A method and system for calculating fatigue life of road assembled box culvert

Abstract

The present invention provides a method and system for calculating the fatigue life of a prefabricated box culvert on a road, relating to the fields of material mechanics and civil engineering technology. The method establishes a three-dimensional finite element model of the box culvert, screens fatigue hotspots, and, based on fatigue stress analysis, installs strain sensors at the fatigue hotspots to measure stress values. Calibration coefficients are generated using vehicle weight and speed data to correct the stress values. Temperature sensors are deployed for real-time monitoring, and a temperature compensation model is established to correct the stress data. Ultimately, after calibration and compensation, the true stress values of the fatigue hotspots are obtained, the cumulative damage degree is defined, and the fatigue life of each hotspot is calculated based on Miner's law. By establishing a three-dimensional finite element model and implementing stress and temperature monitoring and calibration, the present invention accurately assesses the fatigue performance and service life of the box culvert.

Description

Technical Field

[0001] The present invention relates to the technical field of material mechanics and civil engineering, and in particular to a method and system for calculating the fatigue life of a road assembled box 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, box culverts, as common drainage and traffic channel structures, need to ensure their safety and reliability during use. By implementing fatigue life calculations, engineers can assess the fatigue damage that box culverts may suffer during actual operation, thereby optimizing the design and material selection and increasing the service life of the structure. Secondly, in the renovation and reinforcement projects of old infrastructure, fatigue life calculation methods can be used to monitor the health of existing box culverts, helping engineers to regularly evaluate their status and formulate appropriate maintenance or reinforcement strategies to ensure road safety and smooth traffic.

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

[0004] In the existing technology, traditional box culvert fatigue analysis methods often rely on static analysis or simplified theoretical models, ignoring the impact of dynamic traffic loads and environmental factors. This simplistic approach can easily lead to underestimation or overestimation of fatigue damage, which in turn affects the safety and service life of the box culvert.

[0005] Secondly, existing technologies have limitations in predicting fatigue life under dynamic loads. Most methods fail to fully consider the impact of vehicle dynamic loads on box culvert structures, and often perform analysis based on static loads. They cannot accurately capture stress fluctuations that may occur in actual use. For example, traditional finite element analysis methods usually rely on static load models and often lack systematic calibration and compensation mechanisms 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 operation, vehicles will produce significant dynamic load changes, which have a significant impact on the fatigue life of the box culvert.

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

[0007] The above information disclosed in this Background section is only for enhancement of understanding of the background of the present disclosure and therefore it may contain information that does not form the prior art that is already known to a person of ordinary skill in the art. Summary of the Invention

[0008] The purpose of the present invention is to provide a method and system for calculating the fatigue life of a road assembled box culvert to solve the problems raised in the above background technology.

[0009] To achieve the above object, the present invention provides the following technical solutions:

[0010] A method for calculating the fatigue life of a road prefabricated box culvert comprises the following steps:

[0011] Step 1: Create a 3D finite element model of the box culvert based on its size, wall thickness, and opening location. Set the material characteristic parameters and boundary conditions for the box culvert's fatigue resistance. Grid the finite element model and apply a static load. Calculate the displacement data for each grid cell and establish an ultimate displacement threshold to identify fatigue hotspots in the box culvert. These hotspots are defined as cells whose displacement data exceeds the ultimate displacement threshold.

[0012] Step 2: Based on the fatigue stress analysis method, strain sensors are installed at each fatigue hotspot of the box culvert to measure the stress value of each fatigue hotspot of the box culvert. Traffic data on the road is obtained to generate stress calibration coefficients. The generated stress calibration coefficients are used to calibrate the stress values of each fatigue hotspot of the box culvert to eliminate the influence of extreme stress values on the measurement results.

[0013] Step 3: Place temperature sensors at each fatigue hotspot of the box culvert to conduct real-time temperature monitoring and record temperature changes. Based on the relationship between temperature and calibrated stress, establish a temperature compensation model. Use the established model to correct the collected stress data to eliminate the influence of temperature on the stress measurement results.

[0014] Step 4: After extreme stress value calibration and temperature compensation, the true stress value of the fatigue hotspot of the box culvert is obtained. Based on the strain-stress relationship, the damage variables of each fatigue hotspot of the box culvert are defined. Multiple damage degrees are superimposed to represent the cumulative damage degree of each fatigue hotspot of the box culvert. Based on the definition of damage variables, the fatigue damage degree of the box culvert is derived.

[0015] Step 5: Based on Miner's law, analyze the true stress value at each box culvert fatigue hotspot to obtain the corresponding material stress limit cycle number. Combined with the fatigue damage degree of the box culvert, the fatigue life of the box culvert in actual use and operation is obtained.

[0016] Furthermore, a three-dimensional finite element model of the box culvert was established, the strain and displacement data of each unit were calculated, the displacement data of each grid unit was calculated, and the limit displacement threshold was established to screen out the fatigue hotspots of the box culvert. The method used was:

[0017] Use CAD software to create a 3D box culvert model and define its length, width, height, and wall thickness. Adjust the opening of the box culvert to face the road surface. Use finite element analysis software to mesh the 3D box culvert model, generate tetrahedral elements, set material property parameters, including tensile strength, yield strength, elastic modulus, Poisson's ratio, residual stress, and thermal expansion coefficient, and apply simulated vehicle loads.

[0018] For tetrahedral elements, linear shape functions are used to represent the displacement inside the element. Let the four vertices of the tetrahedral element be 、 、 、 , then the expression of the shape function of each vertex is:

[0019] ;

[0020] ;

[0021] ;

[0022] ;

[0023] in, 、 、 、 are the four vertices of the same tetrahedral unit, is the volume of the tetrahedral unit, 、 、 、 are the horizontal coordinates of the four vertices in the tetrahedron unit, 、 、 、 are the ordinates of the four vertices in the tetrahedron unit;

[0024] The displacement calculation of the tetrahedron element is based on the method of nonlinear finite element analysis and local deformation calculation. The formula is:

[0025] ;

[0026] ;

[0027] in, represents the displacement of the tetrahedral element, Indicates the tetrahedral element The displacement of the vertices, 、 、 Represents vertices exist 、 、 The displacement component in the direction, Indicates the tetrahedral element The increment of the vertex displacement, is the partial derivative of the shape function with respect to the coordinates of the four vertices, which describes the rate at which the shape function changes with the coordinates. is the index of the vertex in the tetrahedral cell, and ;

[0028] Establishing a limit displacement threshold , the displacement data exceeds The tetrahedral elements are marked as fatigue hot spots in the box culvert.

[0029] Furthermore, the stress values of each fatigue hotspot of the box culvert are obtained, and the stress values of each fatigue hotspot of the box culvert are calibrated using the generated stress calibration coefficient. The method is as follows:

[0030] A strain sensor is installed at each fatigue hotspot. The strain data is measured in real time to obtain the elastic modulus of the material. Combined with the strain measured at each fatigue hotspot, the corresponding stress value is calculated using the stress formula. The formula is:

[0031] ;

[0032] in, represents the stress value measured at the fatigue hotspot, is the elastic modulus of the material, is the strain at the fatigue hot spot;

[0033] Obtaining road traffic data to generate stress calibration coefficients is based on the following formula:

[0034] ;

[0035] in, represents the stress calibration coefficient, is the average speed of vehicles passing through the road, is the weight of the vehicle, is the acceleration due to gravity;

[0036] The obtained stress calibration coefficient is used to calibrate the stress values measured at each fatigue hotspot of the box culvert to eliminate the influence of extreme stress values. The formula for obtaining the calibrated stress value is:

[0037] ;

[0038] in, Represents the stress value measured at the fatigue hotspot after calibration.

[0039] Furthermore, based on the relationship between temperature and calibrated stress, a temperature compensation model is established, and the collected stress data is corrected using the established model. The method is as follows:

[0040] Temperature sensors are installed at the fatigue hotspots of the box culvert to record the ambient temperature changes in real time. Stress data after stress calibration are collected for the corresponding time period. A polynomial regression model is used to fit the effect of temperature on stress changes. The polynomial model is set as:

[0041] ;

[0042] in, Indicates the stress deviation value that changes with temperature under the temperature compensation model, 、 、 is the regression coefficient solved by the least squares method, is the temperature variable;

[0043] Substitute the stress data after stress calibration into the temperature model for correction based on the following formula:

[0044] ;

[0045] in, It represents the true stress value of the box culvert fatigue hotspot after extreme stress value calibration and temperature compensation.

[0046] Furthermore, the damage variables of each fatigue hotspot of the box culvert are defined based on the strain-stress relationship. The cumulative damage degree of each fatigue hotspot of the box culvert is represented by the superposition of multiple damage degrees. The fatigue damage degree of the box culvert is derived based on the definition of damage variables. The method is as follows:

[0047] Based on the damage mechanics theory, the damage degree is expressed by defining the damage variable of the box culvert. The damage variable is defined by the stress-strain relationship, and the following relationship is introduced:

[0048] ;

[0049] ;

[0050] in, Indicates the damage degree at the fatigue hotspot of the box culvert, is the damage variable, ranging from 0 to 1, It is the maximum stress that the material can withstand at the fatigue hotspot. is the ultimate strength of the material;

[0051] Based on the definition of damage variables, the fatigue damage degree of the box culvert is derived. The fatigue damage degree is expressed as the superposition of damage of multiple cycles. The formula is:

[0052] ;

[0053] in, Indicates the fatigue damage degree of the box culvert, Indicates box culvert The damage degree at each fatigue hotspot is is the index of the fatigue hotspot in the box culvert, and , is the total number of fatigue hot spots in the box culvert, Indicates box culvert The damage variable at each fatigue hotspot.

[0054] Furthermore, the true stress value and the corresponding material stress limit cycle number at each box culvert fatigue hotspot are obtained, and the fatigue damage degree of the box culvert is combined to obtain the fatigue life of the box culvert in actual use and operation. The method is based on:

[0055] The Miner rule is used to obtain the true stress value of each fatigue hotspot. The stress limit cycle number of the corresponding box culvert fatigue hotspot at this stress level is determined according to the stress-life curve of the material. The formula is:

[0056] ;

[0057] in, Indicates the box culvert The number of stress limit cycles of a fatigue hotspot, is the material constant, is the fatigue strength index of the material, For the The true value of stress at each fatigue hotspot;

[0058] Combined with the fatigue damage degree of the box culvert, the formula for deriving the fatigue life of the box culvert is:

[0059] ;

[0060] in, Indicates the fatigue life of the box culvert.

[0061] The present invention further provides a fatigue life calculation system for a road-assembled box culvert, wherein the fatigue life calculation system is used to execute the above-mentioned method for calculating the fatigue life of a road-assembled box culvert, and comprises:

[0062] A box culvert three-dimensional model establishment module is used to establish a three-dimensional finite element model of the box culvert based on the box culvert's size, wall thickness, and opening position, set material characteristic parameters and boundary conditions for the box culvert's fatigue resistance, apply loads to the finite element model and perform grid cell division, calculate the displacement data of each grid cell, and establish an extreme displacement threshold to screen out fatigue hotspots in the box culvert. The fatigue hotspot is a cell whose displacement data exceeds the extreme displacement threshold;

[0063] A stress measurement and data calibration module, based on fatigue stress analysis, installs strain sensors at various fatigue hotspots of the box culvert to measure stress values at each fatigue hotspot, obtains vehicle traffic data on the road to generate stress calibration coefficients, and uses the generated stress calibration coefficients to calibrate the stress values at each fatigue hotspot of the box culvert to eliminate the influence of extreme stress values on the measurement results;

[0064] A temperature compensation module is used to place temperature sensors at various fatigue hotspots in the box culvert to perform real-time temperature monitoring and record temperature changes. A temperature compensation model is established based on the relationship between temperature and calibrated stress. The established model is used to correct the collected stress data to eliminate the influence of temperature on the stress measurement results.

[0065] A damage analysis and cumulative assessment module is used to obtain the true stress value of the box culvert fatigue hotspot after extreme stress value calibration and temperature compensation, and define the damage variables of each fatigue hotspot of the box culvert based on the strain-stress relationship. The cumulative damage degree of each fatigue hotspot of the box culvert is represented by the superposition of multiple damage degrees, and the fatigue damage degree of the box culvert is derived based on the definition of the damage variable;

[0066] The life assessment module analyzes the true stress value under each box culvert fatigue hotspot based on Miner's law, obtains the corresponding material stress limit cycle number, and combines the fatigue damage degree of the box culvert to obtain the fatigue life of the box culvert in actual use and operation.

[0067] Compared with the prior art, the present invention has the following beneficial effects:

[0068] This invention significantly improves the calculation accuracy of the fatigue life of prefabricated box culverts on roads by establishing a precise three-dimensional finite element model and dynamic monitoring system. By utilizing real-time strain and temperature data, combined with stress calibration and temperature compensation models, the working status of the box culvert during actual operation can be more accurately reflected. This method effectively addresses the problem of neglecting dynamic loads and environmental factors in traditional static analysis, making the identification of fatigue hotspots and damage assessment of box culverts more scientific and reasonable, thus providing a reliable basis for engineering design and maintenance.

[0069] Furthermore, this solution implements systematic analysis and cumulative assessment of fatigue damage, deriving overall fatigue life calculations based on Miner's law, providing more comprehensive assurance of structural safety. Through detailed damage degree definitions and comprehensive assessment of multiple fatigue hotspots, engineers can clearly identify and address potential risks, thereby extending the service life of the box culvert and reducing maintenance costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 Schematic diagram of the overall method of the present invention.

[0071] Figure 2 This is a schematic diagram of fatigue damage analysis of the box culvert of the present invention.

[0072] Figure 3 This is a schematic diagram of the analysis of the number of stress limit cycles of the box culvert of the present invention.

[0073] Figure 4 It is a schematic diagram of the system module flow of the present invention. DETAILED DESCRIPTION

[0074] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to specific embodiments.

[0075] It should be noted that, unless otherwise defined, the technical or scientific terms used in the present invention should have the usual meanings understood by people with ordinary skills in the field to which the present invention belongs. The "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative position relationships. When the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0076] Example:

[0077] See also Figure 1 A method for calculating the fatigue life of a road assembled box culvert includes the following steps:

[0078] Step 1: Create a 3D finite element model of the box culvert based on its size, wall thickness, and opening location. Set the material characteristic parameters and boundary conditions for the box culvert's fatigue resistance. Grid the finite element model and apply a static load. Calculate the displacement data for each grid cell and establish an ultimate displacement threshold to identify fatigue hotspots in the box culvert. These hotspots are defined as cells whose displacement data exceeds the ultimate displacement threshold.

[0079] Step 2: Based on the fatigue stress analysis method, strain sensors are installed at each fatigue hotspot of the box culvert to measure the stress value of each fatigue hotspot of the box culvert. Traffic data on the road is obtained to generate stress calibration coefficients. The generated stress calibration coefficients are used to calibrate the stress values of each fatigue hotspot of the box culvert to eliminate the influence of extreme stress values on the measurement results.

[0080] Step 3: Place temperature sensors at each fatigue hotspot of the box culvert to conduct real-time temperature monitoring and record temperature changes. Based on the relationship between temperature and calibrated stress, establish a temperature compensation model. Use the established model to correct the collected stress data to eliminate the influence of temperature on the stress measurement results.

[0081] Step 4: After extreme stress value calibration and temperature compensation, the true stress value of the fatigue hotspot of the box culvert is obtained. Based on the strain-stress relationship, the damage variables of each fatigue hotspot of the box culvert are defined. Multiple damage degrees are superimposed to represent the cumulative damage degree of each fatigue hotspot of the box culvert. Based on the definition of damage variables, the fatigue damage degree of the box culvert is derived.

[0082] Step 5: Based on Miner's law, analyze the true stress value at each box culvert fatigue hotspot to obtain the corresponding material stress limit cycle number. Combined with the fatigue damage degree of the box culvert, the fatigue life of the box culvert in actual use and operation is obtained.

[0083] It should be noted that by setting the ultimate strain and displacement thresholds, potential fatigue hotspots can be effectively screened, providing a scientific basis for subsequent fatigue life assessment and maintenance decisions. This method can identify and locate potential structural weaknesses in advance.

[0084] The use of shape functions to define the vertices of tetrahedral elements is to accurately describe the displacement changes within the element. In finite element analysis, the shape function can interpolate the displacement of any position within the entire element through a linear combination of the element vertices, which is particularly important for nonlinear problems and local deformation calculations. The tetrahedral element is chosen as the basic element because of its flexibility and adaptability in shape, which can better adapt to the discretization of complex geometries. Especially when dealing with complex three-dimensional structures, the tetrahedral element can provide higher accuracy and more effective computational efficiency. This makes it possible to more comprehensively capture the true response of the box culvert under different loading conditions when performing stress analysis, thereby improving the reliability of fatigue life prediction.

[0085] Therefore, it is necessary to establish a three-dimensional finite element model of the box culvert, calculate the strain and displacement data of each unit, and set the ultimate strain threshold and ultimate displacement threshold to screen out the fatigue hotspots of the box culvert. The method is based on:

[0086] Use CAD software to create a 3D model of the box culvert and define its length, width, height, and wall thickness. Adjust the opening of the box culvert to face the road surface. Use finite element analysis software to mesh the 3D box culvert model, generating tetrahedral elements. Ensure that the mesh density is sufficiently fine in the fatigue hotspot area. Set material property parameters, including tensile strength, yield strength, elastic modulus, Poisson's ratio, residual stress, and thermal expansion coefficient, and apply simulated vehicle loads.

[0087] For a tetrahedral element, a linear shape function is used to represent the displacement inside the element. Let the four vertices of the tetrahedral element be 、 、 、 , then the expression of the shape function of each vertex is:

[0088] ;

[0089] ;

[0090] ;

[0091] ;

[0092] in, 、 、 、 are the four vertices of a tetrahedron unit, is the volume of a tetrahedron unit, 、 、 、 are the horizontal coordinates of the four vertices in the tetrahedron unit, 、 、 、 are the ordinates of the four vertices in the tetrahedron unit;

[0093] The displacement calculation of a tetrahedron element is performed based on the method of nonlinear finite element analysis and local deformation calculation. The formula is:

[0094] ;

[0095] ;

[0096] in, represents the displacement of a tetrahedral unit, Indicates the The displacement of the vertices, 、 、 Represents vertices exist 、 、 The displacement component in the direction, Indicates the The displacement increment of each vertex, is the partial derivative of the shape function with respect to the coordinates of the four vertices, which describes the rate at which the shape function changes with the coordinates. is the index of the vertex in the tetrahedral cell, and ;

[0097] Establishing a limit displacement threshold , the displacement data exceeds The tetrahedral elements are marked as fatigue hot spots in the box culvert.

[0098] It should be noted that during normal road traffic, certain key parts of the box culvert, such as the support points, anchor point connections, opening positions, reserved holes, etc., will instantly generate high stress when heavy vehicles pass through. Therefore, if the extreme stress values are not eliminated, the actual fatigue life of the material may be overestimated or underestimated, thereby affecting the safety and reliability of the structure. Through stress calibration, the influence of extreme stress values can be eliminated, so that the stress value can more accurately reflect the actual stress state of the material, thereby improving the reliability of the measurement.

[0099] Therefore, it is necessary to obtain the stress values of each fatigue hotspot of the box culvert and use the generated stress calibration coefficient to calibrate the stress values of each fatigue hotspot of the box culvert. The method is as follows:

[0100] A strain sensor is installed at each fatigue hotspot. The strain data is measured in real time to obtain the elastic modulus of the material. Combined with the strain measured at each fatigue hotspot, the corresponding stress value is calculated using the stress formula. The formula is:

[0101] ;

[0102] in, represents the stress value measured at the fatigue hotspot, is the elastic modulus of the material, is the strain at the fatigue hot spot;

[0103] Obtaining road traffic data to generate stress calibration coefficients is based on the following formula:

[0104] ;

[0105] in, represents the stress calibration coefficient, is the average speed of vehicles passing through the road, is the weight of the vehicle, is the acceleration due to gravity; in the above calculation formula of stress calibration coefficient It reflects the effect of vehicle speed on stress. According to the basic principles of momentum and energy, when a vehicle passes, the square of its speed is proportional to the dynamic load it applies. Therefore, the greater the speed, the greater the dynamic stress generated by the vehicle. Therefore, the speed is designed to be in square form. Represents the weight of the vehicle. The greater the weight, the greater the static and dynamic loads applied to the box culvert, and the resulting stress also increases accordingly. Therefore, the natural logarithm is used to represent the effect of weight on stress in a nonlinear manner, so that the stress changes caused by vehicles of different weights can be more accurately reflected. It represents an adjustment factor that is used to effectively convert the influence of vehicle load into a stress calibration coefficient, ensuring that the stress value measured by the strain sensor can more accurately reflect the actual situation. The size of reflects the degree of influence of vehicle dynamic load on the box culvert structure stress;

[0106] As shown in the vehicle dynamic load test table, in order to obtain the stress calibration coefficient under different types of vehicles, the present invention selected 20 sets of experimental data to demonstrate the reliability of the formula. The experiment selected seven different types of vehicles and passed through the road at speeds from small to large, obtaining 20 different sets of stress data. The data analysis showed that:

[0107] Different types of vehicles have different weights and stress values. For example, heavy trucks are significantly heavier than cars, and their corresponding stress calibration coefficients are also higher, indicating that heavy vehicles have a greater impact on the structure. For vehicles of the same type, as the speed increases, It usually shows an upward trend, which indicates that the dynamic load generated by the vehicle increases significantly when it is traveling at high speed;

[0108] Through the above analysis, it can be considered that the data and formulas in the table are logical and reasonable. The dynamic load test table provides an important reference for structural design and maintenance, especially when considering the impact of different types of vehicles on the structure. Calculation and analysis can help engineers better understand and predict the performance of structures under different loading conditions, and promote the formulation of safe design and maintenance strategies.

[0109] ;

[0110] Table 1-Automobile dynamic load test table

[0111] The obtained stress calibration coefficient is used to calibrate the stress values measured at each fatigue hotspot of the box culvert to eliminate the influence of extreme stress values. The formula for obtaining the calibrated stress value is:

[0112] ;

[0113] in, Represents the stress value measured at the fatigue hotspot after calibration; in the above formula, the measured stress value is Divide by the stress calibration factor It can effectively eliminate the extreme stress value caused by dynamic load. When the extreme stress value occurs, the corresponding The stress calibration factor will also increase, which will reduce the influence of extreme stress values on the measurement results and effectively convert these instantaneous values into long-term, stable stress states;

[0114] ;

[0115] Table 2 - Comparison of Calibrated Stress Values

[0116] As can be seen from the calibration stress value comparison table, the same vehicle type in Table 1 will be affected by extreme stress values due to different speeds. After calibration, the stress values generated when the same type of vehicle passes will not differ too much. Some stress values are significantly increased after calibration, reflecting that the influence of dynamic loads on stress measurement has been effectively reduced, weakening the influence of extreme stress values on measurement.

[0117] It should be noted that temperature changes will significantly affect the physical properties of the material, and thus affect the stress performance of the box culvert under different environmental conditions. Therefore, considering the impact of temperature on the stress value can more realistically reflect the working status of the box culvert in actual operation. The reason for setting up the temperature compensation model is that changes in ambient temperature will not only affect the elastic modulus and other mechanical properties of the material, but may also lead to stress concentration and deformation unevenness. If the temperature effect is not corrected, it may lead to deviations in the assessment of the fatigue life of the box culvert, thereby affecting the safety of the structure. Under high or low temperature conditions, the fatigue properties of the material may change. Therefore, establishing a polynomial regression model that can reflect this relationship can effectively capture the complex relationship between temperature and stress, making stress analysis more accurate.

[0118] Therefore, it is necessary to establish a temperature compensation model based on the relationship between temperature and calibrated stress, and use the established model to correct the collected stress data. The method is based on:

[0119] Temperature sensors are installed at the fatigue hotspots of the box culvert to record the ambient temperature changes in real time. Stress data after stress calibration are collected for the corresponding time period. A polynomial regression model is used to fit the effect of temperature on stress changes. The polynomial model is set as:

[0120] ;

[0121] in, Indicates the stress deviation value that changes with temperature under the temperature compensation model, 、 、 is the regression coefficient solved by the least squares method, is the temperature variable;

[0122] Substitute the stress data after stress calibration into the temperature model for correction based on the following formula:

[0123] ;

[0124] in, It represents the true stress value of the box culvert fatigue hotspot after extreme stress value calibration and temperature compensation.

[0125] It should be noted that defining damage variables for each fatigue hotspot in a box culvert based on the strain-stress relationship and expressing the cumulative damage through the superposition of multiple damage cycles is a key step in assessing structural health and fatigue life. This method can quantify the degree of damage sustained by each fatigue hotspot during actual use, thus providing a scientific basis for structural safety analysis. By introducing damage mechanics theory, the complex stress-strain relationship can be effectively converted into a quantifiable damage index, making the overall damage degree calculation more accurate, thereby providing guidance for subsequent maintenance decisions and structural reinforcement.

[0126] Therefore, it is necessary to define the damage variables of each fatigue hotspot of the box culvert based on the strain-stress relationship, and use multiple damage degrees to represent the cumulative damage degree of each fatigue hotspot of the box culvert. Based on the definition of damage variables, the fatigue damage degree of the box culvert is derived according to the following method:

[0127] Based on the damage mechanics theory, the damage degree is expressed by defining the damage variable of the box culvert. The damage variable is defined by the stress-strain relationship, and the following relationship is introduced:

[0128] ;

[0129] ;

[0130] in, Indicates the damage degree at the fatigue hotspot of the box culvert, is the damage variable, ranging from 0 to 1, It is the maximum stress that the material can withstand at the fatigue hotspot. is the ultimate strength of the material;

[0131] Based on the definition of damage variables, the fatigue damage degree of the box culvert is derived. The fatigue damage degree is expressed as the superposition of damage of multiple cycles. The formula is:

[0132] ;

[0133] in, Indicates the fatigue damage degree of the box culvert, Indicates box culvert The damage degree at each fatigue hotspot is is the index of the fatigue hotspot in the box culvert, and , is the total number of fatigue hot spots in the box culvert, Indicates box culvert The damage variable at each fatigue hotspot.

[0134] It's important to note that obtaining the true stress value, material fatigue limit, and actual number of stress cycles at each box culvert fatigue hotspot, combined with fatigue damage to assess the fatigue life of the box culvert, is a core component of structural health monitoring and assessment. This method not only accurately calculates the number of cycles and damage severity at each fatigue hotspot based on stress data under actual operating conditions, but also effectively quantifies the cumulative damage using Miner's law, thereby deriving the overall fatigue life of the box culvert.

[0135] Therefore, it is necessary to obtain the true stress value and the corresponding material stress limit cycle number at each box culvert fatigue hotspot, and combine the fatigue damage degree of the box culvert to obtain the fatigue life of the box culvert in actual use and operation. The method is based on:

[0136] The Miner rule is used to obtain the true stress value of each fatigue hotspot. The stress limit cycle number of the corresponding box culvert fatigue hotspot at this stress level is determined according to the stress-life curve of the material. The formula is:

[0137] ;

[0138] in, Indicates the box culvert The number of stress limit cycles of a fatigue hotspot, is the material constant, is the fatigue strength index of the material, For the The true value of stress at each fatigue hotspot;

[0139] Combined with the fatigue damage degree of the box culvert, the formula for deriving the fatigue life of the box culvert is:

[0140] ;

[0141] in, Indicates the fatigue life of the box culvert; in the above formula, the fatigue damage degree of the box culvert is The larger the box culvert is, the longer its fatigue life The smaller it is, the greater the ratio of the number of fatigue cycles experienced during use to the number of fatigue limit cycles of the material, which increases the degree of damage to the material and reduces the fatigue life. The larger the value, the greater the fatigue life, because It is the sum of the maximum number of cycles at all fatigue hot spots of the box culvert. The larger the sum, the more maximum cycles the structure can withstand at all fatigue hot spots, thus providing a higher potential fatigue life.

[0142] It can be seen from the fatigue life analysis table of the box culvert that as the number of ultimate stress cycles increases, the fatigue life of the box culvert also increases. This trend shows that when the number of ultimate stress cycles that the box culvert can withstand increases, the fatigue bearing capacity of the material is enhanced, so that it has a longer service life in actual use; fatigue damage degree Fatigue life of box culverts There is a significant negative correlation between the fatigue life of the box culvert and the fatigue damage degree, that is, as the fatigue damage degree increases, the fatigue life of the box culvert gradually decreases; when When it is 1, the fatigue life is the lowest, only 1, and when When it drops to 0.1, the fatigue life soars to 190. This result shows that the fatigue damage degree reflects the degree of damage to the material during the fatigue cycle. The higher the damage degree, the greater the ratio of the number of fatigue cycles the material withstands to its fatigue limit, which leads to increased damage to the material and significantly shortens its service life.

[0143] ;

[0144] Table 3 - Box culvert fatigue life analysis table

[0145] See also Figure 2 ,It can be seen from the box culvert fatigue damage analysis diagram that the X-axis represents the fatigue damage degree, ranging from 0 to 1, reflecting the degree of damage of the box culvert material in the fatigue cycle, and the Y-axis represents the fatigue life of the box culvert, 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 damage degree on the durability of the box culvert structure, especially at low damage degree, close to 0, the fatigue life of the box culvert reaches its maximum value, while at high damage degree, the fatigue life decreases rapidly. By reducing the damage degree, the service life of the box culvert can be effectively extended, providing an important reference basis for engineering practice.

[0146] See also Figure 3 In the box culvert stress limit cycle analysis diagram, it can be seen that with the increase of stress limit cycle number, fatigue life gradually increases. This shows that when the box culvert can withstand more stress cycles, its overall fatigue life is also extended accordingly. At low stress cycle number, the fatigue life growth rate is small, but after reaching a certain value, the fatigue life growth rate is significantly accelerated, especially when it is close to The fatigue life is greatly improved during the cycle. This chart shows that with the increase of the number of stress limit cycles, the fatigue life of the box culvert is significantly improved, emphasizing the importance of reasonable control and optimization of the number of fatigue cycles during the design and maintenance process. By increasing the bearing capacity of the material and optimizing the design, the service life of the box culvert can be effectively extended, providing a reliable basis for actual engineering.

[0147] See also Figure 4 The present invention further provides a fatigue life calculation system for a road assembled box culvert, wherein the fatigue life calculation system is used to execute the above-mentioned method for calculating the fatigue life of a road assembled box culvert, comprising:

[0148] A box culvert three-dimensional model establishment module is used to establish a three-dimensional finite element model of the box culvert based on the box culvert's size, wall thickness, and opening position, set material characteristic parameters and boundary conditions for the box culvert's fatigue resistance, apply loads to the finite element model and perform grid cell division, calculate the displacement data of each grid cell, and establish an extreme displacement threshold to screen out fatigue hotspots in the box culvert. The fatigue hotspot is a cell whose displacement data exceeds the extreme displacement threshold;

[0149] A stress measurement and data calibration module, based on fatigue stress analysis, installs strain sensors at various fatigue hotspots of the box culvert to measure stress values at each fatigue hotspot, obtains vehicle traffic data on the road to generate stress calibration coefficients, and uses the generated stress calibration coefficients to calibrate the stress values at each fatigue hotspot of the box culvert to eliminate the influence of extreme stress values on the measurement results;

[0150] A temperature compensation module is used to place temperature sensors at various fatigue hotspots in the box culvert to perform real-time temperature monitoring and record temperature changes. A temperature compensation model is established based on the relationship between temperature and calibrated stress. The established model is used to correct the collected stress data to eliminate the influence of temperature on the stress measurement results.

[0151] A damage analysis and cumulative assessment module is used to obtain the true stress value of the box culvert fatigue hotspot after extreme stress value calibration and temperature compensation, and define the damage variables of each fatigue hotspot of the box culvert based on the strain-stress relationship. The cumulative damage degree of each fatigue hotspot of the box culvert is represented by the superposition of multiple damage degrees, and the fatigue damage degree of the box culvert is derived based on the definition of the damage variable;

[0152] The life assessment module analyzes the true stress value under each box culvert fatigue hotspot based on Miner's law, obtains the corresponding material stress limit cycle number, and combines the fatigue damage degree of the box culvert to obtain the fatigue life of the box culvert in actual use and operation.

[0153] The above formulas are all dimensionless and numerical calculations. The formulas are obtained by collecting a large amount of data and performing software simulation to obtain the most recent real situation. The preset parameters in the formulas are set by technicians in this field according to actual conditions.

[0154] The above embodiments can be implemented in whole or in part by software, hardware, firmware, or any other combination thereof. 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 will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed by hardware or software depends on the specific application and design constraints of the technical solution.

[0155] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, and may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment as needed.

[0156] The above is only a specific implementation method of the present application, but the scope of protection of the present application is not limited thereto. Any technician familiar with this technical field can easily think of changes or replacements within the technical scope disclosed in this application, which should be covered by the scope of protection of the present application.

Claims

1. A method for calculating the fatigue life of a road prefabricated box culvert, characterized in that: The specific steps include: Step 1: Create a 3D finite element model of the box culvert based on its size, wall thickness, and opening location. Set the material characteristic parameters and boundary conditions for the box culvert's fatigue resistance. Grid the finite element model and apply a static load. Calculate the displacement data for each grid cell and establish an ultimate displacement threshold to identify fatigue hotspots in the box culvert. These hotspots are defined as cells whose displacement data exceeds the ultimate displacement threshold. Step 2: Based on the fatigue stress analysis method, strain sensors are installed at each fatigue hotspot of the box culvert to measure the stress value of each fatigue hotspot of the box culvert. Traffic data on the road is obtained to generate stress calibration coefficients. The generated stress calibration coefficients are used to calibrate the stress values of each fatigue hotspot of the box culvert to eliminate the influence of extreme stress values on the measurement results. Step 3: Place temperature sensors at each fatigue hotspot of the box culvert to conduct real-time temperature monitoring and record temperature changes. Based on the relationship between temperature and calibrated stress, establish a temperature compensation model. Use the established model to correct the collected stress data to eliminate the influence of temperature on the stress measurement results. Step 4: After extreme stress value calibration and temperature compensation, the true stress value of the fatigue hotspot of the box culvert is obtained. Based on the strain-stress relationship, the damage variables of each fatigue hotspot of the box culvert are defined. Multiple damage degrees are superimposed to represent the cumulative damage degree of each fatigue hotspot of the box culvert. Based on the definition of damage variables, the fatigue damage degree of the box culvert is derived. Step 5: Based on Miner's law, analyze the true stress value at each box culvert fatigue hotspot to obtain the corresponding material stress limit cycle number. Combined with the fatigue damage degree of the box culvert, the fatigue life of the box culvert in actual use and operation is obtained.

2. A method for calculating fatigue life of a road assembled box culvert according to claim 1, characterized in that: A three-dimensional finite element model of the box culvert was established, and the strain and displacement data of each unit were calculated. The displacement data of each grid unit was calculated, and the limit displacement threshold was established to screen out the fatigue hotspots of the box culvert. The method used was: Use CAD software to create a 3D box culvert model and define its length, width, height, and wall thickness. Adjust the opening of the box culvert to face the road surface. Use finite element analysis software to mesh the 3D box culvert model, generate tetrahedral elements, set 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 tetrahedral elements, linear shape functions are used to represent the displacement inside the element. Let the four vertices of the tetrahedral element be 、 、 、 , then the expression of the shape function of each vertex is: ； ； ； ； in, 、 、 、 are the four vertices of the same tetrahedral unit, is the volume of the tetrahedral unit, 、 、 、 are the horizontal coordinates of the four vertices in the tetrahedron unit, 、 、 、 are the ordinates of the four vertices in the tetrahedron unit; The displacement calculation of the tetrahedron element is based on the method of nonlinear finite element analysis and local deformation calculation. The formula is: ； ； in, represents the displacement of the tetrahedral element, Indicates the tetrahedral element The displacement of the vertices, 、 、 Represents vertices exist 、 、 The displacement component in the direction, Indicates the tetrahedral element The increment of the vertex displacement, is the partial derivative of the shape function with respect to the coordinates of the four vertices, which describes the rate at which the shape function changes with the coordinates. is the index of the vertex in the tetrahedral cell, and ; Establishing a limit displacement threshold , the displacement data exceeds The tetrahedral elements are marked as fatigue hot spots in the box culvert.

3. A method for calculating fatigue life of a road assembled box culvert according to claim 1, characterized in that: Obtain the stress values of each fatigue hotspot of the box culvert, and use the generated stress calibration coefficient to calibrate the stress values of each fatigue hotspot of the box culvert. The method is as follows: A strain sensor is installed at each fatigue hotspot. The strain data is measured in real time to obtain the elastic modulus of the material. Combined with the strain measured at each fatigue hotspot, the corresponding stress value is calculated using the stress formula. The formula is: ； in, represents the stress value measured at the fatigue hotspot, is the elastic modulus of the material, is the strain at the fatigue hot spot; Obtaining road traffic data to generate stress calibration coefficients is based on the following formula: ； in, represents the stress calibration coefficient, is the average speed of vehicles passing through the road, is the weight of the vehicle, is the acceleration due to gravity; The obtained stress calibration coefficient is used to calibrate the stress values measured at each fatigue hotspot of the box culvert to eliminate the influence of extreme stress values. The formula for obtaining the calibrated stress value is: ； in, Represents the stress value measured at the fatigue hotspot after calibration.

4. A method for calculating fatigue life of a road assembled box culvert according to claim 3, characterized in that: Based on the relationship between temperature and calibrated stress, a temperature compensation model is established, and the collected stress data is corrected using the established model. The method is based on: Temperature sensors are installed at the fatigue hotspots of the box culvert to record the ambient temperature changes in real time. Stress data after stress calibration are collected for the corresponding time period. A polynomial regression model is used to fit the effect of temperature on stress changes. The polynomial model is set as: ； in, Indicates the stress deviation value that changes with temperature under the temperature compensation model, 、 、 is the regression coefficient solved by the least squares method, is the temperature variable; Substitute the stress data after stress calibration into the temperature model for correction based on the formula: ； in, It represents the true stress value of the box culvert fatigue hotspot after extreme stress value calibration and temperature compensation.

5. A method for calculating fatigue life of a road assembled box culvert according to claim 1, characterized in that: Based on the strain-stress relationship, the damage variables of each fatigue hotspot of the box culvert are defined. Multiple damage degrees are superimposed to represent the cumulative damage degree of each fatigue hotspot of the box culvert. Based on the definition of damage variables, the fatigue damage degree of the box culvert is derived. The method is as follows: Based on the damage mechanics theory, the damage degree is expressed by defining the damage variable of the box culvert. The damage variable is defined by the stress-strain relationship, and the following relationship is introduced: ； ； in, Indicates the damage degree at the fatigue hotspot of the box culvert, is the damage variable, ranging from 0 to 1, It is the maximum stress that the material can withstand at the fatigue hotspot. is the ultimate strength of the material; Based on the definition of damage variables, the fatigue damage degree of the box culvert is derived. The fatigue damage degree is expressed as the superposition of damage of multiple cycles. The formula is: ； in, Indicates the fatigue damage degree of the box culvert, Indicates box culvert The damage degree at each fatigue hotspot is is the index of the fatigue hotspot in the box culvert, and , is the total number of fatigue hot spots in the box culvert, Indicates box culvert The damage variable at each fatigue hotspot.

6. A method for calculating fatigue life of a road assembled box culvert according to claim 5, characterized in that: The true stress value and the corresponding material stress limit cycles at each box culvert fatigue hotspot are obtained, and the fatigue damage degree of the box culvert is combined to obtain the fatigue life of the box culvert in actual use. The method is based on: The Miner rule is used to obtain the true stress value of each fatigue hotspot. The stress limit cycle number of the corresponding box culvert fatigue hotspot at this stress level is determined according to the stress-life curve of the material. The formula is: ； in, Indicates the box culvert The number of stress limit cycles of a fatigue hotspot, is the material constant, is the fatigue strength index of the material, For the The true value of stress at each fatigue hotspot; Combined with the fatigue damage degree of the box culvert, the formula for deriving the fatigue life of the box culvert is: ； in, Indicates the fatigue life of the box culvert.

7. A fatigue life calculation system for road assembled box culverts, characterized in that: The fatigue life calculation system is used to execute the method for calculating the fatigue life of a road-assembled box culvert according to any one of claims 1 to 6, comprising: A box culvert three-dimensional model establishment module is used to establish a three-dimensional finite element model of the box culvert based on the box culvert's size, wall thickness, and opening position, set material characteristic parameters and boundary conditions for the box culvert's fatigue resistance, apply loads to the finite element model and perform grid cell division, calculate the displacement data of each grid cell, and establish an extreme displacement threshold to screen out fatigue hotspots in the box culvert. The fatigue hotspot is a cell whose displacement data exceeds the extreme displacement threshold; A stress measurement and data calibration module, based on fatigue stress analysis, installs strain sensors at various fatigue hotspots of the box culvert to measure stress values at each fatigue hotspot, obtains vehicle traffic data on the road to generate stress calibration coefficients, and uses the generated stress calibration coefficients to calibrate the stress values at each fatigue hotspot of the box culvert to eliminate the influence of extreme stress values on the measurement results; A temperature compensation module is used to place temperature sensors at various fatigue hotspots in the box culvert to perform real-time temperature monitoring and record temperature changes. A temperature compensation model is established based on the relationship between temperature and calibrated stress. The established model is used to correct the collected stress data to eliminate the influence of temperature on the stress measurement results. A damage analysis and cumulative assessment module is used to obtain the true stress value of the box culvert fatigue hotspot after extreme stress value calibration and temperature compensation, and define the damage variables of each fatigue hotspot of the box culvert based on the strain-stress relationship. The cumulative damage degree of each fatigue hotspot of the box culvert is represented by the superposition of multiple damage degrees, and the fatigue damage degree of the box culvert is derived based on the definition of the damage variable; The life assessment module analyzes the true stress value under each box culvert fatigue hotspot based on Miner's law, obtains the corresponding material stress limit cycle number, and combines the fatigue damage degree of the box culvert to obtain the fatigue life of the box culvert in actual use and operation.

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