Geometric irregularity state deterioration characterization method for longitudinally-connected ballastless track on high-speed railway bridge under transverse earthquake

Abstract

The invention discloses a geometric irregularity state deterioration characterization method for a longitudinally-connected ballastless track on a high-speed railway bridge under a transverse earthquake, and the method comprises the steps: building a refined finite element model of a longitudinally-connected ballastless track-bridge system, and analyzing the damage characteristics and distribution rules of key components of the earthquake-caused track-bridge system; the characteristic of damage state degradation of key components of the earthquake-induced track-bridge system and a mapping mechanism are disclosed; then, based on the second theorem of Castlliano and the superposition principle, a geometric irregularity state deterioration characterization model of the longitudinally-connected ballastless track on the high-speed railway bridge under the action of the transverse earthquake is constructed, the geometric irregularity state of the longitudinally-connected ballastless track on the simply-supported / continuous beam bridge is mapped based on the deterioration characterization model, deformation data of the steel rail under the action of the earthquake are accurately quantified, and the accuracy of the deformation of the steel rail under the action of the transverse earthquake is improved. The method provides a theoretical basis for quickly judging the post-earthquake traffic capacity and maintenance engineering of a track-bridge system, ensures the operation safety of a high-speed railway, provides a theoretical basis for the design of a high-speed railway track-bridge, is beneficial to post-earthquake track repair and train operation recovery, and has a good practical value and a good popularization prospect.

Description

Technical Field

[0001] This invention relates to a method for characterizing the deterioration of geometric irregularities in longitudinally connected ballastless track on high-speed railway bridges under lateral earthquakes. Background Art

[0002] my country is one of the countries with the most earthquakes globally, with at least 495 seismic fault zones within its borders. Existing, under-construction, and planned high-speed railway lines inevitably pass near or cross earthquake zones. Influenced by climate, geology, and environmental factors, bridges account for over 50% of my country's high-speed railway lines, ranging in length from several kilometers to tens of kilometers, posing a significant earthquake threat to these bridges. Under earthquakes, varying degrees of deformation and stiffness damage to the high-speed railway track-bridge system are largely reflected in the rails, deteriorating track smoothness and jeopardizing line safety. my country's high-speed railway track-bridge system has already experienced earthquake damage, such as the Menyuan earthquake, which caused severe damage to the track system and supports on an eight-span simply supported beam bridge, including support detachment and block failure, lateral displacement and deflection of the main beam, lateral displacement and fracture of the track slab, and lateral displacement and fastener failure of the rails. To ensure safe train operation after earthquakes, it is necessary to characterize the geometric irregularities of ballastless tracks on high-speed railway bridges under seismic loading to assess post-earthquake train traffic capacity.

[0003] Currently, although some progress has been made in the research on the characterization of geometric irregularities of ballastless tracks for high-speed railway bridges, most of these studies are mapping studies of track irregularities related to pier settlement. For example, He Chunyan et al. revealed the mapping relationship between uneven settlement of road-bridge transition sections and rail deformation; Chen Zhaowei et al. derived the mapping relationship between pier settlement and track deformation; Gou et al. proposed an analytical model for mapping typical bridge deformation and rail surface deformation; and Guo Yu et al. proposed a static mapping relationship between foundation settlement and rail surface deformation of double-block and slab ballastless tracks. Research on the mapping relationship between seismic-induced damage in ballastless track-bridge systems is still in its early stages. Existing studies include: Lai Zhipeng et al., who used the energy variational principle to construct a general model of the lateral deformation of the bridge-track system and the track surface mapping deformation, and then combined this with the typical damage and failure characteristics of the track-bridge system under seismic loading to establish a general model for solving the rail mapping deformation caused by the residual deformation of interlayer components; Zhou Wangbao et al., who studied the damage evolution mechanism of key components in the track-bridge coupled system under various seismic intensities and explored the distribution characteristics of track geometric deformation after seismic loading; and the simplified seismic-induced damage characterization model proposed by the inventors of this application, which constructs the correspondence between seismic damage and track irregularities. However, these studies do not consider the influence of interlayer deformation of the bridge system under seismic loading, cannot quantitatively describe track deformation, and there are differences between the track surface mapping deformation and the actual residual track irregularities, affecting the assessment results of post-earthquake train traffic capacity. In addition, existing high-speed railway bridge models are mostly established using the finite element method, which takes a long time to calculate and cannot provide timely assessment results of post-earthquake train traffic capacity, affecting post-earthquake track repair and train operation recovery.

[0004] Therefore, how to accurately quantify the cumulative damage effect of earthquake-induced damage to key components of high-speed railway bridge systems on the deterioration of track geometry and smoothness, and how to quickly assess the post-earthquake traffic capacity of longitudinal ballastless track-bridge systems, remains an urgent problem to be solved. Summary of the Invention

[0005] To address the shortcomings of existing research, such as the failure to consider the impact of inter-layer deformation of bridge systems on the degradation of track geometry under earthquakes, the inability to accurately quantify the cumulative damage effect on the track surface caused by earthquakes, and the long calculation time of models hindering timely assessment of post-earthquake train traffic capacity, this invention proposes a method for characterizing the degradation of geometric irregularities of longitudinally connected ballastless track on high-speed railway bridges under lateral earthquakes. This method involves establishing a refined finite element model of the longitudinally connected ballastless track-bridge system to analyze the damage characteristics and distribution patterns of key components in the track-bridge system under earthquakes, revealing the degradation characteristics and mapping mechanism of the damage state of key components. Then, based on Castigliano's second theorem and the superposition principle, a characterization model for the degradation of geometric irregularities of longitudinally connected ballastless track on high-speed railway bridges under lateral earthquake loading is constructed. This model is then used to map the geometric irregularities of longitudinally connected ballastless track on simply supported / continuous beam bridges, obtaining rail deformation data under earthquake loading. This provides a theoretical basis for rapidly assessing the post-earthquake traffic capacity and maintenance engineering of the track-bridge system, ensuring the safe operation of high-speed railways. The specific technical solution is as follows:

[0006] The present invention proposes a method for characterizing the deterioration of geometric irregularities in longitudinally connected ballastless track on high-speed railway bridges under lateral seismic events, comprising the following steps:

[0007] S1: Establish a refined finite element model of the longitudinal ballastless track-bridge system;

[0008] S2: Select the seismic wave and input the refined finite element model established in step S1 laterally;

[0009] S3: Analyze the seismic damage characteristics and distribution patterns of key components between track layers in the longitudinal ballastless track-bridge system after inputting seismic waves in step S2, and reveal the characteristics and mapping mechanism of the deterioration of the damage state of key components in the longitudinal ballastless track-beam bridge system caused by seismic waves.

[0010] S4: Based on the analysis results of step S3, establish a characterization model for the deterioration of the geometric irregularity of the longitudinal ballastless track on the bridge under transverse earthquake.

[0011] S5: Linearly superimpose the displacement at the top of the support with the inter-layer displacement of the track at the corresponding position, and input it into the characterization model of the deterioration of the geometric irregularity of the longitudinal ballastless track on the bridge under transverse earthquake established in step S4. Solve the model to obtain the rail displacement, thereby evaluating the traffic capacity of the longitudinal ballastless track-bridge system after the earthquake.

[0012] As a preferred technical solution, the refined finite element model of the longitudinally connected ballastless track-beam bridge system established in step S1 includes a finite element model of the ballastless track-simply supported beam bridge system and a finite element model of the ballastless track-continuous beam bridge system; wherein:

[0013] The finite element model of the ballastless track-continuous beam bridge system shows that the main continuous beam bridge is a 32m+48m+32m double-track single-box single-cell variable height continuous box girder bridge, and the approach bridges on both sides are 32m mixed simply supported beam bridges.

[0014] The simply supported beam bridge of the ballastless track-simply supported beam bridge system adopts a 32m standard span concrete box girder;

[0015] All piers are solid structures with rounded ends, and all bearing systems use pot-type rubber bearings. The pile foundations at the bottom of the piers are all considered as consolidation constraints.

[0016] BEAM188 elements were used to simulate continuous beam bridges, simply supported beam bridges, and track structures at each level.

[0017] COMBIN39 nonlinear spring elements were used to simulate the connection between the track and the main beam layers, and between the track and the roadbed.

[0018] The rigid constraints between the master and slave nodes are simulated using MPC184 elements.

[0019] Boundary conditions are simulated using displacement constraints, and the displacement of the roadbed under external forces is ignored. A Rayleigh damping model is adopted, and a modal damping ratio of 5% is set.

[0020] As a preferred technical solution, step S2 selects three seismic waves that have the highest matching degree with the site characteristics, specifically:

[0021] The site fortification intensity is 8.5 degrees, the site category is Class III, the epicentral distance group is Group 2, and the generated design earthquake response spectrum has a characteristic period of 0.55s and a PGA of 0.3g.

[0022] Import the response spectrum into the NGA-West2 ground motion database and select the three ground motions with the highest spectral matching degree.

[0023] The original acceleration data was multiplied by a scaling factor, and a 10s zero-value segment was added to the end of the data. The seismic excitation direction was laterally.

[0024] As a preferred technical solution, step S3 describes analyzing the seismic damage characteristics and distribution patterns of key components between track layers in the longitudinally connected ballastless track-bridge system after inputting seismic waves, including seismic damage analysis of key components between ballastless track layers and seismic damage analysis of key bridge components.

[0025] The seismic damage analysis of key interlayer components of the ballastless track includes the displacement of fasteners on different bridges under different seismic intensities, the displacement of mortar layers on different bridges under different seismic intensities, and the displacement of sliding layers on different bridges under different seismic intensities.

[0026] Seismic damage analysis of key bridge components: including residual displacements of bridge supports under different seismic intensities and residual displacements of pier tops under different seismic intensities.

[0027] As a preferred technical solution, the process of establishing a characterization model for the deterioration of the geometric irregularity of the longitudinally connected ballastless track on the bridge under lateral seismic conditions, as described in step S4, is as follows:

[0028] S4-1: Basic Assumptions: Basic assumptions are made regarding the lateral displacement and action modes among the components of the characterization model of the deterioration of the geometric irregularity of the longitudinally connected ballastless track on the bridge under lateral earthquake.

[0029] S4-2: Rail displacement at fastener nodes: Treating the rail as a simply supported structure, based on the Saint-Venant principle, a rail calculation length much larger than the bridge displacement influence zone is selected to eliminate boundary constraint effects. Equidistantly distributed virtual fastener forces are added between adjacent fasteners to establish the rail static equilibrium equation, and the support reactions at both ends of the rail are obtained by solving it. Then, based on Castigliano's second theorem and the superposition principle, the rail displacement at any fastener node except the endpoints is obtained. The rail displacements at all fastener nodes are expressed in matrix form as follows:

[0030] V r =H r F r (7)

[0031] In the formula: V r Here is the lateral displacement matrix of the rail at the fastener node, where r represents the rail; H r F is the matrix of influence coefficients of fastener force on the lateral displacement of the rail. r This is the matrix of lateral forces acting on the rails from each fastener;

[0032] S4-3: Track slab displacement at each mortar support point: Due to the combined action of the fastener system and the elastic support of the mortar layer, the longitudinal track slab achieves mechanical equilibrium through coordinated displacement with the base plate. The displacement of the track slab at each mortar support point is obtained and expressed in matrix form as follows:

[0033] V s =C s F s +D s P s (10)

[0034] In the formula: V s This represents the displacement matrix of the track slab at the mortar spring support point, where s represents the track slab; C s The matrix showing the influence coefficients of fastener force on the lateral displacement of the track slab is as follows:

[0035] C s =-Hr (11);

[0036] D s The matrix showing the influence coefficients of the mortar spring force on the lateral displacement of the track slab is as follows:

[0037]

[0038] si represents the position of the i-th mortar spring, and sj represents the position of the j-th mortar spring; l si Let l be the distance from the i-th mortar spring to the left support. sj Let l be the distance from the j-th mortar spring to the left support. s F is the length of the track slab; s P represents the fastener force matrix acting on the track slab; s The matrix representing the mortar spring force acting on the track slab;

[0039] S4-4: Base plate displacement: Due to the combined action of the mortar spring force and the sliding layer contact force, the base plate achieves mechanical equilibrium through coordinated displacement, resulting in the base plate displacement, expressed in matrix form as follows:

[0040] V p =A p P p +B p N p (13)

[0041] In the formula: V p A represents the displacement matrix of the base plate at the contact spring node; p The matrix representing the influence coefficients of the mortar spring force on the displacement of the base plate is as follows:

[0042] A p =-D s (14)

[0043] B p The matrix representing the influence coefficients of the contact spring force on the displacement of the base plate is as follows:

[0044]

[0045] In the formula: p represents the base plate; pi represents the position of the i-th contact spring; pj represents the position of the j-th contact spring; l pi Let l be the distance from the i-th contact spring to the left support. pj Let l be the distance from the j-th contact spring to the left support. p P is the length of the base plate; p N represents the matrix of mortar spring forces acting on the base plate. p The matrix of contact spring forces acting on the base plate;

[0046] S4-5: Establish the characterization matrix for the deterioration of the geometric irregularities of the longitudinally connected ballastless track on the bridge under lateral earthquakes: By simultaneously solving the displacement matrices and influence coefficient matrices from steps S4-2 to S4-4, the characterization matrix for the deterioration of the geometric irregularities of the longitudinally connected ballastless track on the bridge under lateral earthquakes can be obtained, as follows:

[0047]

[0048] In the formula: E is the identity matrix.

[0049] As a further preferred technical solution, the basic assumptions in step S4-1 are specifically as follows:

[0050] Assume that the track slab-base plate-bridge meet the requirements for lateral displacement coordination;

[0051] The base plate, track plate, and rail are simplified into a simply supported beam model. The interaction between the rail, track plate, and base plate is considered, while the reaction of the base plate on the bridge displacement is ignored.

[0052] The mortar layer support is simplified as a nonlinear spring distributed along the centerline of the rail, and the base plate-bridge contact relationship is simplified as a unidirectional spring. The spring spacing is taken as 1 / 20 of the fastener spacing. The entire fastener system, including the pad and fastener spring strip, is considered as a spring. Virtual fastener springs are added to maintain the uniformity of the matrix dimension, and their distribution spacing is consistent with that of the mortar springs.

[0053] As a further preferred technical solution, in step S4-2, the static equilibrium equation of the rail is:

[0054]

[0055] In the formula: r represents the rail; F rj The distance between the j-th fastener and the left end of the rail; l rj M0 represents the distance from the j-th fastener to the left support; M0 represents the total bending moment of the system; rj represents the location of the j-th fastener; l r F represents the selected rail length. r0 F is the reaction force at the left end support of the rail. r(n+1) This is the reaction force at the right end support of the rail;

[0056] The solution yields the support reactions at both ends of the rail, expressed as follows:

[0057]

[0058] The displacement of the rail at any fastener node, excluding the endpoints, is expressed as:

[0059]

[0060] In the formula: y ri M(x) represents the displacement of the rail at any fastener node except at the endpoints; M(x) represents the bending moment.

[0061] A(l ri ,l rj ,l r ), B(l ri ,l rj ,l r ), B(l rj ,l ri ,l r ), C(l ri ,l rj ,l r ) and C(l rj ,l ri ,l r Substitute the following formula into the equation:

[0062]

[0063] In the formula: A is the structural compliance coefficient under symmetrical load, B is the structural compliance coefficient under asymmetrical load, and C is the structural compliance coefficient for end boundary effects; ri Let l be the distance from the i-th fastener to the left support. rj Let l be the distance from the j-th fastener to the left support. r The length of one span of rail; x1, x2, x3 represent placeholder variables in the formula; E r Indicates the elastic modulus of the rail; I r The moment of inertia of the rail section;

[0064] The influence coefficient matrix H of the fastener force on the lateral displacement of the rail r Represented as:

[0065]

[0066] As a further preferred technical solution, in step S4-3, the displacement of the track slab at each mortar support point is:

[0067]

[0068] In the formula: F sj P represents the force applied by the j-th fastener; sj Represents the force of the j-th mortar spring; l sj The distance between the j-th fastener and the left end of the track plate; l si l is the distance between the i-th fastener and the left end of the track plate; s E represents the length of the track slab. s I represents the elastic modulus of the track slab. sLet be the moment of inertia of the track slab section.

[0069] As a further preferred technical solution, the lateral force matrix F acting on each fastener of the rail is... r for:

[0070] F r =k c (V s -V r (16)

[0071] The lateral force matrix F of each fastener acting on the track slab s for:

[0072] F s =-k c (V s -V r )

[0073] In the formula: k c The stiffness matrix of the fastener spring;

[0074] The mortar spring force matrix P acting on the track slab s for:

[0075] P s =k ca (V p -V s (17)

[0076] The mortar spring force matrix P acting on the base plate s for:

[0077] P p =-k ca (V p -V s )

[0078] In the formula: k ca The mortar spring stiffness matrix;

[0079] Contact spring force matrix N acting on the base plate p for:

[0080] N p =k p (V b -V p (18)

[0081] In the formula: k p V is the stiffness matrix of the contact spring. b V is the bridge displacement matrix corresponding to the contact spring position. p This represents the displacement matrix of the base plate at the contact spring node.

[0082] As a preferred technical solution, step S5 involves pre-superimposing the displacement at the top of the support under seismic action with the inter-layer displacement of the track at the corresponding location to obtain the superimposed lateral displacement of the support, as follows:

[0083]

[0084] V bmk =α k d m-1 +β k d m (twenty one)

[0086] d m =d z +d g (twenty two)

[0088]

[0089] In the formula: V bmk Let be the lateral displacement at the k-th location of the m-th span of the bridge under seismic action, where m ranges from 1 to 5 and k ranges from 1 to 1. b ;

[0090] d m-1 The displacement is the superimposed displacement of the left support of the m-th span of the bridge;

[0091] d m The displacement is the superimposed displacement of the right-side support of the m-th span of the bridge;

[0092] d z This refers to the displacement of the top of the support under seismic loading.

[0093] d g This represents the inter-story displacement of the track at the corresponding support location under seismic action;

[0094] x mk Let be the longitudinal displacement of the bridge at the k-th position of the m-th span.

[0095] l b0 The length of the expansion joint between bridge sections;

[0096] l b1 This is the distance between the beam end and the centerline of the support;

[0097] l b For Liang Chang;

[0098] α k This is the matrix showing the influence of the left support displacement on the bridge displacement.

[0099] β k This is the matrix showing the influence of the right-side support displacement on the bridge displacement.

[0100] The bridge displacement matrix corresponding to the contact spring position is expressed as:

[0101]

[0102] In the formula: b represents the bridge, and b1, b2...b3 are 1 to m bridge displacement matrices.

[0103] The beneficial effects of this invention are as follows:

[0104] 1) This invention establishes a refined finite element model of the longitudinally connected ballastless track-bridge system, analyzes the damage characteristics and distribution patterns of key components of the track-bridge system caused by earthquakes, and reveals the characteristics and mapping mechanism of the deterioration of the damage state of key components of the track-bridge system caused by earthquakes. Then, based on Castigliano's second theorem and the superposition principle, a deterioration characterization model of the geometric irregularity state of the longitudinally connected ballastless track on high-speed railway bridges under lateral seismic loading is constructed. Based on this deterioration characterization model, the geometric irregularity state of the longitudinally connected ballastless track on simply supported / continuous beam bridges is mapped, and the deformation data of the rails under seismic loading is accurately quantified. This provides a theoretical basis for quickly assessing the post-earthquake traffic capacity and maintenance engineering of the track-bridge system, ensuring the safety of high-speed railway operation, and providing a theoretical basis for the design of high-speed railway track-bridges.

[0105] 2) The geometric irregularity characterization model of longitudinally connected ballastless track on high-speed railway bridges under transverse seismic action constructed in this invention is a MATLAB-based model. Its calculation speed is much faster than that of the finite element model. It can quickly characterize the geometric irregularity of high-speed railway track after the earthquake and accurately quantify the deformation data of the rail under seismic action. It saves the time for assessing the post-earthquake traffic capacity of the track-bridge system and is conducive to post-earthquake track repair and train operation recovery.

[0106] 3) The method of this invention found that the interlayer damage of the track in continuous bridge systems is mainly concentrated in the sliding layer; while in simply supported beam bridge systems, it mainly occurs in the mortar layer, sliding layer, and fasteners; under different ground motions and intensities, the maximum error between the rail residual deformation solved by the deterioration characterization model and the rail residual deformation calculated by the finite element model is within 5%, and the rail residual deformation curves are in good agreement, verifying the accuracy of the established deterioration characterization model in solving the residual deformation of the earthquake-induced ballastless track-bridge system; the overall trend of the rail peak mapping solution and the finite element solution is in good agreement, providing a way to quickly assess the rail residual deformation after an earthquake. Attached Figure Description

[0107] Figure 1 A schematic diagram of a high-speed railway longitudinal ballastless track-bridge system established for this invention;

[0108] Figure 2 The seismic response spectrum selected for this invention;

[0109] Figure 3 The earthquake motion results are input for this invention;

[0110] Figure 4 This invention analyzes the peak displacement results of fasteners on different bridges under different seismic intensities;

[0111] Figure 5 This invention analyzes the peak displacement results of mortar layers on different bridges under different seismic intensities;

[0112] Figure 6 This invention analyzes the peak displacement results of the sliding layer on different bridges under different ground motion intensities;

[0113] Figure 7 This invention describes the residual displacement of bridge supports under different ground motion intensities.

[0114] Figure 8 This invention describes the residual displacement of the pier top under different seismic intensities.

[0115] Figure 9 A schematic diagram of the rail stress in the deterioration characterization model established for this invention;

[0116] Figure 10 A schematic diagram of the stress on a longitudinally connected plate track slab, which is used in the degradation characterization model established for this invention.

[0117] Figure 11 A schematic diagram of the stress on the longitudinally connected plate base plate of the degradation characterization model established for this invention;

[0118] Figure 12 A schematic diagram of bridge displacement caused by superimposed displacement of supports in the deterioration characterization model established in this invention.

[0119] Figure 13 This is a flowchart of the solution process for the degradation characterization model of this invention;

[0120] Figure 14 This invention provides a comparison of superimposed residual displacement of continuous beam supports, mapped residual displacement of rails, and finite element residual displacement of rails under earthquakes of different intensities.

[0121] Figure 15 This invention provides a comparison of the superimposed peak displacement of continuous beam supports, the mapped peak displacement of rails, and the peak displacement of rails using finite element analysis under rare earthquakes.

[0122] Figure 16 This invention provides a comparison of superimposed residual displacement of simply supported beam supports, mapped residual displacement of rails, and finite element residual displacement of rails under earthquakes of different intensities.

[0123] Figure 17This invention compares the superimposed peak displacement of simply supported beam supports, the mapped peak displacement of rails, and the peak displacement of rails using finite element analysis under rare earthquakes. Detailed Implementation

[0124] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments and accompanying drawings. Obviously, the described embodiments are only preferred embodiments of the present invention, and not all embodiments, nor are they intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications or equivalent variations based on the disclosed technical content. However, any simple modifications, equivalent variations, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention's technical solution are still within the protection scope of the present invention's technical solution. Specific embodiments are as follows:

[0125] This embodiment presents a method for characterizing the deterioration of geometric irregularities in longitudinally connected ballastless track on high-speed railway bridges under lateral seismic loading. By establishing a refined finite element model of the longitudinally connected ballastless track-bridge system, the damage characteristics and distribution patterns of key components in the track-bridge system induced by seismic loading are analyzed, revealing the characteristics and mapping mechanism of the deterioration of the damage state of key components in the track-bridge system induced by seismic loading. Then, based on Castigliano's second theorem and the superposition principle, a characterization model for the deterioration of geometric irregularities in longitudinally connected ballastless track on high-speed railway bridges under lateral seismic loading is constructed. Based on this characterization model, the geometric irregularities of longitudinally connected ballastless track on simply supported / continuous beam bridges are mapped, obtaining the deformation data of the rails under seismic loading. This provides a theoretical basis for rapidly assessing the post-earthquake traffic capacity and maintenance engineering of the track-bridge system, ensuring the safe operation of high-speed railways. The specific process is as follows:

[0126] 1. To investigate the damage mechanism of ballastless track-bridge system under earthquake.

[0127] High-speed railway bridge structures mainly include simply supported beam bridges and continuous beam bridges. This embodiment establishes refined finite element models of both a longitudinally connected ballastless track-continuous beam bridge system and a longitudinally connected ballastless track-simply supported beam bridge system. Simplified model diagrams are shown below. Figure 1 (a) and Figure 1 (b) shows the following: Then, three ground motions with the highest matching degree with the site characteristics were selected to carry out damage mechanism analysis of the ballastless track-bridge system under seismic action.

[0128] 1.1 Finite element model of ballastless track-simply supported / continuous beam bridge system

[0129] The refined finite element model of the longitudinal ballastless track-continuous beam bridge system established in this embodiment features a (32+48+32)m double-track single-box single-cell variable-height continuous box girder bridge, with 32m simple-supported concrete girder bridges on both sides as approach bridges. The simply-supported beam bridge in the refined finite element model of the longitudinal ballastless track-simply supported beam bridge system established in this embodiment adopts a 32m standard span concrete box girder. Both models have round-ended solid piers, and the bearing system uses pot bearings. The pile foundations at the bottom of the piers are considered as consolidated. BEAM188 elements are used to simulate the continuous beam bridge, simply supported beam bridge, and track structures at each layer. COMBIN39 nonlinear spring elements are used to simulate the connections between the track and main beam layers, and between the track and the roadbed. MPC184 elements are used to simulate the rigid constraints between master and slave nodes. Boundary conditions are simulated through displacement constraints, and the displacement of the roadbed under external forces is ignored. A Rayleigh damping model is used, with a modal damping ratio of 5%. Both models have been validated through shaking table tests. Materials and some parameters are shown in Table 1. Seismic damage evaluation indices for key components of the ballastless track-bridge system have also been established, as shown in Table 2.

[0130] Table 1. Materials and properties of various components in the high-speed railway track-continuous beam bridge system

[0131]

[0132] Table 2. Seismic damage evaluation indicators for key components of the ballastless track-bridge system

[0133]

[0134] 1.2 Seismic Motion Selection

[0135] In this embodiment, the site fortification intensity is selected as 8.5 degrees, the site category is Class III, and the epicentral distance is grouped as Group 2. A design seismic response spectrum is generated with a characteristic period of 0.55s and a PGA of 0.3g. This response spectrum is imported into the NGA-West2 seismic ground motion database, and the three seismic ground motion groups with the highest spectral matching are selected as follows: Figure 2 As shown in Table 3, the selected seismic motion parameters are as follows. To obtain the post-earthquake time history response of the ballastless track-bridge system, the original acceleration data were multiplied by a scaling factor, and a 10s zero-value segment was added to the end of the data, as shown in Table 3. Figure 3 As shown. Due to the influence of the roadbed constraint effect, the longitudinal and vertical seismic responses of the bridge are significantly weaker than the lateral seismic responses. Therefore, the direction of seismic excitation is lateral.

[0136] Table 3. Seismic Ground Motion Records

[0137]

[0138] 1.3 Seismic Damage Analysis of Key Interlayer Components of Ballastless Track

[0139] The three selected seismic ground motions were input into the refined finite element models of the longitudinally connected ballastless track-continuous beam bridge system and the longitudinally connected ballastless track-simply supported beam bridge system, respectively. According to the specifications, the peak ground acceleration (PGA) was adjusted to 0.3g for design and 0.57g for rare events, respectively. The results are as follows... Figures 4 to 8 As shown.

[0140] 1) Seismic damage analysis of key components between ballastless track layers

[0141] From such Figure 4 As can be seen from (a) to (b), on continuous beam bridges, the maximum lateral peak displacement of the fasteners under rare earthquakes is 0.03 mm, while under design earthquakes it is 0.02 mm. Table 2 shows that the fastener displacement under both earthquake intensities is far below the limit, indicating that the fasteners remain in good condition. Figure 4 As can be seen from (c) to (d), on the simply supported beam bridge, under the rare R3 earthquake and the design earthquake, the maximum peak displacement of the fasteners reached 2.73 mm and 2.56 mm respectively, both exceeding the 2 mm damage limit. However, under the R1 and R2 earthquakes, the peak displacement of the fasteners did not exceed the limit.

[0142] from Figure 5 As can be seen from (a) to (b), on the continuous beam bridge, the maximum lateral peak displacement of the mortar layer under rare earthquakes is 0.2 mm, and under the design earthquake, it is 0.08 mm, both below the 0.5 mm limit for minor damage, indicating that the mortar layer on the continuous beam bridge is not damaged under earthquakes of different intensities. Figure 5 As can be seen from (c) to (d), on simply supported beam bridges, under rare and design earthquakes, the maximum peak displacements reach 2.94 mm and 2.75 mm, respectively, both exceeding the 2 mm limit for complete failure.

[0143] from Figure 6 As can be seen from (a) to (b), on continuous beam bridges, under both design and rare earthquake conditions, the peak displacement of the sliding layer under various ground motions exceeded the minor damage limit of 0.5 mm. Specifically, under the rare earthquake R1, the peak displacement of the sliding layer exceeded the complete failure limit of 2 mm. Figure 6 As can be seen from (c) to (d), on simply supported beam bridges, under both design and rare earthquake conditions, the peak displacement of the sliding layer exceeds the minor damage limit of 0.5 mm.

[0144] 2) Seismic damage analysis of key bridge components

[0145] like Figures 7-8As shown in Table 2, under rare and design earthquakes, the support displacements of both continuous beam bridges and simply supported beam bridges exceeded the limits for all local ground motions. Table 2 shows that the fixed supports were completely destroyed under the aforementioned earthquakes. Comparison reveals that the support displacement response of simply supported beam bridges is significantly greater than that of continuous beam bridges. This is mainly due to the difference in stiffness characteristics between the two. The stiffness distribution of simply supported beams is usually more uniform, while the stiffness distribution of continuous beams may exhibit local variations due to different support conditions. Under various local ground motions, the maximum ratio of residual displacement at the top of piers (2# to 5#) to the residual displacement of supports for continuous beam bridges was 8.87%, and the maximum ratio of residual displacement at the top of abutments (1#, 6#) to the residual displacement of supports was 43.77%. For simply supported beam bridges, the maximum ratio of residual displacement at the top of piers (2# to 5#) to the residual displacement of supports was 13.18%, and the maximum ratio of residual displacement at the top of abutments (1#, 6#) to the residual displacement of supports was 74.18%. Therefore, the residual displacement of the main beam is controlled by the supports, piers, and abutments.

[0146] 2. Characterization Model of Geometric Irregularities in Longitudinal Ballastless Track on Bridge under Lateral Seismic Conditions

[0147] In this implementation, based on the characteristics and mapping mechanism of the damage state deterioration of key components of the earthquake-induced track-bridge system revealed above, and according to Castigliano's second theorem and the superposition principle, a characterization model for the deterioration of the geometric irregularity state of longitudinally connected ballastless track on high-speed railway bridges under lateral seismic loading is constructed as follows:

[0148] 2.1 Basic Assumptions

[0149] The three-dimensional lateral seismic action-induced geometric irregularity degradation model of longitudinally connected ballastless track on high-speed railway bridges constructed in this embodiment (hereinafter referred to as the degradation model) is a MATLAB model. Its calculation speed is much faster than that of the finite element model. It can quickly characterize the geometric irregularity of high-speed railway track after the earthquake and accurately quantify the deformation data of the rail under seismic action. It saves the time for assessing the post-earthquake traffic capacity of the track-bridge system and is conducive to post-earthquake track repair and train operation recovery.

[0150] First, the following assumptions are made regarding the basic structure of this degradation characterization model:

[0151] (1) Considering the lateral restraint effect of key inter-story components such as shear toothed grooves, shear studs, mortar layers, shear reinforcement and lateral stops, the connection stiffness of the corresponding area of ​​the restraining components is increased according to the material properties of the restraining components, so as to simulate the influence of the restraining components on the inter-story displacement transmission and connection contact of the track-bridge system. It is assumed that the track slab-base slab-bridge meet the lateral displacement coordination.

[0152] (2) The base plate, track plate and rail are simplified into a simply supported beam model. The interaction between rail, track plate and base plate is considered, and the reaction of base plate on bridge displacement is ignored.

[0153] (3) The mortar layer support is simplified as a nonlinear spring distributed along the centerline of the rail, and the contact relationship between the base plate and the bridge is simplified as a unidirectional spring. The spring spacing is taken as 1 / 20 of the fastener spacing. The entire fastener system (including pads and fastener springs) is considered as a spring. Virtual fastener springs are added to maintain the uniformity of the matrix dimension, and their distribution spacing is consistent with that of the mortar springs.

[0154] 2.2 Rail Model Establishment

[0155] When a bridge experiences lateral displacement, the various structural layers between the bridge and the rails (such as track slabs and base plates) interact under interlayer coordination, causing the bridge displacement to be transmitted layer by layer to the rail surface, ultimately leading to changes in the rail surface's geometry. This paper treats the rails as simply supported structures and, based on the Saint-Venant principle, selects a rail calculation length much larger than the bridge displacement influence zone to eliminate boundary constraint effects. While the actual rails are infinitely long beams with elastic point supports, the influence range of bridge displacement on the rails is limited; therefore, only a sufficiently long segment needs to be analyzed in the calculation, such as... Figure 9 As shown. To ensure that the structural matrix dimensions of each layer of the track are consistent, virtual fastener forces are added at equal intervals between adjacent fasteners.

[0156] based on Figure 9 The stress state of the rail shown is represented by the following static equilibrium equation:

[0157]

[0158] In the formula: r represents the rail; F rj The distance between the j-th fastener and the left end of the rail; l rj M0 represents the distance from the j-th fastener to the left support; M0 represents the total bending moment of the system; rj represents the location of the j-th fastener; l r F represents the selected rail length. r0 F is the reaction force at the left end support of the rail. r(n+1) This represents the reaction force at the right end support of the rail.

[0159] Solving for the support reactions at both ends of the rail, we can obtain the following:

[0160]

[0161] Based on Castigliano's second theorem and the superposition principle, the displacement y of the rail at any fastener node (excluding the endpoints) is... ri It can be represented as:

[0162]

[0163] In the formula: y riM(x) represents the displacement of the rail at any fastener node except for the endpoints; M(x) represents the bending moment; A(l) represents the displacement of the rail at any fastener node. ri ,l rj ,l r ), B(l ri ,l rj ,l r ), B(l rj ,l ri ,l r ), C(l ri ,l rj ,l r ) and C(l rj ,l ri ,l r Substitute the following formula into the equation:

[0164]

[0165] In the formula: A is the structural compliance coefficient under symmetrical load, B is the structural compliance coefficient under asymmetrical load, and C is the structural compliance coefficient for end boundary effects; ri Let l be the distance from the i-th fastener to the left support. rj Let l be the distance from the j-th fastener to the left support. r The length of one span of rail; x1, x2, x3 represent placeholder variables in the formula; E r I represents the elastic modulus of the rail. r This represents the moment of inertia of the rail section.

[0166] Express the rail displacement values ​​at all fastener nodes in matrix form:

[0167] V r =H r F r (7)

[0168] In the formula: V r Let H be the lateral displacement matrix of the rail at the fastener node. r The matrix of influence coefficients of fastener force on the lateral displacement of rail, F r This is the matrix of lateral forces acting on the rails from each fastener; where:

[0169]

[0170] 2.3 Establishment of the longitudinal ballastless track model

[0171] 2.3.1 Track slab displacement

[0172] Under the combined action of the fastener system and the elastic support of the mortar layer, the longitudinally connected track slab achieves mechanical equilibrium through coordinated displacement with the base plate. The forces acting on the longitudinally connected track slab are as follows: Figure 10As shown. The displacement response of the track slab at each mortar support point can be described as follows:

[0173]

[0174] In the formula: F sj P represents the force applied by the j-th fastener; sj Represents the force of the j-th mortar spring; l sj The distance between the j-th fastener and the left end of the track plate; l si l is the distance between the i-th fastener and the left end of the track plate; s E represents the length of the track slab. s I represents the elastic modulus of the track slab. s Let be the moment of inertia of the track slab section.

[0175] Equation (9) can be expressed in matrix form as follows:

[0176] V s =C s F s +D s P s (10)

[0177] In the formula: V s This represents the displacement matrix of the track slab at the mortar spring support point, where s represents the track slab; C s D is the matrix of influence coefficients of fastener force on the lateral displacement of the track slab. s F is the matrix of influence coefficients of mortar spring force on the lateral displacement of the track slab. s P represents the fastener force matrix acting on the track slab; s This represents the matrix of mortar spring forces acting on the track slab. Wherein:

[0178] C s =-H r (11)

[0179]

[0180] In the formula: si represents the position of the i-th mortar spring, sj represents the position of the j-th mortar spring; l si Let l be the distance from the i-th mortar spring to the left support. sj Let l be the distance from the j-th mortar spring to the left support. s This is the length of the track slab.

[0181] 2.3.2 Base plate displacement

[0182] Under the combined action of the mortar spring force and the sliding layer contact force, the base plate achieves mechanical equilibrium through coordinated displacement. Its force characteristics are similar to those of the track slab, and the force distribution is as follows: Figure 11 As shown.

[0183] Referring to the way the track slab displacement is expressed, the base plate displacement can be represented in the following matrix form:

[0184] V p =A p P p +B p N p (13)

[0185] In the formula: p represents the base plate; V p This represents the displacement matrix of the base plate at the contact spring node; A p and B p P represents the matrix of influence coefficients of mortar spring force and contact spring force on the displacement of the base plate; p and N p These are the mortar spring force matrix and the contact spring force matrix acting on the base plate, respectively. Wherein:

[0186] A p =-D s (14)

[0187]

[0188] In the formula: pi represents the position of the i-th contact spring; pj represents the position of the j-th contact spring; l pi Let l be the distance from the i-th contact spring to the left support. pj Let l be the distance from the j-th contact spring to the left support. p P is the length of the base plate; p N represents the matrix of mortar spring forces acting on the base plate. p This represents the contact spring force matrix acting on the base plate.

[0189] 2.3.3 Analytical Representation Expression

[0190] Based on the relationship between fastener force and the displacement of the track slab and rail, a fastener force matrix expression can be established:

[0191] The lateral force matrix F acting on each fastener of the rail r for:

[0192] F r =k c (V s -V r (16)

[0193] The lateral force matrix F of each fastener acting on the track slab s for:

[0194] F s =-k c(V s -V r )

[0195] In the formula: k c The stiffness matrix of the fastener spring;

[0196] The mortar spring force matrix P acting on the track slab s for:

[0197] P s =k ca (V p -V s (17)

[0198] The mortar spring force matrix P acting on the base plate s for:

[0199] P p =-k ca (V p -V s )

[0200] In the formula: k ca The mortar spring stiffness matrix;

[0201] Contact spring force matrix N acting on the base plate p for:

[0202] N p =k p (V b -V p (18)

[0203] In the formula: k p V is the stiffness matrix of the contact spring. b V is the bridge displacement matrix corresponding to the contact spring position. p This represents the displacement matrix of the base plate at the contact spring node.

[0204] Combining and simplifying equations (7), (10), (11), (12), (13), (14), and (15), we obtain:

[0205]

[0206] In the formula: E is the identity matrix.

[0207] 3. Solution and Verification of Deterioration Characterization Model

[0208] 3.1 Solution of the Geometric Irregularity Characterization Model for Longitudinal Ballastless Track on Bridge

[0209] Based on the aforementioned seismic damage analysis results of key components between ballastless track layers, we found that: for continuous beam bridges, both the sliding layer and the supports suffered damage; for simply supported beam bridges, the mortar layer, sliding layer, and supports all suffered damage, with the fastener layer also showing damage under certain seismic conditions. The main critical component of the bridge was the support, which sustained damage.

[0210] Therefore, it is necessary to consider the impact of seismic damage on key components between ballastless track layers and key components of bridges simultaneously. Then, based on the previously constructed characterization model of the deterioration of the geometric irregularity of longitudinal ballastless track, the rail displacement under seismic action can be mapped to accurately quantify the cumulative damage effect caused by seismic action.

[0211] Since the degradation characterization model in this embodiment simplifies the base plate, track slab, and rail into a simply supported beam system, the model input parameter is selected as the support displacement. To simplify the influence of seismic damage to key inter-track components (such as fasteners and sliding layers) on the degradation characterization relationship of track geometric irregularities, this embodiment adopts a pre-superposition method. The inter-track displacements (post-earthquake residual displacements or peak displacements during the earthquake) at the corresponding support locations are pre-superimposed with the upper support displacements (post-earthquake residual displacements or peak displacements during the earthquake), thus obtaining the superimposed support displacements and simplifying the computational complexity of the rail displacement response under seismic loading. The bridge displacement considering the seismic damage to key inter-track components and key bridge components under seismic loading is as follows: Figure 12 As shown.

[0212] according to Figure 12 As shown, the bridge displacement caused by the superimposed displacement of the supports indicates that the lateral displacement at the k-th position of the m-th span under seismic action is:

[0213]

[0214] V bmk =α k d m-1 +β k d m (twenty one)

[0216] d m =d z +d g (twenty two)

[0218]

[0219] In the formula: V bmk Let m be the lateral displacement at the k-th location of the m-th span of the bridge under seismic action, where m ranges from ~5 and k ranges from 1 to l. b ;d m-1 d represents the superimposed displacement of the left support of the m-th span of the bridge; md represents the superimposed displacement of the right-side support of the m-th span of the bridge; z d represents the displacement of the top of the support under seismic loading; g x represents the inter-story drift of the track at the corresponding support location under seismic loading; mk Let l be the longitudinal displacement of the bridge at position k of the m-th span; b0 The length of the expansion joint between bridge sections; l b1 The distance between the beam end and the centerline of the support; l b α is the beam length; k The matrix representing the influence of the left support displacement on the bridge displacement; β k This is the matrix showing the influence of the right-side support displacement on the bridge displacement.

[0220] The bridge displacement matrix at the corresponding contact spring position can be expressed as:

[0221]

[0222] In the formula: b represents the bridge, b1, b2...b3 are 1 to m bridge displacement matrices, and m ranges from 1 to 5.

[0223] 3.2 Validation of the Geometric Irregularity Characterization Model for Longitudinal Ballastless Track on Continuous Beam Bridges

[0224] This embodiment verifies the degradation characterization model of geometric irregularities of longitudinally connected ballastless tracks on continuous beam bridges and simply supported beam bridges, respectively. The solution process is as follows: Figure 13 As shown.

[0225] 3.2.1 Residual Displacement

[0226] Under rare earthquakes, the residual displacement of supports superimposed on the residual displacement of rails and the residual displacement mapped by rails under earthquakes of different intensities are as follows: Figure 14 As shown in Table 4.

[0227] Table 4. Comparison of maximum values ​​of finite element solutions and mapped solutions under different seismic motions and intensities.

[0228]

[0229] according to Figure 14 As shown in Table 4, under rare earthquakes, the maximum error between the residual rail displacement obtained by the superimposed residual displacement of the supports and the mapped residual displacement of the rail under different earthquake intensities and the finite element model does not exceed 4.65%. Under design earthquakes, the maximum error of the obtained residual rail displacement does not exceed 4.68%. This indicates that the residual rail displacement obtained by the degradation characterization model and the finite element model under different earthquake motions and intensities is in good agreement, verifying the accuracy of the established degradation characterization model for the geometric irregularities of the longitudinal ballastless track on the continuous beam bridge in solving the post-earthquake residual displacement.

[0230] 3.2.2 Peak Displacement

[0231] To further verify the universality of the established deterioration characterization model, the peak displacement of the upper part of the support under a rare earthquake was pre-stacked with the earthquake-induced peak displacement of the corresponding damaged key components of the track. The peak displacement of the rail during the earthquake calculated by the deterioration characterization model and the finite element model was then compared. Figure 15 As shown in the figure. The results show that the calculation results of the degradation characterization model and the finite element model are in good agreement overall, with only slight differences in some sections. The reason is that the degradation characterization model uses Euler beams, which ignore the influence of transverse shear displacement, while the finite element model uses BEAM188 elements based on Timoshenko beam theory. These beam elements consider the cross-sectional rotation caused by bending moment and shear force. Therefore, the degradation characterization model underestimates the peak displacement of the rail during earthquakes.

[0232] 3.3 Validation of the Geometric Disorder Characterization Model for Longitudinal Ballastless Track on Simply Supported Beam Bridges

[0233] 3.3.1 Residual Displacement

[0234] Under rare earthquakes, the residual rail displacement solved by the degradation characterization model and the finite element model is as follows: Figure 16 As shown in Table 5.

[0235] Table 5. Comparison of maximum values ​​of finite element solutions and mapped solutions under different seismic motions and intensities.

[0236]

[0237] according to Figure 16 As shown in Table 5, under rare earthquakes, the maximum error in the residual rail displacement calculated by the deterioration characterization model and the finite element model does not exceed 3.64%, and under design earthquakes, the maximum error in the residual rail displacement does not exceed 3.86%. This indicates that the residual rail displacement calculated by the deterioration characterization model and the finite element model is in good agreement under different earthquake motions and intensities, verifying the accuracy of the established deterioration characterization model for the geometric irregularities of longitudinally connected ballastless track on simply supported beam bridges in solving for post-earthquake residual displacement.

[0238] 3.3.2 Peak Displacement

[0239] Similarly, under rare earthquakes, the peak displacement of the upper part of the support is pre-superimposed with the earthquake-induced peak displacement of key track components such as fasteners, mortar layers, and sliding layers. The mapped rail peak displacement is then compared with that obtained by the deterioration characterization model and the finite element model. Figure 17 As shown in the figure. The results show that the calculation results of the degradation characterization model and the finite element model are in good agreement overall, further verifying the universality of the established degradation characterization model.

[0240] Analysis using the method of this invention yielded the following conclusions:

[0241] (1) Under earthquakes of different intensities, the damage to the ballastless track-continuous beam system was mainly concentrated in the sliding layer and the support area; while the ballastless track-simply supported beam system showed significant earthquake-induced damage in the mortar layer, sliding layer and supports, and the fasteners were also damaged under rare earthquakes. It can be seen that the simply supported beam bridge suffered more severe post-earthquake damage than the continuous beam bridge.

[0242] (2) Under different ground motions and intensities, the maximum error of the residual displacement of the rails on the continuous beam and simply supported beam after the earthquake, calculated by the established deterioration characterization model and the finite element model, does not exceed 5%, which verifies the accuracy of the established deterioration characterization model of the geometric irregularity state of the longitudinal ballastless track on the continuous / simply supported beam in solving the residual displacement after the earthquake.

[0243] (3) Under different ground motions and intensities, the peak displacement curves of the rails of continuous beams and simply supported beams during earthquakes, obtained by the established deterioration characterization model and finite element model, show some deviations in local areas, but the overall curves are in good agreement. This is mainly due to the difference in theoretical assumptions of the deterioration characterization model, which further verifies the universality of the established deterioration characterization model.

[0244] (4) Subsequent work will consider introducing Timoshenko beam theory or establishing a shear correction coefficient correction model, incorporating existing track defects from long-term service into the model, and further improving the accuracy of the model in solving the peak displacement of the seismically induced ballastless track-bridge system.

[0245] In summary, this invention presents a method for characterizing the deterioration of geometric irregularities in longitudinally connected ballastless track on high-speed railway bridges under lateral seismic loading. By establishing a refined finite element model of the longitudinally connected ballastless track-bridge system, it analyzes the damage characteristics and distribution patterns of key components in the track-bridge system induced by earthquakes, revealing the characteristics and mapping mechanisms of the deterioration of the damage state of these key components. Then, based on Castigliano's second theorem and the superposition principle, it constructs a characterization model for the deterioration of geometric irregularities in longitudinally connected ballastless track on high-speed railway bridges under lateral seismic loading. Based on this characterization model, it maps the geometric irregularities of longitudinally connected ballastless track on simply supported / continuous beam bridges, accurately quantifying the deformation data of the rails under seismic loading. This provides a theoretical basis for rapidly assessing the post-earthquake traffic capacity and maintenance engineering of the track-bridge system, ensuring the safety of high-speed railway operation, and providing a theoretical basis for the design of high-speed railway track-bridges. It also facilitates post-earthquake track repair and train operation recovery, demonstrating good practical value and promising prospects for wider application.

[0246] 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 invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered exemplary and not restrictive in all respects. Furthermore, it should be understood that although this specification describes embodiments, it does not encompass only one technical solution. This descriptive method is merely for clarity, and those skilled in the art should consider the specification as a whole. 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 method for characterizing the deterioration of geometric irregularities in longitudinally connected ballastless track on high-speed railway bridges under lateral earthquakes, characterized in that: Includes the following steps: S1: Establish a refined finite element model of the longitudinal ballastless track-bridge system; S2: Select the seismic wave and input the refined finite element model established in step S1 laterally; S3: Analyze the seismic damage characteristics and distribution patterns of key components between track layers in the longitudinal ballastless track-bridge system after inputting seismic waves in step S2, and reveal the characteristics and mapping mechanism of the deterioration of the damage state of key components in the longitudinal ballastless track-beam bridge system caused by seismic waves. S4: Based on the analysis results of step S3, establish a characterization model for the deterioration of the geometric irregularity of the longitudinal ballastless track on the bridge under transverse earthquake. S5: Linearly superimpose the displacement at the top of the support with the inter-layer displacement of the track at the corresponding position, and input it into the characterization model of the deterioration of the geometric irregularity of the longitudinal ballastless track on the bridge under transverse earthquake established in step S4. Solve the model to obtain the rail displacement, thereby evaluating the traffic capacity of the longitudinal ballastless track-bridge system after the earthquake.

2. The method for characterizing the deterioration of geometric irregularities of longitudinally connected ballastless track on a high-speed railway bridge under lateral earthquakes, as described in claim 1, is characterized in that: The refined finite element model of the longitudinally connected ballastless track-beam bridge system established in step S1 includes a finite element model of the ballastless track-simply supported beam bridge system and a finite element model of the ballastless track-continuous beam bridge system; wherein: The finite element model of the ballastless track-continuous beam bridge system shows that the main continuous beam bridge is a 32m+48m+32m double-track single-box single-cell variable height continuous box girder bridge, and the approach bridges on both sides are 32m mixed simply supported beam bridges. The simply supported beam bridge of the ballastless track-simply supported beam bridge system adopts a 32m standard span concrete box girder; All piers are solid structures with rounded ends, and all bearing systems use pot-type rubber bearings. The pile foundations at the bottom of the piers are all considered as consolidation constraints. BEAM188 elements were used to simulate continuous beam bridges, simply supported beam bridges, and track structures at each level. COMBIN39 nonlinear spring elements were used to simulate the connection between the track and the main beam layers, and between the track and the roadbed. The rigid constraints between the master and slave nodes are simulated using MPC184 elements. Boundary conditions are simulated using displacement constraints, and the displacement of the roadbed under external forces is ignored. A Rayleigh damping model is adopted, and a modal damping ratio of 5% is set.

3. The method for characterizing the deterioration of geometric irregularities of longitudinally connected ballastless track on a high-speed railway bridge under lateral seismic conditions as described in claim 1, characterized in that: Step S2 selects three seismic waves that have the highest matching degree with the site characteristics, specifically: The site's seismic intensity is 8.5 degrees, the site category is Class III, and the epicentral distance is grouped as Group 2. A design seismic response spectrum is generated. Its characteristic period is 0.55s, and its PGA content is 0.3g; Import the response spectrum into the NGA-West2 ground motion database and select the three ground motions with the highest spectral matching degree. The original acceleration data was multiplied by a scaling factor, and a 10s zero-value segment was added to the end of the data. The seismic excitation direction was laterally.

4. The method for characterizing the deterioration of geometric irregularities of longitudinally connected ballastless track on a high-speed railway bridge under lateral seismic conditions, as described in claim 1, is characterized in that: Step S3 describes the analysis of the seismic damage characteristics and distribution patterns of key components between track layers in the longitudinally connected ballastless track-bridge system after inputting seismic waves, including seismic damage analysis of key components between ballastless track layers and seismic damage analysis of key bridge components. The seismic damage analysis of key interlayer components of the ballastless track includes the displacement of fasteners on different bridges under different seismic intensities, the displacement of mortar layers on different bridges under different seismic intensities, and the displacement of sliding layers on different bridges under different seismic intensities. Seismic damage analysis of key bridge components: including residual displacements of bridge supports under different seismic intensities and residual displacements of pier tops under different seismic intensities.

5. The method for characterizing the deterioration of geometric irregularities of longitudinally connected ballastless track on a high-speed railway bridge under lateral seismic conditions as described in claim 1, characterized in that: Step S4 describes the process of establishing a characterization model for the deterioration of the geometric irregularities of the longitudinally connected ballastless track on a bridge under lateral seismic conditions. S4-1: Basic Assumptions: Basic assumptions are made regarding the lateral displacement and action modes among the components of the characterization model of the deterioration of the geometric irregularity of the longitudinally connected ballastless track on the bridge under lateral earthquake. S4-2: Rail displacement at fastener nodes: Treating the rail as a simply supported structure, based on the Saint-Venant principle, the calculated length of the rail is selected to be much larger than the bridge displacement influence zone to eliminate the boundary constraint effect. Virtual fastener forces are added at equal intervals between adjacent fasteners to establish the rail static equilibrium equation and solve for the support reaction forces at both ends of the rail. Then, based on Castigliano's second theorem and the superposition principle, the rail displacement at any fastener node, excluding the endpoints, is obtained; and the rail displacements at all fastener nodes are expressed in matrix form as follows: V r =H r F r (7) In the formula: V r This is the lateral displacement matrix of the rail at the fastener node, where r represents the rail. H r This is the matrix of coefficients representing the influence of fastener force on the lateral displacement of the rail. F r This is the matrix of lateral forces acting on the rails from each fastener; S4-3: Track slab displacement at each mortar support point: Due to the combined action of the fastener system and the elastic support of the mortar layer, the longitudinal track slab achieves mechanical equilibrium through coordinated displacement with the base plate. The displacement of the track slab at each mortar support point is obtained and expressed in matrix form as follows: V s =C s F s +D s P s (10) In the formula: V s This represents the displacement matrix of the track slab at the mortar spring support point, where s represents the track slab. C s The matrix showing the influence coefficients of fastener force on the lateral displacement of the track slab is as follows: C s =-H r (11); D s The matrix showing the influence coefficients of the mortar spring force on the lateral displacement of the track slab is as follows: si represents the position of the i-th mortar spring, and sj represents the position of the j-th mortar spring; l si Let l be the distance from the i-th mortar spring to the left support. sj Let l be the distance from the j-th mortar spring to the left support. s The length of the track slab; F s The matrix representing the fastener forces acting on the track slab; P s The matrix representing the mortar spring force acting on the track slab; S4-4: Base plate displacement: Due to the combined action of the mortar spring force and the sliding layer contact force, the base plate achieves mechanical equilibrium through coordinated displacement, resulting in the base plate displacement, expressed in matrix form as follows: V p =A p P p +B p N p (13) In the formula: V p This represents the displacement matrix of the base plate at the contact spring node; A p The matrix representing the influence coefficients of the mortar spring force on the displacement of the base plate is as follows: A p =-D s (14) B p The matrix representing the influence coefficients of the contact spring force on the displacement of the base plate is as follows: p represents the base plate; pi represents the position of the i-th contact spring; pj represents the position of the j-th contact spring. l pi Let l be the distance from the i-th contact spring to the left support. pj Let l be the distance from the j-th contact spring to the left support. p The length of the base plate; P p The matrix of mortar spring forces acting on the base plate; N p The matrix of contact spring forces acting on the base plate; S4-5: Establish the characterization matrix for the deterioration of the geometric irregularities of the longitudinally connected ballastless track on the bridge under lateral earthquakes: By simultaneously solving the displacement matrices and influence coefficient matrices from steps S4-2 to S4-4, the characterization matrix for the deterioration of the geometric irregularities of the longitudinally connected ballastless track on the bridge under lateral earthquakes can be obtained, as follows: In the formula: E is the identity matrix.

6. The method for characterizing the deterioration of geometric irregularities of longitudinally connected ballastless track on a high-speed railway bridge under lateral earthquakes, as described in claim 5, is characterized in that: The basic assumptions mentioned in step S4-1 are as follows: Assume that the track slab-base plate-bridge meet the requirements for lateral displacement coordination; The base plate, track plate, and rail are simplified into a simply supported beam model. The interaction between the rail, track plate, and base plate is considered, while the reaction of the base plate on the bridge displacement is ignored. The mortar layer support is simplified as a nonlinear spring distributed along the centerline of the rail, and the base plate-bridge contact relationship is simplified as a unidirectional spring. The spring spacing is taken as 1 / 20 of the fastener spacing. The entire fastener system, including the pad and fastener spring strip, is considered as a spring. Virtual fastener springs are added to maintain the uniformity of the matrix dimension, and their distribution spacing is consistent with that of the mortar springs.

7. The method for characterizing the deterioration of geometric irregularities of longitudinally connected ballastless track on a high-speed railway bridge under lateral seismic conditions, as described in claim 5, is characterized in that: In step S4-2, the static equilibrium equation of the rail is: In the formula: r represents the rail; F rj The distance between the j-th fastener and the left end of the rail; l rj This represents the distance from the j-th fastener to the left end support; M0 represents the total bending moment of the system; rj represents the position of the j-th fastener; l r The selected rail length; F r0 This is the reaction force at the left end support of the rail; F r(n+1) This is the reaction force at the right end support of the rail; The solution yields the support reactions at both ends of the rail, expressed as follows: The displacement of the rail at any fastener node, excluding the endpoints, is expressed as: In the formula: y ri This refers to the displacement of the rail at any fastener node, excluding the endpoints. M(x) represents the bending moment; A(l ri ,l rj ,l r ), B(l ri ,l rj ,l r ), B(l rj ,l ri ,l r ), C(l ri ,l rj ,l r ) and C(l rj ,l ri ,l r Substitute the following formula into the equation: In the formula: A is the structural compliance coefficient under symmetrical load, B is the structural compliance coefficient under asymmetrical load, and C is the structural compliance coefficient under end boundary effects. l ri Let l be the distance from the i-th fastener to the left support. rj Let l be the distance from the j-th fastener to the left support. r The length of one span of rail; x1, x2, and x3 represent placeholder variables in the formula; E r This represents the elastic modulus of the rail. I r The moment of inertia of the rail section; The influence coefficient matrix H of the fastener force on the lateral displacement of the rail r Represented as:

8. The method for characterizing the deterioration of geometric irregularities of longitudinally connected ballastless track on a high-speed railway bridge under lateral earthquakes, as described in claim 5, is characterized in that: In step S4-3, the displacement of the track slab at each mortar support point is: In the formula: F sj This represents the force applied to the j-th fastener; P sj This represents the force of the j-th mortar spring; l sj The distance between the j-th fastener and the left end of the track plate; l si The distance between the i-th fastener and the left end of the track plate; l s The length of the track slab; E s The elastic matrix of the track slab, I s Let be the cross-sectional inertia matrix of the track slab.

9. The method for characterizing the deterioration of geometric irregularities of longitudinally connected ballastless track on a high-speed railway bridge under lateral earthquakes, as described in claim 5, is characterized in that: The lateral force matrix F acting on each fastener of the rail r for: F r =k c (V s -V r ) (16) The lateral force matrix F of each fastener acting on the track slab s for: F s =-k c (V s -V r ) In the formula: k c The stiffness matrix of the fastener spring; The mortar spring force matrix P acting on the track slab s for: P s =k ca (V p -V s ) (17) The mortar spring force matrix P acting on the base plate s for: P p =-k ca (V p -V s ) In the formula: k ca The mortar spring stiffness matrix; Contact spring force matrix N acting on the base plate p for: N p =k p (V b -V p ) (18) In the formula: k p V is the stiffness matrix of the contact spring. b V is the bridge displacement matrix corresponding to the contact spring position. p This represents the displacement matrix of the base plate at the contact spring node.

10. The method for characterizing the deterioration of geometric irregularities of longitudinally connected ballastless track on a high-speed railway bridge under lateral seismic conditions, as described in claim 1, is characterized in that: Step S5 involves pre-superimposing the displacement at the top of the support under seismic action with the inter-layer displacement of the track at the corresponding location to obtain the superimposed lateral displacement of the support, as follows: V bmk =a k d m-1 +b k d m (21) d m =d z +d g (22) In the formula: V bmk Let be the lateral displacement at the k-th location of the m-th span of the bridge under seismic action, where m ranges from 1 to 5 and k ranges from 1 to 1. b ; d m-1 The displacement is the superimposed displacement of the left support of the m-th span of the bridge; d m The displacement is the superimposed displacement of the right-side support of the m-th span of the bridge; d z This refers to the displacement of the top of the support under seismic loading. d g This represents the inter-story displacement of the track at the corresponding support location under seismic action; x mk Let be the longitudinal displacement of the bridge at the k-th position of the m-th span. l b0 The length of the expansion joint between bridge sections; l b1 This is the distance between the beam end and the centerline of the support; l b For Liang Chang; α k This is the matrix showing the influence of the left support displacement on the bridge displacement. β k This is the matrix showing the influence of the right-side support displacement on the bridge displacement. The bridge displacement matrix corresponding to the contact spring position is expressed as: In the formula: b represents the bridge, b1, b2...b3 are 1 to m bridge displacement matrices, and m ranges from 1 to 5.

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