; C c represents the damping matrix of the high-speed train; K c represents the stiffness matrix of the high-speed train; Q c represents the external load matrix of the high-speed train; x c represents the displacement vector of the high-speed train; represents the velocity vector of the high-speed train; represents the acceleration vector of the high-speed train; c Stands for high-speed train.

[0023] As a preferred technical solution, the aforementioned transverse bridge post-seismic driving safety analysis method considering the seismic damage state of the longitudinal ballastless track-continuous beam bridge system, the wheel-rail contact relationship of the high-speed railway longitudinal ballastless track-continuous beam bridge system model is a knife-edge contact constraint, the lateral clearance between the wheel and rail is 10 mm, the lateral contact stiffness is 1.617×107 N / m, the contact angle is 1 / 40 rad, the creep force is calculated using the Kaller linear creep theory, and the wheel-rail normal force is calculated using the Hertz nonlinear contact theory;

[0024] The Hertz nonlinear contact theory solution calculation formula is:

[0025]

[0026] Where: wr represents the wheel-rail, δ wr is the relative displacement between wheel and rail, G is the wheel-rail contact stiffness;

[0027] The calculation formula for solving the Kaller linear creep theory is:

[0028]

[0029] Where: F x is the longitudinal creep force, x represents along the x-axis; F y is the lateral creep force, y represents along the y-axis; M z is the creep torque, z represents the rotation around the z axis; x is the longitudinal creep rate, ζ y is the lateral creep rate, is the spin creep rate; f 11 、f 22 、f 23 、f 33 is the creep coefficient; respectively expressed as:

[0030]

[0031] Where: G' is the composite shear modulus of the wheel-rail material; a is the major semi-axis of the wheel-rail contact ellipse, b is the minor semi-axis of the wheel-rail contact ellipse, C 11 、C 22 、C 23 、C 33 is the Kalker coefficient, which is a function of the wavelength ratio L / a, where L is the wavelength of the creep rate and a is half the longitudinal diameter of the contact spot.

[0032] As a preferred technical solution, in the aforementioned transverse bridge direction post-earthquake traffic safety analysis method considering the earthquake damage state of the longitudinal ballastless track-continuous beam bridge system, in steps 1-2), the damage indicators of the key inter-layer components of the high-speed railway longitudinal ballastless track-continuous beam bridge system are shown in the following table:

[0033]

[0034] As a preferred technical solution, in the aforementioned transverse bridge post-earthquake traffic safety analysis method considering the seismic damage state of the longitudinal ballastless track-continuous beam bridge system, in steps 1-3), the dynamic equations of the train-ballastless track-continuous beam bridge coupled vibration model considering the seismic damage state are expressed as follows:

[0035]

[0036] Where: M' B is the overall mass matrix of the longitudinal ballastless track-continuous beam bridge system considering the earthquake damage state; C' B is the overall damping matrix of the longitudinal ballastless track-continuous beam bridge system considering the earthquake damage state; K' B is the overall stiffness matrix of the longitudinal ballastless track-continuous beam bridge system considering the seismic damage state; is the acceleration of the longitudinal ballastless track-continuous beam bridge system considering the earthquake damage state; is the velocity of the longitudinal ballastless track-continuous beam bridge system considering the earthquake damage state; x' B is the displacement of the longitudinal ballastless track-continuous beam bridge system considering earthquake damage; Q bg is the vehicle structure gravity vector; Q cg is the gravity vector of the track-continuous beam bridge structure; F bl is the wheel-rail contact force vector; B It represents the longitudinal ballastless track-continuous beam bridge system. c represents a high-speed train, bg represents a vehicle structure, cg represents a track-continuous beam bridge structure, and bl represents a wheel-rail structure.

[0037] In the aforementioned method for analyzing post-earthquake traffic safety in the transverse direction of the longitudinal ballastless track-continuous beam bridge system considering the seismic damage state, in step 2), the post-earthquake traffic safety analysis in the transverse direction of the longitudinal ballastless track-continuous beam bridge system considering the seismic damage state includes a train operation safety analysis considering the seismic damage state and a post-earthquake train operation safety threshold analysis considering the seismic damage state.

[0038] As a preferred technical solution, the aforementioned transverse bridge post-earthquake traffic safety analysis method considering the earthquake damage state of the longitudinal ballastless track-continuous beam bridge system is

[0039] The conclusion of the post-earthquake train operation safety threshold analysis considering the earthquake damage state is:

[0040] The train safety index exceeds the limit when considering the earthquake damage state, which is significantly stronger than that without considering the earthquake damage state. Failure to consider the earthquake damage state will underestimate the judgment of post-earthquake train safety.

[0041] When considering or not considering the earthquake damage state, the risk of exceeding the limit of train safety index does not increase linearly with the earthquake intensity;

[0042] When the earthquake damage state is taken into account, the derailment coefficient and the axle lateral force will exceed the limit when the earthquake motion intensity reaches 0.2g. However, when the earthquake damage state is not taken into account, the derailment coefficient and the axle lateral force will exceed the limit only when the earthquake motion intensity reaches 0.3g.

[0043] When the local vibration intensity reaches 0.5g, the effects on the derailment coefficient exceeding the limit are greater when considering or not considering the earthquake damage state, while the effects on the axle lateral force exceeding the limit are not much different.

[0044] The beneficial effects of the present invention are as follows:

[0045] 1) This paper analyzes the post-earthquake damage patterns of a longitudinally connected ballastless track-continuous beam bridge system. By establishing a vehicle-track-bridge coupled dynamic model that considers the seismic damage state, the paper analyzes the post-earthquake damage patterns of the longitudinally connected ballastless track-continuous beam bridge system to clarify the seismic damage state of key inter-layer components. This paper also conducts a post-earthquake safety performance assessment of trains considering the seismic damage state, providing further improved reference and suggestions for the safe operation of trains after an earthquake.

[0046] 2) The train-ballastless track-continuous beam bridge coupled dynamic model established in this invention, which takes into account the seismic damage state, has been verified to have good accuracy and good agreement with the results in the literature. It can be used for subsequent research and further high-speed rail risk assessment applications.

[0047] 3) The analysis method of the present invention clearly shows that the risk of train safety index exceeding the limit is significantly greater when considering the earthquake damage state than when not considering the earthquake damage state. Not considering the earthquake damage state will underestimate the judgment of post-earthquake driving safety. When considering and not considering the earthquake damage state, the risk of train safety index exceeding the limit does not increase linearly with the earthquake motion intensity. Moreover, when the earthquake damage state is considered, the derailment coefficient and wheel axle lateral force will exceed the limit when the earthquake motion intensity reaches 0.2g, while when the earthquake damage state is not considered, the derailment coefficient and wheel axle lateral force will exceed the limit only after the earthquake motion intensity reaches 0.3g. When the earthquake damage state is reached, the derailment coefficient exceeds the limit when considering and not considering the earthquake damage state. The difference in the effect on the wheel axle lateral force exceeding the limit is not significant. It is clear that when conducting post-earthquake driving safety analysis of the longitudinal ballastless track-continuous beam bridge system, considering the earthquake damage state of the ballastless track-bridge system can more accurately judge post-earthquake driving safety, provide more sufficient protection for avoiding post-disaster driving risks, and have important practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1(a) is a schematic diagram of the existing ballastless track-bridge system model that only considers the rail mapping residual deformation in the ballastless track-bridge system;

[0049] FIG1( b ) is a schematic diagram of a coupled dynamic model of a train-longitudinal ballastless track-continuous beam bridge system considering earthquake damage conditions according to the present invention;

[0050] Figure 2 This is a schematic diagram of the longitudinal ballastless track-continuous beam bridge system model;

[0051] Figure 3 This is a schematic diagram of a high-speed train model in the system of the present invention;

[0052] Figure 4 Schematic diagram of the wheel-rail contact relationship in the system of the present invention;

[0053] Figure 5 is the lateral residual displacement of the fixed support under different earthquake intensities;

[0054] Figure 6 is the lateral residual deformation of the lateral block under different earthquake intensities;

[0055] Figure 7 is the lateral residual displacement of the sliding layer and friction plate under different earthquake intensities;

[0056] Figure 8 The residual deformations of rails, main beams, base plates, track plates, and supports under different earthquake intensities under the R3 earthquake.

[0057] Figure 9 The residual deformations of rails, main beams, base plates, track plates, and supports under different earthquake intensities under the R2 earthquake.

[0058] Figure 10 This is the Ansys-Matlab joint simulation flow chart;

[0059] Figure 11 Comparison of the dynamic response calculation results of the three-span continuous beam bridge under the action of trains calculated by the model of the present invention and the verification model;

[0060] Figure 12 100 ground motions selected for the present invention;

[0061] Figure 13 The effects of considering and ignoring earthquake damage state on train operation performance are explained for the two working conditions of the present invention;

[0062] Figure 14 The safety index of train operation under frequent earthquakes of the present invention;

[0063] Figure 15 Design the safety index of train operation during earthquake for the present invention;

[0064] Figure 16 This is the safety index of train operation in the event of a rare earthquake according to the present invention;

[0065] Figure 17 is the maximum value of the train operation safety performance index under different earthquake intensities and running speeds;

[0066] Figure 18 The diagram shows the post-earthquake operational safety threshold with and without considering earthquake damage. DETAILED DESCRIPTION

[0067] The following will be combined with the embodiments and drawings to clearly and completely describe the technical solutions of the present invention. Obviously, the embodiments described are only preferred embodiments of the present invention, not all embodiments, and are not intended to limit the present invention in any other form. Any person skilled in the art may use the disclosed technical content to make changes or modifications. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall still fall within the scope of protection of the technical solution of the present invention.

[0068] Example 1

[0069] This embodiment is aimed at the existing post-earthquake driving safety analysis of ballastless track-bridge systems. Most of them only consider the residual deformation of the rail mapping in the ballastless track-bridge system, but do not consider the earthquake damage state such as the stiffness and seismic defects of the key components between the layers of the ballastless track-bridge system. The present invention provides a transverse bridge-direction post-earthquake driving safety analysis method that considers the earthquake damage state of the longitudinal ballastless track-continuous beam bridge system, constructs a coupled dynamic model of the train-longitudinal ballastless track-continuous beam bridge system that considers the earthquake damage state, and conducts transverse bridge-direction post-earthquake driving safety analysis of the longitudinal ballastless track-continuous beam bridge system that considers the earthquake damage state, providing further improved reference and suggestions for the safe operation of trains after an earthquake. The details are as follows:

[0070] 1. Construct a coupled dynamic model of the train-longitudinal ballastless track-continuous beam bridge system considering earthquake damage

[0071] Most existing post-earthquake driving safety analyses of ballastless track-bridge systems only consider the residual deformation of the rails in the ballastless track-bridge system, as shown in Figure 1(a), without considering seismic damage states such as seismic defects in the stiffness of key interlayer components of the ballastless track-bridge system. This embodiment establishes a simulation model of a longitudinally connected ballastless track-continuous beam bridge system. Seismic motions with significant impacts were selected from existing studies to conduct a post-earthquake damage analysis of the longitudinally connected ballastless track-continuous beam bridge system. This analysis clarifies the seismic damage states of key interlayer components and the residual deformation laws of each layer of the longitudinally connected ballastless track-continuous beam bridge system. Furthermore, the residual deformations and seismic damage states of each layer of the structure in the simulation model are imported into the dynamic model of the train-longitudinal ballastless track-continuous beam bridge coupled system, forming a vehicle-track-bridge coupled dynamic model that considers seismic damage states, as shown in Figure 1(b). The model was then used to carry out a post-earthquake operation safety performance assessment of trains with and without considering the earthquake damage status, in order to clarify the impact of considering and not considering the earthquake damage status on the post-earthquake traffic capacity of trains, and to provide a guidance diagram of the safety threshold of post-earthquake operation of trains.

[0072] 1.1 Longitudinal ballastless track-continuous beam bridge system model

[0073] Based on the high-speed railway engineering drawings, a longitudinal ballastless track-continuous beam bridge system model is constructed, such as Figure 2 As shown in the figure, the main bridge in this model is a (32+48+32)m double-track single-box single-chamber variable-height continuous box girder bridge. The approach bridges on both sides of the main bridge are 32m concrete simply supported box girder bridges with a single-box single-chamber section. The roadbed section is 200m long. Six springs at the pier bottom are used to simulate the pile-soil interaction, and the spring stiffness is calculated using the m method.

[0074] According to the Lagrange equation, the dynamic equation of the longitudinal ballastless track-continuous beam bridge system is established:

[0075]

[0076] Where M B 、C B , K B , Q B They represent the overall mass matrix, overall damping matrix, overall stiffness matrix, and total node load matrix of the longitudinal ballastless track-continuous beam bridge system respectively. B represents the displacement vector of the longitudinal ballastless track-continuous beam bridge system; represents the velocity vector of the longitudinal ballastless track-continuous beam bridge system; represents the acceleration vector of the longitudinal ballastless track-continuous beam bridge system; B represents the longitudinal ballastless track-continuous beam bridge system.

[0077] 1.2 Vehicle Model

[0078] The high-speed train model used in the longitudinal ballastless track-continuous beam bridge system model of this embodiment is a four-axle vehicle model. Figure 3 As shown, it is simplified into a multi-rigid body system running on the track structure, and the entire carriage contains 31 degrees of freedom. According to the D'Alembert principle, the vehicle dynamics equation of this high-speed train model can be expressed in matrix form as follows:

[0079]

[0080] Where M c 、C c , K c , Q c They represent the mass matrix, damping matrix, stiffness matrix and external load matrix of the high-speed train respectively. c represents the displacement vector of the high-speed train; represents the velocity vector of the high-speed train; represents the acceleration vector of the high-speed train; c Stands for high-speed train.

[0081] 1.3 Wheel-rail contact relationship

[0082] When the vehicle and the track make wheel-rail contact, wheel-rail normal force and creep force will be generated. In this embodiment, it is assumed that the wheel-rail contact relationship is a knife-edge contact constraint, such as Figure 4 As shown, the lateral clearance between the wheel and rail is 10 mm, the lateral contact stiffness is 1.617×107 N / m, the contact angle is 1 / 40 rad, the creep force is calculated using Kaller linear creep theory, and the wheel-rail normal force is calculated using Hertz nonlinear contact theory. The calculation formula for Hertz nonlinear contact theory is as follows:

[0083]

[0084] Where: wrrepresents the wheel rail, δ wr is the relative displacement between the wheel and rail, and G is the wheel-rail contact stiffness.

[0085] The calculation formula of Kalker linear creep theory is as follows:

[0086]

[0087] Where: F x is the longitudinal creep force, x represents along the x-axis; F y is the lateral creep force, y Indicates along the y-axis; M z is the creep torque, z represents the rotation around the z axis; x is the longitudinal creep rate, ζ y is the lateral creep rate, is the spin creep rate;

[0088] f 11 、f 22 、f 23 、f 33 is the creep coefficient; respectively expressed as:

[0089]

[0090] Where: G' is the composite shear modulus of the wheel-rail material; a is the major semi-axis of the wheel-rail contact ellipse, b is the minor semi-axis of the wheel-rail contact ellipse, C 11 、C 22 、C 23 、C 33 is the Kalker coefficient, which is a function of the wavelength ratio L / a, where L is the wavelength of the creep rate and a is half the longitudinal diameter of the contact spot; 11 represents the position of the first row and first column of the matrix, 22 represents the position of the second row and second column of the matrix, 23 Indicates the position of the second row and third column of the matrix, 33 Represents the position of the third row and third column of the matrix.

[0091] 1.4 Extraction of seismic damage status of longitudinal ballastless track and continuous beam main beam

[0092] Appropriate ground motions were selected, specifically those with a greater seismic response for the longitudinal ballastless track-continuous girder bridge system. Combined with the damage indicators for key interlayer components of the longitudinal ballastless track-continuous girder bridge system (see Table 1), a post-earthquake damage analysis was conducted to extract the seismic damage status of the longitudinal ballastless track and continuous girder.

[0093] Table 1. Damage indicators of key components between layers of the high-speed railway longitudinal ballastless track-continuous beam bridge system

[0094]

[0095] The selected earthquake was applied laterally to the dynamics model of a coupled longitudinally connected ballastless track and continuous beam bridge system. The post-earthquake damage of the longitudinally connected ballastless track and continuous beam bridge system was analyzed. The damage to key interlayer components, such as supports, lateral blocks, and sliding layers, was assessed. The post-earthquake residual deformation patterns of each layer of the longitudinally connected ballastless track and continuous beam system were revealed. The results are as follows:

[0096] (1) Fixed support

[0097] like Figure 5 As shown in the figure, under a frequent earthquake of magnitude 8, the maximum lateral peak displacement of the fixed supports is 0.27 mm, and the deformation of each fixed support is still in the linear stage and has not reached the damage limit. Under a design earthquake of magnitude 8, most of the fixed supports have suffered minor damage, and a few have been destroyed. The maximum lateral residual displacement is 39 mm. Under a rare earthquake of magnitude 8, most of the fixed supports have been destroyed, with a maximum lateral residual displacement of 44 mm. It can also be found that the lateral residual displacement of support 1F is basically smaller than that of supports 2F and 3F. This is mainly because when the transition section structure is not damaged, the constraint provided by the transition section track structure reduces the relative displacement between the beam and the support. However, under the rare earthquake R2 earthquake motion, the lateral residual displacement of support 1F is greater than that of supports 2F and 3F, indicating that the transition section track structure at both ends of the bridge has suffered significant damage under the R2 earthquake motion.

[0098] (2) Side block

[0099] like Figure 6 As shown in the figure, under the 8-magnitude frequent and design earthquakes, the maximum lateral residual displacements of the lateral stops were 0.018mm and 0.85mm, respectively. Neither deformation reached the damage limit, indicating that the lateral stops had not yet been damaged. This suggests that the relative deformations between the track and the main beam remain within a safe range under both the 8-magnitude frequent and design earthquakes. Under the 8-magnitude rare earthquake, some of the lateral stops at both ends of the bridge exceeded the damage limit of 2mm, and a small number of them had maximum lateral residual displacements exceeding the failure limit of 5mm. This indicates that the lateral stops have failed, necessitating speed restrictions when passing through this area to avoid the risk of derailment. Furthermore, under the 8-magnitude rare earthquake, lateral stop failure primarily occurred at the junction of the bridge ends and the transition section. This is primarily due to the shaking of the bridge under earthquakes, particularly at mid-span. The inertial forces of this shaking are often transmitted through the bridge deck and structure to the ends. Due to the concentrated inertial forces, the lateral stops at both ends experience significant impact forces, leading to their failure.

[0100] (3) Sliding layer and friction plate

[0101] like Figure 7 As shown in the data, under an 8-magnitude frequent earthquake, the maximum lateral residual displacements of the sliding layer and friction plate were 0.024 mm and 0.004 mm, respectively, and the lateral deformations did not reach the damage limit. Under an 8-magnitude design earthquake, both the sliding layer and the friction plate were essentially damaged. The maximum lateral residual displacement of the sliding layer was 1.50 mm, which did not exceed the 2 mm damage limit, indicating that the sliding layer had not yet failed. The maximum lateral residual displacement of the friction plate was 4.370 mm, which exceeded the 2 mm damage limit, indicating that the friction plate had already failed under the design earthquake. Under an 8-magnitude rare earthquake, the sliding layer was partially damaged, with a maximum lateral residual displacement of 15.2 mm. The friction plate also suffered varying degrees of damage, requiring trains to limit speed when passing through this area. Furthermore, under rare earthquakes, damage to the sliding layer and friction plate primarily occurred at the ends of the bridge. This is primarily due to the shaking of the bridge during earthquakes. The inertial forces of this shaking are often transmitted through the bridge deck and structure to the ends, causing damage to the sliding layer and friction plate at both ends.

[0102] (4) Analysis of residual deformation of each layer of the longitudinal ballastless track-continuous beam system after earthquake

[0103] Taking the R3 and R2 earthquake motions as examples, the post-earthquake residual deformation law of each layer structure of the longitudinal ballastless track-continuous beam system is revealed. The calculation results are as follows: Figure 8 and Figure 9 shown.

[0104] like Figure 8 、 9 As shown, the residual displacements of the rails, base plate, and track plate are similar. Furthermore, under frequent and design earthquakes, the relative residual deformations of the rails and main beams are similar. However, under rare earthquakes, the rails and main beams exhibit significant displacement at their ends. Under the R3 earthquake, the displacements were 7.22mm and 9.82mm, respectively, and under the R2 earthquake, the displacements were 13.12mm and 15.65mm, respectively. This indicates that under rare earthquakes, when trains pass through the junction of the bridge ends and the transition section, there is a safety hazard.

[0105] 1.5 Train-Ballastless Track-Continuous Beam Bridge Coupled Vibration Model Considering Seismic Damage

[0106] Based on the post-seismic damage analysis of the longitudinally connected ballastless track and continuous beam bridge system in Section 1.4, the stiffness of components in the post-seismic damaged area is modified based on the damage mechanics performance indicators of key components in the high-speed railway track-bridge system. The connection spring stiffness of components in the fully damaged area is assumed to be zero, the stiffness of areas without minor damage is assumed to be the original stiffness, and the connection spring stiffness of components between the minor damage and fully damaged limits is calculated using linear interpolation. A modal analysis is then performed on the modified track-bridge system to obtain a .FULL binary file containing the overall stiffness, mass, and damping matrices of the earthquake damage. The binary file is converted to a HARWELL-BOEING format using the HBMAT command, and then converted to a sparse matrix using programming. The sparse matrix is ​​then combined with the .MAPPING node degree of freedom mapping file generated by the HBMAT command. The node degree of freedom mapping file is then called to obtain the overall mass, stiffness, and damping matrices of the track-bridge system.

[0107] Based on the above wheel-rail contact relationship, combined with the dynamic equations of each subsystem (i.e., vehicle system and ballastless track-continuous beam bridge system),

[0108] The dynamic equations of the vehicle-track-continuous beam bridge coupled vibration system are established as follows:

[0109] Not considering earthquake damage status

[0110]

[0111] Considering earthquake damage

[0112]

[0113] Where, M' B , C' B , K' B are the overall mass, damping and stiffness matrices of the longitudinal ballastless track-continuous beam bridge system considering the earthquake damage state; x' B are the acceleration, velocity and displacement of the longitudinal ballastless track-continuous beam bridge system considering the earthquake damage state; Q bg , Q cg are the vehicle and track-continuous beam bridge structure gravity vectors, F bl is the wheel-rail contact force vector. The meanings of the other parameters are the same as above.

[0114] The dynamic response is calculated by Ansys-Matlab joint simulation method, such as Figure 10As shown in the figure, the impact of post-earthquake damage of key inter-layer components on driving safety performance is analyzed, and a driving safety threshold diagram considering post-earthquake damage of key inter-layer components is established, which provides certain references and suggestions for the safe operation of trains after the earthquake.

[0115] 1.6 Verification of the coupled dynamic model of train-ballastless track-continuous beam bridge considering earthquake damage

[0116] In order to verify the accuracy of the constructed train-ballastless track-continuous beam bridge coupling dynamic model considering the earthquake damage state, this embodiment established a 3-span (32+48+32)m prestressed continuous beam bridge. The train model uses the ICE3 high-speed train, each group consists of 8 carriages (2M+6T), the running speed is 275km / h, and the random unevenness time domain samples generated by the Chinese ballastless track spectrum are used to perform track unevenness analysis. The mean displacement of the first and second spans of the beam under the train solved by the constructed train-ballastless track-continuous beam bridge coupling dynamic model considering the earthquake damage state is compared with the calculation results under the model. The results are as follows: Figure 11 As shown, it can be seen that the calculation results of the train-ballastless track-continuous beam bridge coupled dynamic model considering the earthquake damage state constructed by the present invention are in good agreement with the verification model, which verifies the accuracy of the model of the present invention.

[0117] 2. Post-earthquake driving safety analysis of the longitudinal ballastless track-continuous beam bridge system with and without considering earthquake damage

[0118] The 100 selected earthquake motions, such as Figure 12 As shown in the figure, five earthquake motions with larger responses (numbered R1 to R5) were selected, as shown in Table 2. The PGA of the seismic wave was adjusted to 8 degrees, with a common earthquake of 0.1g, a design earthquake of 0.3g, and a rare earthquake of 0.57g. The earthquake input was lateral.

[0119] Table 2. Earthquake records

[0120]

[0121] Two operating conditions are used to illustrate the impact of considering and ignoring the earthquake damage state on the train operation performance:

[0122] Condition 1: Only the residual deformation of the rail after the earthquake is considered without considering the earthquake damage state, such as Figure 13 (a)

[0123] Working condition 2: Considering the residual deformation and earthquake damage state of rails, such as Figure 13 (b) shown.

[0124] The initial track irregularity adopts the Chinese ballastless track spectrum.

[0125] 2.1 Train operation safety analysis with and without considering earthquake damage

[0126] This time, the above-mentioned train-ballastless track-continuous beam bridge coupled dynamic model considering earthquake damage was used to conduct train operation safety analysis with and without considering earthquake damage under different speeds and different ground motions. The results are as follows Figures 14 to 16 shown.

[0127] Depend on Figure 14 (a) to Figure 14 As shown in Figure (b), under the 0.1g earthquake, the longitudinal ballastless track-continuous beam bridge system suffered no significant damage, and the train operation safety indicators remained within the limits. Therefore, considering or ignoring the earthquake damage state has no impact on the train operation safety indicators, indicating that no minor damage occurred.

[0128] Depend on Figure 15 (a) to Figure 15 (d) It can be seen that under the design earthquake of 0.3g, the train operation safety index exceeds the limit. The train safety index exceeds the limit significantly more when considering the earthquake damage state than when not considering the earthquake damage state. Taking the R2 earthquake motion as an example, when considering the earthquake damage state, the derailment coefficient exceeds the limit at a speed of around 270km / h, and the axle lateral force exceeds the limit at a speed of around 260km / h. When the earthquake damage state is not considered, the speeds corresponding to the derailment coefficient and axle lateral force exceeding the limit are 330% and 330%, respectively. It can be seen that not considering the earthquake damage state will underestimate the assessment of post-earthquake train safety, increasing the risk by 21%. Therefore, the post-earthquake train performance assessment of the longitudinal ballastless track-continuous beam bridge system under a 0.3g earthquake should take the earthquake damage state into account.

[0129] Depend on Figure 16 (a) to Figure 16 (d) It can be seen that under the rare 0.57g earthquake, the selected seismic motion exceeds the train operation safety index limit. The derailment coefficient exceeds the limit significantly when considering the seismic damage state than when not considering the seismic damage state, while the wheel axle lateral force exceeds the limit similarly with and without considering the seismic damage state. Taking the R2 seismic motion as an example, after considering the seismic damage state, the derailment coefficient exceeds the limit at a speed of around 210 km / h. When not considering the seismic damage state, the speed corresponding to the derailment coefficient exceeding the limit is 250 km / h. The speed corresponding to the wheel axle lateral force exceeding the limit is 250 km / h both with and without considering the seismic damage state. Without considering the seismic damage state, the exceedance risk increases by 16%, slightly lower than the train safety exceedance risk under the design earthquake of 0.3g. Therefore, the post-seismic performance assessment of the longitudinal ballastless track-continuous beam bridge system under a 0.57g earthquake should consider the seismic damage state. However, the risk of exceeding the train safety index limit does not increase linearly with the seismic motion intensity, whether considering or not considering the seismic damage state.

[0130] 2.2 Analysis of post-earthquake train operation safety thresholds with and without considering earthquake damage

[0131] In order to clarify the relationship between earthquake intensity and train operation safety, the R2 earthquake motion with the largest response is selected, and the calculation results are as follows: Figure 17 and Figure 18 shown.

[0132] from Figure 17 It can be seen that when the earthquake damage state is considered, the derailment coefficient and the wheel axle lateral force will exceed the limit when the earthquake motion intensity reaches 0.2g, and the corresponding speeds are 320km / h and 280km / h respectively. When the earthquake damage state is not considered, the derailment coefficient and the wheel axle lateral force will exceed the limit only after the earthquake motion intensity reaches 0.3g, and the corresponding speeds are 328km / h and 337km / h respectively. When the earthquake damage state is considered, the derailment coefficient exceeds the limit when the earthquake damage state is considered. When the earthquake damage state is considered, the train speed reaches 210km / h, and when the earthquake damage state is not considered, the derailment coefficient exceeds the limit at a speed of 250km / h. There is little difference between the wheel axle lateral force exceeding the limit when the earthquake damage state is considered and when the earthquake damage state is not considered, and both exceed the limit at a train speed of 250km / h.

[0133] In order to more intuitively reflect the relationship between different earthquake intensities and the safe speed of train operation after the earthquake, the post-earthquake operation safety threshold considering the earthquake damage state and the post-earthquake operation safety threshold not considering the earthquake damage state are established, such as Figure 18 The results are shown in the paper, hoping to provide a theoretical basis for the guidance of post-earthquake driving safety of the longitudinal ballastless track-continuous beam bridge system.

[0134] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, the embodiments should be viewed as exemplary and non-restrictive in all respects. Furthermore, it should be understood that although this specification is described in terms of implementation methods, it does not encompass only one technical solution. This narrative is provided for clarity only, and those skilled in the art should consider the specification as a whole. The technical solutions in the embodiments may also be appropriately combined to form other implementation methods that are understandable to those skilled in the art.

Claims

1. A post-earthquake traffic safety analysis method for a longitudinally connected ballastless track-continuous beam bridge system, taking into account the seismic damage state of the bridge, is characterized by: The steps include: 1) Constructing a coupled dynamic model of the train-longitudinal ballastless track-continuous beam bridge system considering earthquake damage; including the following sub-steps: 1-1) Establish a high-speed railway longitudinal ballastless track-continuous beam bridge system model with the CRTS II ballastless track, continuous beam bridge, simply supported beam approach bridge, and roadbed as the research objects; 1-2) Select appropriate earthquake motions to conduct post-earthquake damage analysis. Define the damage states of key interlayer components of the high-speed railway longitudinal ballastless track-continuous beam bridge system model using damage indicators for these components. These key components include fixed supports, sliding layers, friction plates, fasteners, and lateral blocks. 1-3) Based on the damage mechanical performance indicators from step 1-2), the stiffness of the components in the post-earthquake damaged area is modified; a modal analysis is then performed on the modified track-bridge system to obtain the overall mass, stiffness, and damping matrix of the track-bridge system; then, based on the wheel-rail contact relationship and combined with the dynamic equations of the various subsystem models of the high-speed railway longitudinal ballastless track-continuous beam bridge system, a set of dynamic equations for the vehicle-track-continuous beam bridge coupled vibration system is established, thereby obtaining a train-ballastless track-continuous beam bridge coupled vibration model that considers the earthquake damage state; 1-4) Calculate the dynamic response using the Ansys-Matlab co-simulation method, analyze the impact of post-earthquake damage to key inter-story components on driving safety performance, and establish a driving safety threshold diagram considering post-earthquake damage to key inter-story components; 1-5) Verify the accuracy of the established coupled dynamic model of the train-longitudinal ballastless track-continuous beam bridge system considering earthquake damage, in preparation for conducting a transverse post-seismic safety analysis of the longitudinal ballastless track-continuous beam bridge system considering earthquake damage; 2) Conduct post-earthquake train safety analysis in the transverse direction of the longitudinal ballastless track-continuous beam bridge system considering earthquake damage, including train operation safety analysis considering earthquake damage and post-earthquake train operation safety threshold analysis considering earthquake damage.

2. The method for analyzing transverse bridge post-earthquake vehicle safety considering the seismic damage state of the longitudinally connected ballastless track-continuous beam bridge system according to claim 1 is characterized by: In step 1-1), the high-speed railway longitudinal ballastless track-continuous beam bridge system model is specifically as follows: The main bridge is a 32m+48m+32m double-track single-box single-chamber variable-height continuous box girder bridge. The approach bridges on both sides of the main bridge are 32m concrete simply supported box girder bridges with a single-box single-chamber section. The roadbed section is 200m long. Six springs at the pier bottom are used to simulate pile-soil interaction, and the spring stiffness is calculated using the m method.

3. The method for analyzing transverse bridge post-earthquake vehicle safety considering the seismic damage state of the longitudinally connected ballastless track-continuous beam bridge system according to claim 2 is characterized by: The dynamic equation of the high-speed railway longitudinal ballastless track-continuous beam bridge system model is expressed as: Where: M B represents the overall mass matrix of the longitudinal ballastless track-continuous beam bridge system; C B represents the overall damping matrix of the longitudinal ballastless track-continuous beam bridge system; K B represents the overall stiffness matrix of the longitudinal ballastless track-continuous beam bridge system; Q B represents the total nodal load matrix of the longitudinal ballastless track-continuous beam bridge system; x B represents the displacement vector of the longitudinal ballastless track-continuous beam bridge system; represents the velocity vector of the longitudinal ballastless track-continuous beam bridge system; represents the acceleration vector of the longitudinal ballastless track-continuous beam bridge system; B stands for the longitudinal ballastless track-continuous beam bridge system.

4. The method for analyzing transverse bridge post-earthquake vehicle safety considering the seismic damage state of the longitudinally connected ballastless track-continuous beam bridge system according to claim 3 is characterized by: The vehicle model in the high-speed railway longitudinal ballastless track-continuous beam bridge system model is a four-axle vehicle model, and its entire carriage contains 31 degrees of freedom; the dynamic equation of the vehicle model is expressed in matrix form as follows: Where, M c represents the mass matrix of the high-speed train; C c represents the damping matrix of the high-speed train; K c represents the stiffness matrix of the high-speed train; Q c represents the external load matrix of the high-speed train; x c represents the displacement vector of the high-speed train; represents the velocity vector of the high-speed train; represents the acceleration vector of the high-speed train; c stands for high-speed train.

5. The method for analyzing transverse bridge post-earthquake vehicle safety considering the seismic damage state of the longitudinally connected ballastless track-continuous beam bridge system according to claim 4 is characterized by: The wheel-rail contact relationship of the high-speed railway longitudinal ballastless track-continuous beam bridge system model is knife-edge contact constraint, the lateral clearance between the wheel and rail is 10 mm, the lateral contact stiffness is 1.617×107 N / m, the contact angle is 1 / 40 rad, the creep force is calculated using Kaller linear creep theory, and the wheel-rail normal force is calculated using Hertz nonlinear contact theory; The Hertz nonlinear contact theory solution calculation formula is: Where: wr stands for wheel rail, δ wr is the relative displacement between the wheel and rail, G is the wheel-rail contact stiffness; The calculation formula for solving the Kaller linear creep theory is: Where: F x is the longitudinal creep force, x represents along the x-axis; F y is the lateral creep force, y represents along the y axis; M z is the creep force torque, z represents the torque around the z axis; ζ x is the longitudinal creep rate, ζ y is the lateral creep rate, is the spin creep rate; f 11 、f 22 、f 23 、f 33 is the creep coefficient; respectively expressed as: G′ is the composite shear modulus of the wheel / rail material; a is the major semi-axis of the wheel-rail contact ellipse, b is the minor semi-axis of the wheel-rail contact ellipse, C 11 、C 22 、C 23 、C 33 is the Kalker coefficient, which is a function of the wavelength ratio L / a, where L is the wavelength of the creep rate and a is half the longitudinal diameter of the contact spot.

6. The method for analyzing transverse bridge post-earthquake vehicle safety considering the seismic damage state of the longitudinally connected ballastless track-continuous beam bridge system according to claim 1 is characterized by: In step 1-2), the damage indicators of key components between layers of the high-speed railway longitudinal ballastless track-continuous beam bridge system are shown in the following table:

7. The method for analyzing transverse bridge post-earthquake vehicle safety considering the seismic damage state of the longitudinally connected ballastless track-continuous beam bridge system according to claim 1 is characterized by: In step 1-3), the dynamic equations of the train-ballastless track-continuous beam bridge coupled vibration model considering the earthquake damage state are expressed as: Where: M' B is the overall mass matrix of the longitudinal ballastless track-continuous beam bridge system considering the seismic damage state; C' B is the overall damping matrix of the longitudinal ballastless track-continuous beam bridge system considering the seismic damage state; K' B is the overall stiffness matrix of the longitudinal ballastless track-continuous beam bridge system considering the seismic damage state; is the acceleration of the longitudinal ballastless track-continuous beam bridge system considering the earthquake damage state; is the speed of the longitudinal ballastless track-continuous beam bridge system considering the earthquake damage state; x' B The displacement of the longitudinal ballastless track-continuous beam bridge system considering the earthquake damage state; Q bg is the vehicle structure gravity vector; Q cg is the gravity vector of the track-continuous beam bridge structure; F bl is the wheel-rail contact force vector; B represents the longitudinal ballastless track-continuous beam bridge system. c represents high-speed train, bg represents the vehicle structure, cg represents the track-continuous beam bridge structure, bl represents the wheel-rail structure.

8. The method for analyzing transverse bridge post-earthquake vehicle safety considering the seismic damage state of the longitudinally connected ballastless track-continuous beam bridge system according to claim 1 is characterized by: The conclusion of the post-earthquake train operation safety threshold analysis considering the earthquake damage state is: The train safety index exceeds the limit when considering the earthquake damage state, which is significantly stronger than that without considering the earthquake damage state. Failure to consider the earthquake damage state will underestimate the judgment of post-earthquake train safety. When considering or not considering the earthquake damage state, the risk of exceeding the limit of train safety index does not increase linearly with the earthquake intensity; When the earthquake damage state is taken into account, the derailment coefficient and the axle lateral force will exceed the limit when the earthquake motion intensity reaches 0.2g. However, when the earthquake damage state is not taken into account, the derailment coefficient and the axle lateral force will exceed the limit only when the earthquake motion intensity reaches 0.3g. When the local vibration intensity reaches 0.5g, the effects on the derailment coefficient exceeding the limit are greater when considering or not considering the earthquake damage state, while the effects on the axle lateral force exceeding the limit are not much different.

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