Seamless track response simulation method for ballastless track on bridge under earthquake based on site characteristics and displacement loading

Abstract

The invention discloses a site characteristic and displacement loading-based on-bridge ballastless track seamless track response simulation method under an earthquake. The method comprises the following steps: S1, constructing a site soil layer model containing a non-uniform soil layer; s2, inputting transverse and vertical seismic waves at the boundary of the field soil layer model at the same time, and simulating dual-path seismic oscillation transmission; s3, extracting a three-way displacement time history of surface nodes of the field soil layer model; and S4, inputting the three-way displacement time history into a bridge-track coupling model, and obtaining the dynamic response and damage state of the track structure. According to the method, the amplification and attenuation effects of a real site on seismic oscillation can be simulated, and the simulation precision of a real seismic situation is improved, so that the prediction capability of local failure and residual deformation of the ballastless track under a strong earthquake is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of rail transit anti-seismic technology, more particularly to a response simulation method for a bridge on a ballastless track under an earthquake based on site characteristics and displacement loading. BACKGROUND

[0002] With the rapid development of rail transportation, the seismic design and safety evaluation of bridge and track systems under earthquake action have become increasingly important. As the main structural form of high-speed rail, ballastless track is widely used in bridge sections due to its high stability and durability. However, recent earthquake events have shown that the coupling effect of earthquake action on bridge and track systems has a significant impact, resulting in residual deformation, slip and local failure of track structures, which seriously threatens train operation safety.

[0003] Traditional seismic design methods usually focus on bridge structures, ignoring the complex dynamic coupling between track systems and piers, abutments and bridges. Existing researches mainly focus on dynamic response analysis of bridges or tracks under single-direction seismic loading, while the propagation characteristics of seismic waves in complex site conditions and the coupling effects caused by multi-directional seismic action have not been fully considered. In fact, the non-uniformity of site soil layers, interlayer reflection and refraction effects significantly affect the propagation of seismic waves, and the site amplification effect can greatly increase the destructive effect of seismic waves on bridge and track systems. At the same time, the phase difference between seismic waves in different directions and dynamic coupling also have a key impact on the overall dynamic response of the system.

[0004] Currently, the research on the coupling response of site soil layers and track systems is still in its early stages. Some scholars attempt to simulate site conditions through simplified models, but ignore the influence of multi-layer structure, shear wave velocity (Vs) distribution and damping characteristics of soil layers on seismic wave propagation. In addition, the application of multi-path seismic wave input method (combination of horizontal and vertical propagation) and multi-point vibration response analysis technology is also relatively scarce.

[0005] The interaction between bridge pier and track system further increases the complexity of dynamic analysis. As the connecting part of bridge and foundation, the dynamic response of pier pile is significantly affected by site soil layers, which may cause large residual deformation and slip of track slabs in bridge sections, especially when the earthquake intensity is high, this phenomenon is particularly prominent.

[0006] Therefore, how to establish a high-precision site soil layer model and accurately simulate the propagation path and dynamic response of seismic waves has become a major problem in improving the anti-seismic design capability of rail transportation. SUMMARY

[0007] In view of this, in order to at least partially solve the above technical problems, the present application provides a method for simulating the response of a ballastless track on a bridge under an earthquake based on site characteristics and displacement loading, aiming to solve the problems of insufficient simulation of earthquake wave propagation characteristics and lack of research on dynamic coupling effects in the prior art, and to provide a scientific basis for the seismic design and post-disaster evaluation of the rail transit system.

[0008] In order to achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0009] A method for simulating the response of a ballastless track on a bridge under an earthquake based on site characteristics and displacement loading, comprising,

[0010] S1. Constructing a site soil layer model containing non-uniform soil layers;

[0011] S2. Inputting horizontal and vertical seismic waves simultaneously at the boundary of the site soil layer model to simulate double-path seismic wave transmission;

[0012] S3. Extracting the three-dimensional displacement time history of the nodes on the ground surface of the site soil layer model;

[0013] S4. Performing response analysis on the three-dimensional displacement time history and inputting the three-dimensional displacement time history into a bridge-track coupling model to obtain the dynamic response and damage state of the track structure.

[0014] Preferably, step S1 comprises:

[0015] Determining the horizontal range and vertical range of the site soil layer model;

[0016] Layering the soil layer parameters according to soft soil layers, clay layers and bedrock layers for input;

[0017] Simulating local differences in soil layers within the same layer by random field or zoned assignment method, including adjusting the local differences in Poisson's ratio and density parameters within the same layer, setting a gradual transition zone for soil layer parameters to avoid sudden changes in mechanical properties;

[0018] And setting a perfectly matched layer (PML) absorbing boundary at the boundary of the site soil layer model.

[0019] Preferably, the soil layer parameters include soil layer thickness, density, elastic modulus, cohesion and internal friction angle, shear wave velocity, Poisson's ratio and damping ratio.

[0020] Preferably, step S2 comprises:

[0021] Synchronously applying the horizontal and vertical seismic waves to the horizontal boundary and bottom boundary of the site soil layer model;

[0022] The horizontal seismic wave is a long-period wave corrected by site characteristics;

[0023] The vertical seismic wave is a seismic wave that has undergone frequency modulation to ensure that the input waveform is consistent with the actual seismic characteristics of the site.

[0024] Preferably, in step S3, the locations of multiple bridge pier pile foundations laid on the ground surface are used as ground nodes.

[0025] Preferably, the response analysis includes: extracting key dynamic indicators, including the maximum displacement, velocity, acceleration and spectral characteristics of each monitoring point in three directions;

[0026] In addition, the time series and frequency domain characteristics of the vibration response were analyzed, and the vibration phase difference and the influence of site non-uniformity at different pier and pile foundation locations were extracted.

[0027] Phase difference: Observe the phase difference of vibration displacement at the four piers of the simulated three-span simply supported beam within the same time step to identify the asynchronous ground motion phenomenon caused by site non-uniformity.

[0028] The site amplification effect is determined by comparing the input waveform (at the bedrock) with the response spectrum or peak response at the surface to determine the soil amplification factor and frequency band.

[0029] Preferably, the bridge-track coupling model in step S4 includes:

[0030] For piers and bridges, solid elements are used to simulate the nonlinear hysteresis characteristics of the supports.

[0031] The track, track slab and mortar layer adopt cohesion model, the track slabs adopt separable friction contact model, and the limiting structure adopts extended finite element damage model to simulate the shear and tensile stress damage propagation between layers caused by seismic load.

[0032] The fasteners and rails are simulated using nonlinear spring elements, with linear stiffness in the vertical and lateral directions and frictional contact with resistance considered in the longitudinal direction; the rails are simulated using solid elements.

[0033] Preferably, in step S4, the dynamic response and damage state of the track structure include:

[0034] Displacement response is the time history of displacement in the X, Y, and Z directions of the rail, fasteners, track slab, and mortar layer.

[0035] Internal force distribution, including shear stress, tensile stress and their distribution characteristics between ballastless track layers;

[0036] Damage propagation refers to the extent of cohesive damage between the track slab and the mortar layer, as well as the cracking behavior of fasteners and limiting structures.

[0037] Preferably, the method further includes step S5, which involves assessing the load-bearing capacity and analyzing residual deformation based on the dynamic response and damage state of the track structure.

[0038] This invention also provides a simulation system for the response of seamless track ballastless track on bridges under earthquake conditions based on site characteristics and displacement loading, used to execute the simulation method for the response of seamless track ballastless track on bridges under earthquake conditions based on site characteristics and displacement loading as described above, including:

[0039] The site soil modeling module is used to build site soil models that include non-uniform soil layers.

[0040] The dual-path seismic wave loading module is used to simultaneously input transverse and vertical seismic waves at the boundary of the soil layer model of the site to simulate the transmission of ground motion along two paths.

[0041] The displacement response extraction module is used to extract the three-dimensional displacement time history of the surface nodes of the site soil model; and output the phase difference data across the pier.

[0042] The track damage assessment module is used to perform response analysis on the three-dimensional displacement time history and input the three-dimensional displacement time history into the bridge-track coupling model to obtain the dynamic response and damage status of the track structure.

[0043] As can be seen from the above technical solution, this invention, based on a comprehensive consideration of the heterogeneity of site soil layers, multipath seismic wave propagation, and three-directional vibration coupling, proposes a multi-directional seismic wave response analysis method based on a site soil layer model. Compared with the prior art, the beneficial effects of this application include:

[0044] 1) By differentiating the Poisson's ratio, density, thickness, etc. of the multi-layer soil model through actual survey data, the amplification and attenuation effects of the site on seismic motion can be realistically simulated.

[0045] 2) By comprehensively considering the multi-layered soil and multi-path seismic wave propagation, the three-dimensional ground motion time history at the bridge pier location can be obtained more accurately, thereby greatly improving the simulation accuracy of real earthquake scenarios and providing reliable input for subsequent seismic design of ballastless track.

[0046] 3) By acquiring multi-point coupled vibration response, the multi-point synchronous / asynchronous vibration response caused by site non-uniformity and soil layer differences can be more comprehensively reflected, providing refined input conditions for the seismic design of bridges and ballastless tracks.

[0047] 4) In the bridge-track coupling model, a cohesion model is introduced to dynamically simulate the stress concentration and crack evolution at the interface between the track slab and the mortar layer under seismic load. At the same time, an extended finite element model is introduced to dynamically simulate the damage of the limiting protrusions located in the interlayer concealed layer under seismic load. This application can significantly improve the ability to predict the local failure and residual deformation of ballastless track under strong earthquakes. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0049] Figure 1 This is a flowchart of the simulation method for the response of seamless track without ballast on bridges under seismic conditions based on site characteristics and displacement loading, according to the present invention.

[0050] Figure 2 This is a schematic diagram of the soil layer model for the site of this invention;

[0051] Figure 3 This is a schematic diagram of the structure of each component in the bridge-track coupling model of the present invention;

[0052] Figure 4 This is a hysteresis curve diagram of the bridge support of the present invention;

[0053] Figure 5 This is a diagram showing the stress distribution of the track slab under different earthquake conditions according to the present invention;

[0054] Figure 6 This is a time history curve of the lateral displacement of the track slab under different earthquake conditions according to the present invention;

[0055] Figure 7 This is a time history curve of the lateral relative displacement between the rail and the track slab at the bridge pier under different earthquake conditions according to the present invention;

[0056] Figure 8 This is a diagram showing the displacement distribution of the isolation layer under different earthquake conditions according to the present invention. Detailed Implementation

[0057] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0059] This invention discloses a simulation method for the response of seamless track on bridge under seismic loading based on site characteristics and displacement loading. Through four main steps—site soil layer modeling (including non-uniformity and multi-layer absorbing boundaries), dual-path input of seismic waves (horizontal and vertical), multi-point vibration displacement response extraction, and dynamic coupling analysis of ballastless track on bridge—it demonstrates how to use finite element simulation technology to study the dynamic response characteristics of the ballastless track-bridge-soil system under seismic loading.

[0060] The numerical methods and procedures provided by this invention are applicable to the seismic design and earthquake hazard assessment of bridge-track-line systems. They can not only provide a reference for the seismic design and disaster reduction assessment of ballastless tracks on high-speed railway bridges, but also be extended to the seismic analysis of other soil-structure coupled systems such as urban rail transit and highway bridges.

[0061] In one embodiment, such as Figure 1 The method includes the following steps:

[0062] S1. Construct a site soil layer model that includes non-uniform soil layers;

[0063] S2. Simultaneously input transverse and vertical seismic waves at the boundary of the soil layer model of the site to simulate the transmission of ground motion along two paths;

[0064] S3. Extract the three-dimensional displacement time history of the surface nodes of the soil layer model at the site;

[0065] S4. Input the three-dimensional displacement time history into the bridge-track coupling model to obtain the dynamic response and damage state of the track structure.

[0066] Further, the following examples illustrate this:

[0067] Taking a high-speed railway bridge as an example, a CRTSⅢ type slab track is laid on it. The bridge adopts a 32m simply supported box girder structure, with a total length of approximately 640m and a pier height of 15m. The pier pile foundation penetrates from the upper soft soil layer to the hard soil layer. The track system includes rails, fastening system, track slabs, self-compacting concrete, geotextile isolation layer and elastic buffer layer, and base. The limiting structure is set between the self-compacting concrete and the base, consisting of two 0.7m×1.0m×0.9m rectangular columns. For the sake of simplifying the analysis, the following embodiment only selects three consecutive spans as the research object.

[0068] Furthermore, the venue information is as follows:

[0069] According to the site survey report, the site can be mainly divided into three layers: the upper soft soil layer (Layer 1): about 10m thick, with high water content and weak engineering properties; the middle clay-silty clay layer (Layer 2): about 20m thick, with improved mechanical properties compared to the upper layer; and the bedrock layer (Layer 3): from 30m below to 100m deep, consisting of argillaceous sandstone or sandy mudstone with a low degree of weathering.

[0070] The simplified physical and mechanical parameters of the soil layer are shown in the table below:

[0071]

[0072] In one embodiment, the site soil model is as follows: Figure 2 As shown, step S1 specifically includes:

[0073] 1.1 Determine the modeling scope

[0074] Horizontal range: In this embodiment, the range is extended to more than 1km × 1km in the XY plane to cover the bridge piers and surrounding areas to be evaluated.

[0075] Vertical range: The simulated depth in the Z direction extends more than 100m downwards from the ground surface to cover typical soil layers (soft soil, hard soil, bedrock, etc.).

[0076] 1.2 Parametric Modeling

[0077] Soil layer parameter input: Based on the table above, input the thickness, elastic modulus, density, damping ratio, Poisson's ratio, shear wave velocity and other parameters of Layer 1, Layer 2 and Layer 3 into the soil layer model respectively.

[0078] Then, non-uniformity processing is performed: within the same soil layer, random fields or zonal assignment methods can be considered to adjust Poisson's ratio, density, thickness, etc., thereby simulating the local differences of the soil layer in the horizontal and vertical directions to truly reflect the complexity of the site.

[0079] When applying different soil mechanical parameters to each unit, set reasonable soil layer transitions to avoid excessive jumps.

[0080] 1.3 Boundary Conditions

[0081] A Perfectly Matched Layer (PML) absorbing boundary is set up by placing PML elements on the unloaded edges of the model to effectively absorb the boundary reflection energy generated by the propagation of seismic waves and eliminate the impact of seismic wave reflection on the simulation accuracy.

[0082] 1.4 Numerical Methods

[0083] A three-dimensional soil layer model of the site is constructed using the finite element method to accurately describe the propagation characteristics of seismic waves in multi-layered soil. Specifically, in this embodiment, three-dimensional solid elements are used to discretize the site soil; the vertical direction can be further refined by dividing the elements according to the characteristics of the soil layers.

[0084] The cell size should be combined with the highest analysis frequency (f max ) and shear wave velocity (V s The determination is based on comprehensive consideration to meet the accuracy requirements of fluctuation analysis (e.g., ).

[0085] In one embodiment, step S2 specifically includes:

[0086] 2.1 Input Method

[0087] Horizontal propagation: Simultaneous input of seismic wave accelerations with more pronounced long-period components at the lateral boundaries and bottom. El-Centro waves, after site correction, are selected as input, emphasizing the amplification effect of low-frequency components: long-period wave input corrected for site characteristics.

[0088] Vertical propagation: Simultaneously input real vertical seismic waves (such as El-Centro waves) or artificially synthesized seismic waves with adjusted spectral characteristics and amplitudes at the horizontal boundary and bottom to simulate the influence of vertical seismic waves in real seismic events.

[0089] In one embodiment, seismic wave spectrum amplitude modulation is used to ensure that the input waveform is consistent with the actual seismic characteristics of the site. This includes appropriately adjusting the spectrum and amplitude of the input waveform based on the site's seismic motion characteristics, so that the simulated seismic motion matches the design or measured spectrum in both frequency domain and intensity. For example, for an area with an 8-degree seismic fortification intensity, the peak ground acceleration (PGA) of the input wave can be adjusted to approximately 0.2–0.3g, ensuring that the energy distribution in each frequency band matches the specifications or actual measurements. This embodiment simulates seismic intensities of 7, 8, and 9 degrees.

[0090] 2.2 Transmission Path

[0091] In finite element analysis, viscous damping and mass damping terms are set to more closely approximate the dissipation of wave energy by real soil, thereby simulating the reflection, refraction, attenuation and amplification effects of seismic waves in soil layers and enhancing the model's realism.

[0092] In one embodiment, step S3 specifically includes:

[0093] Output node settings

[0094] Multiple bridge pier and abutment pile foundation locations were selected on the site surface as monitoring points, with a node spacing of 32.6m, the same as the bridge pier and abutment spacing. By changing the direction of the monitoring points, the locations of different earthquake sources can be simulated, such as arranging the monitoring points parallel to the lateral loading edge, perpendicular to the lateral loading edge, or at a certain angle to the lateral loading edge.

[0095] Output: Obtain vibration displacement-time curves in the X, Y, and Z directions (u x (t),u y (t),u z (t)).

[0096] In one embodiment, step S4 includes:

[0097] Key dynamic indicators were extracted, including the maximum displacement, velocity, acceleration, and spectral characteristics of each monitoring point in three directions;

[0098] In addition, the time series and frequency domain characteristics of the vibration response were analyzed, and the vibration phase difference and the influence of site non-uniformity at different pier and pile foundation locations were extracted.

[0099] Phase difference: Observe the phase difference of vibration displacement at the four piers of the simulated three-span simply supported beam within the same time step to identify the asynchronous ground motion phenomenon caused by site non-uniformity.

[0100] The site amplification effect is determined by comparing the input waveform (at the bedrock) with the response spectrum or peak response at the surface to determine the soil amplification factor and frequency band.

[0101] In one embodiment, step S4 further includes: establishing a bridge-track coupling model;

[0102] To more accurately analyze the multi-directional dynamic response of bridge piers, bridges, ballastless track, and seamless track under seismic loading, a high-precision finite element model needs to be rebuilt based on the site soil simulation results. The model structure is as follows: Figure 3 As shown, (a) is a bridge model, (b) is a bridge pier model, and (c) is a ballastless track model; in this embodiment,

[0103] Piers and Bridges: Solid elements are used to simulate the pier and bridge structures to model the nonlinear hysteresis characteristics of the bearings. In this application, the hysteresis curves of the bridge bearings are as follows: Figure 4 As shown, (a) is the restoring force model of the sliding bearing, and (b) is the restoring force model of the fixed bearing; the material properties are based on the mechanical parameters of concrete in the actual design (including elastic modulus, Poisson's ratio, damping ratio, and density, etc.). In this embodiment, the bearing model between the bridge and the pier needs to input nonlinear or linear spring stiffness, friction coefficient, etc. according to the design situation to reflect the mechanical characteristics of the bridge end or bearing isolation pad.

[0104] In one embodiment, E c =3.6×10 4 MPa, ν=0.2, ρ=2500kg / m 3 ξ = 0.05. The bridge bearings are KTPZ5500 type pot bearings, with four bearings per span: one fixed type (GD), one transversely movable type (HX), one longitudinally movable type (ZX), and one multi-directional movable type (DX). Under repeated horizontal loading, the hysteresis model of the pot bearing is similar to an ideal elastic-plastic model, with kxy = μN (where μ is the coefficient of sliding friction of the bearing, taken as 0.03; N is the upper dead load borne by the bearing; k is the horizontal shear stiffness of the inner rubber of the bearing, taken as 23MN / m); and xy is the shear displacement of the bearing. The failure shear force Fmax of the fixed bearing is 0.3 times the vertical bearing capacity, which is 1650kN. After the fixed bearing is sheared, the interaction between the upper beam and the top is considered to be only sliding friction, with a friction coefficient of 0.03 and a sliding friction force Fcr of 165kN.

[0105] Ballastless track: For CRTSⅡ type slab ballastless track: a cohesive model is used between the track slab and the mortar layer, with parameters such as shear strength, tensile strength, and crack propagation energy set. This model can simulate the propagation of shear and tensile stress damage between layers caused by seismic loads. For CRTSⅠ, CRTSⅢ, and bi-block types: a separable frictional contact model is used between the upper and lower layers, with contact parameters including the friction coefficient and separation strength limit. An XFEM extended finite element model is introduced for the restraint structure to simulate cracking behavior under horizontal shear force.

[0106] In this embodiment, for the CRTSⅢ type slab track: common-node binding constraints are set between the base plate and the bridge deck, and between the track plate and the self-compacting concrete; a separable contact with a friction coefficient of 0.5 is set between the self-compacting concrete and the base; and a separable elastic contact with a pressure of 3000 MPa / m is set between the limiting boss of the self-compacting concrete and the groove of the base. Furthermore, to address potential shear failure of the limiting boss, a cracking strength of 1.6 MPa and a critical fracture energy of 12 J / m are set within the boss concrete. 2 The extended finite element model was used, with the initial fracture location set around the perimeter where the boss contacts the self-compacting concrete.

[0107] Fasteners and rails: Fasteners are simulated using nonlinear spring elements, with linear stiffness in the vertical and lateral directions, and frictional contact in the longitudinal direction considering a certain resistance, reflecting the constraint performance of the fasteners. Rails are simulated using solid elements. Specifically, in this embodiment, the fasteners use three nonlinear spring elements, with linear total stiffness of 30kN / mm in the vertical and lateral directions, and 45kN / mm in the lateral direction. The maximum longitudinal total resistance is considered to be 9kN, and the ultimate slip displacement is 0.5mm. Rails are simulated using solid elements, and rail E...c =210GPa, ν=0.2, ρ=7800kg / m 3 ξ = 0.05.

[0108] The three-directional displacement responses at different pier locations calculated using the site soil model are used as boundary conditions for the finite element model and applied to the bottom of the pier, including:

[0109] X direction: Horizontal displacement time history data;

[0110] Y-direction: Vertical displacement time history data;

[0111] Z-direction: Time history data of the longitudinal horizontal displacement of the bridge.

[0112] In one embodiment, step S4 further includes: calculating the following dynamic response results by applying seismic loads (multi-directional displacement responses input from the site soil model):

[0113] Displacement response: Analyze the displacement time history, relative displacement, and residual displacement of the rails, fasteners, track slabs, and mortar layer in the X, Y, and Z directions, with a focus on the displacement peaks near the middle of the bridge span or the top of the piers, to determine whether they exceed the allowable relative deformation limit of the track.

[0114] Internal force distribution: Extract the shear stress, tensile stress and their distribution characteristics between the ballastless track layers, and predict the evolution of the shear force between the limiting boss and the base over time.

[0115] Damage propagation: Analyze the cohesive damage range of the track slab and mortar layer, as well as the cracking behavior of fasteners and limiting structures. Specifically, observe the maximum stress distribution area at the interface between the track and the bridge deck, and at the interface between the track slab and the self-compacting concrete, to determine whether there is contact surface failure or structural damage.

[0116] In this embodiment, the dynamic performance response of the ballastless track system on the bridge under different earthquake conditions is as follows: Figures 5-8 ;in,

[0117] Figure 5 The figure shows the stress distribution of the track slab under different earthquake intensities. As can be seen from the figure, under the three earthquake intensities, the maximum transverse stress of the track structure composite slab in the bridge section is 6.29 MPa, which is less than its compressive strength value. The composite slab does not suffer compressive damage, but it is greater than the stress limit for concrete cracking. Therefore, the concrete cracks. Figure 5 The stress distribution of the composite plate in the bridge section is serrated. This is mainly because the CRTSШ type ballastless track adopts a unit arrangement on the bridge, with six composite plates arranged in each span of the beam. Therefore, the stress distribution of the composite plate in the bridge section consists of six "serrations" as shown in the figure.

[0118] Figure 6 The figure shows the time history curves of lateral displacement of the track slab under different earthquake magnitudes. As can be seen from the figure, under the action of El Centro wave earthquakes of magnitudes 7, 8, and 9, the maximum lateral displacement amplitudes of the track slab were 26.131 mm, 70.830 mm, and 159.570 mm, respectively, and the minimum lateral displacement amplitudes were -28.671 mm, -79.644 mm, and -177.383 mm, respectively. There was no relative lateral displacement between the rail and the track slab at the mid-span of the ballastless track. The time history curves indicate that the seismic response of the rail and the track slab to lateral displacement is consistent.

[0119] Figure 7 The time history curves of the relative lateral displacement between the rail and the track slab at the bridge pier under different earthquake magnitudes are shown. Under the action of three earthquake accelerations of magnitude 7, 8, and 9, the relative lateral displacement between the rail and the track slab at the ballastless track bridge pier reaches its maximum value at 2.22s, with maximum values ​​of 0.010mm, 0.026mm, and 0.054mm, respectively. Therefore, the relative lateral displacement between the rail and the track slab at the bridge pier is relatively small.

[0120] Figure 8 This diagram shows the displacement distribution of the isolation layer under different earthquake magnitudes. Since the isolation layer is made of geotextile, its sliding friction coefficient is relatively low; therefore, the displacement limit is 0.5 mm. (Isolation layer displacement distribution) Figure Three The displacement distribution trends of the isolation layer were basically the same under earthquakes of different intensities. The displacement of the isolation layer did not exceed the displacement limit under earthquakes of all three intensities, indicating that the isolation layer maintained good performance and was not damaged.

[0121] Furthermore, based on the simulation results, the bearing capacity was assessed and residual deformation was determined. Combining the stress distribution and residual deformation characteristics of the bridge-track system, optimization suggestions for the seismic design of ballastless track were proposed.

[0122] 1) Bearing capacity assessment;

[0123] The maximum lateral stress of the track structure composite slab in the bridge section under the action of three seismic accelerations of El Centro wave intensity 7, 8 and 9 was 6.29 MPa, which is less than its compressive strength value and the composite slab did not suffer compressive damage. However, it is greater than the stress limit for concrete cracking. Therefore, the concrete cracking did not occur. In high-intensity seismic zones, the reinforcement of self-compacting concrete should be appropriately increased.

[0124] 2) Determination of residual deformation;

[0125] As the earthquake intensity increases, the maximum displacement also increases accordingly. For every degree increase in intensity, the peak displacement increases by a factor of 1. The maximum lateral displacement is 0.383 mm, and the maximum vertical displacement is 0.075 mm. Generally, the lateral displacement is about five times the vertical displacement. The dominance of lateral displacement indicates that the seismic waves have a significant lateral impact on the track structure; however, because the peak values ​​are relatively small, they do not cause damage to the track geometry.

[0126] To further optimize the above technical solution, the simulation results were compared with actual site monitoring data to verify their accuracy. Additionally, the site amplification effect and attenuation pattern in seismic wave propagation were analyzed.

[0127] This application achieves the following objectives through the integrated seismic response simulation of site-bridge-ballastless track in this embodiment:

[0128] 1) Taking into account multi-layered soil and multi-path seismic wave propagation;

[0129] Compared with the traditional single-direction, single-point input method, it can obtain the triaxial ground motion time history at the location of bridge piers and abutments more accurately, providing reliable input for the subsequent seismic design of ballastless track.

[0130] 2) Capture the key effects of site non-uniformity and dynamic coupling of track on bridge;

[0131] The phase difference and amplitude difference of ground motion at different pier locations will lead to differentiated stress and deformation within the same bridge span, which is more in line with the actual earthquake disaster scenario.

[0132] 3) Identify the possibility of interlayer contact damage and local failure in ballastless track;

[0133] By using the cohesion model, stress concentration and crack evolution at the interface between the track slab and mortar layer under seismic load can be dynamically simulated. By using the extended finite element model, damage to the limiting protrusions located in the interlayer concealed layer under seismic load can be dynamically simulated, providing technical support for rapid post-disaster assessment of the track.

[0134] 4) Provide targeted suggestions for subsequent design and reinforcement;

[0135] Based on the simulation results, engineers can make targeted optimizations to the pier pile foundations, restraint structures, structural layer parameters, etc., to further improve the seismic safety level of the seamless track of ballastless track on the bridge.

[0136] In another embodiment, the present invention also provides a simulation system for the response of seamless track ballastless track on bridges under seismic conditions based on site characteristics and displacement loading, comprising:

[0137] The site soil modeling module is used to build site soil models that include non-uniform soil layers.

[0138] The dual-path seismic wave loading module is used to simultaneously input transverse and vertical seismic waves at the boundary of the soil layer model of the site to simulate the transmission of ground motion along two paths.

[0139] The displacement response extraction module is used to extract the three-dimensional displacement time history of the surface nodes of the site soil model; and output the phase difference data across the pier.

[0140] The track damage assessment module is used to input the triaxial displacement time history into the bridge-track coupling model to obtain the dynamic response and damage status of the track structure.

[0141] Since this system implements the simulation method for seamless track response of ballastless track on bridge under earthquake conditions based on site characteristics and displacement loading as described above, it will not be repeated here.

[0142] Compared with the prior art, the advantages of this application include:

[0143] 1) More comprehensive site soil layer modeling;

[0144] Traditional studies often focus on simplified single- or double-layer soil structures, neglecting the heterogeneity of soil layers and the impact of multi-layer structures on seismic wave propagation. This invention employs a multi-layer soil model and allows for differentiation of Poisson's ratio, density, thickness, etc., based on actual survey data, thereby more realistically simulating the amplification and attenuation effects of ground motion on the site.

[0145] 2) Multi-path, multi-directional seismic input;

[0146] Previous analyses mostly considered only a single direction (horizontal or vertical) or a single point of seismic input. This invention simultaneously inputs seismic waves in the horizontal and vertical directions, taking into account the three-directional coupling effect in actual earthquakes and the multi-path propagation characteristics of seismic waves in the site (such as reflection, refraction, attenuation, etc.), thereby significantly improving the simulation accuracy of real earthquake scenarios.

[0147] 3) Acquisition of multi-point coupled vibration response;

[0148] Existing technologies often only acquire seismic responses at bridge foundations or single measuring points. This invention, by arranging multiple measuring points on the site surface to monitor displacement, acceleration time histories, and phase differences in the X, Y, and Z directions, can more comprehensively reflect the multi-point synchronous / asynchronous vibration response caused by site inhomogeneity and soil layer differences, providing refined input conditions for the seismic design of bridges and ballastless tracks.

[0149] 4) Dynamic analysis of ballastless track on coupled bridge;

[0150] Traditional methods focus on the separate analysis of the "bridge body" or "track body," making it difficult to accurately account for the complex interactions between track slabs, fasteners, mortar layers, and pier pile foundations. This invention, based on obtaining the actual dynamic boundary conditions of the site soil layers, establishes a three-dimensional refined finite element model of the pier-bridge-ballastless track. Through methods such as cohesion models and frictional contact, it simulates potential damage and slippage between track layers, significantly improving the ability to predict local failure and residual deformation of ballastless track under strong earthquakes.

[0151] 5) High-precision, scalable numerical analysis workflow;

[0152] This invention employs a "two-step coupling" or "multi-point input" approach between the soil layer model and the structural model, allowing for flexible adjustment of the soil-structure interaction implementation as needed, ensuring both computational efficiency and accuracy. This method can also be extended to seismic analysis of other complex soil-structure systems (such as urban rail transit and highway bridges), demonstrating good versatility and portability.

[0153] In summary, this invention accurately characterizes the propagation of seismic waves in the soil layer and incorporates multi-point ground motion into the dynamic analysis of the bridge-track system, comprehensively reflecting the real soil-bridge-track coupling effect. This significantly improves the accuracy and reliability of seismic response simulation results for ballastless track in bridge sections, providing more scientific and systematic technical support for the seismic design and post-disaster assessment of high-speed rail and other rail transit systems.

[0154] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0155] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A simulation method for the response of seamless track with ballastless track on a bridge under seismic conditions based on site characteristics and displacement loading, characterized in that, include: S1. Construct a site soil layer model that includes non-uniform soil layers; S2. Simultaneously input transverse and vertical seismic waves at the boundary of the soil layer model of the site to simulate the transmission of ground motion along two paths; S3. Extract the three-dimensional displacement time history of the surface nodes of the soil layer model at the site; S4. Perform response analysis on the three-dimensional displacement time history, and input the three-dimensional displacement time history into the bridge-track coupling model to obtain the dynamic response and damage status of the track structure.

2. The earthquake-induced response simulation method for seamless track on ballastless track over bridges according to claim 1, characterized in that, Step S1 includes: Determine the horizontal and vertical extent of the site soil layer model; Input the soil layer parameters in layers: soft soil layer, clay layer, and bedrock layer; Local differences in soil layers within the same layer are simulated using random fields or partitioned assignment methods. And a perfectly matched layer (PML) absorbing boundary is set at the boundary of the soil layer model of the site.

3. The earthquake-induced response simulation method for seamless track on ballastless track over bridges according to claim 2, characterized in that, The soil parameters include soil thickness, density, elastic modulus, cohesion, internal friction angle, shear wave velocity, Poisson's ratio, and damping ratio.

4. The earthquake-induced response simulation method for seamless track on ballastless track over bridges according to claim 1, characterized in that, Step S2 includes: The lateral and vertical seismic waves are simultaneously applied to the lateral and bottom boundaries of the site soil model; Lateral seismic waves are long-period waves corrected for site characteristics; Vertical seismic waves are seismic waves that have undergone frequency modulation.

5. The earthquake-induced response simulation method for seamless track on ballastless track over bridges according to claim 1, characterized in that, In step S3, the locations of multiple bridge pier pile foundations laid on the ground are used as ground nodes.

6. The earthquake-induced response simulation method for seamless track on ballastless track over bridges according to claim 1, characterized in that, The bridge-track coupling model in step S4 includes: For piers and bridges, solid elements are used to simulate the nonlinear hysteresis characteristics of the supports. The track, track slab and mortar layer adopt cohesion model, the track slabs adopt separable friction contact model, and the limiting structure adopts extended finite element damage model to simulate the shear and tensile stress damage propagation between layers caused by seismic load. The fasteners and rails are simulated using nonlinear spring elements, with linear stiffness in the vertical and lateral directions and frictional contact with resistance considered in the longitudinal direction; the rails are simulated using solid elements.

7. The earthquake-induced response simulation method for seamless track on ballastless track over bridges according to claim 1, characterized in that, In step S4, the dynamic response and damage state of the track structure include: Displacement response is the time history of displacement in the X, Y, and Z directions of the rail, fasteners, track slab, and mortar layer. Internal force distribution, including shear stress, tensile stress and their distribution characteristics between ballastless track layers; Damage propagation refers to the extent of cohesive damage between the track slab and the mortar layer, as well as the cracking behavior of fasteners and limiting structures.

8. The earthquake-induced response simulation method for seamless track on ballastless track over bridges according to claim 1, characterized in that, It also includes step S5, which assesses the load-bearing capacity and analyzes residual deformation based on the dynamic response and damage state of the track structure.

9. A simulation system for the response of seamless track with ballastless track on a bridge under seismic conditions based on site characteristics and displacement loading, characterized in that, The method for simulating the response of seamless track ballastless track on bridges under seismic conditions based on site characteristics and displacement loading, as described in any one of claims 1–8, includes: The site soil modeling module is used to build site soil models that include non-uniform soil layers. The dual-path seismic wave loading module is used to simultaneously input transverse and vertical seismic waves at the boundary of the soil layer model of the site to simulate the transmission of ground motion along two paths. The displacement response extraction module is used to extract the three-dimensional displacement time history of the surface nodes of the site soil model; The track damage assessment module is used to perform response analysis on the three-dimensional displacement time history and input the three-dimensional displacement time history into the bridge-track coupling model to obtain the dynamic response and damage status of the track structure.

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