Multi-scale modeling method for ballastless track on bridge
By using a multi-scale finite element modeling method, the problem of nonlinear damage characterization of ballastless track under strong earthquakes was solved, achieving efficient and accurate damage simulation of ballastless track on bridges and reducing modeling costs.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-31
- Publication Date
- 2026-04-10
AI Technical Summary
Existing multi-scale simulation methods for ballastless tracks cannot accurately characterize the strong nonlinear damage behaviors of ballastless tracks on bridges under strong earthquakes, such as rail fracture, fastener failure, and interlayer separation of structural slabs. Furthermore, full solid modeling is costly and cannot be applied to full bridge models.
A multi-scale finite element modeling method is adopted. The model is reasonably divided according to the stress or damage state of different regions of the components. The base plate and track bed plate are established as elastic solid elements, the rail is a multi-scale model, and the fastener system is a multi-scale model. The ballastless track-bridge system multi-scale finite element model is assembled in finite element software. The explicit central difference method and multi-dimensional verification indicators are combined to ensure computational efficiency and accuracy.
It achieves accurate characterization of the strong nonlinear damage behavior of ballastless track on bridges, while taking into account computational efficiency. It can accurately simulate seismic damage such as rail fracture, fastener failure and track slab separation, and reduces modeling and computation costs.
Smart Images
Figure CN121835284A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of railway bridge modeling and analysis technology, specifically relating to a multi-scale modeling method for ballastless track on bridges. Background Technology
[0002] In assessing the seismically induced nonlinear mechanical behavior and damage evolution of railway bridges, multi-scale finite element numerical simulation methods, with their advantages of both accuracy and efficiency, can serve as a core technology in the analysis process. However, existing methods have many shortcomings in establishing multi-scale models of ballastless track, especially when simulating seismic damage to ballastless track on multi-span bridges. Ballastless track has key components such as rails, fasteners, and structural slabs. Under strong earthquakes, ballastless track on bridges is prone to strong nonlinear damage behaviors such as rail buckling or even fracture, fastener failure, and interlayer separation of structural slabs. Existing multi-scale simulation methods for ballastless track all treat rails as equivalent beam elements, fastener stress as equivalent to linear elastic or ideal elastoplastic constitutive models, and structural slabs as equivalent to shell elements or beam elements. Although the modeling and computational analysis efficiency is very high, it cannot characterize the strong nonlinear damage behavior of ballastless track under seismic damage; and the high modeling and computational costs caused by establishing a solid model make it unsuitable for full-bridge models.
[0003] Therefore, a new multi-scale finite element modeling method is urgently needed, which can not only ensure high computational efficiency but also maintain performance accuracy to accurately characterize the strong nonlinear damage behavior of ballastless track components, especially seismic damage such as rail fracture, fastener failure, and interlayer separation of structural slabs. Summary of the Invention
[0004] In view of this, the purpose of this invention is to provide a multi-scale modeling method for ballastless track on bridges, which addresses the shortcomings of existing technologies, such as the inability of traditional multi-scale models to characterize the strong nonlinear damage behavior of ballastless track caused by seismic damage including rail fracture, fastener failure, and ballast slab separation, as well as the high modeling and computational costs resulting from building entirely solid models. This invention rationally divides the multi-scale model and allocates computational resources by considering the stress or damage states of different regions of the components, balancing computational efficiency with the accuracy of strong nonlinear simulation. This allows for the accurate characterization of the strong nonlinear damage behavior of ballastless track caused by seismic damage, including rail fracture, fastener failure, and ballast slab separation.
[0005] To achieve the above objectives, the present invention provides the following technical solution: This invention provides a multi-scale modeling method for ballastless tracks on bridges, comprising the following steps: S1: Establish a multi-scale finite element model of the bridge system, and define the nonlinear constitutive model of each component of the ballastless track on the bridge according to the characteristics of stress and damage; S2: Establish the base plate and the track bed plate as an elastic solid element model to characterize the seismic damage caused by the gap between the plates and the lifting of the track bed plate; S3: Establish a simplified model of the contact between the base plate and the track slab, as well as the geotextile, elastic pad, and vertical bonding force; S4: Establish a multi-scale model of the rail and its contact with the sleeper; S5: Establish a multi-scale model of the fastener system and its coupling with rails and sleepers; S6: Assemble the multi-scale finite element model of the bridge system, the solid element model of the base plate and the track slab, the multi-scale model of the rail and the multi-scale model of the fastener system in the finite element software to form a multi-scale finite element model of the ballastless track-bridge system, and verify the model.
[0006] Furthermore, in step S1, the nonlinear constitutive model of each component includes: The elastic pad is simulated by the pressure-displacement constitutive relationship to simulate compression deformation; The vertical bonding between the base plate and the track bed plate adopts the bond force-displacement constitutive relationship with failure criteria; The fastening system employs a triaxial resistance-displacement constitutive relation to characterize lateral / longitudinal / vertical failures; Rails are modeled differently according to region: elastic-plastic solid elements with maximum stress failure control are used at beam joints, while elastic-plastic fiber beam elements without failure criteria are used at the mid-span of the beam.
[0007] Furthermore, step S3 specifically includes: S3.1 Establish an automatic surface-to-surface contact model between the base plate and the track bed plate. The normal direction is set to hard contact, the tangential direction is controlled by frictional contact, and the friction coefficient is set to the friction coefficient between the track bed plate / base plate and the geotextile. S3.2 Establish a simplified model of the elastic pad: use nonlinear spring elements that are only under compression for simulation. The central node of the spring is fixedly coupled to the boss node under the track bed plate, and the outer node of the spring is fixedly coupled to the side wall node of the groove in the base plate. S3.3 Establish a simplified model of vertical bonding force: Use nonlinear spring elements for simulation. Arrange spring elements symmetrically and vertically around the track bed slab. The upper node of the spring is fixedly coupled to the track bed slab, and the lower node is fixedly coupled to the base plate.
[0008] Furthermore, step S4 specifically includes: S4.1 Establish a multi-scale model of the rail: The rail at the beam joint adopts a refined solid element model, and the cross section of the solid element is the original cross section of the rail; the rail in the middle of the beam span adopts a fiber beam element model, and the cross section of the fiber beam element is an equivalent I-shaped fiber cross section, and the area of the equivalent I-shaped cross section and the strong and weak axis moments of inertia are equal to the original cross section. S4.2 Establishing contact between rail and sleeper: A surface-to-surface hard contact is established between the rail solid unit and the sleeper; a point-to-surface hard contact is established between the rail fiber beam unit and the sleeper, which is achieved by solid coupling between the sleeper upper surface node and the rail fiber beam unit node. S4.3. Solid elements and fiber beam elements are connected by consolidation coupling.
[0009] Furthermore, step S5 specifically includes: establishing a multi-scale model of the fastener system, wherein the fastener system includes a sleeper, a three-dimensional nonlinear spring unit for the fastener, and a rail; wherein the three-dimensional nonlinear spring unit for the fastener is equivalent to a gap unit in the transverse and vertical directions and a friction unit in the longitudinal direction, and the spring center node is fixedly coupled to the rail node and the outer node is fixedly coupled to the sleeper upper surface node.
[0010] Furthermore, step S6 specifically includes: in the finite element software, assembling the multi-scale finite element model of the bridge system established in S1, the solid element model of the base plate and track slab established in S2, the multi-scale model of the rail established in S4, and the multi-scale model of the fastener system established in S5 to obtain the multi-scale finite element model of the ballastless track-bridge system, and verifying the model by comparing simulation data with actual data.
[0011] Furthermore, in step S4.1, the equivalent I-shaped fiber cross-section must satisfy the following constraints: Area equivalence: ,in, This represents the actual cross-sectional area of the original rail section. The cross-sectional area of the equivalent I-shaped section of the fiber beam element Equivalence of moment of inertia: , ,in, , These are the moments of inertia of the equivalent cross-section of the fiber beam element about the y-axis and z-axis, respectively. , These are the actual moments of inertia of the original cross section of the track about the y-axis and the strong axis z-axis, respectively. Shear Stiffness Correction: Shear Stiffness of Fiber Beam Elements Corrected based on the shear deformation energy of solid elements: In the formula, This is the shear deformation energy correction factor. This is the correction factor for bending deformation energy. This refers to the shear modulus of the rail material. The elastic modulus of the rail material. The length of the fiber beam element; The maximum stress of the equivalent I-shaped fiber cross section satisfies the failure criterion for solid elements: In the formula, This represents the maximum stress on the equivalent cross section of the fiber beam element under load. This is the reduction factor for the yield strength of the rail material. This represents the yield strength of the rail material.
[0012] Furthermore, the explicit central difference method is used in the dynamic simulation of steps S3.2, S4.2, and S5, including the following steps: A1. Time step constraint: based on minimum cell size and material wave velocity Sure: In the formula, The stability coefficient, For the time step of dynamic simulation, The elastic modulus of the material. The density of the material; A2. Interface force transmission: nodal forces of nonlinear spring elements According to displacement difference renew: In the formula, For time step in The nodal force of the nonlinear spring element at any given time. For time step in The nodal force of the nonlinear spring element at any given time. Let be the tangential stiffness of the spring element. They are respectively Time and The relative displacement of the interface at any given moment. The damping coefficient; A3. Real-time Failure Detection: When the inter-plate bonding spring shifts... Or the displacement of the fastener gap unit Failure triggered when threshold is exceeded: in, The threshold value for the inter-plate bonding spring displacement. =2.5~4.0mm, The displacement threshold of the fastener gap unit. =1.2~2.0mm.
[0013] Furthermore, the model validation employs the following quantitative metrics: B1. Modal confidence criterion satisfies: In the formula, For the first Modal confidence values of the first mode. For the simulation model First-order mode vector, The first one measured on site First-order mode vector, The symbol for vector transpose; B2. Damage area error (DRE) must meet the following requirement: rail fracture location error at beam joint ≤ 5%. In the formula, This is the coordinate vector of the rail fracture location obtained from the simulation. The coordinate vector of the rail fracture location in the actual earthquake damage is obtained through the three-dimensional coordinates of the fracture point recorded in the field survey. This refers to the length of the main girder of the bridge. B3. Energy Dissipation Ratio (EDR): Energy dissipation ratio of seismic wave input. Energy dissipation of structures error : In the formula, The duration of the seismic waves, , These are the force vectors and velocity vectors of the key nodes in the simulation model, respectively. These are the force vector and velocity vector measured on-site, respectively.
[0014] The beneficial effects of this invention are as follows: 1. This invention establishes the track bed slab and the base plate as elastic solid units, and equates the bonding and failure process between the plates to vertical nonlinear spring units arranged around the plates, which can simulate the failure process of track bed slab separation and lifting; 2. The multi-scale finite element model of rail established in this invention overcomes the shortcomings of existing all-equivalent beam element models in simulating rail fracture damage at beam joints. 3. This invention equates the horizontal and vertical directions of the fastener to gap elements and the longitudinal direction to friction elements, and uses a nonlinear spring to describe its force process, thus ensuring the three-dimensional failure characteristics of the fastener. 4. The multi-scale finite element model of ballastless track on bridges established in this invention takes into account both computational efficiency and simulation accuracy, and can accurately characterize the seismic-induced nonlinear damage process of ballastless track on bridges.
[0015] Other advantages, objectives, and features of the invention will be set forth in the following description and will be apparent to those skilled in the art in some respects, or may be learned by practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description
[0016] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 This is a flowchart of the modeling method of the present invention; Figure 2 This is a schematic diagram of the nonlinear constitutive structure of the component of the present invention; wherein, Figure 2 (a) is a schematic diagram of the pressure-displacement constitutive model of the elastic pad; Figure 2 (b) is a schematic diagram of the bond force-displacement constitutive model of the plates; Figure 2 (c) is a constitutive model of the transverse resistance-displacement of the bridge; Figure 2 (d) is a schematic diagram of the constitutive frictional resistance part of the transverse bridge resistance of the fastener; Figure 2 (e) is a schematic diagram of the constitutive shoulder and bolt resistance of the transverse bridge resistance-displacement of the fastener; Figure 2 (f) is a constitutive diagram of the vertical resistance-displacement of the fastener; Figure 2 (g) is a constitutive diagram of the longitudinal resistance-displacement of the fastener; Figure 2 (h) is a schematic diagram of the elastic-plastic stress-strain constitutive model of the rail; Figure 3 This is a schematic diagram of the base plate and track bed plate of the present invention; wherein, Figure 3 (a) is a top view of the base plate; Figure 3 (b) is a bottom view of the side of the track bed slab; Figure 3 (c) is a top view of the track bed slab from the side; Figure 4 This is a schematic diagram of the elastic pad model of the present invention; Figure 5 This is a simplified modeling diagram of the vertical spring for the bonding force between the base plate and the track bed plate of the present invention. Figure 6 This is a schematic diagram of the multi-scale modeling of the rail in this invention; wherein, Figure 6 (a) is a multi-scale model of the rail and a schematic diagram of its coupling; Figure 6 (b) is a schematic diagram of the cross-section of a solid element; Figure 6 (c) is a schematic diagram of the cross-section of a fiber beam element; Figure 7 This is a schematic diagram illustrating the contact between the multi-scale model of the rail and the sleeper in this invention; wherein, Figure 7 (a) is a schematic diagram of the contact between the rail solid unit and the sleeper; Figure 7(b) is a schematic diagram of the contact between the steel rail fiber beam unit and the sleeper; Figure 8 This is a schematic diagram of the multi-scale model of the fastener of the present invention; Figure 9 This is a schematic diagram of the multi-scale model of the ballastless track of the present invention; Figure 10 This is a schematic diagram of a multi-scale model of the ballastless track-bridge system of the present invention; Figure 11 This is a model verification diagram for the present invention; wherein, Figure 11 (a) is a schematic diagram of the fastener failure structure; Figure 11 (b) is a schematic diagram of the track bed slab lifting structure; Figure 11 (c) is a schematic diagram of the rail buckling structure; Figure 11 (d) is a schematic diagram of the rail fracture structure. Detailed Implementation
[0017] like Figures 1-11 As shown, this invention provides a multi-scale modeling method for ballastless tracks on bridges, comprising the following steps: S1. Establish a multi-scale finite element model of the bridge system based on existing methods, and define nonlinear constitutive models for each component of the ballastless track on the bridge according to the characteristics of stress and damage: First, decompose the ballastless track into different components and determine the strongly nonlinear stress components and their interactions; based on the actual damage state of each component, combined with existing experimental, research results, or refined finite element simulation results, define constitutive models for the strongly nonlinear stress components and their interactions, specifically including: Based on the elastic deformation characteristics of the elastic pad under compression, the overall stress process of its components is defined as the extrusion force-displacement constitutive model, such as... Figure 2 As shown in (a), the compressive stress is 0 when the compressive deformation displacement is 0, and the compressive deformation displacement is... At that time, the longitudinal bridge compressive force on the elastic pad is The compressive force of the transverse bridge towards the elastic pad is ; Based on the characteristics of vertical bond failure between the base plate and the track slab, the vertical opposing action process between the plates is defined as the bond force-displacement constitutive model, such as... Figure 2 As shown in (b), the inter-plate back-to-back displacement is When the maximum adhesion is reached The displacement between the plates is The adhesive force completely fails at this time; Based on the characteristics of fastener failure in the transverse direction, breakage of the vertical elastic clip, and longitudinal rail friction slippage, the three-dimensional overall damage stress process between the rail and the fastener constraint components is defined as a resistance-displacement constitutive model. The transverse direction includes the superposition of two parts: the friction between the rail and the rail pad, and the resistance of the concrete shoulder and the spiral spike. It should be noted that in the following description of the fastener force-displacement constitutive model, "displacement" refers to the displacement between the rail and the sleeper. The transverse destructive force-displacement constitutive model of the fastener is as follows: Figure 2 As shown in (c), This represents the initial transverse bridge sliding displacement. Transverse displacement of the bridge when the peak resistance of the concrete shoulder is reached. The transverse displacement of the bridge when the concrete shoulder fails under shear stress. This refers to the lateral displacement of the bridge when the spiral spike fails. This refers to the frictional force between the rail and the rail pad. The peak shear failure force of the concrete shoulder is the resultant force of the superposition of the frictional force. The resultant force is the superposition of the yield resistance of the spiral spike and the frictional force; the frictional resistance part of the transverse bridge breaking force-displacement constitutive model of the fastener is as follows: Figure 2 As shown in (d); the concrete shoulder and spiral spike resistance portion of the transverse destructive force-displacement constitutive model of the fastener are as follows: Figure 2 As shown in (e), The peak shear failure force of the concrete shoulder. The yield resistance of the spiral spike; the constitutive model of the vertical breaking force-displacement of the fastener is as follows: Figure 2 As shown in (f), This represents the vertical displacement when the elastic bar yields. This refers to the vertical displacement before the elastic clip separates from the rail. This refers to the initial clamping force of the fastener clip on the rail. This refers to the reaction force exerted on the rail by the spring clip when the rail is pulled upwards and yields. The maximum force before the elastic clip and rail are about to detach; the constitutive model of the longitudinal bridge destructive force-displacement of the fastener is as follows: Figure 2 As shown in (g), The longitudinal displacement is the yield point of longitudinal frictional slip of the rail. It represents the longitudinal frictional slip yield force.
[0018] Based on the post-earthquake fracture phenomenon of rails at the beam joints, the rails at the beam joints are subjected to an elastic-plastic stress-strain constitutive model of steel based on failure control at the maximum stress value; the elastic-plastic constitutive model of the rails is as follows: Figure 2 As shown in (h), For the rail yield stress, This corresponds to the yield point strain. This refers to the rail failure stress (stress limit). This represents the corresponding failure strain.
[0019] Based on the fact that there is no breakage of the rail in the middle of the beam span, the steel rail in the middle of the beam span adopts the elastoplastic stress-strain constitutive model of steel without adding failure.
[0020] S2. Establish the base plate and track slab as solid element models: The base plate and track slab have no obvious plastic damage and are established as elastic solid element models; the top-down view of the 3D mesh of the base plate is as follows. Figure 3 As shown in (a), a groove is provided on each side of the longitudinal bridge; the three-dimensional mesh of the track bed slab is viewed from below at an angle as shown in (a). Figure 3 As shown in (b), a boss is provided on each side of the longitudinal bridge; the top view of the three-dimensional mesh of the track bed slab is as follows. Figure 3 As shown in (c), sleepers are provided on both sides of the transverse bridge along the longitudinal bridge direction; this ensures that the seismic damage caused by the separation between slabs and the lifting of the track slab can be accurately characterized. S3. Establish a simplified model of the contact between the base plate and the track slab, as well as the geotextile, elastic pad, and vertical bonding force: The base plate and the track slab are established as automatic surface-to-surface contact, the normal direction is set as hard contact, and the tangential direction is controlled by frictional contact and set as the friction coefficient between the track slab / base plate and the geotextile. The simplified model of the elastic pads uses two opposing elastic pads as equivalent gap elements, simulated using nonlinear spring elements, and established as compression-only springs. The longitudinal and transverse elastic pads are simplified into two sets of compression-only springs in corresponding directions. Each set contains two spring elements with a common central node. The central node is rigidly coupled to the boss node below the track bed slab, and the outer nodes of the springs are coupled to the corresponding groove sidewall nodes of the base plate. Figure 4 As shown; the simplified model of the vertical adhesion force between the plates is simulated using a nonlinear spring, such as... Figure 5 As shown, six spring units are symmetrically arranged vertically around the track bed slab, located at the four corners and the middle of the two side plates. Each spring at the corner is given 1 / 8 of the force, and each spring in the middle is given 1 / 4 of the force. The upper nodes of the springs are fixedly coupled to the track bed slab, and the lower nodes are fixedly coupled to the base plate, ensuring accurate simulation of the vertical bonding force between the plates. S4. Establish a multi-scale model of the rail and its contact with the sleeper: The multi-scale model of the rail includes a refined solid element model at the beam joint and a fiber beam element model at the middle of the beam span, such as... Figure 6 As shown in (a); the cross-section of the solid unit adopts the original cross-section of the rail ( Figure 6 (b) The fiber beam unit section adopts an equivalent I-shaped fiber section to ensure that the area of the equivalent I-shaped section and the moments of inertia of the strong and weak axes are equal to those of the original section. Figure 6 (c) Assign the corresponding node mass to the beam element nodes; The rail solid unit and the sleeper are established in a surface-to-surface hard contact. Figure 7(a)); The steel rail fiber beam unit is set in point-to-surface contact with the sleeper. The nodes of the beam unit are above the sleeper in the vertical direction. Two free nodes are established on the upper surface of the sleeper. First, the two free nodes are fixedly coupled with the corresponding nodes of the steel rail fiber beam unit. Then, a point-to-surface hard contact is established between the beam unit and the sleeper. Figure 7 (b) The connection between the solid unit and the beam unit is a fixed coupling; S5. Establish a multi-scale model of the fastener system and its coupling with the rail and sleeper: The multi-scale model of the fastener system includes sleepers, three-dimensional nonlinear spring elements of the fasteners, and the rail; the three-dimensional nonlinear spring elements of the fasteners are equivalent to gap elements in the transverse and vertical directions and friction elements in the longitudinal direction, using nonlinear springs to describe their three-dimensional force process. Specifically, in the transverse direction, it is equivalent to two sets of symmetrical spring elements; in the vertical direction, it is equivalent to one spring element; and in the longitudinal direction, it is equivalent to one set of symmetrical spring elements. All springs share a common central node, with the central node rigidly coupled to the rail node and the outer nodes rigidly coupled to the nodes on the upper surface of the sleeper. Figure 8 As shown, this ensures accurate characterization of the damage caused by the failure of the fastener's shoulder in the transverse bridge direction, the shearing of the spiral spike, the breakage of the vertical elastic bar, and the frictional slippage of the rail in the longitudinal bridge direction when the fastener and the sleeper undergo three-way relative displacement.
[0021] The fastener has two sets of symmetrical spring units in the transverse direction, each set consisting of two springs symmetrical in the transverse direction, representing the transverse friction force and the resistance force between the sleeper and the spiral spike, respectively; the fastener has one set of nonlinear spring units in the longitudinal direction, which are symmetrical in the longitudinal direction, representing the longitudinal friction resistance. S6. Establish multi-scale models of each component in finite element software, assemble them into a multi-scale model of the ballastless track on the bridge, and assemble it into the bridge multi-scale model system to obtain a multi-scale finite element model of the ballastless track-bridge system and conduct model verification: A multi-scale model of the ballastless track was established using the LS-DYNA dynamic finite element software. The modeling operation included the following steps: It should be noted that the term "keywords" used in the following description refers to the modeling operation commands of LS-DYNA.
[0022] Based on the design drawings of the ballastless track on the bridge, the model, specifications and dimensions of each component were determined, and then the nonlinear constitutive models of each component were determined: elastic pad extrusion pressure-displacement constitutive model, inter-plate bonding force-displacement constitutive model, fastener triaxial resistance-displacement constitutive model, and rail failure elastoplastic stress-strain constitutive model. The elastic pad compression-displacement constitutive model adopts material keywords. The MAT_SPRING_NONLINEAR_ELASTIC definition specifies that the inter-plate adhesion-displacement constitutive model and the fastener triaxial resistance-displacement constitutive model use material keywords. The MAT_SPRING_GENERAL_NONLINEAR definition specifies that the rail's elastoplastic constitutive model uses material keywords. The MAT_PLASTIC_KINEMATIC definition; the rail failure and non-failure elastoplastic constitutive model requires defining two material indices, where the material indices for defining failure are defined using material failure keywords. MAT_ADD_EROSION imparts failure stress to the rail material; The base plate and track bed plate do not consider nonlinearity, and material keywords are used. Define MAT_ELASTIC; Solid element sections use keywords SECTION_SOLID is defined, and the beam element section uses keywords. SECTION_BEAM definition, spring element cross-section uses keywords SECTION_DISCRETE definition; The solid element models of the base plate and track slab adopt element keywords. The ELEMENT_SOLID definition divides the material into an eight-node hexahedral mesh and assigns it the corresponding index of the elastic material and solid element section keywords. The base plate and the track bed plate are connected by keywords. CONTACT_AUTOMATIC_SURFACE_TO_SURFACE establishes the contact, with the normal direction set as hard contact. The geotextile is simplified to tangential contact friction between plates, and the corresponding sliding friction coefficient is assigned within this keyword to complete the geotextile simplification settings. The vertical adhesion force between the elastic pad and the plate is simplified using the element keyword for the nonlinear spring. The `ELEMENT_DISCRETE` definition assigns serial numbers to the keywords for the defined elastic pad material, inter-plate bonding material, and spring section. The simplified nonlinear springs of the elastic pad are simplified into two sets of springs in the longitudinal and transverse directions, respectively. Each set contains two spring units with a common central node. The central node and the boss node below the track bed slab are connected via keywords. CONSTRAINED_NODAL_RIGID_BODY is a fixed coupling condition where the outer node of the spring is connected to the corresponding base plate groove sidewall node via the keyword. CONSTRAINED_NODAL_RIGID_BODY are respectively fixedly coupled; the simplified nonlinear springs for the inter-plate adhesion force are arranged with 6 spring units symmetrically vertically around the track bed slab, respectively located at the four corners and the middle of the two side plates. Each spring at the corners is given 1 / 8 of the force, and each spring at the middle is given 1 / 4 of the force. The upper nodes of the springs are connected to the track bed slab, and the lower nodes are connected to the base plate via keywords. CONSTRAINED_NODAL_RIGID_BODY ensures accurate simulation of vertical bond forces between plates; The multi-scale model of the steel rail: the solid element model at the beam joint uses element keywords. The ELEMENT_SOLID definition divides the data into an eight-node hexahedral mesh. The mesh elements are then finely subdivided and assigned corresponding rail failure material and solid element section keyword numbers. The fiber section of the equivalent I-beam of the rail at mid-span is represented using integral point beam element section keywords. INTEGRATION_BEAM is defined and assigned to the keyword. SECTION_BEAM completes the creation of fiber beam element sections, using keywords. The ELEMENT_BEAM definition assigns the corresponding rail non-failure material and fiber beam element section; Keyword is used at the interface between the solid rail element and the equivalent fiber beam element. CONSTRAINED_NODAL_RIGID_BODY performs consolidation coupling to form a bound rigid arm, making it bear the force as a whole; The multi-scale model of the rail is in contact with the sleeper: the solid element model of the rail and the sleeper use keywords. CONTACT_AUTOMATIC_SURFACE_TO_SURFACE establishes contact; Since the equivalent fiber beam element of the rail cannot establish contact with the sleeper, two free nodes are created on the upper surface of the sleeper in the transverse direction, and these free nodes are then connected to the sleeper. CONTACT_AUTOMATIC_NODES_TO_SURFACE establishes contact and uses keywords to connect with the rail. CONSTRAINED_NODAL_RIGID_BODY performs consolidation coupling and generates rigid arms, which transmit contact forces. The contact settings normals are all automatically established as hard contact, the tangential friction coefficient between the rail and the sleeper is set to 0, and the friction between the two is given to the fastener multi-scale model. The triaxial nonlinear spring element of the fastener multi-scale model adopts the element keyword. The SECTION_DISCRETE definition represents two sets of spring elements in the transverse direction, one spring element in the vertical direction, and one set of spring elements in the longitudinal direction. Each set of springs in the transverse and longitudinal directions consists of two symmetrically arranged spring elements, each assigned a corresponding fastener failure resistance material and spring element section number. All springs in the fastener share a common center node, located at the center of the sleeper's top surface and connected to the rail node using keywords. CONSTRAINED_NODAL_RIGID_BODY is used for consolidation coupling, and the outer node and the sleeper upper surface node are connected using the keyword. CONSTRAINED_NODAL_RIGID_BODY performs consolidation coupling; The force-displacement constitutive curves assigned to the spring unit are such that when the force and displacement of the curve are positive, the spring is under tension; when the force and displacement of the curve are negative, the spring is under compression. Assemble and model all the multi-scale models of the components in the modeling order to build a multi-scale model of the ballastless track on the bridge. Figure 8 The modeling results of the ballastless track are displayed, with the illustration showing a multi-scale model of the ballastless track on both sides of the longitudinal beam joint and the one-way section. The multi-scale model of the ballastless track on the bridge is assembled into the bridge multi-scale model system to obtain a multi-scale finite element model of the ballastless track-bridge system, as shown below. Figure 10 As shown; Ballastless track system boundary: the contact surface between the ballastless track base plate and the upper surface of the main beam; Ballastless track system boundary setting: the ballastless track base plate and the upper surface of the main beam are fixedly coupled to simulate the constraint effect of the shear steel bar; Ballastless track-bridge system boundary: pile foundation model; Ballastless track-bridge system boundary setting: apply near-fault pulse-type ground motion time history to the pile foundation model; Near-fault pulse-type seismic time-history loading was applied to the pile foundation of the ballastless track-bridge system. The accuracy of the simulation under strong nonlinear conditions was verified by successfully reproducing seismic damage caused by rail buckling, rail fracture, fastener failure, and track slab lifting on the bridge. Figure 11 As shown, the reliability verification of the model is completed.
[0023] In one embodiment of the present invention, the equivalent I-shaped fiber cross-section must satisfy the following constraints: Area equivalence: ,in, This represents the actual cross-sectional area of the original rail section. This represents the cross-sectional area of the equivalent I-shaped section of the fiber beam element. Equivalence of moment of inertia: , ,in, , These are the moments of inertia of the equivalent cross-section of the fiber beam element about the y-axis and z-axis, respectively. , These are the actual moments of inertia of the original cross section of the track about the y-axis and the strong axis z-axis, respectively. Shear Stiffness Correction: Shear Stiffness of Fiber Beam Elements Corrected based on the shear deformation energy of solid elements: In the formula, This is the shear deformation energy correction factor. This is the correction factor for bending deformation energy. This refers to the shear modulus of the rail material. The elastic modulus of the rail material. The length of the fiber beam element; The maximum stress of the equivalent I-shaped fiber cross section satisfies the failure criterion for solid elements: In the formula, This represents the maximum stress on the equivalent cross section of the fiber beam element under load. This is the reduction factor for the yield strength of the rail material. This represents the yield strength of the rail material.
[0024] This scheme breaks through the traditional equivalent model that only considers geometric parameters, and introduces shear stiffness correction and failure control compatibility to solve the problems of shear deformation distortion and fracture misjudgment of fiber beam elements in earthquake damage simulation.
[0025] In one embodiment of the present invention, the simplified model of the elastic pad, the rail-sleeper contact, and the coupling of the fastener system are simulated using the following explicit central difference method: A1. Time step constraint: based on minimum cell size and material wave velocity Sure: In the formula, The stability coefficient, For the time step of dynamic simulation, The elastic modulus of the material. The density of the material; A2. Interface force transmission: nodal forces of nonlinear spring elements According to displacement difference renew: In the formula, For time step in The nodal force of the nonlinear spring element at any given time. For time step in The nodal force of the nonlinear spring element at any given time. Let be the tangential stiffness of the spring element. They are respectively Time and The relative displacement of the interface at any given moment. The damping coefficient; A3. Real-time Failure Detection: When the inter-plate bonding spring shifts... Or the displacement of the fastener gap unit Failure triggered when threshold is exceeded: in, The threshold value for the inter-plate bonding spring displacement. =2.5~4.0mm, The displacement threshold of the fastener gap unit. =1.2~2.0mm.
[0026] This scheme proposes a multi-scale interface collaborative solution algorithm to solve the convergence problem of traditional implicit iteration at contact / failure. By using explicit time step constraints and damped force updates, it ensures the stability of high-frequency impacts in earthquake damage simulation; the failure criterion enables real-time damage propagation.
[0027] In one embodiment of the present invention, the model validation employs the following quantitative metrics: B1. Modal confidence criterion satisfies: In the formula, For the first Modal confidence values of the first mode. For the simulation model First-order mode vector, The first one measured on site First-order mode vector, The symbol for vector transpose; B2. Damage area error (DRE) must meet the following requirement: rail fracture location error at beam joint ≤ 5%. In the formula, This is the coordinate vector of the rail fracture location obtained from the simulation. The coordinate vector of the rail fracture location in the actual earthquake damage is obtained through the three-dimensional coordinates of the fracture point recorded in the field survey. This refers to the length of the main girder of the bridge. B3. Energy Dissipation Ratio (EDR): Energy dissipation ratio of seismic wave input. Energy dissipation of structures error : In the formula, The duration of the seismic waves, , These are the force vectors and velocity vectors of the key nodes in the simulation model, respectively. These are the force vector and velocity vector measured on-site, respectively.
[0028] This scheme overcomes the limitations of traditional methods that only compare displacement / force by establishing a multi-dimensional verification index system (dynamic characteristics / damage location / energy conservation); MAC ensures modal accuracy, DRE constrains the location error of key earthquake damage, and EDR verifies the authenticity of nonlinear energy consumption, forming a closed-loop verification chain.
[0029] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made to it in form and detail without departing from the scope defined by the claims of the present invention.
Claims
1. A multi-scale modeling method for ballastless track on bridges, characterized in that, Includes the following steps: S1: Establish a multi-scale finite element model of the bridge system, and define the nonlinear constitutive model of each component of the ballastless track on the bridge according to the characteristics of stress and damage; S2: Establish the base plate and the track bed plate as an elastic solid element model to characterize the seismic damage caused by the gap between the plates and the lifting of the track bed plate; S3: Establish a simplified model of the contact between the base plate and the track slab, as well as the geotextile, elastic pad, and vertical bonding force; S4: Establish a multi-scale model of the rail and its contact with the sleeper; S5: Establish a multi-scale model of the fastener system and its coupling with rails and sleepers; S6: Assemble the multi-scale finite element model of the bridge system, the solid element model of the base plate and the track slab, the multi-scale model of the rail and the multi-scale model of the fastener system in the finite element software to form a multi-scale finite element model of the ballastless track-bridge system, and verify the model.
2. The multi-scale modeling method for ballastless track on bridges according to claim 1, characterized in that: In step S1, the nonlinear constitutive model of each component includes: The elastic pad is simulated by the pressure-displacement constitutive relationship to simulate compression deformation; The vertical bonding between the base plate and the track bed plate adopts the bond force-displacement constitutive relationship with failure criteria; The fastening system employs a triaxial resistance-displacement constitutive relation to characterize lateral / longitudinal / vertical failures; Rails are modeled differently according to region: elastic-plastic solid elements with maximum stress failure control are used at beam joints, while elastic-plastic fiber beam elements without failure criteria are used at the mid-span of the beam.
3. The multi-scale modeling method for ballastless track on bridges according to claim 2, characterized in that: Step S3 specifically includes: S3.1 Establish an automatic surface-to-surface contact model between the base plate and the track bed plate. The normal direction is set to hard contact, the tangential direction is controlled by frictional contact, and the friction coefficient is set to the friction coefficient between the track bed plate / base plate and the geotextile. S3.2 Establish a simplified model of the elastic pad: use nonlinear spring elements that are only under compression for simulation. The central node of the spring is fixedly coupled to the boss node under the track bed plate, and the outer node of the spring is fixedly coupled to the side wall node of the groove in the base plate. S3.3 Establish a simplified model of vertical bonding force: Use nonlinear spring elements for simulation. Arrange spring elements symmetrically and vertically around the track bed slab. The upper node of the spring is fixedly coupled to the track bed slab, and the lower node is fixedly coupled to the base plate.
4. The multi-scale modeling method for ballastless track on bridges according to claim 3, characterized in that: Step S4 is as follows: S4.1 Establish a multi-scale model of the rail: The rail at the beam joint adopts a refined solid element model, and the cross section of the solid element is the original cross section of the rail; the rail in the middle of the beam span adopts a fiber beam element model, and the cross section of the fiber beam element is an equivalent I-shaped fiber cross section, and the area of the equivalent I-shaped cross section and the strong and weak axis moments of inertia are equal to the original cross section. S4.2 Establishing contact between rail and sleeper: A surface-to-surface hard contact is established between the rail solid unit and the sleeper; a point-to-surface hard contact is established between the rail fiber beam unit and the sleeper, which is achieved by solid coupling between the sleeper upper surface node and the rail fiber beam unit node. S4.
3. Solid elements and fiber beam elements are connected by consolidation coupling.
5. The multi-scale modeling method for ballastless track on bridges according to claim 4, characterized in that: Step S5 specifically includes: establishing a multi-scale model of the fastener system, which includes a sleeper, a three-dimensional nonlinear spring unit for the fastener, and a rail; wherein, the three-dimensional nonlinear spring unit for the fastener is equivalent to a gap unit in the transverse and vertical directions and a friction unit in the longitudinal direction, with the spring center node being fixedly coupled to the rail node and the outer node being fixedly coupled to the sleeper upper surface node.
6. The multi-scale modeling method for ballastless track on bridges according to claim 1, characterized in that: Step S6 specifically includes: in the finite element software, assembling the multi-scale finite element model of the bridge system established in S1, the solid element model of the base plate and track slab established in S2, the multi-scale model of the rail established in S4, and the multi-scale model of the fastener system established in S5 to obtain the multi-scale finite element model of the ballastless track-bridge system, and verifying the model by comparing simulation data with actual data.
7. The multi-scale modeling method for ballastless track on bridges according to claim 4, characterized in that: In step S4.1, the equivalent I-shaped fiber cross-section must satisfy the following constraints: Area equivalence: ,in, This represents the actual cross-sectional area of the original rail section. The cross-sectional area of the equivalent I-shaped section of the fiber beam element Equivalence of moment of inertia: , ,in, , These are the moments of inertia of the equivalent cross-section of the fiber beam element about the y-axis and z-axis, respectively. , These are the actual moments of inertia of the original cross section of the track about the y-axis and the strong axis z-axis, respectively. Shear Stiffness Correction: Shear Stiffness of Fiber Beam Elements Corrected based on the shear deformation energy of solid elements: In the formula, This is the shear deformation energy correction factor. This is the correction factor for bending deformation energy. This refers to the shear modulus of the rail material. The elastic modulus of the rail material. The length of the fiber beam element; The maximum stress of the equivalent I-shaped fiber cross section satisfies the failure criterion for solid elements: In the formula, This represents the maximum stress on the equivalent cross section of the fiber beam element under load. This is the reduction factor for the yield strength of the rail material. This represents the yield strength of the rail material.
8. The multi-scale modeling method for ballastless track on bridges according to claim 5, characterized in that: The explicit central difference method is used in the dynamic simulation of steps S3.2, S4.2, and S5, and includes the following steps: A1. Time step constraint: based on minimum cell size and material wave velocity Sure: In the formula, The stability coefficient, For the time step of dynamic simulation, The elastic modulus of the material. The density of the material; A2. Interface force transmission: nodal forces of nonlinear spring elements According to displacement difference renew: In the formula, For time step in The nodal force of the nonlinear spring element at any given time. For time step in The nodal force of the nonlinear spring element at any given time. Let be the tangential stiffness of the spring element. They are respectively Time and The relative displacement of the interface at any given moment. The damping coefficient; A3. Real-time Failure Detection: When the inter-plate bonding spring shifts... Or the displacement of the fastener gap unit Failure triggered when threshold is exceeded: in, The threshold value for the inter-plate bonding spring displacement. =2.5~4.0mm, The displacement threshold of the fastener gap unit. =1.2~2.0mm.
9. The multi-scale modeling method for ballastless track on bridges according to claim 6, characterized in that: The model validation uses the following quantitative metrics: B1. Modal confidence criterion satisfies: In the formula, For the first Modal confidence values of the first mode. For the simulation model First-order mode vector, The first one measured on site First-order mode vector, The symbol for vector transpose; B2. Damage area error (DRE) must meet the following requirement: rail fracture location error at beam joint ≤ 5%. In the formula, This is the coordinate vector of the rail fracture location obtained from the simulation. The coordinate vector of the rail fracture location in the actual earthquake damage is obtained through the three-dimensional coordinates of the fracture point recorded in the field survey. This refers to the length of the main girder of the bridge. B3. Energy Dissipation Ratio (EDR): Energy dissipation ratio of seismic wave input. Energy dissipation of structures error : In the formula, The duration of the seismic waves, , These are the force vectors and velocity vectors of the key nodes in the simulation model, respectively. These are the force vector and velocity vector measured on-site, respectively.