Ballastless track load subitem coefficient calculation method in foundation large deformation area

Abstract

The invention relates to the technical field of ballastless tracks, and discloses a ballastless track load subitem coefficient calculation method in a foundation large deformation area, comprising the following steps: S10, ballastless track load data collection and statistical analysis: comprehensively collecting train load data and temperature gradient data borne by a ballastless track, and calculating a ballastless track load subitem coefficient; comprising but not limited to train axle load, running speed, running frequency, seasonal temperature change and the like, performing statistical analysis on the collected data, calculating to obtain a mean value, a standard value and a variable coefficient of train load and temperature gradient, determining an override probability based on an extreme value theory and in combination with a design reference period of a ballastless track, and calculating the override probability of the ballastless track. And a load standard value matched with the design reference period is obtained, so that the scientificity and rationality of the design are ensured. According to the ballastless track load subitem coefficient calculation method for the foundation large-deformation area, factors such as foundation deformation characteristics, load variability, structural importance grades and design service life are comprehensively considered.

Description

Technical Field

[0001] The present invention relates to the technical field of ballastless tracks, and in particular to a method for calculating load partial factors of ballastless tracks in areas with large foundation deformations. Background Art

[0002] In the modernization process of ballastless track structure design, it has become an industry consensus and trend to gradually adopt the limit state method. This transformation aims to evaluate the performance of the structure under specific limit states through a more scientific and rigorous method, ensuring that the ballastless track structure can meet high safety standards and achieve optimal economy throughout the entire life cycle of design, construction, and operation. Therefore, determining a reasonable load combination mode and its partial factors for ballastless tracks has become a core link in the design work.

[0003] In the traditional ballastless track structure design method, the allowable stress method is adopted, which cannot scientifically consider the influence of various factors on ballastless track design. At present, the parameter values in the ballastless track limit state design code are based on the allowable stress method, and the values of load standard values and partial factors lack scientificity and rationality and cannot be linked to engineering goals. The load combination mode in the ballastless track limit state design code is only applicable to general areas, and there is no special design method for the limit state of ballastless track structures in large deformation areas. Summary of the Invention

[0004] (I) Technical Problems to be Solved

[0005] The purpose of the present invention is to propose a method for calculating load partial factors of ballastless tracks in areas with large foundation deformations by comprehensively considering factors such as foundation deformation characteristics, load variability, structural importance level, and design service life.

[0006] (II) Technical Solutions

[0007] The technical solutions of the present invention for solving the above technical problems are as follows:

[0008] A method for calculating load partial factors of ballastless tracks in areas with large foundation deformations includes the following steps:

[0009] S10. Collect and statistically analyze ballastless track load data, comprehensively collect train load data and temperature gradient data borne by the ballastless track, including but not limited to train axle load, running speed, running frequency, and seasonal temperature changes, etc. Statistically analyze the collected data, calculate the mean value, standard value, and coefficient of variation of the train load and temperature gradient. Based on the extreme value theory, combined with the design reference period of the ballastless track, determine the exceedance probability, and then obtain the load standard value matching the design reference period to ensure the scientificity and rationality of the design;

[0010] S20. Basic large deformation characterization and model construction: Statistically analyze the test data of basic large deformations, establish the relational formula between basic large deformations and factors such as geological conditions and time. In finite element software, use non-linear spring elements to simulate basic large deformations, and construct a finite element model of ballastless track beam slabs including basic large deformations to improve the accuracy and efficiency of structural bending moment calculations.

[0011] S30. Determination of basic random variables and bending moment calculation: Determine the main random variables affecting the bending moment of ballastless track structures, including train loads, fastener stiffness, stiffness of the subgrade under the track, elastic modulus of track slabs, etc., and obtain their statistical parameters. Use the point estimation - finite element method, combined with the finite element model constructed in step S20, to calculate the mean values, standard deviations, and skewness of the first three moments of the bending moment of ballastless track structures under train loads.

[0012] S40. Calculation of load partial factors: Based on the third - moment method, use the first three moments calculated in step S30, combined with the structural limit state equation, to solve the load partial factors of ballastless tracks, verify and adjust the load partial factors to ensure that they can not only meet the safety requirements of structural design but also avoid unnecessary material waste and cost increase.

[0013] Based on the above technical solutions, the present invention can also be improved as follows.

[0014] Furthermore, the specific operation steps in step S10 include the following:

[0015] S101. Data collection: Identify the sources of train load data and temperature gradient data, including but not limited to train operation records, meteorological observation data, track monitoring systems, etc. Collect train load data, record the axle weight data of trains with different models and formations, collect the actual running speed data of trains when passing through the ballastless track section, count the number of trains or train trips passing through the ballastless track per unit time, record the temperature changes in the four seasons of the area where the ballastless track is located, especially the extreme high - temperature and low - temperature data, and use temperature sensors to monitor the temperature gradient changes of track slabs in different seasons and different time periods.

[0016] S102. Data pre - processing: Eliminate data that does not meet requirements such as outliers and missing values to ensure the accuracy and integrity of the data. Classify, sort, and format the collected data for subsequent statistical analysis.

[0017] S103. Statistical analysis: Calculate descriptive statistics such as the mean, median, and mode of train load axle weight, speed, frequency, and temperature gradient to understand the basic distribution of the data. Calculate standard values such as standard deviation to evaluate the degree of dispersion of the data, calculate the coefficient of variation to evaluate the degree of variation of train load and temperature gradient data, and provide a basis for subsequent analysis.

[0018] S104. Determination of the standard load value based on the extreme value theory. According to the design service life of the ballastless track and relevant specifications, determine the design reference period, select a suitable extreme value distribution model, fit the extreme values of the train load and temperature gradient, and calculate the corresponding standard load value using the extreme value distribution model according to the design reference period and the required exceedance probability. Compare and verify the calculated standard load value with existing specifications, similar project experiences, etc., and make adjustments if necessary to ensure the scientificity and rationality of the design.

[0019] Furthermore, in step S10, the collected data, statistical analysis process, calculation results of the standard load value, etc. can also be summarized, and the analysis results can be compiled into a report, including data collection situation, statistical analysis methods, calculation results of the standard load value and their bases, etc., to provide a scientific basis for the subsequent design and construction of the ballastless track.

[0020] Furthermore, step S20 specifically includes the following operation steps:

[0021] S201. Statistical analysis of the large foundation deformation data. Collect the large foundation deformation test data, which may be from on-site monitoring, laboratory tests, historical records, etc. These data should include specific values of the foundation deformation, occurrence time, geological conditions and other relevant information. Clean and sort the collected data, remove outliers and incomplete data to ensure the accuracy and reliability of the data. Use statistical methods to analyze the relationship between the large foundation deformation and factors such as geological conditions and time, which may include regression analysis, correlation analysis, etc., to establish a mathematical relationship formula between the large foundation deformation and these factors.

[0022] S202. Determine the model type: Based on the statistical analysis results, determine a suitable model type to characterize the large foundation deformation. This is usually a complex non-linear model that needs to consider the influence of multiple factors. Select a suitable finite element software for constructing the finite element model of the ballastless track beam slab.

[0023] S203. Simulation with non-linear spring elements. In the finite element software, use non-linear spring elements to simulate the large foundation deformation. These spring elements can simulate the non-linear deformation characteristics of the foundation under the action of external loads. Set the stiffness, damping and other parameters of the spring elements to reflect the actual situation of the foundation deformation. These parameters can be determined according to the relationship formula obtained from the statistical analysis. According to the actual dimensions, material properties and other information of the ballastless track beam slab, construct a geometric model in the finite element software, connect the non-linear spring elements with the foundation part in the geometric model to simulate the influence of the large foundation deformation on the ballastless track beam slab, and set the boundary conditions, loading conditions, etc. of the model to ensure that the model can accurately reflect the actual situation.

[0024] S204. Model verification and adjustment: Verify the constructed finite element model to ensure its accuracy and reliability. This can be achieved by comparing it with experimental data, on-site monitoring data, etc. If errors or deficiencies are found in the model, make timely adjustments and optimizations to improve the model's precision and efficiency.

[0025] Furthermore, in step S204, summarize the results of the statistical analysis of the large deformation data of the foundation, the process and results of model construction, and compile the analysis results and the model construction process into a report, including data collection and processing, statistical analysis methods, model type selection, simulation process of nonlinear spring elements, finite element model construction and verification results, etc.

[0026] Furthermore, step S30 specifically includes the following operating steps:

[0027] S301. Determination of basic random variables: Identify and determine the main random variables that affect the bending moment of the ballastless track structure. These variables usually include train loads such as axle load, speed, frequency, etc., but may be simplified to a comprehensive load effect, fastener stiffness, subgrade stiffness including the influence of large foundation deformation (already considered in the model construction in step S20), elastic modulus of the track slab, etc. For each random variable, collect or estimate its statistical parameters, including mean, standard deviation, etc. These parameters can be obtained through historical data, experimental tests, code recommended values, or expert experience, etc.

[0028] S302. Bending moment calculation: Use the ballastless track beam-slab finite element model containing large foundation deformation constructed in step S20, ensuring that the model has been verified and can accurately reflect the mechanical behavior of the actual structure. Set the input method of random variables in the finite element model, which usually involves defining these variables as variable parameters in the model and assigning corresponding statistical parameters to them. Combine the point estimation method and the finite element method for calculation. For each random variable, select its mean or design value as the input and conduct finite element analysis to obtain the corresponding bending moment value of the ballastless track structure. Repeat the above process by changing the input values of random variables, such as selecting multiple sample points within their distribution ranges, to obtain multiple sets of bending moment values. Use the obtained multiple sets of bending moment values to calculate the first three moments of the bending moment: mean, standard deviation, and skewness. The mean reflects the average level of the bending moment; the standard deviation reflects the degree of dispersion of the bending moment; the skewness describes the degree of skewness of the bending moment distribution pattern.

[0029] S303. Result Analysis and Verification: Analyze and calculate the results of the first three moments, evaluate the variability and uncertainty of the bending moments of the ballastless track structure, explore the influence degree of different random variables on the bending moments, identify the key influencing factors, and compare and verify the calculated results with experimental data, on-site monitoring data or similar engineering experience to ensure the accuracy and reliability of the calculated results. If a large deviation is found between the calculated results and the actual situation, adjust and optimize the model or calculation process in a timely manner;

[0030] S304. Summary and Report: Summarize the determination process of the basic random variables, the bending moment calculation process and results, and compile the analysis results into a report, including the determination basis, statistical parameters of the random variables, the bending moment calculation process, the results of the first three moments and their analysis, etc.

[0031] Furthermore, the specific operation steps in step S40 include the following:

[0032] S401. Preparation Stage: Collect and confirm the calculated results of the first three moments from step S30 to ensure the accuracy and reliability of these data, providing a solid foundation for the subsequent calculation of the load partial factors. According to the specific design requirements and specifications of the ballastless track, ensure the accuracy and applicability of the limit state equation;

[0033] S402. Solve the Load Partial Factors: Use the third - moment method, combined with the structural limit state equation and the equivalent resistance attenuation coefficient, to construct an objective function for solving the load partial factors. The objective function should be able to reflect the safety and economic requirements of the structural design to ensure the reasonable determination of the load partial factors. Use numerical methods such as the iteration method, optimization algorithm, etc. to solve the objective function to obtain the specific values of the load partial factors. During the solution process, pay attention to considering various constraint conditions such as safety factors, economic indicators, etc. to ensure the rationality and feasibility of the solution results;

[0034] S403. Verification and Adjustment: Through methods such as comparative analysis and simulation experiments, verify whether the solved load partial factors meet the safety requirements of the structural design, especially pay attention to the structural response under extreme working conditions to ensure that the load partial factors can ensure the safety of the structure. If it is found that the load partial factors do not meet the requirements or there is unnecessary material waste and cost increase, necessary adjustments should be made according to the verification results. During the adjustment process, factors such as the safety, economy and construction feasibility of the structural design should be comprehensively considered to ensure that the adjusted load partial factors are more reasonable and applicable;

[0035] S404. Summarize and output. Summarize and analyze the obtained load partial coefficients, clarify their application scope and limiting conditions in the design of ballastless track structures, compile calculation reports or technical documents, record in detail the calculation process, results and verification situations, output the obtained load partial coefficients as important parameters for the design of ballastless track structures to the design department or construction unit, and in the subsequent design, construction and acceptance processes, carry out relevant work strictly in accordance with the requirements of the load partial coefficients to ensure the safety and economy of the ballastless track structure.

[0036] (III) Beneficial effects

[0037] Compared with the prior art, the technical solution of the present application has the following beneficial technical effects:

[0038] The present invention comprehensively collects train load data and temperature gradient data borne by the ballastless track, and conducts in-depth statistical analysis. It not only considers conventional factors such as train axle load, running speed, and running frequency, but also incorporates the influence of seasonal temperature changes on track performance. Based on the extreme value theory and the design reference period, the standard load value is determined. This method overcomes the defect of lack of scientific basis for load value in traditional methods, ensures the comprehensiveness and accuracy of load data, thereby improving the scientificity and rationality of design. Especially in areas with large foundation deformations, such detailed analysis can more truly reflect the load level under extreme working conditions, providing a more reliable basis for structural design. By testing and analyzing large foundation deformation data, a relational formula between large foundation deformation and factors such as geological conditions and time is constructed, and nonlinear spring elements are used for simulation in finite element software to construct a finite element model of the beam slab of the ballastless track including large foundation deformation. This innovative model construction method fully considers the influence of foundation deformation on the track structure performance, improves the accuracy and efficiency of structural bending moment calculation. Compared with traditional models, this model can more accurately reflect the actual situation in areas with large foundation deformations, providing a more precise tool for structural design and analysis. The main random variables affecting the structural bending moment of the ballastless track are determined, and the point estimation - finite element method is combined with the constructed finite element model for calculation. This method not only considers conventional random variables such as train loads, but also incorporates the variability of key parameters such as fastener stiffness, subgrade stiffness, and track slab elastic modulus. By calculating the first three moment means, standard deviations, and skewnesses, the statistical characteristics of the structural bending moment are comprehensively described. The accurate calculation of this step lays a solid foundation for the subsequent solution of load partial coefficients. Based on the third - moment method, using the first three - moment data and combining with the structural limit state equation, the load partial coefficients of the ballastless track are solved. This method not only considers the variability of loads, but also ensures the rationality and safety of load partial coefficients through verification and adjustment. Compared with traditional methods, this method can more accurately reflect the stress characteristics of the ballastless track structure in areas with large foundation deformations, ensuring that the design results can meet safety requirements and avoid unnecessary material waste and cost increase. In summary, by comprehensively collecting and analyzing data, constructing accurate models, determining key random variables, and using scientific methods for calculation, the defects in the background technology are effectively overcome, providing a more scientific, reasonable, and accurate method for the design of ballastless tracks in areas with large foundation deformations. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flow chart of a method for calculating the load partial coefficient of a ballastless track in an area with large foundation deformations according to the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] Next, in combination with the accompanying drawings in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0041] Combined with Figure 1 As shown, a calculation method for load partial coefficients of a ballastless track in a large foundation deformation area of the present invention includes the following steps:

[0042] S10. Collection and statistical analysis of ballastless track load data. Comprehensively collect train load data and temperature gradient data borne by the ballastless track, including but not limited to train axle weight, running speed, running frequency, and seasonal temperature changes, etc. Statistically analyze the collected data, calculate the mean value, standard value, and coefficient of variation of the train load and temperature gradient, and based on the extreme value theory, combined with the design reference period of the ballastless track, determine the exceedance probability, and then obtain the load standard value matching the design reference period to ensure the scientificity and rationality of the design;

[0043] Specifically, the following operation steps are included in step S10:

[0044] S101. Data collection. Clearly define the sources of train load data and temperature gradient data, including but not limited to train operation records, meteorological observation data, track monitoring systems, etc. Collect train load data, record the axle weight data of trains of different models and formations, collect the actual running speed data of trains when passing through the ballastless track section, count the number of trains or shifts passing through the ballastless track per unit time, record the temperature changes in the four seasons of the area where the ballastless track is located, especially the extreme high temperature and low temperature data, and use temperature sensors to monitor the temperature gradient changes of the track slab in different seasons and different time periods;

[0045] S102. Data preprocessing. Eliminate unqualified data such as outliers and missing values to ensure the accuracy and integrity of the data. Classify, sort, format, etc. the collected data to facilitate subsequent statistical analysis;

[0046] S103. Statistical analysis. Calculate descriptive statistics such as the mean value, median value, and mode value of the train load axle weight, speed, frequency, and temperature gradient to understand the basic distribution of the data. Calculate standard values such as the standard deviation to evaluate the degree of dispersion of the data, calculate the coefficient of variation, and evaluate the degree of variation of the train load and temperature gradient data to provide a basis for subsequent analysis;

[0047] S104. Determination of the standard load value based on the extreme value theory. Determine the design reference period according to the design service life and relevant specifications of the ballastless track, select an appropriate extreme value distribution model, fit the extreme values of the train load and temperature gradient, calculate the corresponding standard load value using the extreme value distribution model according to the design reference period and the required exceedance probability, and compare and verify the calculated standard load value with existing specifications, similar project experiences, etc., and make adjustments if necessary to ensure the scientificity and rationality of the design;

[0048] In step S10, the collected data, statistical analysis process, calculation results of the standard load value, etc. can also be summarized, and the analysis results can be compiled into a report, including data collection situation, statistical analysis methods, calculation results of the standard load value and their bases, etc., to provide a scientific basis for the subsequent design and construction of the ballastless track;

[0049] The generalized Pareto distribution theory is used to calculate the standard load value of the ballastless track, and the estimated value x of the p quantile p is:

[0050]

[0051] In the above formula, u is the threshold, n is the sample size, N u is the number of exceedance thresholds, and ξ and σ are the shape parameter and scale parameter respectively.

[0052] The calculation method of the shape parameter ξ is:

[0053]

[0054] In the above formula, is the mean of the exceedance amount, s 2 is the variance of the exceedance amount.

[0055] The calculation method of the scale parameter σ is:

[0056]

[0057] If the number of load applications of the ballastless track load is N, the exceedance probability 1 - p is:

[0058]

[0059] In step S10, through detailed data collection (S101), not only the diversity of data sources was clarified, but also the comprehensive range of train load data and temperature gradient data was covered. Starting from multiple aspects such as train operation records, meteorological observation data, and track monitoring systems, the integrity and representativeness of the data were ensured. This process not only recorded the conventional train axle load, speed, and frequency information, but also particularly focused on the temperature gradient changes under extreme climate conditions, providing detailed and reliable basic data for subsequent statistical analysis. The introduction of the data preprocessing step (S102) effectively improved the data quality. By removing outliers and missing values, as well as classifying, sorting, and formatting the data, not only the accuracy and integrity of the data were guaranteed, but also the subsequent statistical analysis became more efficient and accurate. This process reduced the analysis deviation that might be caused by data quality problems, providing a strong guarantee for drawing scientific conclusions. The statistical analysis step (S103) deeply explored the internal laws of the data. By calculating descriptive statistics and standard values such as mean, median, mode, standard deviation, and coefficient of variation, the basic distribution and dispersion degree of train load and temperature gradient were comprehensively understood. These statistical information provided important basis for subsequent analysis, helping to more accurately grasp the mechanical properties of ballastless tracks in areas with large foundation deformations. The load standard value determination step (S104) based on extreme value theory is the core of the whole method. By selecting an appropriate extreme value distribution model, fitting the extreme values of train load and temperature gradient, and calculating the corresponding load standard values according to the design reference period and required exceedance probability, this process fully considered the randomness and uncertainty of load and temperature gradient, making the calculated load standard values more scientific and reasonable. At the same time, through comparison verification and adjustment with existing codes and similar engineering experiences, the safety and reliability of the design results were further ensured. In addition, in step S10, a link was added to summarize the collected data, statistical analysis process, load standard value calculation results, etc. and compile them into a report. This approach not only facilitated the accumulation and inheritance of knowledge, but also provided a scientific basis and reference for the subsequent design and construction of ballastless tracks. By referring to the report, designers can quickly understand information such as the basic situation of the project, data processing methods, and load standard value calculation results, thus carrying out design and construction work more efficiently and accurately.

[0060] S20. Characterization and model construction of large foundation deformations: Conduct statistical analysis on the measured large foundation deformation data, establish a relational formula between large foundation deformations and factors such as geological conditions and time. In the finite element software, use nonlinear spring elements to simulate large foundation deformations and construct a finite element model of the ballastless track beam slab including large foundation deformations to improve the accuracy and efficiency of structural bending moment calculation;

[0061] The following operating steps are specifically included in step S20:

[0062] S201. Statistical analysis of large foundation deformations: Collect large foundation deformation test data, which may be sourced from on-site monitoring, laboratory tests, or historical records, etc. This data should include specific values of foundation deformations, occurrence times, geological conditions, and other relevant information. Clean and organize the collected data, removing outliers and incomplete data to ensure data accuracy and reliability. Use statistical methods to analyze the relationships between large foundation deformations and factors such as geological conditions and time, which may include regression analysis, correlation analysis, etc., to establish a mathematical relationship formula between large foundation deformations and these factors.

[0063] S202. Determine the model type: Based on the results of statistical analysis, determine an appropriate model type to characterize large foundation deformations. This is usually a complex non-linear model that needs to consider the influence of multiple factors. Select a suitable finite element software for constructing a finite element model of ballastless track girders.

[0064] S203. Simulation with non-linear spring elements: In the finite element software, use non-linear spring elements to simulate large foundation deformations. These spring elements can simulate the non-linear deformation characteristics of the foundation under external loads. Set parameters such as the stiffness and damping of the spring elements to reflect the actual situation of foundation deformations. These parameters can be determined according to the relationship formula obtained from statistical analysis. Based on information such as the actual dimensions and material properties of the ballastless track girders, construct a geometric model in the finite element software. Connect the non-linear spring elements to the foundation part in the geometric model to simulate the influence of large foundation deformations on the ballastless track girders. Set boundary conditions, loading conditions, etc. of the model to ensure that the model can accurately reflect the actual situation.

[0065] S204. Model verification and adjustment: Verify the constructed finite element model to ensure its accuracy and reliability. This can be achieved by comparing it with experimental data, on-site monitoring data, etc. If errors or deficiencies are found in the model, make timely adjustments and optimizations to improve the accuracy and efficiency of the model.

[0066] In step S204, summarize the results of the statistical analysis of large foundation deformation data, the process and results of model construction. Compile the analysis results and the model construction process into a report, including data collection and processing, statistical analysis methods, model type selection, non-linear spring element simulation process, finite element model construction, and verification results, etc.

[0067] First, through the statistical analysis of the basic large deformation data in S201, we can comprehensively collect the basic large deformation data from multiple channels such as on-site monitoring, laboratory tests, and historical records. These data not only include specific deformation values and occurrence times but also are associated with key information such as geological conditions. The cleaning and sorting of the data ensure the accuracy and reliability of the data, laying a solid foundation for subsequent analysis. Using statistical methods for in-depth analysis reveals the internal relationships between basic large deformation and factors such as geological conditions and time, and constructs a mathematical relationship formula. This step provides a scientific basis for accurately understanding the mechanism of basic large deformation and also provides the necessary input parameters for subsequent model construction. Secondly, in the model type determination link of S202, based on the results of statistical analysis, a suitable non-linear model is selected to characterize the basic large deformation. This fully considers the influence of various factors, ensuring the complexity and adaptability of the model. At the same time, selecting a compatible finite element software provides strong technical support for the construction of the finite element model of the ballastless track beam slab, ensuring the scientific nature and effectiveness of the model construction. In S203, the basic large deformation is simulated through non-linear spring elements. This innovative method can accurately reflect the non-linear deformation characteristics of the foundation under external loads. The parameters such as the stiffness and damping of the spring elements are determined according to the results of statistical analysis, ensuring the accuracy and authenticity of the simulation. Combining the non-linear spring elements with the geometric model of the ballastless track beam slab realizes the comprehensive simulation of the influence of basic large deformation. In addition, by reasonably setting the boundary conditions and loading conditions of the model, it is ensured that the model can accurately reflect the actual situation, providing a reliable reference basis for the design. Finally, in the model verification and adjustment link of S204, the constructed finite element model is comprehensively verified by comparing experimental data, on-site monitoring data, etc., ensuring the accuracy and reliability of the model. When errors or deficiencies are found in the model, timely adjustment and optimization are carried out to improve the accuracy and efficiency of the model. This step not only ensures the scientific nature and rationality of the design results but also provides valuable experience and reference for the design of subsequent similar projects. In addition, summarizing the results of the statistical analysis of basic large deformation data, the process and results of model construction, and compiling them into a report not only helps with knowledge accumulation and inheritance but also provides detailed reference materials for subsequent design, construction, and scientific research work. This report details key information such as data collection and processing, statistical analysis methods, model type selection, non-linear spring element simulation process, and finite element model construction and verification results, providing strong guarantee for the scientific nature and standardization of ballastless track design.

[0068] S30. Determination of basic random variables and calculation of bending moment: Identify the main random variables that affect the bending moment of the ballastless track structure, including train load, fastener stiffness, subgrade stiffness, elastic modulus of the track slab, etc., and obtain their statistical parameters. Using the point estimation - finite element method and combining with the finite element model constructed in step S20, calculate the first three - order moment means, standard deviations, and skewnesses of the bending moment of the ballastless track structure under the action of train load;

[0069] Specifically, step S30 includes the following operating steps:

[0070] S301. Determination of basic random variables: Identify and determine the main random variables that affect the bending moment of the ballastless track structure. These variables usually include train loads such as axle load, speed, frequency, etc., but may be simplified to a comprehensive load effect in this step, fastener stiffness, subgrade stiffness including the influence of large - scale foundation deformation (which has been considered through the model construction in step S20), elastic modulus of the track slab, etc. For each random variable, collect or estimate its statistical parameters, including mean, standard deviation, etc. These parameters can be obtained through historical data, experimental tests, code - recommended values, or expert experience, etc.;

[0071] S302. Bending moment calculation: Use the finite - element model of the ballastless track beam and slab containing large - scale foundation deformation constructed in step S20, ensuring that the model has been verified and can accurately reflect the mechanical behavior of the actual structure. Set the input method of random variables in the finite - element model, which usually involves defining these variables as variable parameters in the model and assigning corresponding statistical parameters to them. Combine the point - estimation method with the finite - element method for calculation. For each random variable, select its mean or design value as the input and conduct finite - element analysis to obtain the corresponding bending - moment value of the ballastless track structure. Repeat the above process by changing the input values of random variables (such as selecting multiple sample points within their distribution ranges) to obtain multiple sets of bending - moment values. Use the obtained multiple sets of bending - moment values to calculate the first three - order moments of the bending moment: mean, standard deviation, and skewness. The mean reflects the average level of the bending moment; the standard deviation reflects the degree of dispersion of the bending moment; the skewness describes the degree of skewness of the bending - moment distribution pattern;

[0072] S303. Result analysis and verification: Analyze the calculated first three - order moment results, evaluate the variability and uncertainty of the bending moment of the ballastless track structure, explore the influence degree of different random variables on the bending moment, identify key influencing factors, compare and verify the calculated results with experimental data, on - site monitoring data, or similar engineering experience to ensure the accuracy and reliability of the calculated results. If it is found that there is a large deviation between the calculated results and the actual situation, adjust and optimize the model or calculation process in a timely manner;

[0073] S304. Summarization and Reporting: Summarize the determination process of basic random variables, the bending moment calculation process and results, and compile the analysis results into a report, including the determination basis of random variables, statistical parameters, bending moment calculation process, the results and analysis of the first three moments, etc.

[0074] Take the train load, fastener stiffness, subgrade stiffness, and elastic modulus of the track slab as basic random variables, and use the normal distribution to describe the variables. Adopt the 7-point estimation in the standard normal space and calculate the bending moments of the ballastless track structure using the established finite element model, and calculate the first three origin moments μ1, μ2, and μ3 of the bending moments of the ballastless track structure using the Gauss-Hermite integration formula and Rosenblatt transformation.

[0075] According to the relationship between the origin moment and the central moment, the first three central moments of the bending moment of the ballastless track structure are:

[0076]

[0077] In the above formula, α1, α2, and α3 are the first three central moments of the bending moment of the ballastless track structure, namely the mean value, standard deviation, and skewness.

[0078] In S301, by identifying and determining the main random variables that affect the bending moment of the ballastless track structure, such as the comprehensive load effect, fastener stiffness, subgrade stiffness (including the influence of large foundation deformations already considered in the model construction in step S20), and the elastic modulus of the track slab, etc., this step ensures the comprehensiveness and pertinence of subsequent analyses. At the same time, the statistical parameters of these random variables, such as the mean value, standard deviation, etc., are collected or estimated, providing the necessary input data for subsequent bending moment calculations. The acquisition channels of these parameters are diverse, including historical data, experimental tests, code recommended values, and expert experience, etc., ensuring the reliability and accuracy of the data. Secondly, in S302, using the finite element model of the ballastless track beam-slab that includes large foundation deformations and has been constructed and verified in step S20, the point estimation method and the finite element method are combined for calculation, effectively simulating the bending moment response of the ballastless track structure under different random variable conditions. By changing the input values of the random variables and selecting multiple sample points within their distribution ranges for calculation, not only multiple groups of bending moment values are obtained, but also the first three moments of the bending moment are calculated: the mean value, standard deviation, and skewness. These three statistical quantities respectively reflect the average level, dispersion degree, and skewness degree of the distribution form of the bending moment, providing an important basis for comprehensively evaluating the variability and uncertainty of the bending moment of the ballastless track structure. Then, in S303, the results of the first three moments obtained from the calculation are deeply analyzed, the variability and uncertainty of the bending moment of the ballastless track structure are evaluated, and the influence degree of different random variables on the bending moment is discussed, identifying the key influencing factors. In addition, through comparison and verification with experimental data, on-site monitoring data, or similar engineering experience, the accuracy and reliability of the calculation results are ensured. Once it is found that there is a deviation between the calculation results and the actual situation, the model or calculation process can be adjusted and optimized in a timely manner, thereby continuously improving the calculation accuracy and model applicability. Finally, in S304, the entire analysis process is comprehensively summarized, and the analysis results are compiled into a report. This report not only details the determination basis, statistical parameters, bending moment calculation process, and the results of the first three moments of the random variables, etc., but also deeply analyzes and discusses these results. This not only helps with knowledge accumulation and inheritance, but also provides valuable reference and scientific basis for the subsequent design, construction, and maintenance of ballastless tracks.

[0079] S40. Calculation of load partial factors. Based on the third moment method, using the first three moments calculated in step S30 and combining with the structural limit state equation, solve the load partial factors of the ballastless track, verify and adjust the load partial factors to ensure that they can not only meet the safety requirements of structural design but also avoid unnecessary material waste and cost increase.

[0080] First, in the preparation stage of S401, by collecting and verifying the calculated first three moment data from step S30, the accuracy and reliability of these key data are ensured. This step lays a solid foundation for the subsequent calculation of load partial coefficients, avoiding calculation result deviations caused by data errors. At the same time, according to the specific design requirements and specifications of the ballastless track, the accuracy and applicability of the limit state equation are ensured, providing a clear direction and basis for the entire calculation process. Secondly, in the stage of solving the load partial coefficient in S402, using the advanced third-moment method, combined with the structural limit state equation and the equivalent resistance attenuation coefficient, an objective function for solving the load partial coefficient is constructed. This method not only considers the safety requirements of structural design but also takes into account economic requirements, ensuring the reasonable determination of the load partial coefficient. By using numerical methods for solution, such as the iterative method, optimization algorithm, etc., the specific values of the load partial coefficient are obtained. During the solution process, various constraint conditions are fully considered, such as safety factors, economic indicators, etc., ensuring the rationality and feasibility of the solution results. Then, in the verification and adjustment stage of S403, through various methods such as comparative analysis and simulation experiments, the obtained load partial coefficient is comprehensively verified. This step pays special attention to the structural response under extreme working conditions, ensuring that the load partial coefficient can meet the safety requirements of structural design. If it is found that the load partial coefficient does not meet the requirements or there is unnecessary material waste and cost increase, necessary adjustments are made in a timely manner. During the adjustment process, factors such as the safety, economy, and construction feasibility of structural design are comprehensively considered, ensuring that the adjusted load partial coefficient is more reasonable and applicable. Finally, in the summary and output stage of S404, an in-depth summary and analysis of the obtained load partial coefficient are carried out, clarifying its application scope and limiting conditions in the ballastless track structure design. By compiling a calculation report or technical document, the calculation process, results, and verification conditions are detailedly recorded, providing an important reference basis for the design department or construction unit. The obtained load partial coefficient is output as an important parameter for the ballastless track structure design, ensuring that in the subsequent design, construction, and acceptance processes, relevant work can be carried out strictly in accordance with the requirements of the load partial coefficient, thus ensuring the safety and economy of the ballastless track structure.

[0081] When using reliability for the design of ballastless track structures, it should satisfy probabilistically:

[0082] G(X) = R - ∑S i , β...β T Formula (6)

[0083] In the above formula, G(X) is the performance function, and R and S i are the resistance and load effect respectively, and β T is the target reliability index of the performance function G(X).

[0084] To calculate the partial coefficient of load, it is necessary to first estimate the target average resistance μ RT , the initial value of the average resistance μ R0 The estimation method is as follows:

[0085]

[0086] In the above formula, μ Si and σ Si are the mean and standard deviation of the bending moment of the ballastless track structure, and β T is the target reliability index, which is taken as 3.7 for the ballastless track structure.

[0087] The standard deviation σ G of the performance function G(X) is calculated as follows:

[0088]

[0089] In the above formula, σ R is the standard deviation of the structural resistance R, and σ Si is the standard deviation of the load effect S i .

[0090] The skewness α 3G0 of the performance function G(X) is calculated as follows:

[0091]

[0092] In the above formula, α 3R and α 3Si are the skewnesses of the resistance R and the load effect S i respectively.

[0093] The third-order moment reliability index β 3M is calculated as follows:

[0094]

[0095] In the above formula, β 2M is the second-order moment reliability index, and the calculation method is as follows:

[0096] β 2M = μ G / σ G Formula (11)

[0097] In the above formula, μ G is the mean of the performance function G(X), and the calculation method is as follows:

[0098] μ G = μ R -∑μ Si Formula (12)

[0099] Substitute formula (10) into formula (6) to get:

[0100]

[0101] Express the expression on the right side of the above formula with β 2T to obtain:

[0102] β 2M ≥β 2T Formula (14)

[0103] β 2T can be expressed as:

[0104]

[0105] Use formula (8), formula (9) and formula (15) to calculate the initial values σ G , α 3G and β 2T of σ G0 , α 3G0 and β 2T0 , then the calculation method of the target average resistance μ RT is:

[0106]

[0107] Use formula (8), formula (9) and formula (15) to calculate σ G , α 3G and β 2T .

[0108] Substitute formula (8), formula (11) and formula (12) into formula (14) to get:

[0109]

[0110] Through transposition transformation and arrangement, it can be obtained:

[0111]

[0112] Let:

[0113]

[0114] In the above formula, α R and α Si are the direction cosines of the resistance R and the load effect S i respectively (also known as the separation coefficient). Substitute formula (19) into formula (18), then formula (18) can be simplified to:

[0115] μ R (1 - α R V R β2T ) ≥ ∑μ Si (1 + α Si V Si β 2T ) Formula (20)

[0116] In the above formula, V R and V Si are the coefficient of variation of the resistance R and the load effect S respectively i , then the load partial coefficient γ i The calculation method is as follows:

[0117]

[0118] In the above formula, S ni is the load standard value, and the calculation method can be seen in Formula (1).

[0119] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "including a..." does not exclude the existence of another identical element in the process, method, article or device including the said element.

[0120] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the partial coefficient of load of ballastless track in areas with large foundation deformation, characterized in that: The following steps are involved: S10. Collection and statistical analysis of ballastless track load data. Comprehensively collect train load data and temperature gradient data on ballastless track, including but not limited to train axle weight, running speed, running frequency and seasonal temperature changes, etc. Statistical analysis is performed on the collected data to calculate the mean, standard value and coefficient of variation of train load and temperature gradient. Based on extreme value theory and combined with the design reference period of ballastless track, the exceedance probability is determined, and then the load standard value matching the design reference period is obtained to ensure the scientificity and rationality of the design. S20, characterization and model construction of large foundation deformation, statistical analysis of the tested large foundation deformation data, establishment of the relationship formula between large foundation deformation and geological conditions, time and other factors, use of nonlinear spring units to simulate large foundation deformation in finite element software, and construction of a ballastless track beam slab finite element model including large foundation deformation to improve the accuracy and efficiency of structural bending moment calculation; S30, determining basic random variables and calculating bending moments, determining the main random variables that affect the bending moment of the ballastless track structure, including train load, fastener stiffness, offline foundation stiffness, track plate elastic modulus, etc., and obtaining their statistical parameters, using point estimation-finite element method, combined with the finite element model constructed in step S20, to calculate the mean, standard deviation, and skewness of the first three order moments of the bending moment of the ballastless track structure under the train load; S40, calculation of load partial coefficient, based on the third-order moment method, using the first three moments calculated in step S30, combined with the structural limit state equation, solve the load partial coefficient of the ballastless track, verify and adjust the load partial coefficient to ensure that it can meet the safety requirements of the structural design and avoid unnecessary material waste and cost increase.

2. The method for calculating the load partial coefficient of ballastless track in areas with large foundation deformation according to claim 1 is characterized in that: The step S10 specifically includes the following steps: S101. Data collection, clarify the sources of train load data and temperature gradient data, including but not limited to train operation records, meteorological observation data, track monitoring systems, etc., collect train load data, record the axle weight data of trains of different models and different formations, collect the actual running speed data of trains when passing through ballastless track sections, count the number or frequency of trains passing through ballastless track per unit time, record the temperature changes in the area where ballastless track is located throughout the year, especially the extreme high and low temperature data, and use temperature sensors to monitor the temperature gradient changes of track plates in different seasons and time periods; S102, data preprocessing, elimination of outliers, missing values ​​and other data that do not meet the requirements, ensuring the accuracy and completeness of the data, and classifying, sorting, formatting and other processing of the collected data to facilitate subsequent statistical analysis; S103, statistical analysis, calculation of descriptive statistics such as mean, median, mode, etc. of train load axle weight, speed, frequency and temperature gradient, understanding of the basic distribution of data, calculation of standard values ​​such as standard deviation, evaluation of data dispersion, calculation of coefficient of variation, evaluation of the degree of variation of train load and temperature gradient data, and providing a basis for subsequent analysis; S104. Determine the standard load value based on the extreme value theory. According to the design service life of the ballastless track and relevant specifications, determine the design reference period, select a suitable extreme value distribution model, fit the extreme values ​​of the train load and temperature gradient, calculate the corresponding standard load value based on the design reference period and the required exceedance probability using the extreme value distribution model, compare and verify the calculated standard load value with existing specifications, similar engineering experience, etc., and make adjustments when necessary to ensure the scientificity and rationality of the design.

3. The method for calculating the load partial coefficient of ballastless track in areas with large foundation deformation according to claim 1 is characterized in that: In step S10, the collected data, statistical analysis process, load standard value calculation results, etc. can also be summarized, and the analysis results can be compiled into a report, including data collection conditions, statistical analysis methods, load standard value calculation results and their basis, etc., to provide a scientific basis for the subsequent ballastless track design and construction.

4. The method for calculating the load partial coefficient of ballastless track in areas with large foundation deformation according to claim 1 is characterized in that: The step S20 specifically includes the following steps: S201. Statistical analysis of foundation large deformation data. Collect foundation large deformation test data. These data may come from field monitoring, laboratory tests or historical records. These data should include specific values ​​of foundation deformation, occurrence time, geological conditions and other related information. Clean and organize the collected data, remove abnormal values ​​and incomplete data, ensure the accuracy and reliability of the data, and use statistical methods to analyze the relationship between foundation large deformation and geological conditions, time and other factors. This may include regression analysis, correlation analysis, etc., to establish a mathematical relationship formula between foundation large deformation and these factors. S202, determine the model type: based on the statistical analysis results, determine the appropriate model type to characterize the large deformation of the foundation. This is usually a complex nonlinear model that needs to consider the influence of multiple factors. Select the appropriate finite element software to construct the finite element model of the ballastless track beam and slab; S203. Nonlinear spring unit simulation. In the finite element software, nonlinear spring units are used to simulate large deformation of the foundation. These spring units can simulate the nonlinear deformation characteristics of the foundation under the action of external loads. The stiffness, damping and other parameters of the spring units are set to reflect the actual situation of the foundation deformation. These parameters can be determined according to the relationship formula obtained by statistical analysis. According to the actual size, material properties and other information of the ballastless track beam, a geometric model is constructed in the finite element software. The nonlinear spring unit is connected to the foundation part in the geometric model to simulate the influence of large deformation of the foundation on the ballastless track beam. The boundary conditions and loading conditions of the model are set to ensure that the model can accurately reflect the actual situation. S204. Model verification and adjustment. Verify the constructed finite element model to ensure the accuracy and reliability of the model. This can be achieved by comparing it with experimental data, field monitoring data, etc. If errors or deficiencies are found in the model, timely adjustments and optimizations should be made to improve the accuracy and efficiency of the model.

5. The method for calculating the load partial coefficient of ballastless track in areas with large foundation deformation according to claim 4 is characterized in that: In step S204, the results of the statistical analysis of the foundation large deformation data, the process and results of the model construction are summarized, and the analysis results and the model construction process are compiled into a report, including data collection and processing, statistical analysis methods, model type selection, nonlinear spring unit simulation process, finite element model construction and verification results, etc.

6. The method for calculating the load partial coefficient of ballastless track in areas with large foundation deformation according to claim 4 is characterized in that: The step S30 specifically includes the following steps: S301, basic random variables determination, identification and determination of the main random variables that affect the bending moment of the ballastless track structure. These variables usually include train loads such as axle weight, speed, frequency, etc., but in this step they may be simplified to comprehensive load effects, fastener stiffness, offline foundation stiffness including the influence of large foundation deformation, which has been considered through the model construction in step S20, track plate elastic modulus, etc. For each random variable, collect or estimate its statistical parameters, including mean, standard deviation, etc. These parameters can be obtained through historical data, experimental tests, code recommended values ​​or expert experience, etc.; S302, bending moment calculation, using the finite element model of the ballastless track beam and slab including the large deformation of the foundation constructed in step S20, ensuring that the model has been verified and can accurately reflect the mechanical behavior of the actual structure, setting the input method of random variables in the finite element model, which usually involves defining these variables as variable parameters in the model and assigning corresponding statistical parameters to them, combining the point estimation method with the finite element method for calculation, for each random variable, selecting its mean or design value as input, performing finite element analysis, and obtaining the corresponding ballastless track structure bending moment value, repeating the above process, by changing the input value of the random variable such as selecting multiple sample points within its distribution range, obtaining multiple groups of bending moment values, using the obtained multiple groups of bending moment values, calculating the first three moments of the bending moment: mean, standard deviation and skewness, the mean reflects the average level of the bending moment; the standard deviation reflects the degree of dispersion of the bending moment; the skewness describes the degree of skewness of the distribution of the bending moment; S303. Result analysis and verification. Analyze the first three moment results obtained by calculation, evaluate the variability and uncertainty of the bending moment of the ballastless track structure, explore the influence of different random variables on the bending moment, identify the key influencing factors, compare and verify the calculation results with experimental data, on-site monitoring data or similar engineering experience, ensure the accuracy and reliability of the calculation results, and adjust and optimize the model or calculation process in a timely manner if it is found that there is a large deviation between the calculation results and the actual situation; S304. Summary and report. Summarize the determination process of basic random variables, the bending moment calculation process and results, and compile the analysis results into a report, including the basis for determining random variables, statistical parameters, bending moment calculation process, the first three order moment results and their analysis.

7. The method for calculating the load partial coefficient of ballastless track in areas with large foundation deformation according to claim 1 is characterized in that: The step S40 specifically includes the following steps: S401, preparation stage, collecting and confirming the first three moment data calculated in step S30, ensuring the accuracy and reliability of these data, providing a solid foundation for the subsequent calculation of load partial factors, and ensuring the accuracy and applicability of the limit state equation according to the specific design requirements and specifications of ballastless track; S402. Solve the load partial coefficient, use the third-order moment method, combine the structural limit state equation and the equivalent resistance attenuation coefficient, and construct the objective function for solving the load partial coefficient. The objective function should be able to reflect the safety and economic requirements of the structural design, ensure the reasonable determination of the load partial coefficient, and use numerical methods such as iteration method and optimization algorithm to solve the objective function and obtain the specific value of the load partial coefficient. In the solution process, pay attention to various constraints such as safety factor, economic index, etc. to ensure the rationality and feasibility of the solution result; S403. Verification and adjustment. Verify whether the load partial factors obtained by the solution meet the safety requirements of the structural design through comparative analysis, simulation experiments and other methods, pay special attention to the structural response under extreme working conditions, and ensure that the load partial factors can ensure the safety of the structure. If it is found that the load partial factors do not meet the requirements or there is unnecessary waste of materials and cost increase, necessary adjustments should be made according to the verification results. During the adjustment process, the safety, economy and construction feasibility of the structural design should be comprehensively considered to ensure that the adjusted load partial factors are more reasonable and applicable; S404. Summary and output. Summarize and analyze the obtained load partial factors, clarify their application scope and restrictions in the ballastless track structure design, write a calculation report or technical document, record the calculation process, results and verification in detail, and output the solved load partial factors as important parameters for the ballastless track structure design to the design department or construction unit. In the subsequent design, construction and acceptance process, carry out related work in strict accordance with the requirements of the load partial factors to ensure the safety and economy of the ballastless track structure.

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