Transverse-bridge-direction post-earthquake traffic safety analysis method considering earthquake damage state of longitudinally-connected ballastless track-continuous beam bridge system

Abstract

The invention discloses a transverse-bridge-direction post-earthquake traffic safety analysis method considering an earthquake damage state of a longitudinally-connected ballastless track-continuous beam bridge system, and the method comprises the steps: building a vehicle-track-bridge coupling dynamic model considering the earthquake damage state, and carrying out the analysis of a post-earthquake damage rule of the longitudinally-connected ballastless track-continuous beam bridge system; according to the method, the earthquake damage state of the interlayer key component is determined, the post-earthquake operation safety performance evaluation of the train considering the earthquake damage state is carried out, and the judgment that the train safety index ultralimit considering the earthquake damage state is obviously higher than that not considering the earthquake damage state, and the post-earthquake driving safety is underestimated without considering the earthquake damage state is determined; and when the earthquake damage state is considered or not considered, the over-limit risk of the train safety index under different earthquake intensities provides more sufficient guarantee for avoiding the post-disaster driving risk, and the method 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 taking into account the earthquake damage state of a longitudinally connected ballastless track-continuous beam bridge system. Background Art

[0002] The suddenness and destructiveness of earthquakes pose a major threat to the safety of high-speed railway operations. They not only endanger trains and passengers in operation, but may also cause long-term operational interruptions, seriously affecting the normal operation of the railway system. As an important lifeline, high-speed railways are the lifeline for post-earthquake disaster relief and rescue. After an earthquake, key components of the track-bridge system will inevitably produce earthquake damage modes such as stiffness and residual deformation to varying degrees. Whether these damage modes can ensure continued driving safety, how to continue driving, and what type of vehicles to drive are of great significance to the development of post-earthquake disaster relief and rescue work.

[0003] In recent years, some scholars have studied the driving law of high-speed railway ballastless track-bridge system under earthquake-induced damage. For example, a study reported a seismic analysis of the track-bridge system affected by near-field random earthquakes. The track unevenness caused by earthquakes has a significant impact on the derailment coefficient and lateral acceleration of high-speed trains, which increases with the increase of train running speed. The track unevenness caused by earthquakes has little effect on the vertical dynamic performance of high-speed trains. Another study pointed out that by refining the train running index value to define the damage level of the track structure (intact, slight, medium, severe and complete damage state), the influence of the track lateral displacement amplitude and train speed on the safety and stability of the train was studied, and the track lateral displacement was proposed as an indicator to measure the damage of the track structure. Another study conducted a shaking table test of a train running on a high-speed railway bridge based on a four-array shaking table and a 1:10 scale train-track-bridge model, and analyzed the influence of the near-fault vertical earthquake effect on the train derailment on the bridge. The results showed that vertical earthquake excitation reduced the minimum value of the wheel-rail vertical force and increased the possibility of jumping derailment. However, most of the existing post-earthquake driving safety analysis of ballastless track-bridge systems only considers the residual deformation of the rail mapping in the ballastless track-bridge system, but does not consider the earthquake damage state such as the stiffness defects of the key components between layers of the ballastless track-bridge system.

[0004] Therefore, the extent of damage to key components between layers 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 addressed urgently. 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 rail mapping in the ballastless track-bridge system, but do not consider the seismic damage state of the stiffness of the key components between the layers of the ballastless track-bridge system, such as the seismic defects. The present invention provides a transverse bridge direction post-earthquake driving safety analysis method that considers the seismic damage state of the longitudinal ballastless track-continuous beam bridge system, establishes a vehicle-track-bridge coupling dynamic model that considers the seismic damage state, analyzes the post-earthquake damage law of the longitudinal ballastless track-continuous beam bridge system, and clarifies the seismic damage state of the key components between the layers. The post-earthquake running safety performance evaluation of the train considering the seismic damage state is carried out, which provides a further improved reference and suggestion for the safe operation of trains after the earthquake. The specific technical scheme is as follows:

[0006] A post-earthquake driving safety analysis method in the transverse direction of the bridge considering the seismic damage state of a longitudinally connected ballastless track-continuous beam bridge system comprises the following steps:

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

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

[0009] In the aforementioned transverse bridge direction post-earthquake driving safety analysis method considering the seismic damage state of the longitudinally connected ballastless track-continuous beam bridge system, in step 1), the construction of 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 CRTS II ballastless track, continuous beam bridge, simply supported beam approach bridge and roadbed overall system as the research objects;

[0011] 1-2) Select appropriate earthquake motions, conduct post-earthquake damage analysis, and define damage indicators of interlayer key 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 combined with the dynamic equations of each subsystem model 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 to obtain the train-ballastless track-continuous beam bridge coupled vibration model considering the seismic damage state;

[0013] 1-4) The dynamic response is calculated by the Ansys-Matlab joint simulation method, the influence of post-earthquake damage of key components between layers on the driving safety performance is analyzed, and a driving safety threshold diagram considering post-earthquake damage of key components between layers is established, which provides certain references 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-earthquake driving 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 direction post-earthquake driving safety analysis method considering the earthquake damage state of the longitudinally connected ballastless track-continuous beam bridge system, in step 1-1), the high-speed railway longitudinally connected 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 and a roadbed section of 200m. Six springs at the bottom of the pier are used to simulate the pile-soil interaction, and the spring stiffness is calculated using the m method.

[0017] As a preferred technical solution, the above-mentioned transverse bridge post-earthquake driving 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 node 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 driving safety analysis method considering the seismic damage state of the longitudinal ballastless track-continuous beam bridge system, 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 the form of a matrix:

[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 direction post-earthquake 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 the rail is 10mm, the lateral contact stiffness is 1.617×107N / m, the contact angle is 1 / 40rad, 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 force 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 driving safety analysis method considering the earthquake damage state of the longitudinal ballastless track-continuous beam bridge system, in step 1-2), the damage index of the interlayer key components of the high-speed railway longitudinal ballastless track-continuous beam bridge system is shown in the following table:

[0033]

[0034] As a preferred technical solution, in the aforementioned transverse bridge direction post-earthquake driving safety analysis method considering the seismic damage state of the longitudinal ballastless track-continuous beam bridge system, in step 1-3), the dynamic equation group of the train-ballastless track-continuous beam bridge coupled vibration model considering the seismic damage state is expressed as:

[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 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 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 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 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 driving 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 driving 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 above-mentioned transverse bridge post-earthquake driving safety analysis method considering the seismic 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 significantly more than when not considering the earthquake damage state. Not considering the earthquake damage state will underestimate the judgment of post-earthquake driving safety;

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

[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 intensity reaches 0.2g, while 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 intensity reaches 0.3g;

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

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

[0045] 1) The present invention analyzes the post-earthquake damage law of the longitudinally connected ballastless track-continuous beam bridge system. By establishing a vehicle-track-bridge coupling dynamic model that takes into account the earthquake damage state, the post-earthquake damage law of the longitudinally connected ballastless track-continuous beam bridge system is analyzed to clarify the earthquake damage state of key components between layers, and the post-earthquake operation safety performance evaluation of the train taking into account the earthquake damage state is performed, which provides 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 considering the earthquake damage state established in the present invention has been verified to have good accuracy and good agreement with the results in the literature, and can be used for subsequent research and further high-speed rail risk assessment applications.

[0047] 3) The analysis method of the present invention clarifies that the train safety index exceeding the limit when considering the earthquake damage state is significantly stronger than that 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 is not a linear growth relationship with the earthquake intensity; and when the earthquake damage state is considered, the derailment coefficient and the wheel axle lateral force will exceed the limit when the earthquake intensity reaches 0.2g, and when the earthquake damage state is not considered, the derailment coefficient and the wheel axle lateral force will exceed the limit after the earthquake intensity reaches 0.3g. When the local vibration intensity reaches 0.5g, the derailment coefficient exceeding the limit is greatly affected by considering and not considering the earthquake damage state, while the difference in the impact on the wheel axle lateral force exceeding the limit is not much. It is clear that when conducting the 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 the post-earthquake driving safety, provide more sufficient protection to avoid post-disaster driving risks, and have important practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] FIG1( a ) is a schematic diagram of a ballastless track-bridge system model that only considers the residual deformation of rail mapping 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 state according to the present invention;

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

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

[0052] Figure 4 A 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] Fig. 9 The residual deformations of rails, main beams, base plates, track plates and supports under different earthquake intensities under the R2 earthquake;

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

[0059] Fig.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] Fig.12 100 ground motions selected for the present invention;

[0061] Fig.13 The effects of considering and not considering earthquake damage state on train running performance are explained for two working conditions of the present invention;

[0062] Fig.14 It is the safety index of train operation under frequent earthquakes of the present invention;

[0063] Fig.15 Design the safety index of train operation under earthquake for the present invention;

[0064] Fig.16 It is the safety index of train operation under rare earthquake of the present invention;

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

[0066] Fig.18 The following is a diagram of 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 solution of the present invention. Obviously, the described embodiments are only preferred embodiments of the present invention, not all embodiments, and are not intended to limit the present invention in other forms. Any technician familiar with the profession may use the disclosed technical content to make changes or modifications. However, any simple modification, equivalent change and modification 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 still belongs to the protection scope 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 system, which mostly only considers the residual deformation of rail mapping in the ballastless track-bridge system, but does not consider the seismic damage state of the stiffness of the key components between the layers of the ballastless track-bridge system, such as the seismic defects. The present invention provides a transverse bridge post-earthquake driving safety analysis method that considers the seismic 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 seismic damage state, and carries out the transverse bridge post-earthquake driving safety analysis of the longitudinal ballastless track-continuous beam bridge system that considers the seismic damage state, providing further improved references 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 of the post-earthquake driving safety analysis of existing ballastless track-bridge systems only considers the residual deformation of the rail mapping in the ballastless track-bridge system, as shown in Figure 1(a), without considering the seismic damage state such as the seismic defects of the stiffness of the key components between the layers of the ballastless track-bridge system. This embodiment establishes a simulation model of the longitudinal ballastless track-continuous beam bridge system, selects the earthquake motions with greater influence from the existing research, conducts the analysis of the post-earthquake damage law of the longitudinal ballastless track-continuous beam bridge system, clarifies the seismic damage state of the key components between the layers of the longitudinal ballastless track-continuous beam bridge system and the residual deformation law of each layer structure; then, the residual deformation and seismic damage state of each layer structure in the simulation model are introduced into the train-longitudinal ballastless track-continuous beam bridge coupling system dynamics model, forming a vehicle-track-bridge coupling dynamics model considering the seismic damage state, as shown in Figure 1(b). The model was then used to carry out post-earthquake operation safety performance evaluation of trains with and without considering the earthquake damage status, in order to clarify the impact of considering and without considering the earthquake damage status on the post-earthquake traffic capacity of trains, and to provide a guidance chart of the safety threshold of post-earthquake operation of trains.

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

[0073] According to the high-speed railway engineering general drawing, a longitudinal ballastless track-continuous beam bridge system model is constructed, such as Figure 2 As shown in the figure, the main bridge in the 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 and a roadbed section of 200m. Six springs at the bottom of the pier 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. 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 the 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 are in wheel-rail contact, wheel-rail normal force and creep force are 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 play 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. 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 wheel and rail, and G is the wheel-rail contact stiffness.

[0085] The calculation formula for solving 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 represents along the y axis; M z is the creep force 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 represents 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] Select appropriate earthquake motion, that is, select earthquake motion with larger earthquake response of longitudinal ballastless track-continuous beam bridge system. Combined with the damage index of key components between layers of longitudinal ballastless track-continuous beam bridge system, see Table 1, conduct post-earthquake damage analysis and extract earthquake damage status of longitudinal ballastless track and continuous beam main beam.

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

[0094]

[0095] The selected earthquake is laterally input into the dynamic model of the longitudinal ballastless track-continuous beam bridge coupling system, and the post-earthquake damage of the longitudinal ballastless track-continuous beam bridge system is analyzed. The damage of the bearings, lateral blocks, sliding layers, and other key components between the layers is evaluated, and the post-earthquake residual deformation law of each layer structure of the longitudinal ballastless track-continuous beam system is revealed. The results are as follows:

[0096] (1) Fixed support

[0097] like Figure 5 As shown in the figure, under the 8-degree frequent earthquake, the maximum lateral peak displacement of the fixed bearing is 0.27mm, and the deformation of each fixed bearing is still in the linear stage and has not reached the damage limit. Under the 8-degree design earthquake, most of the fixed bearings have been slightly damaged, and a few have been destroyed. The maximum lateral residual displacement is 39mm. Under the 8-degree rare earthquake, most of the fixed bearings have been destroyed, and the maximum lateral residual displacement is 44mm. It can also be found that the lateral residual displacement of bearing 1F is basically smaller than that of bearings 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 bearing. However, under the rare earthquake R2 seismic motion, the lateral residual displacement of bearing 1F is greater than that of bearings 2F and 3F, indicating that the transition section track structure at both ends of the bridge has been greatly damaged under the R2 seismic motion.

[0098] (2) Side stopper

[0099] like Figure 6 As shown in the figure, under the 8-degree frequent and design earthquake, the maximum lateral residual displacement of the lateral block is 0.018mm and 0.85mm respectively, and the deformation of the lateral block has not reached the damage limit, indicating that the lateral block has not been damaged, indicating that under the 8-degree frequent and design earthquake, the relative deformation of the track and the main beam is still within the safe range. Under the 8-degree rare earthquake, some of the lateral blocks at both ends of the bridge exceeded the damage limit of 2mm, and the maximum lateral residual displacement of a small number of lateral blocks exceeded the damage limit of 5mm, which means that the lateral blocks have been damaged. Trains need to limit their speed when passing through this area, otherwise there is a risk of derailment. In addition, it can be found that the damage of the lateral blocks under the action of the 8-degree rare earthquake mainly occurs at the junction of the two ends of the bridge with the transition section. This is mainly because the bridge will shake under the action of the earthquake, especially in the mid-span of the bridge. The inertial force of this shaking is often transmitted to the two ends through the bridge deck and structure. Due to the concentrated effect of the inertial force, the impact force borne by the lateral blocks at both ends will be very large, which will lead to the damage of the lateral blocks.

[0100] (3) Sliding layer and friction plate

[0101] like Figure 7 As shown in the figure, under the 8-degree frequent earthquake, the maximum lateral residual displacements of the sliding layer and the friction plate are 0.024mm and 0.004mm respectively, and the lateral deformation does not reach the damage limit. Under the 8-degree design earthquake, the sliding layer and the friction plate are basically damaged. The maximum lateral residual displacement of the sliding layer is 1.50mm, which does not exceed the damage limit of 2mm, indicating that the sliding layer has not been damaged; the maximum lateral residual displacement of the friction plate is 4.370mm, which exceeds the damage limit of 2mm, which means that the friction plate has been damaged under the design earthquake. Under the 8-degree rare earthquake, the sliding layer has been partially damaged, and its maximum lateral residual displacement is 15.2mm; the friction plates have been damaged to varying degrees, and the train needs to limit the speed when passing through this area. In addition, it can be found that the damage of the sliding layer and the friction plate under the action of rare earthquakes mainly occurs at both ends of the bridge. This is mainly because the bridge will shake under the action of the earthquake. The inertial force of this shaking is often transmitted to both ends through the bridge deck and structure, which leads to the damage of the sliding layer and friction plate at both ends of the bridge.

[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 residual deformation law of each layer of the longitudinal ballastless track-continuous beam system is revealed. The calculation results are as follows: Figure 8 and Fig. 9 shown.

[0104] like Figure 8 , 9 As shown in the figure, the residual displacements of the rails, base plates, and track plates are similar. In addition, under frequent and design earthquakes, the relative residual deformations of the rails and the main beams are similar, but under rare earthquakes, there is a significant displacement of the rails and the main beams at the ends. Under the R3 earthquake, the displacements at both ends are 7.22mm and 9.82mm, respectively, and under the R2 earthquake, the displacements at both ends are 13.12mm and 15.65mm, respectively. This indicates that when a train passes through the position where the two ends of the bridge meet the transition section during a rare earthquake, there are safety hazards in operation.

[0105] 1.5 Train-ballastless track-continuous beam bridge coupled vibration model considering earthquake damage state

[0106] According to the results of the post-seismic damage analysis of the longitudinal ballastless track-continuous beam bridge system in Chapter 1.4, the stiffness of the components in the post-seismic damage area is modified based on the damage mechanical performance indicators of each key component of the high-speed railway track-bridge system. It is assumed that the connection spring stiffness of the components in the completely damaged area is 0, the stiffness of the area without slight damage is the original stiffness, and the connection spring stiffness of the components between the slight damage and complete damage limits is calculated by linear interpolation. Then, a modal analysis is performed on the modified track-bridge system to obtain the .FULL binary file containing the overall stiffness, mass, and damping matrix of the earthquake damage. The binary file is converted into a HARWELL-BOEING format file using the HBMAT command, and converted into a sparse matrix by programming. The sparse matrix is ​​mapped with the .MAPPING node degree of freedom mapping file generated by the HBMAT command, and the node degree of freedom mapping file is called to obtain the overall mass, stiffness, and damping matrix 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] No consideration of earthquake damage

[0110]

[0111] Considering earthquake damage state

[0112]

[0113] In the formula, M' B , C' B , K' B They are the overall mass, damping and stiffness matrices of the longitudinal ballastless track-continuous beam bridge system considering the seismic 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 gravity vectors of the vehicle and track-continuous beam bridge structure, F bl is the wheel-rail contact force vector. The meanings of other parameters are consistent with those in the previous text.

[0114] The dynamic response is calculated by the Ansys-Matlab joint simulation method, such as Fig.10As shown in the figure, the influence 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 seismic 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 has 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 in 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 seismic damage state is compared with the calculation results under the model. The results are as follows: Fig.11 As shown, it can be seen that the calculation results of the train-ballastless track-continuous beam bridge coupling 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 in the transverse direction with and without considering the earthquake damage state

[0118] The 100 selected ground motions are as follows: Fig.12 As shown, five earthquake motions with larger earthquake responses (numbered R1 to R5) are selected, as shown in Table 2. The adjustment of seismic wave PGA is 8 degrees, the most frequent earthquake is 0.1g, the design earthquake is 0.3g, the rare earthquake is 0.57g, and the earthquake adopts lateral input.

[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 running performance:

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

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

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

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

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

[0127] Depend on Fig.14 (a) to Fig.14 (b) It can be seen that under the 0.1g earthquake, the longitudinal ballastless track-continuous beam bridge system did not suffer obvious damage, and the train operation safety indicators were within the limit. Therefore, considering or not considering the earthquake damage state has no effect on the train operation safety indicators, that is, no minor damage occurred.

[0128] Depend on Fig.15 (a) to Fig.15 (d) It can be seen that under the design earthquake of 0.3g, the train operation safety index exceeds the limit value. The train safety index exceeding the limit when considering the earthquake damage state is significantly stronger than that not considering the earthquake damage state. Taking the R2 earthquake motion as an example, after considering the earthquake damage state, the derailment coefficient exceeds the limit when the driving speed is around 270km / h, and the axle lateral force exceeds the limit when the driving speed is around 260km / h. When the earthquake damage state is not considered, the speeds corresponding to the derailment coefficient and the 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 judgment of post-earthquake driving safety, and the risk is increased by 21%. Therefore, under a 0.3g earthquake, the post-earthquake driving performance evaluation of the longitudinal ballastless track-continuous beam bridge system should consider the earthquake damage state.

[0129] Depend on Fig.16 (a) to Fig.16 (d) It can be seen that under the rare earthquake of 0.57g, the train operation safety index under the selected earthquake motion exceeds the limit value. The derailment coefficient exceeds the limit after considering the earthquake damage state, which is significantly stronger than that without considering the earthquake damage state. The axle lateral force exceeds the limit when considering and without considering the earthquake damage state. Taking the R2 earthquake motion as an example, after considering the earthquake damage state, the derailment coefficient exceeds the limit at a driving speed of about 210km / h, while when the earthquake damage state is not considered, the speed corresponding to the derailment coefficient exceeding the limit is 250km / h. Considering and not considering the earthquake damage state, the driving speed corresponding to the axle lateral force exceeding the limit is 250km / h. Without considering the earthquake damage state, the over-limit risk increases by 16%, which is slightly lower than the driving safety over-limit under the design earthquake of 0.3g. Therefore, under the 0.57g earthquake, the post-earthquake driving performance evaluation of the longitudinal ballastless track-continuous beam bridge system should consider the earthquake damage state, but 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 intensity.

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

[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 Fig.17 and Fig.18 shown.

[0132] from Fig.17 It can be seen that when the earthquake damage state is taken into account, 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 local vibration intensity reaches 0.5g, the derailment coefficient exceeds the limit when considering and not considering the earthquake damage state. When the earthquake damage state is considered, the train speed will exceed the limit when it reaches 210km / h, and when the earthquake damage state is not considered, the corresponding speed of the derailment coefficient exceeding the limit is 250km / h; there is little difference between the wheel axle lateral force exceeding the limit when considering and not considering the earthquake damage state, 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 post-earthquake train operation, 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 Fig.18 As shown, it is hoped that a certain theoretical basis will be provided for the guidance of post-earthquake driving safety of the longitudinal ballastless track-continuous beam bridge system.

[0134] It is obvious 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 regarded as exemplary and non-restrictive from any point of view. In addition, it should be understood that although this specification is described in accordance with the embodiments, it does not contain only one technical solution. This narrative of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in the embodiments can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A post-earthquake driving safety analysis method for a longitudinally connected ballastless track-continuous beam bridge system considering the seismic damage state in the transverse direction of the bridge, characterized by: The steps include: 1) Construct a coupled dynamic model of the train-longitudinal ballastless track-continuous beam bridge system considering the earthquake damage state; 2) Conduct post-earthquake driving safety analysis in the transverse direction of the longitudinal ballastless track-continuous beam bridge system considering the earthquake damage status.

2. The method for analyzing the post-earthquake driving safety of a longitudinally connected ballastless track-continuous beam bridge system according to claim 1 is characterized by: In step 1), the construction of a coupled dynamic model of a train-longitudinal ballastless track-continuous beam bridge system considering earthquake damage state comprises the following sub-steps: 1-1) Establish a high-speed railway longitudinal ballastless track-continuous beam bridge system model with CRTS II ballastless track, continuous beam bridge, simply supported beam approach bridge and roadbed overall system as the research objects; 1-2) Select appropriate earthquake motions, conduct post-earthquake damage analysis, and define the damage state of the model's interlayer key components through the damage index of the interlayer key components of the high-speed railway longitudinal ballastless track-continuous beam bridge system model; 1-3) Based on the wheel-rail contact relationship and combined with the dynamic equations of each subsystem model 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 to obtain the train-ballastless track-continuous beam bridge coupled vibration model considering the seismic damage state; 1-4) The dynamic response is calculated by the Ansys-Matlab joint simulation method, the influence of post-earthquake damage of key components between layers on driving safety performance is analyzed, and a driving safety threshold diagram considering post-earthquake damage of key components between layers is established; 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-earthquake driving safety analysis of the longitudinal ballastless track-continuous beam bridge system considering the seismic damage state.

3. The method for analyzing the post-earthquake driving safety of a longitudinally connected ballastless track-continuous beam bridge system according to claim 2 is characterized by: In step 1-1), the high-speed railway longitudinal ballastless track-continuous beam bridge system model is 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 and a roadbed section of 200m. Six springs at the bottom of the pier are used to simulate the pile-soil interaction, and the spring stiffness is calculated using the m method.

4. The method for analyzing the post-earthquake driving safety in the transverse direction of the bridge considering the earthquake damage state of the longitudinally connected ballastless track-continuous beam bridge system according to claim 3 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.

5. The method for analyzing the post-earthquake driving safety in the transverse direction of the bridge considering the earthquake damage state of the longitudinal ballastless track-continuous beam bridge system according to claim 4 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 the form of a matrix as follows: In the formula, 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.

6. The method for analyzing the post-earthquake driving safety of a longitudinally connected ballastless track-continuous beam bridge system according to claim 5 is characterized by: 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 play between the wheel and the 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; The Hertz nonlinear contact theory solution calculation formula is: Where: wr Represents wheel rail, δ wr is the relative displacement between 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 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.

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

8. The method for analyzing vehicle safety after an earthquake in the transverse direction of a bridge considering the earthquake damage state of a longitudinally connected ballastless track-continuous beam bridge system according to claim 2 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.

9. The method for analyzing the post-earthquake driving safety of a longitudinally connected ballastless track-continuous beam bridge system according to claim 1 is characterized by: In step 2), the post-earthquake driving safety analysis of the longitudinal ballastless track-continuous beam bridge system in the transverse direction considering the earthquake damage state includes a train operation safety analysis considering the earthquake damage state and a post-earthquake train operation safety threshold analysis considering the earthquake damage state.

10. The method for analyzing the post-earthquake driving safety of a longitudinally connected ballastless track-continuous beam bridge system according to claim 9 is characterized in that: 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 significantly more 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 or not considering earthquake damage states, the risk of exceeding the limit of train safety indicators does not increase linearly with the intensity of earthquake motion; When the earthquake damage state is taken into account, the derailment coefficient and the axle lateral force will exceed the limit when the earthquake intensity reaches 0.2g, while 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 intensity reaches 0.3g; When the local vibration intensity reaches 0.5g, the influence on the derailment coefficient exceeding the limit is greater when considering or not considering the earthquake damage state, while the influence on the axle lateral force exceeding the limit is not much different.

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