A method for constructing a freeze-thaw-fatigue combined damage analysis model of a track slab

Abstract

The application provides a track slab freeze-thaw-fatigue combined damage analysis model construction method, which comprises the following steps: a combined damage constitutive relationship considering the mutual influence of freeze-thaw cycles and fatigue load is established; a flexible load calculation mechanism is proposed, so that it can adapt to equal-amplitude and non-equal-amplitude loading conditions, real-time and high-precision coupling calculation of damage evolution process and global stress field of the structure is realized, and the stress redistribution law caused by damage is revealed. Through the freeze-thaw-fatigue combined damage constitutive relationship construction, combined damage mechanics parameter coupling calculation and slab track fatigue damage and stress field coupling calculation, the freeze-thaw-fatigue damage accumulation model is introduced into the fatigue constitutive of the track slab, and the global stress redistribution phenomenon inversion of the ballastless track under the mutual influence of damage and stress-strain is realized.

Description

Technical Field

[0001] This invention relates to the field of freeze-thaw fatigue damage analysis technology, and more specifically, to a method for constructing a freeze-thaw-fatigue composite damage analysis model for track slabs. Background Technology

[0002] As a typical component of high-speed railway ballastless track in cold regions, the track slab bears the dual effects of train loads and freeze-thaw cycles. Its concrete material faces the extremely complex scenario of freeze-thaw fatigue damage during long-term service. Under the dual effects of freeze-thaw loads, the track slab and ballast bed slab will suffer damage. Freeze-thaw cycles subject the concrete to continuous frost heave forces, leading to the accumulation of pores and microcracks, resulting in the accumulation of freeze-thaw cycle damage and the deterioration of mechanical properties. Fatigue causes microcracks to accumulate and interconnect, forming numerous main cracks. The decrease in concrete mechanical properties caused by freeze-thaw cycles will further affect fatigue performance. The combined effect of these two factors continuously exacerbates the damage to the track slab concrete.

[0003] The CA mortar layer of CRTS Type I slab track typically serves functions of support, load transfer, leveling, and vibration reduction. Designed for a lifespan of 60 years and designed to withstand tens of millions of train loads, it is prone to fatigue failure. Researchers have gradually developed constitutive equations under different assumptions, with common methods including the linear damage accumulation method, the microscopic plane method, and the competition mechanism method based on damage energy release rate. Among these, the fatigue damage constitutive model for the adjustment layer of ballastless track, based on "SN curve + tensor constitutive equation + finite element coupling" (patent number: ZL202011118898.4), is the most representative.

[0004] However, this model can only handle constant amplitude loads and analyzes damage under the influence of fatigue train loads. It becomes unusable when environmental factors are introduced. Furthermore, it has limitations for variable amplitude loads and is no longer applicable to damage problems in ballastless track concrete subjected to freeze-thaw cycles and high-cycle train loads. Additionally, the selection of freeze-thaw cycle damage and fatigue damage equations requires experimental calibration. Due to the sensitivity of high-cycle fatigue to load types, fatigue curves from other industries differ significantly from the characteristics of high-speed railway ballastless track train loads, meaning that empirical formulas and conclusions from other industries cannot be directly applied. Moreover, freeze-thaw damage requires confirmation of the experimental and practical results based on the actual structural conditions. This includes determining the annual number of freeze-thaw cycles, the ratio of natural to rapid freeze-thaw cycles, and the applicability of the combined freeze-thaw and fatigue characteristics to concrete damage problems under different load characteristics, all of which need to be recalibrated and selected. Currently, there is no scientifically sound calculation method to calculate the freeze-thaw-fatigue combined damage of ballastless track and analyze its evolution within the structure with the number of loading cycles. Summary of the Invention

[0005] To address the technical problems mentioned above, this invention provides a method for constructing a combined freeze-thaw and fatigue damage analysis model for track slabs.

[0006] This invention provides a method for constructing a combined freeze-thaw and fatigue damage analysis model for track slabs, comprising the following steps: S1. Based on full-scale on-site monitoring and indoor freeze-thaw-fatigue composite loading tests, obtain damage evolution curves reflecting the average number of annual freeze-thaw-train load cycles on actual railway lines. Combined with fatigue SN curves and freeze-thaw damage equations, calibrate freeze-thaw damage variable D1, fatigue damage variable D2, and the damage variable D resulting from their interaction. 12 Establish a fatigue damage expression form containing composite effects, including the composite damage variable D; S2. Based on the continuous medium damage theory, a composite damage variable D is introduced to construct a composite damage constitutive relation that is coupled in both freeze-thaw and fatigue modes. S3. Using the composite damage constitutive calculation method, a multi-level load identifier is established to identify the loading mode of the multi-level load, and a closed-loop time-series calculation unit consisting of three analysis steps is constructed for each level of load; the calculation methods of different analysis steps are defined separately to realize the updating of damage and stress state under cyclic loading. S4. Based on the load identifier, generate the corresponding number of analysis steps, and assign stress damage iteration function and load cycling function to each analysis step; determine the number of load amplitude levels to be applied according to the load identifier, and cycle in units of three times the number of levels to cooperate with the calculation of composite fatigue damage. S5. A three-dimensional local refined finite element model is established using the full solid finite element method. The composite damage constitutive calculation method is embedded into the model through secondary development technology. Loads are applied and calculations are performed to achieve real-time interaction and updating of damage and stress fields.

[0007] The core of this invention is to establish freeze-thaw damage variable D1, fatigue damage variable D2, and their interaction with damage variable D. 12 The expression for the composite damage variable D .

[0008] Through rapid freezing experiments, a freeze-thaw damage evolution function D1 = f(N_fr) based on dynamic elastic modulus or mass loss was established, where N_fr is the number of freeze-thaw cycles. Based on the PM fatigue damage criterion and the concrete SN curve, the expression for the fatigue damage variable under a given stress level S is derived. ; This invention innovatively equates the strength degradation caused by freeze-thaw cycles to an increase in fatigue stress level. By establishing the relationship between the number of freeze-thaw cycles and the tensile strength loss rate R of concrete (R = g(N_fr), the nominal stress level S0 is corrected to the true stress level S = S0 / (1 - R). Then, the additional fatigue damage aggravated solely by freeze-thaw cycles is calculated using the corrected S0 / N curve. .

[0009] Based on the principles of continuum damage mechanics and strain equivalence, the composite damage variable D is introduced into the material constitutive relation: , where σ is the stress tensor, C is the fourth-order elastic tensor, and ε is the strain tensor; this constitutive relation defines the law of material stiffness evolution with damage and is the basis for finite element coupled calculation.

[0010] To handle variable amplitude loads, this invention designs a closed-loop timing calculus logic based on identifiers: User-defined load amplitude levels (e.g., level 1, level 2...n), each load level corresponds to a "closed-loop timing calculation unit" consisting of three analysis steps (A, B, C): Analysis Step A (Loading Calculation): Using the damage state D_old from the end of the previous step, apply the target load for this level and calculate the new stress field σ_new. Damage is frozen at this stage.

[0011] Analysis step B (steady-state constant load damage iteration): Keep the load σ_new constant, calculate the damage increment ΔD generated in this round based on the current stress level and accumulated damage, update the total damage D_new = D_old + ΔD, and update (reduce) the material stiffness in real time according to D_new.

[0012] Analysis step C (unloading stress reset): The load is unloaded to zero (or the initial value), but the material stiffness is maintained at the pre-damage stiffness corresponding to D_new. The stress state of the structure after springback is calculated to return it to the reference state before the start of this load cycle, in preparation for the next load cycle.

[0013] Through automated scripts, the corresponding sequence of computational units is automatically generated and assembled based on the load level identifier, thereby simulating complex load histories.

[0014] A refined three-dimensional finite element model of the CRTS III type slab track was established, including rails, fasteners (simulated using triaxial spring elements), track slabs, self-compacting concrete, base plate, and subgrade.

[0015] Through secondary development interfaces such as the User Material Subroutine (UMAT), the aforementioned composite damage constitutive model and multi-level load update logic are embedded into the finite element software and applied to the track slab material.

[0016] The system applies a sequence of measured or designed train loads and performs calculations. In each incremental step, the finite element solver calls the constitutive program: it calculates the stress based on the current strain and updates the damage based on the stress history. The updated damage value is fed back through a freeze-and-release mechanism, modifying the material stiffness matrix and thus affecting the next stress solution. This process achieves complete coupling between damage evolution and stress field calculation.

[0017] The beneficial effects of this invention are as follows: This invention provides a method for constructing a combined freeze-thaw and fatigue damage analysis model for railway track slabs. For the first time, it quantifies the coupling effect of freeze-thaw and fatigue within a unified framework, making the model more closely reflect the actual physicochemical processes of railway track slabs in cold regions, resulting in higher prediction accuracy. The proposed multi-level load closed-loop time-series calculation unit method breaks through the limitation of traditional models only applicable to constant amplitude loading, enabling flexible and efficient simulation of complex variable amplitude train load histories in the field. It achieves real-time, bidirectional coupling between damage variables and the finite element stress-strain field. The development of damage instantly changes local stiffness, causing stress redistribution, thus realistically reproducing key mechanical phenomena such as "intensified stress concentration in the gap region," making the analysis results more valuable for engineering guidance. This model can be directly used to assess the damage state and remaining life of existing railway track slabs in cold regions, and can also provide theoretical basis and optimization directions for the freeze-thaw and fatigue resistance design of new railway lines. Attached Figure Description

[0018] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the nominal stress level and the actual stress level in this invention; Figure 3 This is a schematic diagram of the microscopic pore model of the track slab concrete in this invention; Figure 4 This is a schematic diagram of the tensile stress-strain curve of the track slab concrete after freeze-thaw cycles in this invention. Figure 5 This is a schematic diagram of the constitutive calculation logic for freeze-thaw fatigue damage of track slab concrete in this invention; Figure 6 This is a schematic diagram of the load state variable transfer relationship in this invention; Figure 7 This is a schematic diagram of the finite element model of the CRTSⅢ type slab track in this invention; Figure 8 This is a schematic diagram of the seam separation condition setting in this invention; Figure 9 This is a schematic diagram of the damage and stress curves of the track slab concrete in this invention. Detailed Implementation

[0019] The exemplary embodiments of this disclosure are described below with reference to the accompanying drawings, including various details of the embodiments to aid understanding, and should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this disclosure. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0020] Please see Figure 1 This invention discloses a method for constructing a combined freeze-thaw and fatigue damage analysis model for track slabs, comprising the following steps: S1. Based on full-scale on-site monitoring and indoor freeze-thaw-fatigue composite loading tests, obtain the damage evolution curve reflecting the annual average number of freeze-thaw-train loads on the actual line. Combine the fatigue SN curve and freeze-thaw damage equation, calibrate the freeze-thaw damage variable D1, the fatigue damage variable D2, and the damage variable D12 generated by their mutual influence, and establish the fatigue damage expression form with composite influence, composite damage variable D. S2. Based on the continuous medium damage theory, a composite damage variable D is introduced to construct a composite damage constitutive relation that is coupled in both freeze-thaw and fatigue modes. S3. Using the composite damage constitutive calculation method, a multi-level load identifier is established to identify the loading mode of the multi-level load, and a closed-loop time-series calculation unit consisting of three analysis steps is constructed for each level of load; the calculation methods of different analysis steps are defined separately to realize the updating of damage and stress state under cyclic loading. S4. Based on the load identifier, generate the corresponding number of analysis steps, and assign stress damage iteration function and load cycling function to each analysis step; determine the number of load amplitude levels to be applied according to the load identifier, and cycle in units of three times the number of levels to cooperate with the calculation of composite fatigue damage. S5. A three-dimensional local refined finite element model is established using the full solid finite element method. The composite damage constitutive calculation method is embedded into the model through secondary development technology. Loads are applied and calculations are performed to achieve real-time interaction and updating of damage and stress fields.

[0021] Specifically, this embodiment takes the freeze-thaw fatigue damage calculation of the CRTS III type slab track concrete structure as an example.

[0022] Under freeze-thaw cycle damage, concrete develops microcracks, which further expand under fatigue loading. Therefore, the freeze-thaw damage and fatigue load damage to concrete are not simply linearly added together, but rather mutually influential. The formula for calculating the damage variable D of concrete structures under the combined action of freeze-thaw cycle and fatigue load is: .

[0023] This invention conducted a temperature monitoring test on CRTS Ⅲ type slab track in cold regions at the Subei Slab Plant of China Railway No. 9 Bureau in Sujiatun District, Shenyang City. A full-scale model of the slab track was cast to study the actual temperature field of the track structure.

[0024] Based on measured temperature data from 2022 to 2024, the average number of natural freeze-thaw cycles experienced by the orbital structure in a year was 109.

[0025] Tongji University's statistics show that Shenyang experiences 114 freeze-thaw cycles per year, while Zhejiang University predicts that Shenyang's concrete structures will experience 105 freeze-thaw cycles per year. These figures are very close to the data presented in this invention, therefore the temperature data is considered accurate.

[0026] Natural freeze-thaw cycles take a long time, and it is impractical to spend the same amount of time conducting freeze-thaw cycle tests on concrete. Therefore, it is necessary to convert the number of indoor freeze-thaw cycles to natural freeze-thaw cycles based on the rules in order to ensure the accuracy of indoor rapid freeze-thaw cycle tests.

[0027] Related scholars believe that the deterioration rate of concrete under rapid testing is linearly related to the deterioration rate under natural conditions, and the relationship between the number of rapid freeze-thaw cycles and the number of natural freeze-thaw cycles is as follows: ; In the formula, , These represent the number of indoor rapid freeze-thaw cycles and the number of natural freeze-thaw cycles, respectively, with K being the damage proportionality coefficient.

[0028] Due to significant regional climate differences and large variations in freeze-thaw cycles, the damage ratio coefficient in freeze-thaw tests is not a fixed value.

[0029] The temperature monitoring test set up in Shenyang is located in Northeast China. Based on the average temperature of the coldest month, it belongs to a severely frost-affected area. Therefore, the damage proportion coefficient K is taken as 7. Substituting this into the formula, the equivalent number of indoor freeze-thaw cycles for the number of natural freeze-thaw cycles per year can be calculated as 16. Statistical analysis is conducted over a three-year cycle. The number of freeze-thaw loading cycles for ballastless track over three years is 48. Considering safety and for the convenience of cycle planning for interactive testing, the number of freeze-thaw cycles is taken as 50.

[0030] The distribution of vertical force between the wheel and rail on a certain railway was statistically analyzed in each section, and the frequency distribution of wheel and rail load data during the operation of CRH380A train was obtained.

[0031] This invention, based on practical operational considerations, only considers the most frequently occurring wheel-rail vertical force for calculation, obtaining a probability P of 0.075 for this force. A certain railway operates high-speed trains primarily composed of CRH380A model trains. A total of 110 pairs of trains are deployed on busy sections of the line, with approximately 70% of trains having 16 carriages and 30% having 8 carriages. Based on this, the number of fatigue loading cycles for ballastless track per year is calculated as follows: ; Corresponding to the statistics on freeze-thaw cycles, the fatigue loading number of ballastless track over three years was 491,400. From a safety perspective, the fatigue loading number was set at 500,000.

[0032] Fatigue loading tests also require defining the stress level, which is the ratio of the maximum stress on the concrete specimen to the specimen's stress strength. Deng Shijie et al. from Southwest Jiaotong University established a mechanical calculation model for slab tracks, obtaining a maximum tensile stress level range of approximately 0.298-0.671 under different load combinations. For high-speed trains, a stress level of 0.3 under different load combinations was deemed most suitable.

[0033] The fatigue loading frequency of ballastless track is related to the number of times the track structure is subjected to wheel rolling per unit time, which is a parameter related to train operating speed. The frequency of train load is calculated according to the following formula: ; In the formula, v is the train speed (m / s), and l is the fixed wheelbase between train bogies (2.4 m for passenger cars and 1.75 m for freight cars). Considering the track slab damage of ballastless track on a 350 km / h high-speed railway, the loading frequency for the fatigue test is taken as 40 Hz.

[0034] The ballastless track experiences 16 freeze-thaw cycles and 164,000 fatigue loads per year. Frequent loading and alternating loads would make the experiment overly cumbersome and complex. To simplify the experimental procedures, the research team adopted a 3-year cycle, meaning one cycle involves 16 × 3 = 48 freeze-thaw cycles and 164,000 × 3 = 492,000 fatigue loads. To facilitate calculation, the experiment is rounded down, with one cycle consisting of 50 freeze-thaw cycles and 500,000 fatigue loads.

[0035] Regarding freeze-thaw damage, the ballastless track slab, being a layered structure, has a relatively small thickness compared to its length and width. Furthermore, as the slab is located on the upper layer of the track structure and is exposed to the cold environment, it experiences relatively uniform freeze-thaw cycles. Therefore, for the freeze-thaw damage value D1 of the track slab, the freeze-thaw damage function based on macroscopic mechanical indicators obtained from experiments is used to consider overall deterioration. The accumulated damage of the track slab concrete specimen under freeze-thaw cycle loading is expressed as follows: or ; In the formula, n is the number of freeze-thaw cycles of the track slab concrete.

[0036] According to statistics, every 50 freeze-thaw cycles correspond to 500,000 fatigue loads. Therefore, the relationship between the number of freeze-thaw cycles and the number of fatigue loads within the same service life can be derived as follows: ; In the formula, N represents the number of fatigue loads applied to the track slab concrete.

[0037] Substituting the expression for the accumulated damage from freeze-thaw cycles, we can obtain the expression for the freeze-thaw damage value D1 of the track slab as follows: .

[0038] The concept of the SN curve, used to address fatigue damage, was first proposed by Wöhler and others in Germany and has been used ever since. Its general expression can be represented as: ; In the formula, S represents the stress level, which is the ratio of the stress borne by the concrete to its corresponding strength; Nf represents the material fatigue life; a and b are material parameters, which are generally obtained through statistical analysis based on experimental data. From the literature, the fatigue SN curve parameters for C60 concrete track slabs are a = 1.0718 and b = -0.1048. Based on the experimental results, the tensile strength of the track slab concrete is taken as 3.01 MPa.

[0039] The PM fatigue damage model is applied to accumulate tensile stress damage in the track slab. Assuming the structure is subjected to stress level Si and the number of fatigue cycles at level i is Ni, the work applied to the material corresponds to the number of fatigue cycles. Therefore, the material damage at each stress level is summed and embedded into the SN curve of the track slab concrete to obtain the expression for the fatigue damage value D2 of the track slab: ; To address the damage variables arising from the freeze-thaw-fatigue interaction, the SN curve of concrete fatigue considering freeze-thaw damage was used to calculate the damage value D12 of the track slab concrete caused by the freeze-thaw-fatigue interaction. The fatigue life of concrete is related to the stress level it is subjected to, while microcracks generated by freeze-thaw cycles further exacerbate the effect of fatigue loads.

[0040] This invention considers the strength degradation caused by freeze-thaw cycle damage as an impact on fatigue performance, that is, it equates the effect of freeze-thaw damage on fatigue life to strength loss, thereby leading to increased stress level and reduced fatigue life. The SN curve of concrete fatigue life will change before and after freeze-thaw cycle damage, and its stress level versus fatigue life curve is as follows: Figure 2 As shown.

[0041] Depend on Figure 2 It can be seen that the SN curve of concrete will decrease under freeze-thaw cycles. S and Nf correspond to the true stress level and the true fatigue life, respectively. S0 and Nf0 are the nominal stress level and nominal fatigue life obtained from the SN fatigue curve of track slab concrete without freeze-thaw cycles. Freeze-thaw damage reduces the strength of concrete, resulting in a higher true stress level than nominal stress level under the same stress, which in turn makes the true fatigue life less than the nominal fatigue life.

[0042] The effect of microcracks caused by freeze-thaw damage on fatigue is equated to the additional damage caused by increased stress level, thus realizing the combined effect of freeze-thaw action on fatigue damage. The relationship between nominal stress and actual stress is expressed as follows: ; In the formula, S0 and S are the nominal stress level and the actual stress level, respectively, and R is the corresponding concrete strength loss rate. The fatigue SN curve of concrete considering freeze-thaw damage is as follows: ; The calculated fatigue life Nf of concrete, taking freeze-thaw damage into account, is: ; Based on experimental testing of concrete porosity changes under different freeze-thaw cycles, three-dimensional microstructure models with different porosities were established. Randomly distributed pores were created, and the information was imported into the three-dimensional concrete microstructure model, such as... Figure 3 As shown, the restart function is used to find the restart points with different degrees of pore expansion during freeze-thaw cycle simulation. Then, according to the predefined field function of the load module, different degrees of freeze-thaw damage are set as the initial state of the concrete to study the changes in macroscopic tensile strength of freeze-thaw concrete at different restart points. Figure 4 As shown, the tensile strength loss rate function is obtained by fitting: ; Substituting the PM damage criterion for fatigue damage in track slab concrete and removing the effect of track slab damage accumulation under fatigue-only conditions, the expression for the damage value D12 caused by the interaction of freeze-thaw and fatigue in track slabs is obtained as follows: ; The damage caused by the interaction of freeze-thaw cycles and fatigue does not increase linearly, but rather exhibits an exponential relationship. By superimposing the three damage values, the composite damage variable D of the concrete structure under the combined action of freeze-thaw cycles and fatigue loads can be obtained. According to the Lemaitre damage equivalence principle, and based on thermodynamics and continuum mechanics theory, the stress-strain state of any damaged material can be considered as being represented by the constitutive and damage variables of the undamaged state. ; In the formula, σ and ɛ are the second-order stress and strain tensors, D is the composite damage variable, and C is the fourth-order elastic tensor; Will Substituting, we get: ; A composite damage constitutive calculation method for concrete is adopted, establishing multi-level load amplitude markers. The marker values ​​correspond to different load levels, and each load level is matched with a closed-loop three-stage time-series calculation unit. The time-series units across the entire domain are calculated according to a fixed logical division of labor, adapting to multi-level variable amplitude traffic load fluctuation conditions. The single-level load closed-loop time-series division of labor rules are as follows: First timeline: Load application calculation stage, locking historical cumulative damage values ​​to remain constant, only updating global load stress distribution parameters, without adding new damage increments.

[0043] Second time series: Steady-state constant load damage iteration stage, locking the external load amplitude to be constant, relying on the real-time coupled constitutive formula, superimposing the damage increment of this round of load interaction, updating the cumulative damage value of the whole domain, and simultaneously correcting the equivalent stiffness coefficient of the structure.

[0044] The third time series is the stress unloading and reset stage. The damage boundary parameters before the update are used to deduce the value of the structural rebound stress, so that the stress of the plate returns to the initial reference stress state of this level, and the single-level load closed-loop calculation is completed, connecting to the next level of load time series iteration.

[0045] Because the damage accumulation of concrete under low-frequency freeze-thaw cycles and fatigue loads is not significant, and the calculation cost of renewing damage with a small number of loads is too high.

[0046] This invention utilizes a pre-defined calculation method to update the element stiffness matrix every fixed number of load applications, thereby reducing computation time. When developing the calculation method, the following requirements must be met: ① Update the Jacobian matrix based on the material stiffness degradation caused by damage; ② Update the stress and state variables at the end of the incremental step.

[0047] Based on the above requirements, a constitutive calculation method for freeze-thaw fatigue damage of track slab concrete is developed. The calculation logic is as follows: Figure 5 As shown.

[0048] Multilevel identifiers are set, where 1 represents a single level, 2 represents level 2, and so on. The analysis steps are grouped into groups of 3 for a complete single-level load cycle. If it is a single level, then the multilevel identifier is 1 × the number of analysis steps = 3 for a complete cycle. If it is a level 2, then the multilevel identifier is 2 × the number of analysis steps = 3 = 6 for a complete cycle, and so on.

[0049] In a complete loop, analysis steps 1, 4, 7, etc., are set as the loading stage, where n is a natural number from 0 to the identifier value. At this time, the damage variable D0 from the previous step is used to keep the damage state frozen, and the multi-level loads are assigned to the 3n+1 analysis steps respectively. The analysis step 3n+2 is set to the stress constant stage. At this time, the damage needs to be updated. The analysis step keeps the load constant at each level, uses the current accumulated damage value D, and updates the Jacobian matrix accordingly.

[0050] The 3n+3 analysis step is the unloading stage. At this point, the damage variable D0 from the previous analysis step is updated to recalculate the stress, ensuring that the stress returns to its initial value and is transferred to the damage allocation during the loading and unloading process in the next analysis step. The variable transfer relationship is shown in [link to relevant documentation]. Figure 6 As shown.

[0051] To achieve variable transfer, a large number of analysis steps are required. Furthermore, since these analysis steps have different functions, they also need to cover multi-level load conditions and establish specific load amplitude curves corresponding to each analysis step. Manual input alone is cumbersome. Therefore, this invention can automatically generate a specified number of analysis steps, automatically providing a complete loop array space through multi-level identifiers. It allocates loading, dead load, and unloading functions according to 3n+1, 3n+2, and 3n+3 analysis steps, and simultaneously automatically assigns load magnitudes to analysis steps with different load amplitudes, thereby distinguishing the functions of different analysis steps.

[0052] This invention employs the full-solid finite element method to perform refined modeling of the CRTS III type slab track structure. The physical parameters of each structural component are determined based on actual engineering conditions, and the model is reasonably simplified without compromising the core research accuracy, thereby improving simulation efficiency. To effectively eliminate boundary effects in the finite element model, this invention constructs an overall model encompassing the lengths of three track slabs, selecting the middle track slab as the core research object. All test conditions are set within the middle track slab region, ensuring the accuracy and reliability of the simulation results.

[0053] This invention uses 60kg / m standard steel rails commonly used in high-speed railways and recreates the cross-sectional structure of the rails according to industry standard drawings to ensure that the model is consistent with the actual engineering structure.

[0054] The rail as a whole is discretized and simulated using C3D8R solid elements; the fastening system uses the WJ-8 type fastener commonly used in passenger dedicated lines, with a fastener spacing of 630mm. Since this invention focuses solely on freeze-thaw fatigue combined damage to the track slab concrete, to simplify the modeling process and improve computational efficiency, three sets of Cartesian space linear spring elements are used to simulate the fastener structure, fully considering the triaxial stiffness characteristics of the fasteners. The elastic connection between the rail and the track slab is achieved through these linear spring elements.

[0055] The track slab adopts the engineering-standard P5600 track slab, with geometric dimensions set to 5600mm in length, 2500mm in width, and 200mm in height. A 70mm gap is reserved between adjacent track slabs. The concrete strength grade of the track slab is C60, and C3D8R solid elements are used for simulation. To balance computational accuracy and efficiency, this invention only uses a self-developed constitutive method for calculating freeze-thaw-fatigue composite damage for the central core track slab, while the auxiliary track slabs at both ends use conventional material parameter settings.

[0056] To further optimize mesh generation quality and balance computational efficiency with simulation accuracy, this invention adopts a differentiated mesh generation strategy: conventional sparse mesh generation is used for the non-study track slabs at both ends; fine mesh processing is performed on the middle core track slab, wherein the core area where the load is applied is mesh-refined with a mesh size of 40mm×40mm×40mm, and the mesh size of the remaining areas of the middle track slab is set to 100mm×40mm×40mm. At the same time, a mesh transition area is set to avoid abrupt mesh changes affecting computational accuracy.

[0057] The self-compacting concrete layer uses C40 concrete with a structural height of 90mm, and its planar dimensions perfectly match those of the track slab. The base plate adopts a three-piece longitudinally connected integral structure specifically for ballastless track, simplified to a single integral base plate model. The concrete strength grade is also C40, and the geometric dimensions are set to 16990mm in length, 3100mm in width, and 300mm in height. Both the self-compacting concrete layer and the base plate are simulated using C3D8R solid elements. Since the core research object of this invention is the damage and deterioration law of the track slab, secondary details such as the bottom boss of the self-compacting concrete and the top groove of the base plate are ignored during modeling, achieving a reasonable simplification of the model.

[0058] The roadbed surface layer provides overall support constraints for the base plate. In the modeling, the longitudinal length of the roadbed surface layer is consistent with that of the base plate. Based on the actual engineering parameters, the dimensions are set to 16990mm in length, 3100mm in width, and 400mm in height. C3D8R solid elements are used for simulation.

[0059] This invention assembles components sequentially according to the structural hierarchy of rails, track slabs, self-compacting concrete layers, base plates, and subgrade surface layers, constructing a complete finite element model of the CRTS III type slab track on the subgrade. The overall model is as follows: Figure 7 As shown in Table 1, the material and geometric parameters of each component of the track structure are set according to Table 1. The intermediate track plate, which is the core of the study, adopts the freeze-thaw-fatigue composite damage material parameters customized in this invention.

[0060] Table 1 Parameters of various components of CRTS Type III slab track

[0061] This invention imposes the following limitations on the model boundary conditions and the interaction relationships between each structural layer to ensure that the simulation model closely matches the actual engineering conditions: (1) The track slab has built-in portal steel bars, which can effectively enhance the interlayer connection performance between the track slab and the self-compacting concrete, restrict the relative slippage between the two layers, and achieve excellent overall composite bonding performance. Based on this structural characteristic, the present invention adopts a tie-bonding contact method to simulate the contact relationship between the track slab and the self-compacting concrete layer.

[0062] (2) In actual engineering practice, a geotextile interlayer is laid between the self-compacting concrete layer and the base plate. Accordingly, the present invention sets the normal contact between the two as a hard contact mode, considers the interlayer friction in the tangential direction, adopts the penalty contact property, and sets the friction coefficient to 0.7.

[0063] (3) The base plate is directly cast onto the surface of the roadbed, and there is frictional constraint at the interface between the two. In this invention, the normal direction between the base plate and the surface of the roadbed is set as hard contact, and the tangential direction adopts the penalty contact property, with the friction coefficient set to 0.5.

[0064] (4) In order to fit the actual working conditions of the seamless high-speed railway and eliminate the boundary effect of numerical simulation, three-dimensional displacement constraints are applied to both ends of the rail and the base plate.

[0065] (5) The present invention uses a wire spring unit to simulate the fastener system. This simulation method has no rotational degree of freedom, so rotational constraints are applied to the connection position between the wire spring and the track plate.

[0066] (6) In order to restore the actual stress effect of the fastener pad and avoid the problem of local stress concentration, a coupling constraint is applied to the corresponding area of ​​the pad at the connection between the end of the fastener spring and the track plate.

[0067] (7) To realistically simulate the rigid support effect of the subgrade layer, full displacement constraint is applied to the bottom surface of the subgrade surface layer.

[0068] To verify the freeze-thaw fatigue damage evolution of the designed track structure, a train load with an axle load of 15 t and a dynamic load factor of 3 was selected as the working condition for the study.

[0069] During the service life of ballastless track, the location of train loads directly affects the stress distribution of the track slab. Research shows that the stress is most concentrated at the end of the slab. Therefore, the first fastener at the end of the slab was selected as the load application location, as this area is a sensitive region for the initiation and propagation of gaps.

[0070] Interlayer gaps in CRTS III type ballastless track mainly develop at the interface between the track slab and self-compacting concrete, easily leading to track slab delamination and threatening track smoothness. According to the "Maintenance Rules for High-Speed ​​Railway Ballastless Track Lines," gaps are classified into two levels of damage, I and II, based on length (100mm, 300mm boundary) and width (0.5mm, 1.0mm boundary). This invention focuses on the end-plate gap condition (the dominant type accounting for 68%), referencing a common 2mm gap height in engineering, and sets up a transversely continuous, 0.6m long condition. The geometric characteristics of the end-plate gap are shown in […]. Figure 8 .

[0071] Based on the cumulative constitutive model of freeze-thaw-fatigue composite damage, the damage evolution law of track slabs in the open state under real train load is calculated. With stress gradient and damage degree as the core indicators, the structural deterioration mechanism in cold service environment is revealed.

[0072] The damage evolution curve under operating conditions is shown in the figure. Figure 9 , Figure 9 The damage accumulation shows a linear characteristic, corresponding to the uniform development of freeze-thaw damage; while the peak stress shows a "decline-rise" fluctuation: in the early stage, the stress decreases due to the reduction of stiffness caused by local damage, and in the later stage, as the stress concentration effect increases with the expansion of the gap, the peak stress rises by 12%, revealing the intrinsic mechanism that the gap state exacerbates the risk of fatigue failure.

[0073] The specific embodiments described above do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A method for constructing a combined freeze-thaw and fatigue damage analysis model for track slabs, characterized in that, Includes the following steps: S1. Based on full-scale on-site monitoring and indoor freeze-thaw-fatigue composite loading tests, obtain damage evolution curves reflecting the average number of annual freeze-thaw-train load cycles on actual railway lines. Combined with fatigue SN curves and freeze-thaw damage equations, calibrate freeze-thaw damage variable D1, fatigue damage variable D2, and the damage variable D resulting from their interaction. 12 Establish a fatigue damage expression form containing composite effects, including the composite damage variable D; S2. Based on the continuous medium damage theory, a composite damage variable D is introduced to construct a composite damage constitutive relation that is coupled in both freeze-thaw and fatigue modes. S3. Using the composite damage constitutive calculation method, a multi-level load identifier is established to identify the loading mode of the multi-level load, and a closed-loop time-series calculation unit consisting of three analysis steps is constructed for each level of load. The calculation methods for different analysis steps are defined separately to achieve the updating of damage and stress states under cyclic loading; S4. Based on the load identifier, generate the corresponding number of analysis steps, and assign stress damage iteration function and load cycling function to each analysis step; determine the number of load amplitude levels to be applied according to the load identifier, and cycle in units of three times the number of levels to cooperate with the calculation of composite fatigue damage. S5. A three-dimensional local refined finite element model is established using the full solid finite element method. The composite damage constitutive calculation method is embedded into the model through secondary development technology. Loads are applied and calculations are performed to achieve real-time interaction and updating of damage and stress fields.

2. The method according to claim 1, characterized in that, In step S1, the freeze-thaw damage variable D1 is obtained by fitting the freeze-thaw damage function based on the mechanical property degradation test data; The fatigue damage variable D2 is derived from the PM fatigue damage model considering the stress level S and the SN curve of concrete.

3. The method according to claim 1, characterized in that, In step S1, the damage variable D 12 The relationship between the nominal stress level S0 and the actual stress level S is calculated by equating the deterioration of concrete strength caused by freeze-thaw damage to an increase in fatigue stress level. That is, after considering freeze-thaw damage, the relationship is as follows: ； Where R is the concrete strength loss rate.

4. The method according to claim 1, characterized in that, In step S1, the freeze-thaw damage variable D1, the fatigue damage variable D2, and the damage variable D resulting from their interaction are calibrated. 12 They are respectively: ； ； ； Where n is the number of freeze-thaw cycles of concrete, N is the number of fatigue loads on concrete; Si is the stress level, Ni is the number of fatigue loads at level i, Nfi is the fatigue life of the material, and a and b are material parameters; The composite damage variable is represented as: .

5. The method according to claim 4, characterized in that, In step S2, the stress-strain state of the material after damage is represented by the constitutive and damage variables in the undamaged state: ； Where σ and ɛ are the second-order stress and strain tensors, and C is the fourth-order elastic tensor; Substituting D into the equation, the constitutive relation of the combined damage caused by the freeze-thaw and fatigue bidirectional coupling is as follows: 。 6. The method according to claim 5, characterized in that, In step S3, the calculation logic of the closed-loop timing calculation unit is as follows: First timeline: Load application calculation stage, lock the historical cumulative damage value to keep it constant, only update the global load stress distribution parameters, and do not add new damage increments; Second time sequence: Steady-state constant load damage iteration stage, locking the external load amplitude to be constant, relying on the real-time coupled constitutive formula, superimposing the damage increment of this round of load interaction, updating the cumulative damage value of the whole domain, and simultaneously correcting the equivalent stiffness coefficient of the structure. The third time series is the stress unloading and reset stage. The damage boundary parameters before the update are used to deduce the value of the structural rebound stress, so that the stress returns to the initial reference stress state of this level, and the single-level load closed-loop calculation is completed, connecting to the next level of load time series iteration.

7. The method according to claim 6, characterized in that, In step S4, an automated scripting language is used to automatically generate a sequence of analysis steps based on the load identifier, and the functions of loading, constant load damage update and unloading are assigned to each analysis step according to the rule of 3n+1, 3n+2, 3n+3, where n is a natural number not greater than the value of the load identifier.

8. The method according to claim 7, characterized in that, In step S5, the finite element model is a CRTS III type slab track model, including rails, WJ-8 type fastening system, track slab, self-compacting concrete layer, base plate and subgrade surface layer; the constitutive relation automatic analysis step proposed in step S4 and the corresponding constitutive relation mentioned in step S3 are embedded into the finite element track slab material properties in step 5 to form a track structure deterioration analysis model calculated according to freeze-thaw-fatigue composite damage, and the corresponding damage evolution and stress redistribution of the track slab are analyzed.

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