Track irregularity calculation method of high-speed railway track bridge system
By establishing a mapping relationship between the vertical deformation of the beam and the additional deformation of the rail, the Rayleigh-Ritz method is used to calculate the rail irregularity, which solves the problem that the existing technology cannot quantify the rail irregularity and provides a theoretical basis for assessing the safety of train operation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HEFEI UNIV OF TECH
- Filing Date
- 2026-03-19
- Publication Date
- 2026-04-17
AI Technical Summary
Existing technologies lack effective methods for quantifying earthquake-induced rail irregularities in high-speed railway track and bridge systems, making it impossible to accurately assess the degree of rail irregularities under seismic loading and their impact on train operation safety.
By establishing the mapping relationship between the vertical deformation of the beam and the additional deformation of the rail, the rail displacement matrix is derived using the Rayleigh-Ritz method. The ratio of the rail deformation amplitude to the length of the deformation area is defined as the rail irregularity. The rail irregularity under different vertical deformation conditions of the beam is then calculated.
It enables a comprehensive quantification of rail irregularities under seismic loading, providing a reliable theoretical basis for the safety and stability of high-speed railway train operation after an earthquake, and enabling a more accurate assessment of the impact of rail irregularities on train operation.
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Figure CN121881484A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of bridge safety analysis technology, specifically a method for calculating track irregularities in a high-speed railway track bridge system. Background Technology
[0002] CRTS III slab track is an emerging high-speed railway track system suitable for the construction of lines with speeds of 300 km / h and above. CRTS III slab track consists of components such as rails, elastic fasteners, track slabs, self-compacting concrete filling layers, and bases. Together with widely used simply supported beam bridges, it forms the CRTS III slab track simply supported beam bridge system for high-speed railways.
[0003] Based on the structural characteristics of simply supported beam bridge systems, the CRTS III type slab track is a unit slab, and its base plate is tightly connected to the main beam through pre-embedded steel bars. Therefore, under seismic loading, when the main beam undergoes vertical deformation, the base plate will move along with the main beam under the action of the tensile force of the pre-embedded steel bars and its own weight, and its own deformation will be almost negligible.
[0004] The composite slab, consisting of the base plate, the self-compacting concrete filling layer, and the track slab, experiences almost no vertical tension due to the presence of an isolation layer. However, the presence of grooves and bosses between the base plate and the self-compacting concrete filling layer, along with the composite slab's own weight, causes it to move along with the base plate. The presence of fasteners ultimately leads to corresponding deformation of the rails. In other words, the bridge-rail interaction results in additional unevenness in the rails. Figure 1 shows a schematic diagram of the vertical deformation of the beam and the mapped deformation of the rail in the CRTS III type slab track simply supported beam bridge system for high-speed railways.
[0005] There is a lack of effective quantitative methods for measuring the additional irregularities in the rails of high-speed railway track bridge systems caused by vibration, which urgently needs to be addressed. Summary of the Invention
[0006] To address the technical problems existing in the prior art, this invention provides a method for calculating track irregularity in a high-speed railway track bridge system. By establishing a mapping relationship between the vertical deformation of the beam and the additional deformation of the rail, and on this basis quantifying the rail irregularity, the method accurately reveals the degree of rail irregularity under seismic loading and its impact on train operation safety.
[0007] To achieve the above objectives, the present invention provides the following technical solution: This invention discloses a method for calculating track irregularity in high-speed railway track bridge systems, applied to CRTSⅢ type slab track simply supported beam bridge systems. The calculation method includes: S1. Based on the Rayleigh-Ritz method, the mapping relationship between the vertical deformation of the beam and the additional deformation of the rail is derived, and the rail displacement matrix at all fastener positions is obtained.
[0008] S2. Define the ratio of rail deformation amplitude to deformation zone length as rail irregularity, and calculate rail irregularity under different beam vertical deformation conditions accordingly; wherein, the rail deformation amplitude is the sum of the positive deformation amplitude and the negative deformation amplitude of the rail, obtained from the rail displacement matrix of all fastener positions.
[0009] As a further improvement to the above scheme, the CRTS Ⅲ type slab track simply supported beam bridge system includes, from top to bottom, rails, fasteners, track slabs, self-compacting concrete filling layer, base plate, box girder, supports, and piers; wherein, the rails are fixed to the track slabs by fasteners, the track slabs, self-compacting concrete filling layer, and base plate form a composite slab, an isolation layer is provided between the self-compacting concrete filling layer and the base plate, the base plate is fixedly connected to the box girder by pre-embedded steel bars, and the box girder is supported on the piers by supports.
[0010] As a further improvement to the above scheme, in step S1, the gravity equilibrium state of the CRTS Ⅲ type slab track simply supported beam bridge system is taken as the initial state. When deriving the mapping relationship between the vertical deformation of the beam and the additional deformation of the rail, the mechanical equilibrium equation used does not include the gravity term. In this case, the base plate and the box girder are modeled as a deformation-coordinated whole. The reaction effect of the rail on the vertical deformation of the bridge structure is not considered in the calculation process. The rail of the roadbed section is simplified to a simply supported boundary. The boundary effect of the roadbed section is eliminated by taking a set calculation length of the roadbed section. The fastener is modeled as a Winker linear spring uniformly distributed along the center line of the rail, and the isolation layer is modeled as a Winker linear spring uniformly distributed along the center line of the base plate.
[0011] As a further improvement to the above scheme, in step S1, the influence coefficient matrix of the fastener force on the rail displacement is... The expression is: ; In the formula, Representation matrix The element in the i-th row and j-th column; ; n is a positive integer greater than 1. This refers to the total length of the rails. The equivalent cross-sectional moment of inertia of the rail; The elastic modulus of the rail; This represents the x-axis coordinate value of the i-th fastener. This represents the x-axis coordinate value of the j-th fastener; M represents the number of track slabs in the CRTS Ⅲ type slab track simply supported beam bridge system. Each track slab has N fasteners, so there are a total of MN fasteners.
[0012] As a further improvement to the above scheme, in step S1, when deriving the mapping relationship between the vertical deformation of the beam and the additional deformation of the rail, a single track slab is modeled as a free beam structure, and trigonometric functions are used as basis functions to approximate the vertical displacement of the track slab. The total potential energy function of the track slab is derived by combining the fastener force and the spring force of the isolation layer in order to solve the deformation of the track slab in the bridge section.
[0013] As a further improvement to the above scheme, the foundation deformation of the roadbed section is simulated using equivalent Winker spring stiffness. The track slab of the roadbed section is subjected to the combined action of fastener force and roadbed spring force. The deformation solution process of the track slab of the roadbed section is the same as that of the track slab of the bridge section.
[0014] This invention also discloses a bridge safety assessment method, comprising: Using the track irregularity calculation method of a high-speed railway track bridge system as described above, the rail irregularity of the CRTS Ⅲ type slab track simply supported beam bridge system to be tested is calculated. The safety of train travel on the bridge is assessed based on the rail irregularity, and the rail irregularity is negatively correlated with the safety of train travel on the bridge.
[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention proposes a method for calculating rail irregularity by establishing a mapping relationship between the vertical deformation of the beam and the additional deformation of the rail. Compared with using only deformation amplitude or length as indicators, this method can more comprehensively and quantitatively reflect the degree of rail irregularity under seismic action and its impact on train operation safety, thus providing a reliable theoretical basis and calculation method for evaluating the safety and stability of high-speed railway train operation after an earthquake. Attached Figure Description
[0016] Figure 1 This is a schematic diagram of the vertical deformation of the CRTS Ⅲ type slab track simply supported beam bridge system for high-speed railways.
[0017] Figure 2 This is a flowchart of the method for calculating track irregularity in a high-speed railway track bridge system according to Embodiment 1 of the present invention.
[0018] Figure 3 This is a diagram of the mechanical model of the rail in Embodiment 1 of the present invention.
[0019] Figure 4 This is a diagram of the bridge mechanics model in Embodiment 1 of the present invention.
[0020] Figure 5 This is a flowchart illustrating the derivation of the refined analytical expression for rail mapping deformation in Embodiment 1 of the present invention. Detailed Implementation
[0021] 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.
[0022] Example 1: Please refer to Figures 1-5 This embodiment provides a method for calculating track irregularity in a high-speed railway track bridge system, applied to a CRTS III type slab track simply supported beam bridge system, in which the rails are fixedly installed on the track slab of the beam by fasteners; the calculation method includes: S1. Based on the Rayleigh-Ritz method, the mapping relationship between the vertical deformation of the beam and the additional deformation of the rail is derived, and the rail displacement matrix at all fastener positions is obtained. The detailed derivation process will be given below.
[0023] S2. Define the ratio of rail deformation amplitude to deformation zone length as rail irregularity, and calculate rail irregularity under different beam vertical deformation conditions accordingly; wherein, the rail deformation amplitude is the sum of the positive deformation amplitude and the negative deformation amplitude of the rail, obtained from the rail displacement matrix of all fastener positions.
[0024] Depend on Figure 1 As shown, the CRTS Ⅲ type slab track simply supported beam bridge system includes, from top to bottom, rails, fasteners, track slabs, self-compacting concrete filling layer, base plate, box girder, supports, and piers. The rails are fixed to the track slabs by fasteners. The track slabs, self-compacting concrete filling layer, and base plate form a composite slab. An isolation layer is provided between the self-compacting concrete filling layer and the base plate. The base plate is fixedly connected to the box girder by pre-embedded steel bars. The box girder is supported on the piers by supports.
[0025] In this embodiment, to establish a theoretical calculation model for the vertical deformation of the beam and the additional irregularities of the rail in the CRTS III type slab track simply supported beam bridge system of high-speed railway, the following basic assumptions are made: (1) When performing force analysis on the system, the gravity equilibrium state of the system is taken as the initial state, and the influence of gravity is ignored during the calculation process.
[0026] (2) Since the base plate and the beam are connected by pre-embedded steel bars, they have a strong inter-layer constraint effect. It is assumed that the deformation of the base plate and the beam is coordinated.
[0027] (3) The vertical bending stiffness of the bridge is much greater than that of the track system, and the influence of the rails on the deformation of the bridge structure is ignored.
[0028] (4) The rails in the roadbed section are simplified to simply supported boundaries, and the boundary effect of the rails in the roadbed section is eliminated by taking a sufficient calculated length of the roadbed section.
[0029] (5) The fastening system is considered to be Winker linear springs evenly distributed along the center line of the rail, and the isolation layer is considered to be Winker linear springs evenly distributed along the center line of the base plate.
[0030] The following section will elaborate on the derivation process of the mapping relationship between the vertical deformation of the beam and the additional deformation of the rail.
[0031] First, calculate the rail displacement, assuming the total number of track slabs in the entire CRTS III type slab track simply supported beam bridge system of the high-speed railway is... Six track slabs are arranged on each standard 32m simply supported beam and on the roadbed at both ends. Each track slab has If there are 10 fasteners, then there are a total of 100 fasteners. individual fasteners and A simply supported beam.
[0032] Based on the above assumptions, the mechanical model diagram of the rail is as follows: Figure 3 As shown. Assume the rail's mapped deformation is... Then the simply supported boundary conditions of the rail can be expressed as (Equation 1): (1) In Equation 1 above, This refers to the total length of the rails. and These represent the mapped deformation of the rail at position x=0 (the starting point of the rail) and the acceleration of the rail at position x=0 (the starting point of the rail), respectively. and Let x = lg and x = lg, respectively, represent the mapped deformation of the rail at position x = lg (the end point of the rail) and the acceleration of the rail at position x = lg (the end point of the rail).
[0033] Taking the sine function as the basis function, the rail mapping deformation curve can be approximately expressed as (Equation 2): (2) In Equation 2 above, It is an arbitrary constant; , where n is an integer greater than 1.
[0034] Total potential energy of the rail under fastener force It can be expressed as (Equation 3): (3) In the formula, The elastic modulus of the rail. The equivalent cross-sectional moment of inertia of the rail, Let the fastening force be that of the i-th fastener. , This represents the mapped deformation of the rail at position x; Let be the mapped deformation of the rail at the i-th fastener position.
[0035] Substituting equation 2 into equation 3, we obtain equation 4, as follows: (4) According to the Rayleigh-Ritz method, when the structure is in equilibrium, for any They all Therefore, we can obtain (Equation 5): (5) Solving for this, we get (Equation 6): (6) Substituting equation 6 into equation 2, we get: (7) Rearranging it into matrix form, it can be represented as (Equation 8): (8) This formula is used to reflect the displacement of the rail.
[0036] Where the matrix (Equation 9) is: (9) for For (Equation 10): (10) In the formula: For the fastener force matrix, Let A be the rail displacement matrix for all fastener positions, and let A be the influence coefficient matrix of fastener force on rail displacement. Let represent the element in the i-th row and j-th column of matrix A, where n is a positive integer greater than 1. This refers to the total length of the rails. The equivalent cross-sectional moment of inertia of the rail; The elastic modulus of the rail; This represents the x-axis coordinate value of the i-th fastener. This represents the x-axis coordinate value of the j-th fastener; M represents the number of track slabs in the CRTS Ⅲ type slab track simply supported beam bridge system. Each track slab has N fasteners, so there are a total of MN fasteners.
[0037] Then, the beam displacement is calculated, and the bridge mechanical model is as follows: Figure 4 As shown. Assume the... If the pier experiences vertical deformation, but the corresponding support does not, then the... Displacement function of the span beam (left span of the deformable pier) It can be expressed as (Equation 11): (11) No. Displacement function of the span beam (right span of the deformable pier) It can be expressed as (Equation 12): (12) According to Equations 11-12, the beam displacement matrix at the corresponding fastener location can be expressed as (Equation 13): (13) In the formula: For the length of a single-span beam, This represents the vertical deformation of the bridge pier. This is the matrix of influence coefficients between the vertical deformation of the bridge piers and the bridge displacement. The beam spacing is [value].
[0038] Next, the track slab displacement is calculated. Considering a single track slab as a free beam structure, and taking trigonometric functions as basis functions, the track slab displacement function is then obtained. It can be approximated as (Equation 14): (14) In the formula: D is an arbitrary constant, Indicates the displacement of the beam. m and m is the influence coefficient matrix of the fastener force on the track slab. This refers to the length of a single track slab.
[0039] Taking the vertical deformation of the first pier as an example, the displacement function of the first track slab on the left side of the first span of the beam (6 track slabs are laid on each of the two roadbed sections, so the first track slab on the left side of the first span of the beam is the 7th track slab in the global coordinate system) is as follows. It can be expressed as (Equation 15): (15) In the formula: , The length of a single track slab. The coordinates are local coordinates with the left end of a certain track slab as the origin. For the spacing between boards, , Taking the vertical deformation of the first pier as an example, the influence coefficient matrix of the fastener force on the first track slab on the left side of the first span of the beam (6 track slabs are laid on each of the two roadbed sections, so the first track slab on the left side of the first span of the beam is the 7th track slab in the global coordinate system) is as follows: This represents the displacement function of the first span beam (the left span of the deformed pier) where the first pier has undergone vertical deformation but the corresponding support has not.
[0040] In the bridge section, the track slab is subjected to the combined forces of the fasteners and the spring forces of the insulating layer, and the total potential energy of the track slab is... It can be expressed as (Equation 16): (16) In the formula: The elastic modulus of the track slab. The moment of inertia of the equivalent cross section of the track slab, The Winker springs distribute the force in the isolation layer of the bridge section. ; The Winker spring stiffness is used for the isolation layer. Let represent the fastening force of the i-th fastener, and D represent the vertical rigid body translation constant term.
[0041] From the torque balance of the track slab, we can obtain (Equation 17): (17) From the vertical force balance of the track slab, we can obtain (Equation 18): (18) In the formula, This indicates that it was calculated.
[0042] Substituting equations 17 and 18 into equation 16 yields equation (19): (19) According to Ruili-Rizfa Thus, we obtain (Equation 20): (20) According to Ruili-Rizfa Thus, we obtain (Equation 21): (twenty one) in, Taking the vertical deformation of the first pier as an example, the influence coefficient matrix of the fastener force on the first track slab on the left side of the first span beam (6 track slabs are laid on each of the two roadbed sections, so the first track slab on the left side of the first span beam is the 7th track slab in the overall coordinate system); Let m be the total number of track slabs, and let p be the matrix representing the influence coefficients of the fastener force on the p-th track slab from the left end. Similarly, for the p-th track slab, we have (Equation 22): (twenty two) Equation 23: (twenty three), Substituting equations 18, 22, and 23 into equation 14, we obtain (as shown in equation 24 below): (twenty four) in, This represents the displacement of the track slab at the j-th fastener position of the p-th track slab. This represents the x-axis coordinate value of the i-th fastener.
[0043] Equation 24 can be expressed in matrix form as follows: As shown in equation 25: (25) in, The fastener force matrix of the p-th track slab The influence coefficient matrix of the fastener force on the p-th track slab. To and , , Identity matrices of the same dimension Let represent the beam displacement matrix of the p-th track slab.
[0044] in, Based on the following equation 26: (26) in, express The element in the pNth row and pNth column of the matrix.
[0045] In this embodiment (Equation 27): (27) in, express The element corresponding to row i and column j in the matrix, This represents the x-axis coordinate value of the j-th fastener.
[0046] Formula 28: (28) Equation 29: (29) in, Representation matrix The elements in.
[0047] Influence coefficient matrix of fastener force on track slab , This can be expressed as (Equations 30 and 31): (30) (31) in, , These represent the influence coefficient matrix of the fastening force on the Mth track slab.
[0048] The displacement matrix of the track plate at all fastener positions can be expressed as (Equation 32): (32)
[0049] in, This represents the beam displacement matrix at all fastener locations. This represents the track plate displacement matrix for all fastener positions.
[0050] For the subgrade section, the foundation deformation is simulated using the equivalent Winker spring stiffness. Therefore, the equivalent Winker spring distributed force... It can be expressed as (Equation 33): (33) In the formula: The equivalent Winker spring stiffness for the foundation deformation of the roadbed section. This represents the displacement of the beam.
[0051] In the subgrade section, the track slab is subjected to the combined forces of fasteners and subgrade springs. The deformation of the track slab in the subgrade section is similar to that in the bridge section. It should be noted that the interaction between the subgrade and the track slab is simulated using springs, and there is a subgrade spring force between them.
[0052] Finally, a mapping relationship parsing model is generated: make For the equivalent stiffness of the fastener, then the first... The force of a fastener can be expressed as (Equation 34): (34) in, Let be the mapped deformation of the rail at the i-th fastener position. For the deformation of the track plate at the i-th fastener position The fastener force is expressed in matrix form as (Equation 35): (35) in, The formula represents the displacement matrix of the track slab at all fastener positions minus the linear deformation of the rail; the entire formula reflects the force relationship of the fasteners.
[0053] The combined formulas 8, 13, 32, and 35 can represent the fastener force matrix as the vertical deformation of the bridge pier. Single-valued function (Formula 36): (36) In the formula: Let be the identity matrix with the same dimensions as A, B, and C.
[0054] Substituting Equation 36 into Equation 8, we obtain the analytical expression for the rail's mapped deformation as a function of the vertical deformation (Equation 37): (37) The derivation process of the refined analytical expression for rail mapping deformation is as follows: Figure 5 As shown.
[0055] In step S2, the ratio of the rail deformation amplitude (the sum of the positive and negative amplitudes) to the length of the rail deformation region is defined as the rail irregularity. Therefore, the rail irregularity can be expressed as (Equation 38): (38) In the formula, This indicates the amplitude of the positive deformation of the rail, in meters (m). This indicates the magnitude of the reverse deformation of the rail, in meters (m). This indicates the length of the rail deformation zone, in meters (m). This indicates the rail irregularity; wherein the rail deformation amplitude is the sum of the positive and negative deformation amplitudes of the rail, obtained from the rail displacement matrix at all fastener positions.
[0056] In this embodiment, the calculation results of rail irregularity corresponding to different vertical deformation amplitudes of the beam were also statistically analyzed, as shown in Table 1.
[0057] Table 1: Rail irregularity under different vertical deformation amplitudes of the beam ; As can be seen from Table 1, as the vertical deformation amplitude of the beam increases, the rail irregularity gradually increases. The greater the rail irregularity, the greater the impact on the safe and stable operation of high-speed trains on the bridge, and in severe cases, it can lead to train derailment.
[0058] Based on the above conclusions, this embodiment also provides a bridge safety assessment method, including: First, the rail irregularity of the CRTS Ⅲ type slab track simply supported beam bridge system to be tested is calculated by applying the track irregularity calculation method of the high-speed railway track bridge system described above. Then, the train safety of the bridge is evaluated based on the rail irregularity, which is negatively correlated with the train safety of the bridge.
[0059] In some embodiments, rail irregularity warning thresholds can be designed for corresponding road sections based on bridge conditions. When the irregularity exceeds the corresponding threshold, a safety warning is issued.
[0060] Furthermore, if the aforementioned function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.
[0061] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.
[0062] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.
[0063] Furthermore, in order to provide a concise description of exemplary embodiments, not all features of actual embodiments (i.e., those features that are not relevant to the best mode of carrying out the invention as currently considered, or those features that are not relevant to implementing the invention) may be omitted.
[0064] It should be understood that numerous specific implementation decisions can be made during the development of any practical implementation, such as in any engineering or design project. Such development efforts may be complex and time-consuming, but for those skilled in the art who benefit from this disclosure, the development effort will be a routine work of design, manufacturing, and production without requiring much experimentation.
[0065] The above 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 with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the protection scope of the technical solutions of the embodiments of the present invention.
Claims
1. A track irregularity calculation method of a high-speed railway track bridge system, characterized by, include: Based on the Ruili-Ritz method, the mapping relationship between the vertical deformation of the beam and the additional deformation of the rail is derived, and the rail displacement matrix at all fastener positions is obtained. The formula is as follows: In the formula, This is the matrix of coefficients representing the influence of fastener force on rail displacement. and This is the matrix of influence coefficients of fastener force on the track slab; To and , and Identity matrices of the same dimension; Equivalent stiffness of the fastener; The equivalent Winker spring stiffness of the isolation layer; This is the matrix of coefficients representing the influence of the vertical deformation of the piers on the bridge displacement. This represents the vertical deformation of the bridge pier. Rail irregularity is established based on the ratio of rail deformation amplitude to deformation zone length. Rail irregularity is calculated under different vertical deformation conditions of the beam, where: The deformation amplitude of the rail is the sum of the positive deformation amplitude and the negative deformation amplitude of the rail.
2. The method according to claim 1, characterized in that, The track irregularity calculation method is applied to the CRTSⅢ type slab track simply supported beam bridge system, wherein the system includes at least: The components arranged from top to bottom are: rails, fasteners, track slabs, self-compacting concrete filling layer, base plate, box girder, supports, and piers. The rails are fixed to the track slab with fasteners. The track slab, the self-compacting concrete filling layer and the base plate form a composite slab. An isolation layer is provided between the self-compacting concrete filling layer and the base plate. The base plate is fixedly connected to the box girder by pre-embedded steel bars. The box girder is supported on the pier by supports.
3. The method according to claim 2, characterized in that, Also includes: In step S1, the gravity equilibrium state of the CRTS Ⅲ type slab track simply supported beam bridge system is taken as the initial state. When deriving the mapping relationship between the vertical deformation of the beam and the additional deformation of the rail, the mechanical equilibrium equation used does not include the gravity term. In this model, the base plate and the box girder are considered as a deformable and coordinated whole. The reaction effect of the rails on the vertical deformation of the bridge structure is not considered in the calculation process. The rails in the roadbed section are simplified to simply supported boundaries. The boundary effect of the roadbed section is eliminated by taking a set calculation length of the roadbed section. The fasteners are modeled as Winker linear springs uniformly distributed along the center line of the rails, and the isolation layer is modeled as Winker linear springs uniformly distributed along the center line of the base plate.
4. The method according to claim 3, characterized in that, In step S1, the influence coefficient matrix of fastener force on rail displacement is calculated. The expression is: In the formula, Let represent the element in the i-th row and j-th column of matrix A. M represents the number of track slabs in the CRTS Ⅲ type slab track simply supported beam bridge system. Each track slab has N fasteners, so there are a total of MN fasteners.
5. The method according to claim 4, characterized in that, The defining relation is: In the formula, n is a positive integer greater than 1. This refers to the total length of the rails. The equivalent cross-sectional moment of inertia of the rail; The elastic modulus of the rail; This represents the x-axis coordinate value of the i-th fastener. This represents the x-axis coordinate value of the j-th fastener.
6. The method according to claim 3, characterized in that, Also includes: In step S1, when deriving the mapping relationship between the vertical deformation of the beam and the additional deformation of the rail, a single track slab is modeled as a free beam structure. Trigonometric functions are used as basis functions to approximate the vertical displacement of the track slab. The total potential energy function of the track slab is derived by combining the fastener force and the spring force of the isolation layer in order to solve the deformation of the track slab in the bridge section.
7. The method according to claim 6, characterized in that, The deformation of the roadbed section is simulated using the equivalent Winker spring stiffness. The track slab in the roadbed section is subjected to the combined action of fastener force and roadbed spring force. The deformation solution process of the track slab in the roadbed section is the same as that of the track slab in the bridge section.
8. A bridge safety assessment method, applied to the method described in any one of claims 1 to 7, characterized in that, include: Calculate the rail irregularity of the CRTS III type slab track simply supported beam bridge to be tested; The safety of train travel on the bridge is assessed based on the rail irregularity, and the rail irregularity is negatively correlated with the safety of train travel on the bridge.
9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1-7.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1-7.
Citation Information
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