Rail slab upwarp analysis method and system based on strength stability synthesis theory

Abstract

The application provides a track slab arching analysis method and system based on strength stability comprehensive theory, and relates to the technical field of health monitoring of high-speed railway ballastless track structure. The method comprises the following steps: obtaining track slab geometric dimensions, material properties and initial arching parameters; establishing a spatial mechanics model considering lateral block transverse constraint; applying equivalent temperature rise load to simulate temperature stress field and deformation field; calculating transverse constraint reaction force and equivalent temperature stress; inputting a strength stability comprehensive theory model to calculate comprehensive factors and strength stability factors; and combining critical condition to judge the arching critical state. The application introduces the strength stability comprehensive theory, integrates the strength failure of the track slab and the structural instability into the same analysis framework, and realizes the precise evaluation of the high-temperature arching critical state.

Description

Technical Field

[0001] This invention relates to the field of health monitoring technology for ballastless track structures of high-speed railways, and in particular to a method and system for analyzing track slab arching based on the comprehensive theory of strength and stability. Background Technology

[0002] Longitudinal continuous ballastless track is one of the track structure types for high-speed railways. A representative structure is the CRTSⅡ type slab track (hereinafter referred to as "Type II slab"), which mainly consists of track slabs, wide and narrow joints, a mortar layer, and a support layer. The track slabs are longitudinally connected through wide and narrow joints, forming a longitudinally continuous track structure system. The mortar layer located between the track slab and the support layer provides vertical support and adjustment for the track slab. Due to large-scale construction operations, complex substructure deformation, and structural degradation over time, under the combined action of multiple coupled loads such as train loads, temperature, and water environment, Type II slabs are prone to defects such as under-slab voids, localized damage, and initial camber. Under extreme high-temperature conditions, this can further lead to camber deformation and pose a potential risk of systemic failure. On bridges, longitudinally continuous ballastless track has lateral blocks (such as...) installed on both sides along the longitudinal direction of the track. Figure 2 As shown in the diagram, the track slab is connected to the beam via embedded parts, providing lateral restraint, improving the overall structural stiffness, and preventing excessive lateral deformation of the track system. At this point, the upward arching deformation of the Type II slab on the bridge under high temperature will exhibit the bending characteristics of a two-dimensional plate shell under bidirectional stress.

[0003] Current technologies are primarily based on classical stability analysis theory, simplifying track slabs into beam elements and focusing on whether they will experience buckling instability. However, this analytical method neglects the structural strength failure that may simultaneously occur during the arching deformation of the track slab—that is, before instability, the concrete inside the track slab may have already reached its compressive strength limit and failed. This method of analyzing stability and strength failure separately cannot accurately assess the true critical state of the track slab at high temperatures, resulting in a lack of scientific basis for engineering design and maintenance. Summary of the Invention

[0004] To address the technical problem in the prior art that separates the analysis of track slab stability and strength failure, resulting in the inability to accurately assess the critical state of track slab arching, this invention provides a track slab arching analysis method and system based on the comprehensive theory of strength stability. By introducing the comprehensive theory of strength stability and considering the lateral constraint effect of the lateral blocks, a comprehensive analysis method that simultaneously assesses strength failure and structural instability is constructed, enabling accurate determination of the critical state of track slab arching.

[0005] To achieve the above objectives, the first aspect of the present invention provides a method for analyzing the arching of a track slab based on the comprehensive theory of strength and stability, comprising: Obtain the basic parameters of the track structure, including the geometric dimensions, material properties, and initial camber of the track slab. f 0 and initial arch chord length l 0; Based on the aforementioned basic parameters, a spatial mechanical analysis model of the track slab considering the lateral constraints of the side stops is established. Equivalent temperature increase T eq The temperature load is applied to the analysis model to simulate the temperature stress field and deformation field of the track slab at high temperature. Based on the simulated temperature stress field and deformation field, the transverse constraint reaction force and equivalent temperature stress of the track slab under temperature load are calculated. The lateral constraint reaction force and equivalent temperature stress are input into a preset strength stability comprehensive theoretical model to calculate the comprehensive factor during the arching process of the track slab. and intensity stability factor ; According to the comprehensive factors and intensity stability factor Based on preset critical conditions, determine whether the track slab has reached the critical state of upward arching, and output the analysis results.

[0006] Furthermore, the establishment of the spatial mechanical analysis model of the track slab considering the lateral constraints of the side stops includes: The lateral restraint reaction force of the lateral blocks on the track slab is equivalent to a uniformly distributed lateral load applied to the side of the track slab. The mortar layer between the track slab and the lower support layer is simplified into a nonlinear elastic support with only unidirectional compression function; The track slab is discretized into shell units, and lateral constraints are applied to the sides of the slab to simulate the limiting effect of lateral stops.

[0007] Further, the lateral constraint reaction force and equivalent temperature stress of the track slab under temperature load are calculated, including: The finite element method was used to simulate the stress response of the track slab under different lateral block spacings and different equivalent temperature rise conditions. Extract the lateral constraint reaction force of the lateral stop from the simulation results; Through numerical fitting, a functional relationship was established between the lateral constraint reaction force, the equivalent temperature rise, and the lateral stop spacing; the functional relationship represents... ,in For lateral constraint reaction force, For elastic modulus, The coefficient of linear expansion is 1 / 3. Poisson's ratio, For equivalent temperature rise, The length of a single track slab. The spacing between the lateral stops; Based on the aforementioned functional relationship, the equivalent stress relationship parameters are determined. satisfy: .

[0008] Furthermore, based on the comprehensive theory of strength stability, the comprehensive factor for calculating the arching process on the track slab is... and intensity stability factor ,include: The relationship parameters of the track slab's bending stiffness, initial camber, gravity load, and equivalent stress. Perform dimensionless processing; Dimensionless parameters include , , , ,in This is the ratio of the upper arch chord length to the initial arch chord length. For the initial arch sag, For cross-sectional area, The section modulus, For density, It is the acceleration due to gravity. For the length of the upper arch chord, The ultimate compressive strength, The width of the track slab, Poisson's ratio, These are the parameters for the equivalent stress relationship. The critical chord length for instability; Substituting the dimensionless parameters into the constitutive equations of the strength stability synthesis theory, the synthesis factor is obtained by solving. and intensity stability factor The comprehensive factor Represented as ; The intensity stability factor Represented as: ; in, It is the ratio of the upper arch chord length to the critical chord length for instability. This represents the ultimate compressive strength of concrete. This is the critical stress for instability; Among them, comprehensive factors Strength stability factor is a property used to characterize the limit equilibrium state of arch bending on a track slab. Used to determine whether a structure experiences strength failure or buckling instability first.

[0009] Furthermore, determining whether the track slab has reached the critical state of upward arching includes: The calculated equivalent temperature stress is compared with the preset concrete compressive strength limit. σ S Compare; if the equivalent temperature stress reaches or exceeds the compressive strength limit. σ S If so, the track slab is determined to have reached the critical state of strength failure; Based on the intensity stability factor The value is used to determine: like If the value is greater than 1, it is determined that the track slab has first experienced structural instability, at which point the critical stress for instability is... Determined by the following formula: ; in, For elastic modulus, Let the moment of inertia of the cross section be... For cross-sectional area, The critical chord length for instability; like If the value is less than 1, the track slab is determined to have failed due to strength first. At this point, the critical state is determined by the ultimate compressive strength of the concrete. σ S control; like = 1, then the track slab is determined to be in a critical equilibrium state where strength failure and structural instability occur simultaneously.

[0010] Furthermore, it also includes: For different lateral block arrangement densities, the corresponding critical stress and comprehensive factor of the upper arch are calculated respectively; Through comparative analysis, the optimal lateral block arrangement scheme was determined; It outputs recommendations to guide the optimization of track structure design.

[0011] A second aspect of the present invention provides a track slab arching analysis system based on strength stability comprehensive theory, comprising: The parameter acquisition module is used to obtain the basic parameters of the track structure, including the geometric dimensions, material properties, and initial camber of the track slab. f 0 and initial arch chord length l 0; The model building module is used to establish a spatial mechanical analysis model of the track slab that considers the lateral constraints of the side stops based on the aforementioned basic parameters. Load application module for applying equivalent temperature rise T eq The temperature load is applied to the analysis model to simulate the temperature stress field and deformation field of the track slab at high temperature. The stress calculation module is used to calculate the lateral constraint reaction force and equivalent temperature stress of the track slab under temperature load based on the simulated temperature stress field and deformation field. The state analysis module is used to input the lateral constraint reaction force and equivalent temperature stress into a preset strength stability comprehensive theoretical model to calculate the comprehensive factor during the arching process of the track slab. and intensity stability factor ; The critical determination module is used to determine the criticality based on the comprehensive factor. and intensity stability factor Based on preset critical conditions, determine whether the track slab has reached the critical state of upward arching, and output the analysis results.

[0012] A third aspect of the present invention provides an electronic device including a memory, a processor, and a program stored in the memory and running on the processor, wherein the processor executes the program to implement the steps in the track slab arching analysis method based on the strength stability comprehensive theory described in the first aspect of the present invention.

[0013] A fourth aspect of the present invention provides a computer-readable storage medium having a program stored thereon that, when executed by a processor, implements the steps in the track slab arching analysis method based on the strength stability comprehensive theory described in the first aspect of the present invention.

[0014] A fifth aspect of the present invention provides a computer program product comprising software code, wherein the program in the software code performs the steps of the track slab arching analysis method based on the strength stability comprehensive theory described in the first aspect of the present invention.

[0015] Compared with existing technologies, the present invention provides a method and system for analyzing track slab arching based on the comprehensive theory of strength stability, which has the following advantages: (1) This invention introduces the Comprehensive Strength Stability Theory (CTSS), incorporating the strength failure and structural instability of the track slab into the same analytical framework. This solves the problem of existing technologies analyzing these two aspects separately, which leads to inaccurate assessment of the critical state of the arching, and achieves accurate assessment of the critical state of the arching at high temperatures. The CTSS theory constructs a comprehensive factor n and a strength stability factor... Two core indicators: the comprehensive factor n characterizes the nature of the ultimate equilibrium state of the track slab's arch bending (n=∞ indicates only axial compression, n=1 indicates critical instability, and n>1 indicates a compression-bending state); and the strength stability factor... Used to determine failure mode ( <1 First, strength failure, >1. Instability first, =1 (occurring simultaneously). By substituting parameters such as the initial camber parameters, material properties, temperature load, and stop constraints of the track slab into the CTSS constitutive equation, these two factors can be solved simultaneously, thereby achieving a comprehensive evaluation of the critical camber state of the track slab.

[0016] (2) This invention establishes a spatial mechanical analysis model of the track slab considering the lateral constraints of the side stops, discretizes the track slab into shell elements, and equates the lateral constraint reaction force of the side stops to a uniformly distributed lateral load. Specifically, the actual constraint characteristics of the side stops are first determined through field surveys and experimental data, and then the action of the stops is equated to a uniformly distributed load distributed along the side of the slab in the finite element model. Simultaneously, the mortar layer is simplified into a nonlinear elastic support with only unidirectional compression function, accurately simulating the actual stress characteristics of the mortar layer during the arching process of the track slab (only under pressure, deformable after voiding). This modeling method upgrades the track slab from a traditional one-dimensional beam element model to a two-dimensional plate and shell model, which can accurately reflect the arching characteristics of the track slab under bidirectional stress, significantly improving the accuracy of the analysis.

[0017] (3) This invention establishes the functional relationship between the lateral constraint reaction force of the lateral block and the equivalent temperature rise and the block spacing through finite element simulation and numerical fitting. By setting multiple sets of different stop intervals (e.g., 3.25m, 6.5m, 8m, ∞) and different equivalent temperature rises The simulation conditions were used to extract the corresponding lateral constraint reaction force data; then, a multivariate nonlinear regression method was used to fit the data, and it was found that... and It shows a linear positive correlation with The correlations are inversely proportional and include cross terms; ultimately, a high-precision fitting formula with a correlation coefficient R² = 0.9871 is obtained. This simplifies the complex contact mechanics problem of the stop-track slab into an explicit mathematical expression, providing a quantitative basis for engineering design and facilitating the arrangement of stops in practical engineering.

[0018] (4) This invention defines dimensionless parameters and constructs comprehensive factors. Intensity stability factor The explicit expression of the track slab is obtained by dimensionless processing of physical quantities such as bending stiffness, initial camber parameters, gravity load, and stop constraints. , , , Four dimensionless parameters were used to eliminate the influence of dimensions; then these parameters were substituted into the CTSS constitutive equation to derive the comprehensive factor. explicit expression and intensity stability factor expression These two expressions transform complex physical processes into programmable mathematical formulas, effectively characterizing the limit equilibrium state and failure modes during the arching process of the track slab, providing clear criteria for determining critical states, and facilitating engineering applications.

[0019] (5) By analyzing the influence of different lateral block arrangement schemes on the critical stress, this invention can optimize the block arrangement and propose the best design scheme. Based on the complete analysis model established above, it traverses different block intervals. L c (e.g., 3.25m, 6.5m, 8m, ∞), calculate the corresponding dimensionless bending stiffness parameters respectively. D and the critical stress of the upper arch σ Tx,eq Comparative analysis revealed that the denser the baffles are set, the better. D The larger (e.g.) l When f0 = 13m and f0 = 10mm, L c =3.25m corresponding D =1.99, an 82.5% increase compared to 1.09 without blocks), and the critical stress for the upward arch is also greater (the critical stress increases by 31.9% under the same conditions). Based on this, the optimal solution is recommended to install two sets of lateral blocks (spaced 3.25m apart) on a single track slab. This can significantly increase the critical stress for the upward arch of the track slab, extend the structural life, and ensure high-speed driving safety. Attached Figure Description

[0020] The accompanying drawings, which form part of this disclosure, are used to provide a further understanding of this disclosure. The illustrative embodiments of this disclosure and their descriptions are used to explain this disclosure and do not constitute an undue limitation of this disclosure.

[0021] Figure 1 A flowchart of the track slab arching analysis method based on the comprehensive theory of strength and stability provided in Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the CRTSⅡ type plate track lateral stop block provided in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the mechanical analysis model of the track slab provided in Embodiment 1 of the present invention; Figure 4 This is a hypothetical deformation curve diagram provided for Embodiment 1 of the present invention; Figure 5 The critical stress curve of track slab arching based on beam element assumption provided in Embodiment 1 of the present invention; Figure 6Provided for Embodiment 1 of the present invention n and Relationship diagram; Figure 7 This is a schematic diagram of the analysis model provided in Embodiment 1 of the present invention; Figure 8 This is a graph showing the vertical force-displacement parameters of the mortar layer provided in Embodiment 1 of the present invention. Figure 9 Provided for Embodiment 1 of the present invention - q z and L 0 / L c , T eq Relationship diagram; Figure 10 Provided for Embodiment 1 of the present invention l When 0 = 6.5m, under the action of lateral blocks at different intervals A schematic diagram illustrating the changing pattern of D; Figure 11 Provided for Embodiment 1 of the present invention l When 0=13m, under the action of lateral blocks at different intervals A schematic diagram illustrating the changing pattern of D; Figure 12 Provided for Embodiment 1 of the present invention l When θ = 6.5m, the effect of different numbers of lateral blocks σ Tx,eq A schematic diagram illustrating the changing pattern; Figure 13 Provided for Embodiment 1 of the present invention l When 0=13m, under the action of different numbers of lateral blocks σ Tx,eq A schematic diagram illustrating the changing pattern; Figure 14 Provided for Embodiment 1 of the present invention l When θ = 6.5m, the effect of different numbers of lateral blocks n A schematic diagram illustrating the changing pattern; Figure 15 Provided for Embodiment 1 of the present invention l When 0=13m, under the action of different numbers of lateral blocks n A schematic diagram illustrating the changing pattern; Figure 16 This is an architecture diagram of the track slab arching analysis system based on the comprehensive theory of strength stability provided in Embodiment 2 of the present invention.

[0022] In the diagram, 1. Rail; 2. Track slab; 3. Temperature load; 4. Mortar layer; 5. Rigid foundation; 6. Cross section; 7. Side baffle. Detailed Implementation

[0023] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0024] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form as well. Furthermore, it should be understood that the terms “comprising” and “having”, and any variations thereof, are intended to cover non-exclusive inclusion, for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0025] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0026] All data acquisition in this embodiment is carried out in accordance with laws and regulations and with user consent, and the data is used legally.

[0027] Example 1 like Figure 1 This embodiment provides a method for analyzing track slab arching based on the comprehensive theory of strength and stability, including: S1. Obtain the basic parameters of the track structure, including the geometric dimensions, material properties, and initial camber of the track slab. f 0 and initial arch chord length l 0.

[0028] S2. Based on the aforementioned basic parameters, establish a spatial mechanical analysis model for the track slab that considers the lateral constraints of the side stops.

[0029] In this step, the model is built based on the following basic assumptions, such as Figure 3 As shown: (1) The track slab is regarded as a plate unit structure with uniform cross section, and the influence of auxiliary structures such as dummy joints and rail support on the bending stiffness of the track slab is ignored; the temperature field distribution in the slab is only related to the depth and is uniformly distributed in the transverse and longitudinal directions.

[0030] (2) The bonding effect of the mortar layer is not considered, and the mortar layer is completely decoupled from the track slab. Due to the influence of multiple fields such as temperature, water and train dynamic load, the bonding state between the track slab and the mortar layer will gradually weaken or even disappear after the line is in operation, and the mortar layer will only play the role of vertical support.

[0031] (3) Since the steel rail contributes less to the bending stiffness of the track slab, the steel rail is simplified to a uniformly distributed vertical load; the lateral restraint reaction force of the side blocks on the track slab is equivalent to a uniformly distributed lateral load.

[0032] S3, Increase the equivalent temperature T eq The temperature load is applied to the analysis model to simulate the temperature stress field and deformation field of the track slab at high temperature.

[0033] In this step, it is assumed that the track slab has an initial arch sagitta and chord length. Since the Type II slab is a longitudinally continuous structure, during the upward arching process of the track slab, the boundary constraints of its upward arching section are in an intermediate state between hinged and fixed, and the upward arching chord length will also change with the temperature rise in the slab. Let its upward arching deformation curve be... y Initial arch deformation curve y Let 0 represent a half-wave quadratic sine curve with no sharp edges at the boundary, i.e., continuous first derivative, as follows: , (1) In the formula, f 0、 l 0 represents the initial arch sagitta and chord length, respectively. f , l These represent the displacement of the upper arch and the chord length, respectively. Assume the curve after the upper arch deformation is as follows: y T ,satisfy y T = y 0+ y Relationships, such as Figure 4 As shown.

[0034] As the overall temperature rise increases, the deformation of the track slab gradually expands until it reaches a state of instability and buckling, during which the total potential energy accumulated by the track slab is... U Mainly composed of the compressive deformation energy of the track slab U 1. Bending deformation energy U 2 and the gravitational potential energy of the track slab U 3 components. Based on the principle of stationary potential energy, the arch displacement on the track slab... f Represented as: (2) In the formula, EI Let be the bending stiffness of the beam element. ρ , g ,A These are the track slab density, gravity parameters, and track slab cross-sectional area, respectively. P T The temperature and pressure during the arching process on the track slab. k It is the ratio of the upper arch chord length to the initial arch chord length. k and P T The relationship is represented as: (3) S4. Based on the simulated temperature stress field and deformation field, calculate the lateral constraint reaction force and equivalent temperature stress of the track slab under temperature load.

[0035] The stress within the track slab during the arching process can be determined using the resisted strain method. Considering that the Type II slab is a typical longitudinally continuous plate-shell structure, its longitudinal stress and deformation are not easily affected by non-uniform temperature fields, and its temperature gradient sensitivity in the vertical direction is much higher than in the other two directions, the temperature field is simplified to only be related to... y Direction-related functions T ( y ).like T ( y )At z Axial asymmetry, temperature stress in plate σ T Under the premise of satisfying the equilibrium of the resultant force, the condition of the equilibrium of the resultant moment should also be satisfied, that is: (4) In the formula, E , α These are the elastic modulus and linear expansion coefficient of the concrete used in the track slab, respectively. h For the track slab along y Thickness in the direction. F The reaction force provided by the lateral stop under temperature action, and the temperature inside the plate T ( y Closely related. Because the longitudinal connecting plate is in x With the directions fully constrained, and combining the analysis results of equation (4), the stress distribution in all directions within the plate can be expressed as follows: (5) In the formula, σ Tx , σ Ty , σ Tz , τ Txy , τ Tyz , τ TxzThese are the stress components of the track slab under temperature effects. υ Poisson's ratio for concrete q z Lateral constraint reaction force provided to the lateral stops. To characterize the temperature characteristics of the track slab under complex temperature conditions, the following assumptions are made: σ Tx,eq , σ Tz,eq For the track slab in x , z The equivalent temperature stress in the direction, where σ Tx,eq , σ Tz,eq Combined with temperature P Tx , P Tz Related.

[0036] To simplify the expression for the anisotropic temperature stress of the track slab, using equivalent temperature... T eq Characterizing the temperature response properties of the track slab: (6) Equation (4) shows that, under the condition that the resultant force and resultant moment are simultaneously balanced, the equivalent temperature stress in the transverse direction of the track slab is only related to the reaction force of the lateral stop. q z Relevant, namely: (7) In high-temperature environments, σ Tx,eq , σ Tz,eq All are equivalent temperatures T eq To clarify the relationship between anisotropic stress components under different temperature conditions, the relevant functions are assumed to be used. σ Tx,eq , σ Tz,eq The following relationship must be satisfied: (8) In the formula, λ As the equivalent stress relationship parameter, according to equations (7) and (8), λ can be expressed as: (9) S5. Input the lateral constraint reaction force and equivalent temperature stress into the preset strength stability comprehensive theoretical model to calculate the comprehensive factor during the arching process of the track slab. and intensity stability factor .

[0037] According to equations (2) and (3), if the initial arch shape of the track slab is fixed, its upper arch displacement... f by f 0、 l 0、 l Joint influence. When the denominator of equation (2) approaches 0, f As the value approaches infinity, the track slab can be considered to be buckling and unstable. P This is the critical load for instability. P cr , l The critical chord length for instability l cr Take 4 EI π 4 -π 2 l cr 2 P cr =0, thus obtaining the track slab in its one-dimensional state. P cr The expression: (10) Equation (10) shows that if the track slab buckles due to instability, the calculation... P cr The equivalent chord length is 0.5. l cr This refers to the case where the beam is fixed at both ends in the Euler buckling equation. Although the position of the boundary point changes during the arching process of the track slab, the boundary of the arched section remains in a state without bends. Therefore, the buckling characteristics of the track slab are the same as those of the Euler beam in the fixed state. According to the analysis results of equation (3), under the influence of the non-uniform temperature field, the track slab in z There are also corresponding temperature stress components in the direction, due to the track slab in y , z Since the directional constraint is a free support, equation (10) can be extended to: (11) In the formula, σ crx , σ crz These are the track slab buckling states under instability. x , z Temperature force and temperature stress in the direction of temperature. D For the bending stiffness of a plate element, the conversion relationship between the bending stiffness of a beam element and the bending stiffness of a plate element is as follows: (12) According to equation (8), equation (11) can also be written as: (13) Next, the stress state of the track slab during the arching process is analyzed. During the arching process of the track slab... The total stress in the z-direction is: , (14) In the formula, W This represents the section modulus of the track slab's bending moment. This occurs during the upward arching process of the track slab. bending moment in the direction M x exist x The maximum value is found at the section where =0, combining equations (1), (2), and (12). M x It can be represented as: (15) According to Mohr's circle theorem, the first and third principal stresses ( σ 1. σ 3) Characterizes the local maximum tensile and compressive stress in concrete, i.e.: (16) in: (17) By combining equations (16) and (17), we can obtain: (18) The analysis of equations (9) and (14) shows that, σ x , σ z The value is always less than 0, meaning that even under the influence of upward camber moment, the track slab remains under full compression under temperature and pressure. Normally, σ x < σ z Therefore, it is possible σ x Reaching the ultimate strength σ S The strength critical state for determining whether the arch on the Type II plate has reached elastic bending deformation is as follows: (19) Dimensionless parameters include: , , , (twenty one) in, k , e , m , D These are dimensionless parameters for the initial arch chord length, initial arch sag, gravity load, and bending stiffness. For the initial arch sag, For cross-sectional area, The section modulus, For density, It is the acceleration due to gravity. For the length of the upper arch chord, The ultimate compressive strength, The width of the track slab, Poisson's ratio, These are the parameters for the equivalent stress relationship. The critical chord length for instability.

[0038] According to CTSS theory, define = k cr 2 σ S / σ cr Let be the strength stability factor. Combining equations (6), (14), (15), and (19), we can obtain the discriminant for the bending limit equilibrium state established using strength theory: (20) In the formula, σ Tx,eq = σ Tx,eq / σ S The dimensionless form of the equivalent temperature stress is, i.e. x Utilization rate of directional load strength.

[0039] Substituting the dimensionless parameters into the constitutive equations of the strength stability synthesis theory, the synthesis factor n and the strength stability factor are obtained by solving. Let n be a comprehensive factor characterizing the properties of the bending limit equilibrium state during the arching process of the track slab. The comprehensive factor n is expressed as: (twenty two) The intensity stability factor Represented as:

[0040] Among them, the comprehensive factor n is used to characterize the properties of the limit equilibrium state of the arch bending on the track slab, and the strength stability factor. Used to determine whether a structure experiences strength failure or buckling instability first. It is the ratio of the upper arch chord length to the critical chord length for instability. This represents the ultimate compressive strength of concrete. The critical stress for instability is given. If the effects of transverse temperature force and lateral stops are not considered, the longitudinal track slab can be simplified to a beam element structure, under which condition D=1.

[0041] Due to the longitudinal continuity of the Type II slab, the track slab undergoing upward arching deformation can be approximated as having the bending characteristics of a beam element. To fundamentally analyze the combined strength and stability performance of the Type II slab during the arching process and clarify the variation patterns of the strength stability factor and the combined factor, the following is based on... D Assuming =1, we initially explore the strength and stability characteristics of the track slab during the arching process. EI =6.035×10 7 N·m 2 , ρ =2400kg / m 3 , A =0.51m 2 , W =0.017m 3 , σ S =35.5MPa, α =1.0×10 -5 Taking track slabs with initial camber chord lengths of 6.5m for one slab and 13m for two slabs as examples, this paper analyzes the critical stress of track slab camber under high-temperature conditions. Field surveys show that for sections with severe camber, the maximum camber sag of the track slab can exceed 10mm; therefore, the initial camber sag is analyzed. f For cases where 0 is 0~20mm. Combining equations (2), (3), and (20), we obtain the result based on the beam element assumption ( D =1) Critical stress for arching of the track slab σ Tx,eq like Figure 5 As shown.

[0042] Figure 5 This indicates that the ultimate compressive stress for camber on the track slab is closely related to the initial camber. If the initial camber chord length is equal to the length of one slab, the critical stress for camber on the track slab decreases approximately linearly with the increase of the initial camber sagitta. When the initial camber chord length is equal to the length of two slabs, if the initial camber sagitta is less than 5 mm, the track slab will hardly camber, i.e. σ Tx,eq = σ x = σ SAfter the initial camber exceeds 5mm, temperature and pressure cause the track slab to arch, and the ultimate stress shows a decreasing trend with a gradually increasing rate of change. Once the initial camber exceeds 10mm, the change in ultimate stress tends to stabilize. Field investigation results show that the overall temperature rise of the track slab will not exceed 60°C, meaning the temperature compressive stress in the slab will not exceed 21.3MPa, with a ratio of 0.6 to the ultimate compressive strength. The results indicate that the ultimate compressive stress of the track slab exceeds the limit of 0.6. Therefore, if the influence of lateral temperature forces and the effect of lateral blocks are not considered, the track slab will not reach the critical state of upward arching.

[0043] Calculated using equation (23), under different initial arch conditions, when D When =1, the comprehensive factor n and Relationship such as Figure 6 As shown. Among them, and l 0, f Related to parameters such as 0, l The values ​​are 3m, 6.5m, 10m, and 13m respectively. f The thicknesses are 1mm, 3mm, 5mm, 7.5mm, 10mm, 15mm, and 20mm respectively.

[0044] Specifically, the calculation of the lateral constraint reaction force and equivalent temperature stress of the track slab under temperature load includes: The finite element method was used to simulate the stress response of the track slab under different lateral stop intervals and different equivalent temperature rises; a model was established as follows: Figure 7 The mechanical analysis model shown is mainly composed of the track slab and CA mortar, neglecting the influence of the support layer, rails, and fastening system on structural deformation. The track slab is constructed as a flexible planar plate element with a size of 0.1m. To eliminate boundary effects, the model uses five plate lengths and focuses on the middle track slab for analysis, simulating the constraint effect of lateral blocks by applying lateral constraints on the sides of the plate. Due to the limited bonding tensile force of the mortar layer, the constraint between the track slab and the support layer in the finite element model is simplified to a nonlinear elastic constraint with only uniaxial compression function, simulating the elastic support stiffness of the mortar layer. The force-displacement relationship curve is obtained by equivalent transformation of the elastic modulus of CA mortar, as shown in the figure. Figure 8 As shown (displacement is positive when the spring is in tension and negative when it is in compression). The temperature and pressure of the track slab in a high-temperature environment are simulated by applying a temperature rise load in the slab, while applying equivalent constraint forces at both ends. P T To achieve a balance between temperature and force on the track slab, satisfying... P T = EαAT eq The relationship between them. The main calculation parameters of the model are shown in Table 1.

[0045] Table 1 Main Calculation Parameters

[0046] The lateral constraint reaction forces of the lateral blocks were extracted from the simulation results. The calculation results show that when the model is taken as 5 plate lengths, the constraint forces of each group of lateral blocks in the middle track slab are... F The forces are all equal, satisfying the force characteristics of a uniformly distributed load. q z and F satisfy q z =( L 0 F ) / ( L c A z The relationship between ) L 0、 L c These represent the length of a single track slab (6.5m) and the distance between each set of lateral stops. A z This represents the side surface area of ​​the track slab. Because the track slab operates in a high-temperature environment... q z Always less than 0, therefore - q z Characterizing different L c and T eq Constraint characteristics of the lateral stop under certain conditions. q z The pattern of change is as follows Figure 9 As shown.

[0047] The results show that, with the change in the temperature rise of the track slab, the lateral restraint reaction force and the number of lateral stop groups show a positive increasing relationship. If... L 0 / L c Remain unchanged, - q z and T eq Maintaining a linear growth relationship, in which T eq When =0, q z =0. According to Figure 8 The shape of the curved surface in the middle can be used to determine - q z and L 0 / L c , T eq The relation contains cross terms.

[0048] Through numerical fitting, a functional relationship between the lateral constraint reaction force, equivalent temperature rise, and lateral stop spacing is established; therefore, it is assumed that the constraint force of the lateral stops satisfies... q z =- EαυT eq f ( L 0 / L c The relationship between ) T eq When =0, q z =0. Through numerical fitting, q z and L c , T eq The relationship can be represented as: (twenty three) For lateral constraint reaction force, For elastic modulus, The coefficient of linear expansion is 1 / 3. Poisson's ratio, For equivalent temperature rise, The length of a single track slab. The lateral stop interval. The correlation coefficient R of equation (23) 2 =0.9871, close to 1, indicating a high overall fit, therefore it can be used to represent the performance of track slabs under high-temperature conditions. q z and N , T eq The changing pattern.

[0049] Based on the aforementioned functional relationship, the equivalent stress relationship parameters are determined. satisfy: .

[0050] S6. Based on the aforementioned comprehensive factors and intensity stability factor Based on preset critical conditions, determine whether the track slab has reached the critical state of upward arching, and output the analysis results.

[0051] The calculated equivalent temperature stress is compared with the preset concrete compressive strength limit. Compare; if the equivalent temperature stress reaches or exceeds the compressive strength limit. If so, the track slab is determined to have reached the critical state of strength failure; Based on the intensity stability factor The value is used to determine: like If the value is greater than 1, it is determined that the track slab has first experienced structural instability, at which point the critical stress for instability is... Determined by the following formula: ; in, For elastic modulus, Let the moment of inertia of the cross section be... For cross-sectional area, This is the critical chord length for instability; at this point, the instability characteristics of the track slab are the same as the buckling of the Euler beam under fixed conditions.

[0052] like If the value is less than 1, the track slab is determined to have failed due to strength first. At this point, the critical state is determined by the ultimate compressive strength of the concrete. control; like = 1, then the track slab is determined to be in a critical equilibrium state where strength failure and structural instability occur simultaneously.

[0053] Furthermore, it also includes: For different lateral block arrangement densities, the corresponding critical stress and comprehensive factor of the upper arch were calculated. To analyze the comprehensive impact of the lateral block arrangement scheme on the stability and strength of the track slab arch, the following was performed: l Taking 0 = 6.5m and 13m as examples, let's analyze... f When 0 = 0~20mm, the track slab is respectively at L c =3.25m, 6.5m, 8m, ∞ (without lateral stops) D The changing patterns, such as Figure 10 and Figure 11 As shown.

[0054] The results show that the bending stiffness-related parameters are closely related to the distribution of lateral stops. (Coefficients) D and f 0 shows a decreasing trend, when l When 0 = 6.5m, the coefficient D exist f When 0 < 5 mm, the deceleration rate is relatively large. f The change tends to level off after 0>5mm; when l When 0 = 13m, the coefficient D exist f When 0 < 10 mm, the deceleration rate is relatively large. f The change tends to level off after 0 > 10 mm; f After 0>10mm, the coefficient D Basically unaffectedl 0 and f The effect of 0. Therefore, it can be... f Taking 0=10mm as an example, let's analyze the relationship between the number of lateral stop block groups and the coefficient. D The impact. Figure 10 and Figure 11 This indicates that, in l 0 = 6.5m f Under the condition of 0=10mm, L c When the value is 3.25m, 6.5m, 8m, or ∞, the coefficient... D The values ​​are 2.07, 1.63, 1.55, and 1.18 respectively, compared to the absence of lateral stops (i.e., ...). L c =0) L c When the height is 3.25m, 6.5m, and 8m, the coefficients increase by 75.4%, 38.1%, and 31.4% respectively; l 0=13m、 f Under the condition of 0=10mm, coefficient D These correspond to 1.99, 1.54, 1.46, and 1.09, respectively, with growth rates of 82.5%, 41.3%, and 33.9%. Therefore, the denser the lateral stops are arranged, the closer the arch of the track slab will be to the bending characteristics of a plate unit. If the track structure does not have lateral stops, f After 0>10mm, the coefficient D Approaching 1.0, the arch on the track slab approximates the bending characteristics of a beam element, therefore... f Under the condition of 0>10mm, the CTSS comprehensive characteristics of the track slab arch can be analyzed based on the assumption of beam elements.

[0055] Through comparative analysis, the optimal lateral block arrangement scheme was determined; l Taking 0 = 6.5m and 13m as examples, let's analyze... f Under the condition of 0=0~20mm, the critical stress of arching on the track slab is L c The variation patterns at 3.25m, 6.5m, 8m, and ∞ are shown in the following figures. Figure 12 and Figure 13 As shown.

[0056] The results show that the denser the longitudinal distribution of the lateral blocks, the greater the critical stress for track slab arching, and the easier it is for the track structure to maintain its original shape under high-temperature conditions. Among these, L c The critical stress for the upward arching of the lateral stop track slab is similar at 6.5m and 8m. l 0 = 6.5mf Under the condition of 0=20mm, the lateral stop is L c When = 3.25m, 6.5m, 8m, ∞, σ Tx,eq The values ​​are 0.908, 0.897, 0.894, and 0.870 respectively, compared to not having side stops. L c =6.5m, 8m σ Tx,eq They increased by 4.4%, 3.1%, and 2.8% respectively; l 0=13m、 f Under the condition of 0=20mm, σ Tx,eq The corresponding values ​​are 0.817, 0.763, 0.746, and 0.619, respectively, with growth rates of 31.9%, 23.3%, and 20.5%. Therefore, in sections with significant upward camber, the lateral blocks provide some constraint on the track slab. Compared to the original arrangement with an 8m interval, the critical stress increase rate for track slab camber is 2.3% and 9.5% for lateral block intervals of 6.5m and 3.25m, respectively.

[0057] The output provides recommendations to guide the optimization of track structure design. Comprehensive analysis indicates that the lateral stops should be arranged at intervals of 3.25m, i.e., two sets of lateral stops should be installed on each track slab to limit the upward arching effect of the track slab.

[0058] Furthermore, the comprehensive factor n and the strength stability factor were analyzed under different lateral block actions. The changing pattern, among which l The values ​​are 3m, 6.5m, 10m, and 13m respectively. f The values ​​for 0 are 1mm, 3mm, 5mm, 7.5mm, 10mm, 15mm, and 20mm, respectively. The results are as follows: Figure 14 and Figure 15 As shown.

[0059] The results show that the lateral blocks have no significant effect on the comprehensive factor of the arch deformation on the track slab. The variation law of the comprehensive factor under the influence of different lateral blocks is similar to the CTSS analysis results based on beam elements, and n is related to... The relationship is roughly inversely proportional to a first-order function. Therefore, the lateral stops do not affect the limit equilibrium properties of the arch bending on the track slab.

[0060] Example 2 like Figure 16 This embodiment provides a track slab arching analysis system based on the comprehensive theory of strength and stability, including: The parameter acquisition module is used to obtain the basic parameters of the track structure, including the geometric dimensions, material properties, and initial camber of the track slab. f 0 and initial arch chord length l 0; The model building module is used to establish a spatial mechanical analysis model of the track slab that considers the lateral constraints of the side stops based on the aforementioned basic parameters. Load application module for applying equivalent temperature rise T eq The temperature load is applied to the analysis model to simulate the temperature stress field and deformation field of the track slab at high temperature. The stress calculation module is used to calculate the lateral constraint reaction force and equivalent temperature stress of the track slab under temperature load based on the simulated temperature stress field and deformation field. The state analysis module is used to input the lateral constraint reaction force and equivalent temperature stress into a preset strength stability comprehensive theoretical model to calculate the comprehensive factor during the arching process of the track slab. and intensity stability factor ; The critical determination module is used to determine the criticality based on the comprehensive factor. and intensity stability factor Based on preset critical conditions, determine whether the track slab has reached the critical state of upward arching, and output the analysis results.

[0061] Example 3 Embodiment 3 of the present invention provides an electronic device.

[0062] An electronic device includes a memory, a processor, and a program stored in the memory and running on the processor. The processor includes, but is not limited to, at least one of a central processing unit (CPU), a graphics processing unit (GPU), a neural network processor (NPU), a tensor processor (TPU), or an artificial intelligence acceleration chip. When executing the program, it implements the steps in the track slab arching analysis method based on strength stability synthesis theory as described in Embodiment 1 of the present invention.

[0063] The detailed steps are the same as the track slab arching analysis method based on the comprehensive theory of strength stability provided in Example 1, and will not be repeated here.

[0064] Example 4 Embodiment 4 of the present invention provides a computer-readable storage medium.

[0065] A computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps in the track slab arching analysis method based on strength stability comprehensive theory as described in Embodiment 1 of the present invention.

[0066] The detailed steps are the same as the track slab arching analysis method based on the comprehensive theory of strength stability provided in Example 1, and will not be repeated here.

[0067] Example 5 Embodiment 5 of the present invention provides a computer program product.

[0068] A computer program product includes software code, wherein the program in the software code executes the steps in the track slab arching analysis method based on strength stability comprehensive theory as described in Embodiment 1 of the present invention.

[0069] The detailed steps are the same as the track slab arching analysis method based on the comprehensive theory of strength stability provided in Example 1, and will not be repeated here.

[0070] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented using various computer languages. For example, in one implementation, the methods and systems can be developed based on deep learning frameworks (such as TensorFlow, PyTorch, etc.) and using the Python language. Those skilled in the art will understand that other suitable programming languages ​​or tools can also be used for implementation without departing from the core ideas of the present invention.

[0071] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0072] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0073] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0074] The above description is merely a preferred embodiment of this practice and is not intended to limit the scope of this practice. Various modifications and variations can be made to this practice by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this practice should be included within the protection scope of this practice.

Claims

1. A method for analyzing the arching of track slabs based on the comprehensive theory of strength and stability, characterized in that, include: Obtain the basic parameters of the track structure, including the geometric dimensions, material properties, and initial camber of the track slab. f 0 and initial arch chord length l 0; Based on the aforementioned basic parameters, a spatial mechanical analysis model of the track slab considering the lateral constraints of the side stops is established. Equivalent temperature increase T eq The temperature load is applied to the analysis model to simulate the temperature stress field and deformation field of the track slab at high temperature. Based on the simulated temperature stress field and deformation field, the transverse constraint reaction force and equivalent temperature stress of the track slab under temperature load are calculated. The lateral constraint reaction force and equivalent temperature stress are input into a preset strength stability comprehensive theoretical model to calculate the comprehensive factor during the arching process of the track slab. and intensity stability factor ; According to the comprehensive factors and intensity stability factor Based on preset critical conditions, determine whether the track slab has reached the critical state of upward arching, and output the analysis results.

2. The method as described in claim 1, characterized in that, The establishment of a spatial mechanical analysis model for the track slab considering the lateral constraints of the side stops includes: The lateral restraint reaction force of the lateral blocks on the track slab is equivalent to a uniformly distributed lateral load applied to the side of the track slab. The mortar layer between the track slab and the lower support layer is simplified into a nonlinear elastic support with only unidirectional compression function; The track slab is discretized into shell units, and lateral constraints are applied to the sides of the slab to simulate the limiting effect of lateral stops.

3. The method as described in claim 1, characterized in that, The calculation of the lateral constraint reaction force and equivalent temperature stress of the track slab under temperature load includes: The finite element method was used to simulate the stress response of the track slab under different lateral block spacings and different equivalent temperature rise conditions. Extract the lateral constraint reaction force of the lateral stop from the simulation results; Through numerical fitting, a functional relationship was established between the lateral constraint reaction force, the equivalent temperature rise, and the lateral stop spacing; the functional relationship represents... ,in For lateral constraint reaction force, For elastic modulus, The coefficient of linear expansion is 1 / 3. Poisson's ratio, For equivalent temperature rise, The length of a single track slab. The spacing between the lateral stops; Based on the aforementioned functional relationship, the equivalent stress relationship parameters are determined. satisfy: .

4. The method as described in claim 3, characterized in that, The comprehensive factor for calculating the arching process of the track slab is based on the comprehensive theory of strength stability. and intensity stability factor ,include: The relationship parameters of the track slab's bending stiffness, initial camber, gravity load, and equivalent stress. Perform dimensionless processing; Dimensionless parameters include , , , ,in This is the ratio of the upper arch chord length to the initial arch chord length. For the initial arch sag, For cross-sectional area, The section modulus, For density, It is the acceleration due to gravity. For the length of the upper arch chord, The ultimate compressive strength, The width of the track slab, Poisson's ratio, These are the parameters for the equivalent stress relationship. The critical chord length for instability; Substituting the dimensionless parameters into the constitutive equations of the strength stability synthesis theory, the synthesis factor is obtained by solving. and intensity stability factor The comprehensive factor Represented as: ； The intensity stability factor Represented as: ； in, It is the ratio of the upper arch chord length to the critical chord length for instability. This represents the ultimate compressive strength of concrete. This is the critical stress for instability; Among them, comprehensive factors Strength stability factor is a property used to characterize the limit equilibrium state of arch bending on a track slab. Used to determine whether a structure experiences strength failure or buckling instability first.

5. The method as described in claim 1, characterized in that, The determination of whether the track slab has reached the critical state of upward arching includes: The calculated equivalent temperature stress is compared with the preset concrete compressive strength limit. σ S Compare; if the equivalent temperature stress reaches or exceeds the compressive strength limit. σ S If so, the track slab is determined to have reached the critical state of strength failure; Based on the intensity stability factor The value is used to determine: like If the value is greater than 1, it is determined that the track slab has first experienced structural instability, at which point the critical stress for instability is... Determined by the following formula: ； in, For elastic modulus, Let the moment of inertia of the cross section be... For cross-sectional area, The critical chord length for instability; like If the value is less than 1, the track slab is determined to have failed due to strength first. At this point, the critical state is determined by the ultimate compressive strength of the concrete. σ S control; like = 1, then the track slab is determined to be in a critical equilibrium state where strength failure and structural instability occur simultaneously.

6. The method according to any one of claims 1 to 5, characterized in that, Also includes: For different lateral block arrangement densities, the corresponding critical stress and comprehensive factor of the upper arch are calculated respectively; Through comparative analysis, the optimal lateral block arrangement scheme was determined; It outputs recommendations to guide the optimization of track structure design.

7. A track slab arching analysis system based on strength stability comprehensive theory, characterized in that, include: The parameter acquisition module is used to obtain the basic parameters of the track structure, including the geometric dimensions, material properties, and initial camber of the track slab. f 0 and initial arch chord length l 0; The model building module is used to establish a spatial mechanical analysis model of the track slab that considers the lateral constraints of the side stops based on the aforementioned basic parameters. Load application module for applying equivalent temperature rise T eq The temperature load is applied to the analysis model to simulate the temperature stress field and deformation field of the track slab at high temperature. The stress calculation module is used to calculate the lateral constraint reaction force and equivalent temperature stress of the track slab under temperature load based on the simulated temperature stress field and deformation field. The state analysis module is used to input the lateral constraint reaction force and equivalent temperature stress into a preset strength stability comprehensive theoretical model to calculate the comprehensive factor during the arching process of the track slab. and intensity stability factor ; The critical determination module is used to determine the criticality based on the comprehensive factor. and intensity stability factor Based on preset critical conditions, determine whether the track slab has reached the critical state of upward arching, and output the analysis results.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the program, it implements the steps of the track slab arching analysis method based on the strength stability comprehensive theory as described in any one of claims 1 to 6.

9. 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 track slab arching analysis method based on the strength stability synthesis theory as described in any one of claims 1 to 6.

10. A computer program product, comprising software code, characterized in that, The program in the software code executes the steps of the track slab arching analysis method based on the strength stability comprehensive theory as described in any one of claims 1 to 6.

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