Method and system for calculating fatigue life of road assembly type box culvert

Abstract

The invention provides a method and system for calculating the fatigue life of a road assembly type box culvert, and relates to the technical field of material mechanics and civil engineering. The fatigue life of the road assembly type box culvert is calculated by establishing a three-dimensional finite element model of the box culvert, screening out fatigue hot spots, installing strain sensors at the fatigue hot spots based on a fatigue stress analysis method, and measuring stress values. A calibration coefficient is generated through vehicle weight and speed data, a stress value is corrected, a temperature sensor is arranged for real-time monitoring, a temperature compensation model is established to correct stress data, finally, a real stress value of a fatigue hot spot is obtained after calibration and compensation, and an accumulated damage degree is defined. And the fatigue life of each hot spot is calculated based on a Miner rule. By establishing the three-dimensional finite element model, stress and temperature monitoring and correction are implemented, and the fatigue performance and the service life of the box culvert are accurately evaluated.

Description

Technical Field

[0001] The present invention relates to the technical fields of material mechanics and civil engineering, and particularly to a method and system for calculating the fatigue life of a road prefabricated culvert. Background Art

[0002] Currently, in urban infrastructure construction, especially in the construction and maintenance of transportation facilities such as highways, urban roads, and bridges, culverts, as common drainage and traffic channel structures, need to ensure their safety and reliability during use. By implementing fatigue life calculations, engineers can evaluate the fatigue damage that culverts may withstand during actual operation, thereby optimizing design and material selection to improve the service life of the structure. Secondly, in the renovation and reinforcement projects of old infrastructure, fatigue life calculation methods can be used for the health monitoring of existing culverts, helping engineers regularly evaluate their status, formulate corresponding maintenance or reinforcement strategies, and ensure road safety and smooth traffic.

[0003] In the current development, there are still some technical problems to be solved. First of all, how to accurately establish the three-dimensional finite element model of the culvert and its material property parameters is a challenge. Especially in complex geological environments and loading conditions, the accuracy of the model directly affects the calculation results of the fatigue life. Secondly, the acquisition and processing of real-time monitoring data are another technical difficulty. How to effectively integrate strain, temperature, and traffic flow data from sensors, and perform precise calibration and compensation to eliminate the interference of external factors and ensure the reliability of the data is crucial for the accurate calculation of the fatigue life. In addition, the establishment and verification of the damage accumulation model are also an important topic. How to accurately describe the evolution process of fatigue damage through a reasonable model to better predict the fatigue life of the culvert requires further research and experimental verification.

[0004] In the prior art, traditional culvert fatigue analysis methods often rely on static analysis or simplified theoretical models, ignoring the influence of dynamic traffic loads and environmental factors. This simplistic approach is likely to lead to underestimation or overestimation of fatigue damage, thereby affecting the safety and service life of the culvert.

[0005] Secondly, there are limitations in the prediction of fatigue life under dynamic loads in the prior art. Most methods fail to fully consider the impact of vehicle dynamic loads on the culvert structure and often analyze it with static loads, unable to accurately capture the stress fluctuations that may occur during actual use. For example, traditional finite element analysis methods usually rely on static load models and often lack a systematic calibration and compensation mechanism in fatigue damage analysis, resulting in insufficient reliability of stress data and failure to fully consider the impact of dynamic loads on the structure. During vehicle operation, significant dynamic load changes will occur, which has an important impact on the fatigue life of the culvert.

[0006] Therefore, it is necessary to provide a calculation method and system for the fatigue life of road prefabricated box culverts to solve the above problems.

[0007] The above information disclosed in the background art section is only used to enhance the understanding of the background of the present disclosure. Therefore, it may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0008] The purpose of the present invention is to provide a calculation method and system for the fatigue life of road prefabricated box culverts to solve the problems raised in the above background art.

[0009] To achieve the above purpose, the present invention provides the following technical solutions: A calculation method for the fatigue life of road prefabricated box culverts, the specific steps include: Step 1: Establish a three-dimensional finite element model of the box culvert according to the size, wall thickness and opening position of the box culvert, set the material property parameters and boundary conditions of the anti-fatigue performance of the box culvert, perform mesh element division on the finite element model and apply static loads, calculate the displacement data of each mesh element, and set a limit displacement threshold to screen out the fatigue hot spots of the box culvert. The fatigue hot spots are the elements whose displacement data exceeds the limit displacement threshold; Step 2: Based on the fatigue stress analysis method, install strain sensors at each fatigue hot spot of the box culvert to measure the stress values of each fatigue hot spot of the box culvert, and obtain the traffic data of the road to generate a stress calibration coefficient. Use the generated stress calibration coefficient to calibrate the stress values of each fatigue hot spot of the box culvert to eliminate the influence of extreme stress values on the measurement results. The traffic data includes the weight of the vehicle and the average speed of the vehicle passing through the road; Step 3: Arrange temperature sensors at each fatigue hot spot of the box culvert, perform real-time temperature monitoring and record the temperature change situation. According to the relationship between temperature and calibrated stress, establish a temperature compensation model, and use the established model to correct the collected stress data to eliminate the influence of temperature on the stress measurement results; Step 4: After calibration of extreme stress values and temperature compensation, obtain the true stress values of the fatigue hot spots of the box culvert, and define the damage variables of each fatigue hot spot of the box culvert based on the strain-stress relationship. Use the superposition of multiple damage degrees to represent the cumulative damage degree of each fatigue hot spot of the box culvert, and deduce the fatigue damage degree of the box culvert based on the definition of damage variables; Step 5: Analyze the true stress values under each fatigue hot spot of the box culvert based on the Miner's rule, obtain the corresponding material stress limit cycle times, and combine with the fatigue damage degree of the box culvert to obtain the fatigue life of the box culvert during actual use and operation.

[0010] Further, a three-dimensional finite element model of the box culvert is established to calculate the strain and displacement data of each element, and the displacement data of each grid element is calculated. A limit displacement threshold is set to screen out the fatigue hot spots of the box culvert. The method is as follows: Use CAD software to establish a three-dimensional model of the box culvert and define its length, width, height, and wall thickness. Adjust the opening position of the box culvert to face the road surface directly. Use finite element analysis software to mesh the three-dimensional box culvert model to generate tetrahedral elements. Set the material property parameters, including tensile strength, yield strength, elastic modulus, Poisson's ratio, residual stress, and coefficient of thermal expansion, and apply simulated vehicle loads; For tetrahedral elements, use linear shape functions to represent the displacements inside the elements. Let the four vertices of the tetrahedral element be , , , , respectively. Then the expressions for the shape functions of each vertex are: ; ; ; ; where, , , , are the four vertices of the same tetrahedral element respectively, is the volume of the tetrahedral element, , , , are the abscissas of the four vertices in the tetrahedral element respectively, , , , are the ordinates of the four vertices in the tetrahedral element respectively; Based on the method of nonlinear finite element analysis and local deformation calculation, the displacement of the tetrahedral element is calculated. The formula is: ; ; where, represents the displacement of the tetrahedral element, represents the displacement of the th vertex in the tetrahedral element, , , represent the vertices in , , The displacement component in the direction, representing the increment of the displacement of the -th vertex in the tetrahedral element. is the partial derivative of the shape function with respect to the coordinates of the four vertices, describing the rate of change of the shape function with the coordinates. is the index of the vertex in the tetrahedral element, and ; Set the limit displacement threshold . Tetrahedral elements with displacement data exceeding are marked as the fatigue hot spots of the culvert.

[0011] Furthermore, obtain the stress values of each fatigue hot spot of the culvert and calibrate the stress values of each fatigue hot spot of the culvert using the generated stress calibration coefficient. The method is as follows: Install strain sensors at each fatigue hot spot. By monitoring the measured strain data in real time, obtain the elastic modulus of the material combined with the strain measured at each fatigue hot spot, and calculate the corresponding stress value using the stress formula. The formula is as follows: ; where represents the stress value measured at the fatigue hot spot, is the elastic modulus of the material, is the strain at the fatigue hot spot; Obtain the stress calibration coefficient by generating road vehicle data. The formula is as follows: ; where represents the stress calibration coefficient, is the average speed of the vehicle passing through the road, is the weight of the vehicle, is the acceleration due to gravity; Use the obtained stress calibration coefficient to calibrate the stress values measured at each fatigue hot spot of the culvert to eliminate the influence of extreme stress values. The formula for obtaining the calibrated stress value is as follows: ; where represents the stress value measured at the fatigue hot spot after calibration.

[0012] Furthermore, according to the relationship between temperature and the calibrated stress, establish a temperature compensation model and use the established model to correct the collected stress data. The method is as follows: Install temperature sensors at the fatigue hot spots of the culvert box, record the ambient temperature changes in real time, and collect the stress data calibrated by stress during the corresponding time period. Use the polynomial regression model to fit the influence of temperature on stress changes. The polynomial model is set as: ; Among them, represents the stress deviation value that changes with temperature under the temperature compensation model, , , are the regression coefficients solved by the least squares method, is the temperature variable; Substitute the stress data calibrated by stress into the temperature model for correction. The formula is: ; Among them, represents the true stress value of the fatigue hot spot of the culvert box after calibration by extreme stress values and temperature compensation.

[0013] Furthermore, based on the strain-stress relationship, define the damage variables of each fatigue hot spot of the culvert box, represent the cumulative damage degree of each fatigue hot spot of the culvert box by superimposing multiple damage degrees, and derive the fatigue damage degree of the culvert box based on the definition of damage variables. The method is: Based on the damage mechanics theory, the damage degree is represented by defining the damage variable of the culvert box, and the definition of the damage variable is represented by the stress-strain relationship. The following relationship is introduced: ; ; Among them, represents the damage degree at the fatigue hot spot of the culvert box, is the damage variable, and its value range is from 0 to 1, is the maximum stress that the material at the fatigue hot spot can withstand, is the ultimate strength of the material; Based on the definition of the damage variable, derive the fatigue damage degree of the culvert box. The fatigue damage degree is expressed as the superposition of damage of multiple cycles. The formula is: ; Among them, represents the fatigue damage degree of the culvert box, represents the damage degree at the th fatigue hot spot of the culvert box, is the index of the fatigue hot spot in the culvert box, and , is the total number of fatigue hot spots in the culvert box, represents the damage variable at the th fatigue hot spot of the culvert box.

[0014] Further, the true stress values at each fatigue hot spot of the culvert and the corresponding material stress limit cycle numbers are obtained, and combined with the fatigue damage degree of the culvert to obtain the fatigue life of the culvert during actual use and operation. The method is as follows: The true stress values of each fatigue hot spot are obtained by using the Miner's rule, and the stress limit cycle numbers corresponding to the fatigue hot spots of the culvert at this stress level are determined according to the stress-life curve of the material. The formula is as follows: ; Wherein, represents the stress limit cycle number of the th fatigue hot spot of the culvert, is a material constant, is the fatigue strength index of the material, is the true stress value at the th fatigue hot spot; Combined with the fatigue damage degree of the culvert, the formula for deriving the fatigue life of the culvert is as follows: ; Wherein, represents the fatigue life of the culvert.

[0015] The present invention also provides a calculation system for the fatigue life of a road prefabricated culvert. The fatigue life calculation system is used to execute the above-mentioned method for calculating the fatigue life of a road prefabricated culvert, and includes: A culvert three-dimensional model establishment module, which is used to establish a three-dimensional finite element model of the culvert according to the size, wall thickness and opening position of the culvert, set the material property parameters and boundary conditions of the anti-fatigue performance of the culvert, apply loads to the finite element model and perform mesh element division, calculate the displacement data of each mesh element, and set a limit displacement threshold to screen out the fatigue hot spots of the culvert. The fatigue hot spots are the units whose displacement data exceed the limit displacement threshold; A stress measurement and data calibration module, which is based on the fatigue stress analysis method, installs strain sensors at each fatigue hot spot of the culvert to measure the stress values of each fatigue hot spot of the culvert, and obtains the road passing vehicle data to generate a stress calibration coefficient, and uses the generated stress calibration coefficient to calibrate the stress values of each fatigue hot spot of the culvert to eliminate the influence of extreme stress values on the measurement results. The passing vehicle data includes the weight of the vehicle and the average speed of the vehicle passing through the road; Temperature compensation module. The temperature compensation module is used to arrange temperature sensors at each fatigue hot spot of the culvert, conduct real-time temperature monitoring and record the temperature change situation. According to the relationship between temperature and calibrated stress, a temperature compensation model is established, and the collected stress data is corrected using the established model to eliminate the influence of temperature on the stress measurement result; Damage analysis and cumulative assessment module. The damage analysis and cumulative assessment module is used to obtain the true stress value of the culvert fatigue hot spot after calibration by extreme stress values and temperature compensation, define the damage variable of each fatigue hot spot of the culvert based on the strain-stress relationship, represent the cumulative damage degree of each fatigue hot spot of the culvert by superimposing multiple damage degrees, and deduce the fatigue damage degree of the culvert based on the definition of the damage variable; Life assessment module. The life assessment module analyzes the true stress value under each culvert fatigue hot spot based on Miner's rule, obtains the corresponding material stress limit cycle times, and combines the fatigue damage degree of the culvert to obtain the fatigue life of the culvert during actual use and operation.

[0016] Compared with the prior art, the beneficial effects of the present invention are: By establishing an accurate three-dimensional finite element model and a dynamic monitoring system, the present invention significantly improves the calculation accuracy of the fatigue life of road precast culverts. Using the real-time collected strain and temperature data, combined with the stress calibration and temperature compensation model, it can more accurately reflect the working state of the culvert during actual operation. This method effectively solves the problem of ignoring dynamic loads and environmental factors in traditional static analysis, making the identification and damage assessment of culvert fatigue hot spots more scientific and reasonable, thus providing a reliable basis for engineering design and maintenance; In addition, this solution realizes the systematic analysis and cumulative assessment of fatigue damage, and deduces the calculation of the overall fatigue life based on Miner's rule, providing a more comprehensive guarantee for structural safety. Through the refined definition of damage degree and the comprehensive assessment of multiple fatigue hot spots, engineers can clearly identify and respond to potential risks, thereby extending the service life of the culvert and reducing maintenance costs. Brief Description of the Drawings

[0017] Figure 1 It is a schematic diagram of the overall method flow of the present invention.

[0018] Figure 2 It is a schematic diagram of the analysis of the fatigue damage degree of the culvert of the present invention.

[0019] Figure 3 It is a schematic diagram of the analysis of the stress limit cycle times of the culvert of the present invention.

[0020] Figure 4 It is a schematic diagram of the system module flow of the present invention. Detailed Embodiments

[0021] To make the objectives, technical solutions, and advantages of the present invention more clear and understandable, the present invention will be further described in detail below in conjunction with specific embodiments.

[0022] It should be noted that unless otherwise defined, the technical terms or scientific terms used in the present invention should have the ordinary meanings understood by those with ordinary skills in the field to which the present invention belongs. The "first", "second", and similar terms used in the present invention do not indicate any order, quantity, or importance, but are only used to distinguish different components. The terms such as "including" or "comprising" mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects. The terms such as "connected" or "linked" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms such as "upper", "lower", "left", "right", etc. are only used to represent relative positional relationships, and when the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0023] Embodiment: Please refer to Figure 1 , a calculation method for the fatigue life of a prefabricated road culvert, and the specific steps include: Step 1: Establish a three-dimensional finite element model of the culvert according to the size, wall thickness, and opening position of the culvert, set the material property parameters and boundary conditions of the anti-fatigue performance of the culvert, perform mesh element division on the finite element model and apply static loads, calculate the displacement data of each mesh element, and set a limit displacement threshold to screen out the fatigue hot spots of the culvert. The fatigue hot spots are the elements whose displacement data exceed the limit displacement threshold; Step 2: Based on the fatigue stress analysis method, install strain sensors at each fatigue hot spot of the culvert to measure the stress values of each fatigue hot spot of the culvert, and obtain the traffic data of passing vehicles on the road to generate a stress calibration coefficient. Use the generated stress calibration coefficient to calibrate the stress values of each fatigue hot spot of the culvert to eliminate the influence of extreme stress values on the measurement results. The traffic data of passing vehicles includes the weight of the vehicle and the average speed of the vehicle passing through the road; Step 3: Arrange temperature sensors at each fatigue hot spot of the culvert, perform real-time temperature monitoring and record the change of temperature. According to the relationship between temperature and the calibrated stress, establish a temperature compensation model, and use the established model to correct the collected stress data to eliminate the influence of temperature on the stress measurement results; Step 4: After calibration of extreme stress values and temperature compensation, obtain the true stress values of the fatigue hot spots of the culvert, and define the damage variables of each fatigue hot spot of the culvert based on the strain-stress relationship. Use the superposition of multiple damage degrees to represent the cumulative damage degree of each fatigue hot spot of the culvert, and deduce the fatigue damage degree of the culvert based on the definition of damage variables; Step 5: Analyze the true stress values at each fatigue hot spot of the culvert based on Miner's rule, obtain the corresponding material stress limit cycle times, and combine with the fatigue damage degree of the culvert to obtain the fatigue life of the culvert during actual operation.

[0024] It should be noted that by setting the limit strain and displacement thresholds, potential fatigue hot spots can be effectively screened out, providing a scientific basis for subsequent fatigue life assessment and maintenance decisions. This method can identify and locate potential weaknesses in the structure in advance.

[0025] The shape function is used to define the vertices of the tetrahedral element to accurately describe the displacement change inside the element. In finite element analysis, the shape function can interpolate the displacement at any position inside the entire element through a linear combination of the element vertices, which is particularly important for non-linear problems and local deformation calculations. The tetrahedral element is chosen as the basic element because of its shape flexibility and adaptability, which can better adapt to the discretization of complex geometries. Especially when dealing with three-dimensional complex structures, the tetrahedral element can provide higher accuracy and more efficient computational efficiency. This enables a more comprehensive capture of the true response of the culvert under different loading conditions during stress analysis, thereby improving the reliability of fatigue life prediction.

[0026] Therefore, it is necessary to establish a three-dimensional finite element model of the culvert, calculate the strain and displacement data of each element, and set the limit strain threshold and limit displacement threshold to screen out the fatigue hot spots of the culvert. The method is as follows: Use CAD software to establish a three-dimensional model of the culvert and define its length, width, height, and wall thickness. Adjust the opening position of the culvert to face the road surface directly. Use finite element analysis software to mesh the three-dimensional culvert model to generate tetrahedral elements, ensuring that the mesh density is fine enough in the fatigue hot spot area. Set the material property parameters, including tensile strength, yield strength, elastic modulus, Poisson's ratio, residual stress, and thermal expansion coefficient, and apply simulated vehicle loads; For a tetrahedral element, use a linear shape function to represent the displacement inside the element. Let the four vertices of the tetrahedral element be , , , , then the expressions of the shape functions of each vertex are: ; ; ; ; where , , , are respectively the four vertices of a tetrahedral element, is the volume of a tetrahedral element, , , , are respectively the abscissas of the four vertices in the tetrahedral element, , , , are respectively the ordinates of the four vertices in the tetrahedral element; Based on the method of nonlinear finite element analysis and local deformation calculation, the displacement of a tetrahedral element is calculated according to the formula: ; ; where, represents the displacement of a tetrahedral element, represents the displacement of the th vertex, , , respectively represent the displacement components of vertex in the , , directions, represents the displacement increment of the th vertex, is the partial derivative of the shape function with respect to the coordinates of the four vertices, describing the rate of change of the shape function with the coordinates, is the index of the vertex in the tetrahedral element, and ; Set the extreme displacement threshold , and mark the tetrahedral elements with displacement data exceeding as the fatigue hot spots of the culvert.

[0027] It should be noted that during normal road vehicle traffic, for some key parts of the culvert, such as the connection points of the support points and anchor points of the culvert, as well as the opening positions and reserved holes of the culvert, these parts will instantaneously generate high stresses when heavy vehicles pass by. Therefore, if the extreme stress values are not eliminated, the actual fatigue life of the material may be overestimated or underestimated, which will in turn affect the safety and reliability of the structure; through stress calibration, the influence of extreme stress values can be eliminated, making the stress values more accurately reflect the actual stress state of the material, thereby improving the reliability of the measurement.

[0028] Therefore, it is necessary to obtain the stress values of each fatigue hot spot of the culvert box and calibrate the stress values of each fatigue hot spot of the culvert box by using the generated stress calibration coefficient. The method is as follows: Install strain sensors at each fatigue hot spot, obtain the elastic modulus of the material by monitoring the measured strain data in real time, and combine the strain measured at each fatigue hot spot. Calculate the corresponding stress value by using the stress formula. The formula is as follows: ; Among them, represents the stress value measured at the fatigue hot spot, is the elastic modulus of the material, is the strain at the fatigue hot spot; Obtain the stress calibration coefficient by generating data of passing vehicles on the road. The formula is as follows: ; Among them, represents the stress calibration coefficient, is the average speed of the vehicle passing through the road, is the weight of the vehicle, is the acceleration due to gravity; in the above calculation formula of the stress calibration coefficient reflects the influence of vehicle speed on stress. According to the basic principles of momentum and energy, when the vehicle passes, the square of its speed is proportional to the dynamic load it exerts. Therefore, the greater the speed, the greater the dynamic stress generated by the vehicle. So the speed is designed in square form; in the formula represents the weight of the vehicle. The greater the weight, the greater the static and dynamic loads applied to the culvert box, resulting in a corresponding increase in stress. Therefore, using the natural logarithm is to non-linearly process the influence of weight on stress, so that under vehicles of different weights, the resulting stress changes can be more accurately reflected; represents an adjustment factor, which is used to effectively convert the influence of vehicle load into a stress calibration coefficient to ensure that the stress value measured by the strain sensor can more accurately reflect the actual situation, The magnitude of reflects the degree of influence of vehicle dynamic load on the stress of the culvert box structure; As shown in the table of vehicle dynamic load experiments, in order to obtain the stress calibration coefficients under different types of vehicles, the present invention selects 20 groups of experimental data to demonstrate the reliability of the formula. The experiment selects seven different types of vehicles and passes through the road at increasing speeds from small to large, obtaining 20 groups of different stress data. Analyzing the data can obtain: Different types of vehicles have different weights and stress values. For example, the weight of heavy trucks is significantly higher than that of sedans, and their corresponding stress calibration coefficients are also higher, indicating that heavy vehicles have a greater impact on the structure. Among vehicles of the same type, as the speed increases, it generally shows an upward trend, suggesting that when vehicles are traveling at high speeds, the dynamic loads generated are significantly increased; Based on the above analysis, it can be considered that the data and formulas in this table are both logical and reasonable. The dynamic load experiment table provides an important reference for structural design and maintenance, especially when considering the impact of different types of vehicles on the structure. The stress calibration coefficient Calculation and analysis can help engineers better understand and predict the performance of the structure under different load conditions, promoting the formulation of safety design and maintenance strategies.

[0029] ; Table 1 - Automobile Dynamic Load Experiment Table Using the obtained stress calibration coefficient, the stress values measured at each fatigue hot spot of the culvert are calibrated to eliminate the influence of extreme stress values. The formula for obtaining the calibrated stress values is: ; Among them, represents the stress value measured at the fatigue hot spot after calibration; in the above formula, by dividing the measured stress value by the stress calibration coefficient the extreme stress values caused by dynamic loads can be effectively eliminated. When extreme stress values occur, the corresponding stress calibration coefficient also increases, thus reducing the influence of extreme stress values on the measurement results and effectively converting these instantaneous values into long-term and stable stress states; ; Table 2 - Calibrated Stress Value Comparison Table It can be seen from the calibrated stress value comparison table that under the same vehicle type in Table 1, the influence of extreme stress values will be brought about due to different speeds. After calibration, the stress values generated when the same type of vehicle passes through will not vary too much. Some stress values are significantly increased after calibration, reflecting that the influence of dynamic loads on stress measurement is effectively reduced, weakening the influence of extreme stress values on the measurement.

[0030] It should be noted that temperature changes will significantly affect the physical properties of materials, and thus affect the stress performance of the culvert under different environmental conditions. Therefore, considering the influence of temperature on the stress value can more realistically reflect the working state of the culvert during actual operation. The reason for setting up the temperature compensation model is that the change of environmental temperature will not only affect the elastic modulus and other mechanical properties of materials, but also may cause stress concentration and non-uniformity of deformation. If the temperature influence is not corrected, it may lead to deviation in the evaluation of the fatigue life of the culvert, and further affect the structural safety. Under high or low temperature conditions, the fatigue characteristics of materials may change. Therefore, establishing a polynomial regression model that can reflect this relationship can effectively capture the complex relationship between temperature and stress, making the stress analysis more accurate.

[0031] Therefore, it is necessary to establish a temperature compensation model according to the relationship between temperature and the calibrated stress, and use the established model to correct the collected stress data. The method is as follows: Install temperature sensors at the fatigue hot spots of the culvert to record the changes in environmental temperature in real time, and collect the stress data after stress calibration during the corresponding time period. Use the polynomial regression model to fit the influence of temperature on stress changes, and set the polynomial model as: ; where, represents the stress deviation value that changes with temperature under the temperature compensation model, , , are the regression coefficients solved by the least squares method, is the temperature variable; Substitute the stress data after stress calibration into the temperature model for correction. The formula is as follows: ; where, represents the true stress value of the fatigue hot spot of the culvert after calibration of the extreme stress value and temperature compensation.

[0032] It should be noted that defining the damage variables of each fatigue hot spot of the culvert based on the strain-stress relationship and representing the cumulative damage degree through the damage superposition of multiple cycles is a key step in evaluating the structural health and fatigue life. This method can quantify the damage degree borne by each fatigue hot spot of the culvert during actual use, thus providing a scientific basis for the safety analysis of the structure. By introducing the damage mechanics theory, the complex stress-strain relationship can be effectively transformed into a quantifiable damage index, making the calculation of the overall damage degree more accurate, and further providing guidance for subsequent maintenance decisions and structural reinforcement.

[0033] Therefore, it is necessary to define the damage variables of each fatigue hot spot of the culvert based on the strain-stress relationship, represent the cumulative damage degree of each fatigue hot spot of the culvert by superimposing multiple damage degrees, and derive the fatigue damage degree of the culvert based on the definition of the damage variable. The method is as follows: Based on the damage mechanics theory, the damage degree is represented by defining the damage variable of the culvert, and the definition of the damage variable is represented by the stress-strain relationship. The following relational expressions are introduced: ; ; where, represents the damage degree at the fatigue hot spot of the culvert, is the damage variable, and its value range is from 0 to 1, is the maximum stress that the material at the fatigue hot spot can withstand, is the ultimate strength of the material; Based on the above definition of the damage variable, the fatigue damage degree of the culvert is derived. The fatigue damage degree is expressed as the superposition of the damage of multiple cycles. The formula is as follows: ; where, represents the fatigue damage degree of the culvert, represents the damage degree at the th fatigue hot spot of the culvert, is the index of the fatigue hot spot in the culvert, and , is the total number of fatigue hot spots in the culvert, represents the damage variable at the th fatigue hot spot of the culvert.

[0034] It should be noted that obtaining the true stress value, material fatigue limit and actual stress cycle number of each fatigue hot spot of the culvert, and combining with the fatigue damage degree to evaluate the fatigue life of the culvert is the core link of structural health monitoring and evaluation. This method can not only accurately calculate the cycle number and damage degree of each fatigue hot spot based on the stress data under actual working conditions, but also effectively quantify the cumulative damage through the Miner's rule, and then derive the overall fatigue life of the culvert.

[0035] Therefore, it is necessary to obtain the true stress value and the corresponding material stress limit cycle number under each fatigue hot spot of the culvert, and combine with the fatigue damage degree of the culvert to obtain the fatigue life of the culvert during actual operation. The method is as follows: The Miner's rule is used to obtain the true stress value of each fatigue hot spot, and the stress limit cycle number corresponding to the fatigue hot spot of the culvert at this stress level is determined according to the stress-life curve of the material. The formula is as follows: ; Among them, represents the stress limit cycle number of the th fatigue hot spot of the box culvert, is a material constant, is the fatigue strength index of the material, is the true stress value at the th fatigue hot spot; Combined with the fatigue damage degree of the box culvert, the formula for deriving the fatigue life of the box culvert is: ; Among them, represents the fatigue life of the box culvert; in the above formula, the fatigue damage degree of the box culvert is the greater, the smaller the fatigue life of the box culvert, which means that the proportion of the fatigue cycle number experienced during use relative to the fatigue limit cycle number of the material increases, resulting in an increase in the damage degree of the material and a decrease in the fatigue life; while is the sum of the limit cycle numbers of all fatigue hot spots of the box culvert. The larger this sum is, the more the maximum cycle number that the structure can withstand at all fatigue hot spots, thus providing a higher potential fatigue life.

[0036] It can be seen from the box culvert fatigue life analysis table that as the limit stress cycle number increases, the box culvert fatigue life also increases. This trend indicates that when the limit stress cycle number that the box culvert can withstand increases, the fatigue bearing capacity of the material increases, so that it has a longer service life in actual use; the fatigue damage degree and the box culvert fatigue life have a significant negative correlation, that is, as the fatigue damage degree increases, the box culvert fatigue life gradually decreases; when is 1, the fatigue life is the lowest, only 1, and when drops to 0.1, the fatigue life soars to 190. This result shows that the fatigue damage degree reflects the damage degree of the material during fatigue cycling. The higher the damage degree, the greater the proportion of the fatigue cycle number that the material withstands relative to its fatigue limit, resulting in an increase in the damage of the material and a significant shortening of its service life.

[0037] ; Table 3 - Box Culvert Fatigue Life Analysis Table Please refer to Figure 2, it can be obtained from the schematic diagram of the fatigue damage degree analysis of the culvert box that the X-axis represents the fatigue damage degree, ranging from 0 to 1, which reflects the damage degree of the culvert box material during the fatigue cycle. The Y-axis represents the fatigue life of the culvert box, indicating the expected service life of the material under a specific fatigue damage degree. As the fatigue damage degree increases, the fatigue life decreases significantly. This trend emphasizes the negative impact of the damage degree on the durability of the culvert box structure. Especially when the damage degree is low, close to 0, the fatigue life of the culvert box reaches the maximum value, while at high damage degrees, the fatigue life drops rapidly. By reducing the damage degree, the service life of the culvert box can be effectively extended, providing an important reference basis for engineering practice.

[0038] Please refer to Figure 3 , it can be seen from the schematic diagram of the analysis of the stress limit cycle times of the culvert box that as the stress limit cycle times increase, the fatigue life gradually rises. This indicates that when the culvert box can withstand more stress cycles, its overall fatigue life is correspondingly extended. At low stress cycle times, the increase in fatigue life is relatively small, but after reaching a certain value, the growth rate of the fatigue life significantly accelerates, especially when approaching cycles, the fatigue life increases significantly. This chart shows that as the stress limit cycle times of the culvert box increase, its fatigue life is significantly improved, emphasizing the importance of reasonably controlling and optimizing the fatigue cycle times during the design and maintenance processes. By increasing the load-bearing capacity of the material and optimizing the design, the service life of the culvert box can be effectively extended, providing a reliable basis for practical engineering.

[0039] Please refer to Figure 4 , the present invention further provides a fatigue life calculation system for a road prefabricated culvert box. The fatigue life calculation system is used to execute the above-mentioned fatigue life calculation method for a road prefabricated culvert box, including: A culvert box three-dimensional model establishment module, which is used to establish a three-dimensional finite element model of the culvert box according to the size, wall thickness, and opening position of the culvert box, set the material property parameters and boundary conditions of the anti-fatigue performance of the culvert box, apply loads to the finite element model and perform mesh element division, calculate the displacement data of each mesh element, and set a limit displacement threshold to screen out the fatigue hot spots of the culvert box. The fatigue hot spots are the elements whose displacement data exceeds the limit displacement threshold; A stress measurement and data calibration module, which, based on the fatigue stress analysis method, installs strain sensors at each fatigue hot spot of the culvert box to measure the stress values of each fatigue hot spot of the culvert box, obtains the road passing vehicle data to generate a stress calibration coefficient, and uses the generated stress calibration coefficient to calibrate the stress values of each fatigue hot spot of the culvert box to eliminate the influence of extreme stress values on the measurement results. The passing vehicle data includes the weight of the vehicle and the average speed of the vehicle passing through the road; Temperature compensation module. The temperature compensation module is used to arrange temperature sensors at each fatigue hot spot of the culvert, conduct real-time temperature monitoring and record the temperature change situation. According to the relationship between temperature and calibrated stress, a temperature compensation model is established, and the established model is used to correct the collected stress data to eliminate the influence of temperature on the stress measurement result; Damage analysis and cumulative assessment module. The damage analysis and cumulative assessment module is used to obtain the true stress value of the fatigue hot spot of the culvert after calibration by extreme stress values and temperature compensation, define the damage variable of each fatigue hot spot of the culvert based on the strain-stress relationship, represent the cumulative damage degree of each fatigue hot spot of the culvert by superimposing multiple damage degrees, and deduce the fatigue damage degree of the culvert based on the definition of the damage variable; Life assessment module. The life assessment module analyzes the true stress value under each fatigue hot spot of the culvert based on the Miner's rule, obtains the corresponding material stress limit cycle times, and combines the fatigue damage degree of the culvert to obtain the fatigue life of the culvert during actual use and operation.

[0040] The above formulas are all dimensionless and take their numerical values for calculation. The formulas are obtained by collecting a large amount of data and performing software simulation to get a formula closest to the actual situation. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0041] The above embodiments can be implemented in whole or in part by software, hardware, firmware or any other combination. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. Those skilled in the art can realize that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are executed by hardware or software methods depends on the specific application and design constraints of the technical solution.

[0042] The units described as separate components may or may not be physically separated. The components shown as units may or may not be physical units, and may be located in one place, or may be distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0043] The above is only the specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present application, and all of them should be covered within the protection scope of the present application.

Claims

1. A calculation method for the fatigue life of a prefabricated road culvert, characterized in that, The specific steps include: Step 1: Establish a three-dimensional finite element model of the box culvert according to the dimensions, wall thickness, and opening position of the box culvert. Set the material property parameters and boundary conditions for the anti-fatigue performance of the box culvert. Perform mesh element division on the finite element model and apply static loads. Calculate the displacement data of each mesh element, and set a limit displacement threshold to screen out the fatigue hot spots of the box culvert. The fatigue hot spots are the elements where the displacement data exceeds the limit displacement threshold. Step 2: Based on the fatigue stress analysis method, install strain sensors at each fatigue hot spot of the box culvert to measure the stress values of each fatigue hot spot of the box culvert, and obtain the traffic data of passing vehicles on the road to generate a stress calibration coefficient. Use the generated stress calibration coefficient to calibrate the stress values of each fatigue hot spot of the box culvert to eliminate the influence of extreme stress values on the measurement results. The passing vehicle data includes the weight of the vehicle and the average speed of the vehicle passing through the road. Step 3: Arrange temperature sensors at each fatigue hot spot of the box culvert to conduct real-time temperature monitoring and record the temperature change. According to the relationship between temperature and calibrated stress, establish a temperature compensation model, and use the established model to correct the collected stress data to eliminate the influence of temperature on the stress measurement results. Step 4: Obtain the true stress values of the fatigue hot spots of the box culvert after calibration of extreme stress values and temperature compensation. Define the damage variables of each fatigue hot spot of the box culvert based on the strain-stress relationship. Use the superposition of multiple damage degrees to represent the cumulative damage degree of each fatigue hot spot of the box culvert, and deduce the fatigue damage degree of the box culvert based on the definition of damage variables. Step 5: Analyze the true stress values under each fatigue hot spot of the box culvert based on the Miner's rule to obtain the corresponding material stress limit cycle times, and combine with the fatigue damage degree of the box culvert to obtain the fatigue life of the box culvert during actual use and operation.

2. The fatigue life calculation method of a road prefabricated culvert according to claim 1, characterized in that, To establish a three-dimensional finite element model of the box culvert, calculate the strain and displacement data of each element, calculate the displacement data of each mesh element, and set a limit displacement threshold to screen out the fatigue hot spots of the box culvert. The method is based on: Use CAD software to establish a three-dimensional model of the box culvert and define its length, width, height, and wall thickness. Adjust the opening position of the box culvert to face the road surface directly. Use finite element analysis software to perform mesh division on the three-dimensional box culvert model to generate tetrahedral elements. Set the material property parameters, including tensile strength, yield strength, elastic modulus, Poisson's ratio, residual stress, and thermal expansion coefficient, and apply simulated vehicle loads. For a tetrahedral element, linear shape functions are used to represent the displacements inside the element. Let the four vertices of the tetrahedral element be , , , , then the expressions for the shape functions at each vertex are: ； ； ； ； Among them, , , , are the four vertices of the same tetrahedron element respectively, is the volume of the tetrahedron element, , , , are the abscissas of the four vertices in the tetrahedron element respectively, , , , are the ordinates of the four vertices in the tetrahedron element respectively; Based on the method of nonlinear finite element analysis and local deformation calculation, calculate the displacement of the tetrahedral elements. The formula is based on: ； ； Among them, represents the displacement of the tetrahedral element, represents the displacement of the th vertex in the tetrahedral element, , , respectively represent the displacement components of vertex in the , , directions, represents the increment of the displacement of the th vertex in the tetrahedral element, is the partial derivative of the shape function with respect to the coordinates of the four vertices, describing the rate of change of the shape function with the coordinates, is the index of the vertex in the tetrahedral element, and ; Set the limit displacement threshold , and mark the tetrahedral elements whose displacement data exceeds as the fatigue hot spots of the culvert box.

3. A method for calculating the fatigue life of a prefabricated road culvert according to claim 1, characterized in that, To obtain the stress values of each fatigue hot spot of the box culvert and use the generated stress calibration coefficient to calibrate the stress values of each fatigue hot spot of the box culvert. The method is based on: Install strain sensors at each fatigue hot spot, measure the strain data through real-time monitoring, obtain the elastic modulus of the material combined with the strain measured at each fatigue hot spot, and calculate the corresponding stress value using the stress formula. The formula is based on: ； Among them, represents the stress value measured at the fatigue hot spot, is the elastic modulus of the material, is the strain at the fatigue hot spot; Obtain the traffic data of passing vehicles on the road to generate a stress calibration coefficient. The formula is based on: ； Among them, represents the stress calibration coefficient, is the average speed of the vehicle passing through the road, is the weight of the vehicle, is the acceleration due to gravity; Using the obtained stress calibration coefficient, calibrate the stress values measured at each fatigue hot spot of the box culvert to eliminate the influence of extreme stress values. The formula for obtaining the calibrated stress value is as follows: ； Among them, represents the stress value measured at the fatigue hot spot after calibration.

4. A method for calculating the fatigue life of a prefabricated road culvert according to claim 3, characterized in that, According to the relationship between temperature and the calibrated stress, establish a temperature compensation model, and use the established model to correct the collected stress data. The method is as follows: Install temperature sensors at the fatigue hot spots of the box culvert, record the ambient temperature changes in real time, and collect the stress data after stress calibration during the corresponding time period. Use the polynomial regression model to fit the influence of temperature on stress changes. Set the polynomial model as: ； Among them, represents the stress deviation value varying with temperature under the temperature compensation model, , , are regression coefficients solved by the least squares method, is the temperature variable; Substitute the stress data after stress calibration into the temperature model for correction. The formula is as follows: ； Among them, represents the true stress value of the fatigue hot spot of the culvert after calibration of extreme stress values and temperature compensation.

5. A calculation method for the fatigue life of a prefabricated road culvert according to claim 1, characterized in that, Define the damage variables at each fatigue hot spot of the box culvert based on the strain-stress relationship. Use the superposition of multiple damage degrees to represent the cumulative damage degree at each fatigue hot spot of the box culvert. Derive the fatigue damage degree of the box culvert based on the definition of damage variables. The method is as follows: Based on the damage mechanics theory, the damage degree is represented by defining the damage variables of the box culvert. The definition of the damage variables is represented by the stress-strain relationship. Introduce the following relationship: ； ； Among them, represents the damage degree at the fatigue hot spot of the box culvert, is the damage variable, and its value range is from 0 to 1, is the maximum stress that the material at the fatigue hot spot can withstand, is the ultimate strength of the material; Based on the above definition of damage variables, derive the fatigue damage degree of the box culvert. The fatigue damage degree is expressed as the superposition of damage in multiple cycles. The formula is as follows: ； Among them, represents the fatigue damage degree of the box culvert, represents the damage degree at the th fatigue hot spot of the box culvert, is the index of the fatigue hot spots in the box culvert, and , is the total number of fatigue hot spots in the box culvert, represents the damage variable at the th fatigue hot spot of the box culvert.

6. A method for calculating the fatigue life of a prefabricated road culvert according to claim 5, characterized in that, Obtain the true stress value and the corresponding material stress limit cycle number at each fatigue hot spot of the box culvert, and combine the fatigue damage degree of the box culvert to obtain the fatigue life of the box culvert during actual use and operation. The method is as follows: Use the Miner's rule to obtain the true stress value at each fatigue hot spot, and determine the stress limit cycle number corresponding to the fatigue hot spot of the box culvert at this stress level according to the stress-life curve of the material. The formula is as follows: ； Among them, represents the stress limit cycle times of the th fatigue hot spot of the culvert box, is a material constant, is the fatigue strength index of the material, is the true stress value at the th fatigue hot spot; Combine the fatigue damage degree of the box culvert, and the formula for deriving the fatigue life of the box culvert is as follows: ； Among them, represents the fatigue life of the culvert box.

7. A fatigue life calculation system for prefabricated road culverts, characterized in that, The fatigue life calculation system is used to execute the road prefabricated box culvert fatigue life calculation method described in any one of claims 1-6, including: A box culvert three-dimensional model establishment module, which is used to establish a three-dimensional finite element model of the box culvert according to the size, wall thickness and opening position of the box culvert, set the material property parameters and boundary conditions of the anti-fatigue performance of the box culvert, apply loads to the finite element model and perform mesh element division, calculate the displacement data of each mesh element, and set a limit displacement threshold to screen out the fatigue hot spots of the box culvert. The fatigue hot spots are the units whose displacement data exceed the limit displacement threshold; A stress measurement and data calibration module, which is based on the fatigue stress analysis method, installs strain sensors at each fatigue hot spot of the box culvert to measure the stress values at each fatigue hot spot of the box culvert, and obtains the road traffic data to generate a stress calibration coefficient. Use the generated stress calibration coefficient to calibrate the stress values at each fatigue hot spot of the box culvert to eliminate the influence of extreme stress values on the measurement results. The traffic data includes the weight of the vehicle and the average speed of the vehicle passing through the road; Temperature compensation module, which is used to arrange temperature sensors at each fatigue hot spot of the culvert, conduct real-time temperature monitoring and record the temperature change situation, establish a temperature compensation model according to the relationship between temperature and calibrated stress, and use the established model to correct the collected stress data to eliminate the influence of temperature on the stress measurement result; Damage analysis and cumulative assessment module, which is used to obtain the true stress value of the culvert fatigue hot spot after calibration with extreme stress values and temperature compensation, define the damage variables of each fatigue hot spot of the culvert based on the strain-stress relationship, represent the cumulative damage degree of each fatigue hot spot of the culvert with the superposition of multiple damage degrees, and deduce the fatigue damage degree of the culvert based on the definition of damage variables; Life assessment module, which analyzes the true stress value under each culvert fatigue hot spot based on the Miner's rule, obtains the corresponding material stress limit cycle times, and combines the fatigue damage degree of the culvert to obtain the fatigue life of the culvert during actual use and operation.

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