Steel bridge deck fatigue crack growth assessment methods, equipment, storage media and products

Abstract

The present invention discloses a method, device, storage medium, and product for assessing fatigue crack growth in steel bridge decks. The method comprises constructing an equivalent stress range prediction model for different vehicle types based on a probability model of measured traffic loads; constructing a probability model for fatigue stress spectra of steel bridge deck welds based on the probability model of measured traffic loads and the equivalent stress range prediction model; constructing a prediction model for the equivalent stress intensity factor range at the crack tip and crack edge; performing a random crack growth analysis based on a probability model of initial crack depth, morphology ratio, and material-related parameters, a stress spectrum probability model, and a prediction model for the equivalent stress intensity factor range at the crack tip and crack edge; and performing a probability evolution analysis of different sensitivity parameters based on the distribution characteristics of the sensitivity parameters during crack growth, as well as assessing the reliability of the steel bridge deck. The present invention improves assessment accuracy while reducing assessment time and increasing assessment efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge structure safety, and in particular relates to a method, device, storage medium and product for evaluating fatigue crack propagation of steel bridge decks based on measured traffic flow. Background Art

[0002] Due to the complex structure, numerous welds, and high residual stresses of steel bridge decks, fatigue cracks initiate and rapidly expand at weld defects under wheel loads, resulting in numerous fatigue cracks on a large number of steel bridge decks within a short service life. These cracks are highly concealed and difficult to detect. Once discovered, they penetrate the top plate, causing a reduction in local stiffness of the bridge deck and damage to the pavement layer, which in turn leads to a series of problems such as driving safety and corrosion. The degree of harm is high and the repair cost is high. In addition to the structural defects of the steel bridge deck itself, there are also special problems such as widespread overloading and rapid growth in traffic volume, which also exacerbate the fatigue problems of existing steel bridge decks. Steel bridge decks are affected by complex factors with multiple sources of uncertainty, and crack propagation is highly random, making the fatigue assessment of steel bridge decks difficult. Currently, the assessment method for the random propagation of fatigue cracks in steel bridge deck welds remains to be explored.

[0003] Traditional fatigue assessment methods for steel bridge decks include the SN curve (i.e., stress-life curve), fracture mechanics methods, and direct probabilistic methods. The SN curve ignores the dynamic changes in crack growth and actual traffic loads. The fracture mechanics method requires extensive meshing during crack growth, increasing computational complexity and complicating probabilistic simulations. These geometry-based methods are relatively conservative and fail to fully reflect the stochastic nature of fatigue cracking. Direct probabilistic methods include the probabilistic stress-life (PSN) curve and the probabilistic fatigue crack growth method based on fracture mechanics. PSN curves typically require fatigue testing, which is costly and inefficient. Furthermore, the use of deterministic fracture mechanics analysis contradicts the stochastic nature of fatigue crack growth and overestimates fatigue life. Fracture mechanics-based probabilistic fatigue crack growth methods are widely accepted for their consideration of the stochastic behavior of fatigue crack growth. However, their reliance on analytical solutions or interpolation of deterministic finite element (FE) results underutilizes the flexibility and accuracy of FE-based fracture mechanics analysis methods, making it difficult to fundamentally address the computational time constraints caused by the uncertainty of fatigue crack growth.

[0004] On the other hand, the uncertainty of traffic flow directly affects the accuracy of fatigue crack growth analysis in steel bridge deck welds. However, direct application of measured traffic flow to fatigue crack growth analysis is currently insufficient. Furthermore, existing research has primarily focused on estimating fatigue damage in steel bridge decks by measuring stress ranges. However, the essence of steel bridge deck degradation is the cumulative damage generated by fatigue crack growth, which carries significant uncertainty. Summary of the Invention

[0005] The purpose of the present invention is to provide a method, equipment, storage medium and product for fatigue crack propagation assessment of steel bridge decks, so as to solve the problem that fatigue cracks in steel bridge deck welds are affected by complex factors of multi-source uncertainty (such as parent material defects, weld defects, residual stress and manufacturing errors) and the randomness of traffic loads, resulting in a high degree of randomness in the crack propagation process, which in turn leads to low accuracy in fatigue crack propagation assessment of steel bridge decks, and the need to perform cycle-by-cycle growth analysis and stress intensity factor calculation on each sample during fatigue crack propagation assessment, resulting in low efficiency in crack propagation assessment.

[0006] The present invention solves the above technical problems through the following technical solutions: A method for evaluating fatigue crack growth in steel bridge decks, comprising:

[0007] Obtaining measured traffic flow data, performing statistical analysis and fitting on the measured traffic flow data, and obtaining a probability model of the measured traffic load;

[0008] Constructing an equivalent stress range prediction model for different vehicle types based on the probability model of the measured traffic load;

[0009] Constructing a fatigue stress spectrum probability model for steel bridge deck welds based on the probability model of the measured traffic load and the equivalent stress range prediction model for different vehicle types;

[0010] Construct a prediction model for the equivalent stress intensity factor range at the crack tip and crack edge;

[0011] Probabilistic models for obtaining initial crack depth, morphology ratio, and material-related parameters;

[0012] Based on the probability model of initial crack depth, morphology ratio and material-related parameters, the probability model of fatigue stress spectrum of steel bridge deck welds, and the equivalent stress intensity factor range prediction model at the crack tip and crack edge, a random crack growth analysis was performed to obtain the distribution characteristics of sensitivity parameters during the random crack growth process.

[0013] According to the distribution characteristics of sensitivity parameters during the random crack propagation process, the probability evolution analysis of different sensitivity parameters and the reliability evaluation of steel bridge deck are carried out.

[0014] Furthermore, a prediction model for the equivalent stress range of different vehicle types is constructed based on the probability model of the measured traffic load, including:

[0015] Designing a plurality of first subsamples based on the probability model of the measured traffic load, and constructing a first subsample data set based on the plurality of first subsamples; wherein each vehicle type corresponds to a first subsample data set, and each first subsample in each first subsample data set includes the vehicle load and wheel track lateral offset distance of the corresponding vehicle type;

[0016] Construct a finite element model of a steel bridge deck;

[0017] For each first subsample data set, simulate the operation of a vehicle on a steel bridge deck finite element model based on each first subsample of the first subsample data set to generate a stress history curve corresponding to the first subsample; use a rain flow counting method to convert the stress history curve into multiple stress ranges and their corresponding number of cyclic actions; calculate the equivalent stress range based on the multiple stress ranges and their corresponding number of cyclic actions for each first subsample; construct a first sample data set corresponding to the vehicle type based on each first subsample of the first subsample data set and its equivalent stress range; wherein each first sample of the first sample data set includes the vehicle load, wheel track lateral offset distance, and equivalent stress range of the corresponding vehicle type;

[0018] Constructing a first prediction model;

[0019] For each first sample data set, the first prediction model is trained and verified using the first sample data set to obtain an equivalent stress range prediction model for the corresponding vehicle model.

[0020] Preferably, the equivalent stress range is calculated according to the multiple stress ranges of each first sub-sample and the corresponding number of cycles, and the specific formula is:

[0021] ΔS eq =(∑ΔS i m n si ) 1 / m ;

[0022] Where, ΔS eq Indicates the equivalent stress range, ΔS i represents the i-th stress range, n si represents the number of cycles i, and m represents material-related parameters.

[0023] Furthermore, based on the probability model of the measured traffic load and the equivalent stress range prediction model of different vehicle models, a probability model of fatigue stress spectrum of steel bridge deck welds is constructed, including:

[0024] Extracting a plurality of second samples from the probability model of the measured traffic load; wherein each second sample includes vehicle loads and lateral wheel track offset distances of different vehicle types;

[0025] Using the equivalent stress range prediction model of different vehicle models to predict the second sample of the corresponding vehicle model, the equivalent stress range of the corresponding second sample is obtained;

[0026] Statistical analysis and fitting are performed on multiple equivalent stress ranges to obtain a probabilistic model of fatigue stress spectrum of steel bridge deck welds.

[0027] Furthermore, a prediction model for the equivalent stress intensity factor range at the crack tip and crack edge is constructed, including:

[0028] Step 4.1: Constructing a third sample data set and a fourth sample data set; wherein each third sample in the third sample data set includes a crack parameter and an equivalent stress intensity factor range at the crack tip; and each fourth sample in the fourth sample data set includes a crack parameter and an equivalent stress intensity factor range at the crack edge;

[0029] Step 4.2: Construct a second prediction model, and use the third sample data set and the fourth sample data set to train and verify the second prediction model respectively to obtain the equivalent stress intensity factor range prediction model of the crack tip and the crack edge.

[0030] Furthermore, constructing a third sample data set and a fourth sample data set includes:

[0031] Step 4.11: Import the steel bridge deck finite element model into FRANC3D software, embed fatigue cracks at the welds between the steel bridge deck top plate and the longitudinal ribs, and construct a solid sub-model containing fatigue cracks;

[0032] Step 4.12: Apply a deterministic load to the solid sub-model containing the fatigue crack and perform simulation calculations to obtain the stress intensity factor history curves at the crack tip and crack edge;

[0033] Step 4.13: Using a rain flow counting method, convert the stress intensity factor history curve at the crack tip into multiple stress intensity factor ranges at the crack tip and their corresponding number of cycles;

[0034] The stress intensity factor history curve of the crack edge is converted into multiple stress intensity factor ranges of the crack edge and their corresponding cyclic action times by using a rain flow counting method;

[0035] Step 4.14: Calculate the equivalent stress intensity factor range at the crack tip based on the multiple stress intensity factor ranges at the crack tip and their corresponding number of cycles;

[0036] Calculate the equivalent stress intensity factor range of the crack edge based on multiple stress intensity factor ranges at the crack edge and their corresponding cyclic action times;

[0037] Step 4.15: Repeat steps 4.11 to 4.14 to obtain the equivalent stress intensity factor range for each fatigue crack and its crack tip and crack edge;

[0038] Step 4.16: Construct a third sample data set based on the range of equivalent stress intensity factors of all fatigue cracks and their crack tips; construct a fourth sample data set based on the range of equivalent stress intensity factors of all fatigue cracks and their crack edges.

[0039] Preferably, the equivalent stress intensity factor range at the crack tip or crack edge is calculated based on multiple stress intensity factor ranges at the crack tip or crack edge and their corresponding number of cycles. The specific formula is:

[0040] ΔK eq =(∑ΔK ri m n Ki ) 1 / m ;

[0041] Where ΔK eq Indicates the range of equivalent stress intensity factors at the crack tip or crack edge, ΔK ri represents the range of the i-th stress intensity factor at the crack tip or crack edge, n Ki represents the number of cycles of action at the crack tip or crack edge, and m represents the material-related parameters.

[0042] Furthermore, a random crack growth analysis was conducted based on a probabilistic model of initial crack depth, morphology ratio, and material-related parameters; a probabilistic model of fatigue stress spectra for steel bridge deck welds; and a model predicting the range of equivalent stress intensity factors at the crack tip and crack edge. Specifically, the analysis included:

[0043] Step 6.1: Extract multiple fifth samples from the probability model of initial crack depth, shape ratio, and material-related parameters, and the probability model of fatigue stress spectrum of steel bridge deck welds; each fifth sample corresponds to a crack, and each fifth sample includes the initial crack depth, crack semi-major axis length, material-related parameters, and equivalent stress range; the crack semi-major axis length is calculated based on the initial crack depth and shape ratio;

[0044] Step 6.2: For each fifth sample, predict the initial crack depth and crack semi-major axis length of the fifth sample using the equivalent stress intensity factor range prediction model at the crack tip and crack edge to obtain the equivalent stress intensity factor range at the crack tip and crack edge under the deterministic load;

[0045] Step 6.3: Obtain the equivalent stress range under the deterministic load; calculate the equivalent stress intensity factor range of the crack tip and crack edge under the measured traffic flow based on the equivalent stress range under the deterministic load, the equivalent stress range of the fifth sample, and the equivalent stress intensity factor range of the crack tip and crack edge under the deterministic load;

[0046] Step 6.4: Define a crack depth growth increment, and calculate a crack semi-major axis length growth increment and a corresponding load cycle increment for the fifth sample based on the crack depth growth increment, material parameters of the fifth sample, and the equivalent stress intensity factor range of the crack tip and crack edge under actual traffic flow.

[0047] Step 6.5: Crack extension is performed according to the crack depth extension increment, the crack semi-major axis extension increment, and the corresponding load cycle number increment to obtain the current crack depth, the current crack semi-major axis length, and the current load cycle number;

[0048] Step 6.6: Determine whether to terminate crack extension based on the current crack depth and critical crack depth; if so, obtain the sensitivity parameters corresponding to the random crack extension process; if not, proceed to step 6.2 based on the current crack depth, the current crack semi-major axis length, and the current number of load cycles.

[0049] Preferably, the calculation formula for the equivalent stress intensity factor range of the crack tip or crack edge under the measured traffic flow is:

[0050]

[0051] Where p represents the crack tip, e represents the crack edge; ΔK i_aeq Indicates the range of equivalent stress intensity factors at the crack tip or crack edge under measured traffic flow; ΔK i_EC1 Indicates the range of equivalent stress intensity factors at the crack tip or crack edge under deterministic load, ΔS eq represents the equivalent stress range of the fifth sample (i.e. the equivalent stress range under the measured traffic flow), ΔS EC1 Indicates the equivalent stress range under deterministic load.

[0052] Furthermore, the sensitivity parameters during the random crack propagation process include the crack semi-major axis length, morphology ratio, number of load cycles, and equivalent stress intensity factor ranges at the crack tip and crack edge for each crack depth; the probabilistic evolution analysis includes equivalent stress intensity factor range evolution analysis, crack morphology evolution analysis, load cycle number evolution analysis, and residual fatigue life evolution analysis;

[0053] The analysis of the evolution of the equivalent stress intensity factor range includes:

[0054] The equivalent stress intensity factor ranges of each crack at the crack tip and crack edge at each crack depth were statistically analyzed and fitted, and the probability evolution models of the equivalent stress intensity factor ranges at the crack tip and crack edge were obtained respectively.

[0055] The crack morphology evolution analysis includes:

[0056] The crack semi-major axis length and morphology ratio of each crack at each crack depth are statistically analyzed to obtain the crack semi-major axis evolution and crack morphology evolution respectively;

[0057] The load cycle evolution analysis includes:

[0058] The load cycle number of each crack at each crack depth is statistically analyzed and fitted to obtain a load cycle number probability evolution model;

[0059] The remaining fatigue life evolution analysis includes:

[0060] The residual fatigue life of each crack at each crack depth is statistically analyzed and fitted to obtain the residual fatigue life probability evolution model;

[0061] The calculation formula for the steel bridge deck reliability is:

[0062] β=norminv(1-P f );

[0063]

[0064] Among them, β represents the fatigue reliability index, norminv represents the inverse function of the normal distribution function, P f represents the failure probability of the steel bridge deck, a(t) represents the crack depth, and a f represents the critical crack depth, I[] i Indicates the true or false indicator of the fifth i-th sample, n MCS Indicates the number of the fifth sample.

[0065] Based on the same concept, the present invention also provides an electronic device, including a memory, a processor, and a computer program / instruction stored in the memory, wherein the processor executes the computer program / instruction to implement the steel bridge deck fatigue crack growth assessment method as described above.

[0066] Based on the same concept, the present invention also provides a computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the steel bridge deck fatigue crack growth assessment method as described above.

[0067] Based on the same concept, the present invention also provides a computer program product, comprising a computer program / instruction, which implements the above-mentioned steel bridge deck fatigue crack growth assessment method when executed by a processor.

[0068] Beneficial effects

[0069] Compared with the prior art, the advantages of the present invention are:

[0070] The present invention adopts the method of constructing a random fatigue crack propagation model, fully considering the uncertainties in the crack structure material properties, load, crack size, etc., obtains the statistical characteristics of the crack propagation sensitivity parameters of the steel bridge deck under the measured traffic flow, and establishes its probabilistic evolution model based on this; based on the measured traffic flow data, it accurately captures the prominent uncertainties in the measured traffic load, ensuring the accuracy of the random fatigue crack propagation analysis; the random fatigue crack propagation analysis is carried out by replacing the time-consuming finite element model with a prediction model, achieving a delicate balance between accuracy, efficiency and flexibility, and solving the problem of low efficiency of crack propagation assessment caused by the need to perform cycle-by-cycle growth analysis and stress intensity factor calculation for each sample when using the finite element model for fatigue crack propagation assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only one embodiment of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0072] Figure 1 is a flow chart of a method for evaluating fatigue crack growth in a steel bridge deck according to an embodiment of the present invention;

[0073] Figure 2 This is a schematic diagram of the suspension bridge structure according to an embodiment of the present invention;

[0074] Figure 3 is the probability model of the gross vehicle weight of the C6 model in the embodiment of the present invention;

[0075] Figure 4 is a probability model of average daily traffic volume in an embodiment of the present invention;

[0076] Figure 5 is a probability model of the wheel track lateral offset distance in an embodiment of the present invention;

[0077] Figure 6 is a finite element model of a steel bridge deck in an embodiment of the present invention;

[0078] Figure 7 It is the RF model based on the bagging algorithm in the embodiment of the present invention;

[0079] Figure 8 2 is a schematic diagram of the verification results of the equivalent stress range prediction model for the C6 vehicle model in an embodiment of the present invention;

[0080] Figure 9 is a probability model of fatigue stress spectrum of steel bridge deck weld in an embodiment of the present invention;

[0081] Figure 10 This is a flowchart of the interactive use of ABAQUS and FRANC3D in an embodiment of the present invention;

[0082] Figure 11 2 is a schematic diagram of the verification results of the equivalent stress intensity factor range prediction model at the crack tip in an embodiment of the present invention;

[0083] Figure 12 2 is a schematic diagram of the verification results of the equivalent stress intensity factor range prediction model of the crack edge in an embodiment of the present invention;

[0084] Figure 13 is a probabilistic evolution model of the equivalent stress intensity factor range at the fatigue crack tip in an embodiment of the present invention;

[0085] Figure 14 is a probability evolution model of the equivalent stress intensity factor range of the fatigue crack edge in the embodiment of the present invention;

[0086] Figure 15 Schematic diagram of the evolution of the semi-major axis length of a crack in an embodiment of the present invention;

[0087] Figure 16 Schematic diagram of crack morphology evolution in an embodiment of the present invention;

[0088] Figure 17 is a probability evolution model of the number of fatigue load cycles in an embodiment of the present invention;

[0089] Figure 18 is the probability evolution model of the remaining fatigue life (or remaining extended life) in the embodiment of the present invention; wherein, E(1 / 6.63×10 7 ) indicates that the expected value is 1 / 6.63×10 7 Exponential distribution, LogN(19.50,1.00 2 ) represents a lognormal distribution with a mean of 19.5 and a standard deviation of 1;

[0090] Figure 19 is a fatigue reliability index curve under the influence of the average daily traffic volume growth in the embodiment of the present invention; wherein α1 represents the overall growth coefficient of the average daily traffic volume;

[0091] Figure 20 is a fatigue reliability index curve under the influence of the vehicle gross weight growth in the embodiment of the present invention; wherein α2 represents the overall growth coefficient of the vehicle gross weight. DETAILED DESCRIPTION

[0092] The following is a clear and complete description of the technical solutions of the present invention in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0093] The following specific embodiments are used to describe the technical solution of the present application in detail. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0094] like Figure 1 As shown, a method for evaluating fatigue crack growth of a steel bridge deck provided by an embodiment of the present invention includes the following steps:

[0095] Step 1: Obtain measured traffic flow data, perform statistical analysis and fitting on the measured traffic flow data, and obtain a probability model of the measured traffic load.

[0096] The present invention obtains measured traffic flow data of a suspension bridge based on a WIM (Weight-in-Motion) system. Figure 2 Figure 2 shows a schematic diagram of a suspension bridge structure, where: Figure 2 (a) is the elevation view of the suspension bridge. Figure 2 (b) is a schematic diagram of the cross section of the steel box girder. Figure 2 (c) is a detailed diagram of the steel bridge deck segment and welding structure. The WIM system has been serving Figure 2 The suspension bridge shown in the figure records measured traffic flow data and statistically classifies it. First, the occupancy rate of each vehicle type is obtained. Then, the probability distribution characteristics of the gross vehicle weight of each vehicle type and the average daily traffic volume are obtained. These are aligned and fitted to obtain probability models for different vehicle types, probability models for the gross vehicle weight of different vehicle types, and probability models for the average daily traffic volume. In other words, the probability model of the measured traffic load in this embodiment includes the probability models for the occupancy rate of different vehicle types, the probability models for the gross vehicle weight of different vehicle types, and the probability model for the average daily traffic volume.

[0097] In this embodiment, six types of vehicle models can be obtained from the measured traffic flow data recorded by the WIM system, and the occupancy rate of each type of vehicle model in all vehicle models is shown in Table 1.

[0098] Table 1 Different models and their market share

[0099]

[0100] Each vehicle model has a corresponding probability model for its gross vehicle weight. This embodiment uses a Gaussian mixture model to fit the gross vehicle weight data of each vehicle model to obtain a probability model for the gross vehicle weight of each vehicle model. Taking the C6 model in Table 1 as an example, its probability model is as follows: Figure 3 As shown, Figure 3 In the example, GMM stands for Gaussian mixture model, and the subscripts 1, 2, and 3 indicate that a Gaussian mixture model containing three Gaussian functions is used for fitting. i Indicates the weight of the i-th Gaussian function in the Gaussian mixture model, μ i represents the mean of the i-th Gaussian function, σ i represents the standard deviation of the i-th Gaussian function, i = 1, 2, 3. This embodiment uses the normal distribution function to fit the average daily traffic volume data to obtain the probability model of the average daily traffic volume, such as Figure 4 shown. Figure 4 In, N (3824, 178 2 ) represents the normal distribution function with a mean of 3824 and a standard deviation of 178.

[0101] The probability model of the measured traffic load also includes a probability model of the wheel track lateral offset distance. By obtaining the probability distribution characteristics of the wheel track lateral offset distance and fitting it, the probability model of the wheel track lateral offset distance can be obtained. There are two ways to obtain the probability distribution characteristics of the wheel track lateral offset distance: one is to obtain it from the measured traffic flow data, and the other is to obtain it from the existing technology. The probability distribution characteristics of the wheel track lateral offset distance of this embodiment are obtained according to the Eurcode1 specification. The Eurcode1 specification can be specifically found in: European committee for standardization.EN 1991:Eurocode 1-Actions on structures-part 2:traffic loadson bridges.Brussels,Belgium:CEN;2003. This embodiment uses the normal distribution function to fit the probability distribution characteristics of the wheel track lateral offset distance, and the obtained probability model of the wheel track lateral offset distance is as follows: Figure 5 As shown, EC1 represents the Eurcode1 standard.

[0102] The probability model of the measured traffic load (i.e., the measured traffic load model) is composed of probability models of the occupancy rate of different vehicle types, the gross vehicle weight of different vehicle types, the average daily traffic volume, and the lateral offset distance of the wheel track. The probability model of the measured traffic load integrates the conditional probability relationship between various traffic variables. The number of axles and wheelbase are considered to be deterministic variables directly related to the vehicle configuration.

[0103] Compared with relying on fatigue design specifications to establish a fatigue vehicle model, the present invention fully considers the uncertainty of traffic loads during the service life of the bridge and establishes a measured traffic load model, which can accurately simulate the crack growth performance of actual steel bridge decks under measured traffic flow.

[0104] Step 2: Construct an equivalent stress range prediction model for different vehicle types based on the probability model of the measured traffic load.

[0105] The influence line of a steel bridge deck weld is relatively short relative to the axle spacing, and each axle passing through the weld will induce a fatigue stress peak. Furthermore, the number of axles corresponding to different vehicle models also varies. Therefore, it is necessary to establish a corresponding equivalent stress range prediction model based on the vehicle model. In a specific embodiment of the present invention, an equivalent stress range prediction model for different vehicle models is constructed based on a probabilistic model of measured traffic loads, including:

[0106] Step 2.1: Design multiple first subsamples based on the probability model of the measured traffic load, and construct a first subsample data set based on the multiple first subsamples.

[0107] For each vehicle model, the uniform design method is used to design N from the probability model of vehicle gross weight and wheel track lateral offset distance. 11 The total vehicle weight and wheel track lateral offset distance of each vehicle model are calculated, so that each total vehicle weight of each vehicle model corresponds to a wheel track lateral offset distance, thereby obtaining a first sub-sample, which is obtained by N 11 The first sub-samples constitute the first sub-sample data set of the vehicle model. That is, each vehicle model corresponds to a first sub-sample data set, and each first sub-sample in each first sub-sample data set includes the gross vehicle weight and lateral wheel track offset distance of the corresponding vehicle model.

[0108] Step 2.2: Construct the finite element model of the steel bridge deck.

[0109] based on Figure 2 Based on the structural design drawings of the suspension bridge, a three-dimensional multi-scale steel bridge deck finite element model is established, including the overall model of the steel bridge deck segment and the local sub-model of the detail area, such as Figure 6 As shown. In the finite element model of the steel bridge deck, the shell element is simulated using SR4, with a total of 43,596 elements; for the key areas, the local solid sub-model is refined and the solid element is simulated using C3D8R, with a total of 62,460 elements. In order to balance calculation accuracy and efficiency, the mesh size of the weld area in the local solid sub-model is finely set to 1mm, and a mesh size of 4mm is used in other non-critical areas. For the overall segment model, the mesh size is uniformly set to 80mm. In addition, the finite element model of the steel bridge deck imposes necessary constraints on the three degrees of freedom: longitudinal, transverse, and vertical to ensure the accuracy of the analysis results.

[0110] Because the steel bridge deck finite element model doesn't directly include pavement elements, a 45° spread angle was used to apply a uniformly distributed wheel load perpendicular to the pavement. Specifically, the pavement thickness was 67 mm, the tire contact area on the front axle was 300 mm × 200 mm (width and length), and the tire contact area on the rear axle was 600 mm × 200 mm. By calculating the load diffusion effect under the influence of the pavement, the corrected load areas were set to 434 mm × 334 mm and 734 mm × 334 mm, respectively.

[0111] Step 2.3: For each first subsample data set, simulate the operation of a vehicle on the steel bridge deck finite element model according to each first subsample of the first subsample data set to generate a stress history curve corresponding to the first subsample.

[0112] According to each first subsample of the first subsample data set, the vehicle gross weight and wheel track lateral offset distance are set in the Dload subroutine in ABAQUS software, and the vehicle operation is simulated to generate the stress history.

[0113] Step 2.4: Use the rainflow counting method to convert the stress history curve into multiple stress ranges and their corresponding number of cycles.

[0114] Step 2.5: Calculate the equivalent stress range based on the multiple stress ranges of each first sub-sample and the corresponding number of cycles. The specific calculation formula is:

[0115] ΔS eq =(∑ΔS i m n si ) 1 / m (1)

[0116] Where, ΔS eq Indicates the equivalent stress range, ΔS i represents the i-th stress range, n si Expressed with ΔS i The corresponding number of cycles is the i-th cycle, and m represents the material-related parameters, which is usually taken as 3.

[0117] Step 2.6: Construct a first sample data set corresponding to the vehicle model according to each first sub-sample of the first sub-sample data set and its equivalent stress range.

[0118] For each vehicle model's first subsample dataset, the equivalent stress range for each first subsample is obtained according to steps 2.3 through 2.6. Based on each first subsample (including the vehicle model's gross vehicle weight and lateral wheel track offset) and its equivalent stress range, the first sample dataset for that vehicle model is constructed. Therefore, each first sample in each vehicle model's first sample dataset includes the vehicle model's gross vehicle weight, lateral wheel track offset, and equivalent stress range.

[0119] Step 2.7: Build the first prediction model.

[0120] In a specific embodiment of the present invention, the first prediction model adopts a random forest model (i.e., RF model). Figure 7 As shown in Figure 1, the RF model, an advanced model based on an ensemble learning strategy using a bagging algorithm, demonstrates broad application prospects in bridge engineering. By constructing multiple decision trees as weak learners and integrating their predictions, the overall model's generalization and accuracy are enhanced. During training, each decision tree randomly selects samples and features for learning. This dual randomness not only ensures diversity and independence among the weak learners but also facilitates effective model training, enabling the model to demonstrate greater robustness and lower random error when faced with unknown sample sets.

[0121] Step 2.8: For each first sample data set, the first prediction model is trained and verified using the first sample data set to obtain an equivalent stress range prediction model for the corresponding vehicle model.

[0122] For each vehicle model, the vehicle gross weight and wheel track lateral offset distance of each first sample of the first sample data set of the vehicle model are used as input, and the corresponding equivalent stress range is used as output. The first prediction model is trained and verified, and the equivalent stress range prediction model of the vehicle model can be obtained. At the same time, the adjusted determination coefficient (AdjustedR 2 ) is 0.9996, indicating that the trained equivalent stress range prediction model has good generalization ability and prediction accuracy. Figure 8 shown.

[0123] Each vehicle model corresponds to an equivalent stress range prediction model.

[0124] Step 3: Based on the probability model of measured traffic loads and the equivalent stress range prediction model of different vehicle models, a probability model of fatigue stress spectrum of steel bridge deck welds is constructed.

[0125] To provide a large number of random samples for subsequent fatigue crack random propagation analysis, the present invention also constructs a probabilistic model of fatigue stress spectrum for steel bridge deck welds. In a specific embodiment of the present invention, based on a probabilistic model of measured traffic loads and a prediction model of equivalent stress ranges for different vehicle types, a probabilistic model of fatigue stress spectrum for steel bridge deck welds is constructed, including:

[0126] Step 3.1: Draw a plurality of second samples from the probability model of the measured traffic load.

[0127] Assuming N2 second samples are required, the number of second samples required for each vehicle type is calculated based on the occupancy rate and N2 in Table 1. Monte Carlo sampling is then used to extract the corresponding number of vehicle gross weights from the probability model for the vehicle gross weight of that vehicle type. The N2 vehicle gross weights are then formed from the vehicle gross weights of all vehicle types. Monte Carlo sampling is also used to extract N2 lateral wheel track offset distances from the probability model for the wheel track offset distance, with each vehicle gross weight corresponding to one lateral wheel track offset distance. This results in N2 second samples. In other words, each second sample includes the vehicle gross weight and lateral wheel track offset distance of the corresponding vehicle type.

[0128] Step 3.2: Use the equivalent stress range prediction model of different vehicle models to predict the second sample of the corresponding vehicle model to obtain the equivalent stress range of the second sample.

[0129] The equivalent stress range prediction model corresponding to the vehicle model of the second sample is used to predict the second sample, so as to predict the equivalent stress range of the second sample.

[0130] Step 3.3: Perform statistical analysis and fitting on the equivalent stress range of all second samples to obtain the probabilistic model of fatigue stress spectrum of steel bridge deck welds.

[0131] The equivalent stress ranges of all second samples were statistically analyzed and fitted using different fitting functions, e.g. Figure 9 As shown in the figure, the lognormal distribution function can best fit the probability model of fatigue stress spectrum of steel bridge deck welds.

[0132] Step 4: Construct a prediction model for the equivalent stress intensity factor range at the crack tip and crack edge.

[0133] In a specific embodiment of the present invention, a prediction model for the equivalent stress intensity factor (SIF) range of crack tips and crack edges is constructed, including:

[0134] Step 4.1: Construct the third sample data set and the fourth sample data set.

[0135] In a specific embodiment of the present invention, constructing the third sample data set and the fourth sample data set includes:

[0136] Step 4.11: Import the finite element model of the steel bridge deck constructed in step 2.2 into FRANC3D software, embed fatigue cracks at the welds between the top plate and the longitudinal ribs of the steel bridge deck, and construct a solid sub-model containing fatigue cracks, such as Figure 10 shown.

[0137] Figure 10 In this example, a represents the crack depth, and c represents the semi-major axis length of the crack. The ABAQUS and FRANC3D joint solution method features adaptive remeshing technology. The crack tip is meshed and remeshed using singular wedge elements or degenerate hexahedral elements, ensuring a high-quality mesh around the crack front and enabling accurate prediction of the SIF and crack propagation process. Specifically, after an initial crack is embedded in the weld between the top plate and the longitudinal rib of a steel bridge deck, the model is adaptively remeshed to obtain a solid sub-model containing the initial crack.

[0138] Step 4.12: Apply a deterministic load to the solid sub-model containing the fatigue crack and perform simulation calculations to obtain the stress intensity factor history curves at the crack tip and crack edge.

[0139] This example applies a deterministic fatigue vehicle model (i.e. Eurcode1 specification), through Figure 10 The interactive technology of ABAQUS and FRANC3D shown in the figure is used to obtain the stress intensity factors at the crack tip and crack edge when vehicle load acts on different positions of the steel bridge deck, thereby obtaining the stress intensity factor history curves at the crack tip and crack edge.

[0140] The stress intensity factors at the crack tip and crack edge can be solved using the M-integral method.

[0141] Step 4.13: Use the rain flow counting method to convert the stress intensity factor history curve at the crack tip into multiple stress intensity factor ranges at the crack tip and their corresponding number of cycles;

[0142] The rain flow counting method is used to convert the stress intensity factor history curve of the crack edge into multiple stress intensity factor ranges of the crack edge and their corresponding number of cycles.

[0143] Step 4.14: Calculate the equivalent stress intensity factor range at the crack tip based on the multiple stress intensity factor ranges at the crack tip and their corresponding number of cycles; calculate the equivalent stress intensity factor range at the crack edge based on the multiple stress intensity factor ranges at the crack edge and their corresponding number of cycles.

[0144] In this embodiment, the equivalent stress intensity factor range at the crack tip or crack edge is calculated based on multiple stress intensity factor ranges at the crack tip or crack edge and their corresponding number of cycles. The specific formula is:

[0145] ΔK eq =(∑ΔK ri m n Ki ) 1 / m (2)

[0146] Where ΔK eq Indicates the range of equivalent stress intensity factors at the crack tip or crack edge, ΔK ri represents the range of the i-th stress intensity factor at the crack tip or crack edge, n Ki represents the number of cycles of action at the crack tip or crack edge, and m represents the material-related parameters.

[0147] According to steps 4.11 to 4.14, a fatigue crack (including crack depth and crack semi-major axis length) and the equivalent stress intensity factor range of the crack tip and crack edge of the fatigue crack can be obtained.

[0148] Step 4.15: Repeat steps 4.11 to 4.14 to obtain the equivalent stress intensity factor range for each fatigue crack and its crack tip and crack edge.

[0149] To obtain the equivalent stress intensity factor ranges of multiple fatigue cracks and their crack tips and crack edges, steps 4.11 to 4.14 are repeated. In this embodiment, Latin hypercube sampling is used based on the critical crack size and the reasonable crack extension range, and the number of fatigue cracks sampled is 80.

[0150] Step 4.16: Construct a third sample data set based on the range of equivalent stress intensity factors of all fatigue cracks and their crack tips; construct a fourth sample data set based on the range of equivalent stress intensity factors of all fatigue cracks and their crack edges.

[0151] Each third sample in the third sample dataset includes crack parameters and a range of equivalent stress intensity factors at the crack tip; each fourth sample in the fourth sample dataset includes crack parameters and a range of equivalent stress intensity factors at the crack edge. In this embodiment, the crack parameters include crack depth and crack semi-major axis length. The number of samples in both the third and fourth sample datasets is 80.

[0152] During the fatigue crack growth process, its morphological evolution is often maintained within a specific range. Therefore, this embodiment considers that the extracted fatigue cracks are evenly distributed within a reasonable crack growth range.

[0153] Step 4.2: Construct a second prediction model, and use the third sample data set and the fourth sample data set to train and verify the second prediction model respectively, to obtain the equivalent stress intensity factor range prediction model of the crack tip and crack edge.

[0154] In this embodiment, the second prediction model uses a random forest model.

[0155] The crack depth and crack semi-major axis length of each third sample in the third sample data set are used as input, and the corresponding equivalent stress intensity factor range of the crack tip is used as output. The second prediction model is trained and verified, and the equivalent stress intensity factor range prediction model of the crack tip can be obtained. At the same time, the adjusted determination coefficient (Adjusted R 2 ) is 0.99238, indicating that the trained crack tip equivalent stress intensity factor range prediction model has good generalization ability and prediction accuracy, such as Figure 11 As shown, where c represents the semi-major axis length of the crack and a represents the crack depth.

[0156] The crack depth and crack semi-major axis length of each fourth sample in the fourth sample data set are used as input, and the equivalent stress intensity factor range of the corresponding crack edge is used as output. The second prediction model is trained and verified, and the equivalent stress intensity factor range prediction model of the crack edge can be obtained. At the same time, the adjusted determination coefficient (Adjusted R 2 ) is 0.99612, indicating that the trained equivalent stress intensity factor range prediction model of crack edge has good generalization ability and prediction accuracy, such as Figure 12 shown.

[0157] Step 5: Obtain the probabilistic model of initial crack depth, morphology ratio and material-related parameters.

[0158] In order to provide a large number of random samples for subsequent fatigue crack random growth analysis, it is also necessary to obtain probability models of initial crack depth, morphology ratio, and material-related parameters. The probability models of these parameters can be obtained using existing technologies. This embodiment obtains the probability models of initial crack depth and morphology ratio from the existing literature (Kountouris IS, Baker MJ. Defect assessment: analysis of the dimensions of defects detected by ultrasonic inspection in an offshore structure, CESLIC Report OR8. London, UK: Imperial College of Science and Technology.). The probability model of material-related parameters is obtained from the BS7910 standard.

[0159] Step 6: Based on the probability model of initial crack depth, morphology ratio, and material-related parameters, the probability model of fatigue stress spectrum of steel bridge deck welds, and the equivalent stress intensity factor range prediction model at the crack tip and crack edge, a random crack growth analysis is performed to obtain the distribution characteristics of the sensitivity parameters during the random crack growth process.

[0160] In a specific embodiment of the present invention, a random crack growth analysis is performed based on a probability model of initial crack depth, morphology ratio, and material-related parameters, a probability model of fatigue stress spectrum of steel bridge deck welds, and a prediction model of equivalent stress intensity factor ranges at crack tips and crack edges, specifically including:

[0161] Step 6.1: Extract a plurality of fifth samples based on the probability model of initial crack depth, morphology ratio and material-related parameters, and the probability model of fatigue stress spectrum of steel bridge deck welds.

[0162] Each fifth sample corresponds to a crack, and each fifth sample includes an initial crack depth, a crack semi-major axis length, material-related parameters, and an equivalent stress range; the crack semi-major axis length is calculated based on the initial crack depth and the morphology ratio.

[0163] Step 6.2: For each fifth specimen, use the equivalent stress intensity factor range prediction model at the crack tip and crack edge to predict the initial crack depth and crack semi-major axis length of the fifth specimen, and obtain the equivalent stress intensity factor range at the crack tip and crack edge under deterministic load.

[0164] The initial crack depth and crack semi-major axis length of the fifth specimen were input into the crack tip equivalent stress intensity factor range prediction model to obtain the crack tip equivalent stress intensity factor range for the fifth specimen under a deterministic load. The initial crack depth and crack semi-major axis length of the fifth specimen were input into the crack edge equivalent stress intensity factor range prediction model to obtain the crack edge equivalent stress intensity factor range for the fifth specimen under a deterministic load. Because a deterministic load was applied to the solid sub-model containing the fatigue crack when constructing the crack tip and crack edge equivalent stress intensity factor range prediction models, the calculated equivalent stress intensity factor ranges for the crack tip and crack edge of the fifth specimen are both the equivalent stress intensity factor ranges under a deterministic load.

[0165] Step 6.3: Obtain the equivalent stress range of the steel bridge deck weld under the deterministic load; based on the equivalent stress range under the deterministic load, the equivalent stress range of the fifth sample, and the equivalent stress intensity factor range at the crack tip and crack edge under the deterministic load, calculate the equivalent stress intensity factor range at the crack tip and crack edge of the fifth sample under the measured traffic flow.

[0166] Using the fatigue vehicle model specified in Eurcode 1 as the vehicle load, the equivalent stress range of the steel bridge deck weld under deterministic load can be obtained by following steps 2.3 to 2.6. The equivalent stress intensity factor range at the crack tip or crack edge under deterministic load can be expressed as:

[0167]

[0168] Where p represents the crack tip, e represents the crack edge; ΔK i_EC1 Indicates the range of equivalent stress intensity factors at the crack tip or crack edge under deterministic load; Y i (a,c) represent the correction factors at the crack tip or crack edge, depending on the geometry of the detail of interest and the crack shape; ΔS EC1 represents the equivalent stress range under deterministic load, a represents the crack depth, and c represents the semi-major axis length of the crack.

[0169] By introducing the stress ratio relationship between the measured traffic flow and the fatigue vehicle model specified in Eurcode1, formula (3) is rewritten as:

[0170]

[0171] Where ΔK i_aeq Indicates the range of equivalent stress intensity factors at the crack tip or crack edge under measured traffic flow, ΔS eq represents the equivalent stress range of the fifth sample (i.e. the equivalent stress range under the measured traffic flow), ΔS EC1 Indicates the equivalent stress range under deterministic load.

[0172] For the same crack shape in the same detail, the SIF range is proportional to the stress range. The essence of the prediction model for the equivalent stress intensity factor range of the crack tip and edge is to predict the equivalent stress intensity factor range of the fatigue crack edge and tip of different sizes (crack depth and crack semi-major axis length) under a certain deterministic vehicle load, and then solve the equivalent stress intensity factor range of the fatigue crack edge and crack tip under the measured traffic flow through the stress ratio relationship between the deterministic vehicle load and the measured traffic flow. Therefore, according to formula (4), the equivalent stress intensity factor range of the crack tip and crack edge under the measured traffic flow can be calculated for each fifth sample (i.e., each crack).

[0173] Step 6.4: Define the crack depth growth increment. Based on the crack depth growth increment, the material parameters of the fifth specimen, and the range of equivalent stress intensity factors at the crack tip and crack edge under measured traffic flow, calculate the crack semi-major axis length growth increment and the corresponding load cycle increment for the fifth specimen.

[0174] A crack growth model is selected to characterize the development relationship between the stress intensity factor range and the crack growth rate. Crack growth models include the Pairs model, the Walker model, and the Forman model. In this embodiment, the Pairs model is selected to characterize the relationship between the stress intensity factor range and the crack growth rate, specifically:

[0175]

[0176] Where a and c represent the crack depth and semi-major axis length respectively, N represents the number of load cycles, and C and m represent material-related parameters. According to BS7910 standard, m of Q345qD steel is set to 3, ΔK p and ΔK e Represent the stress intensity factor ranges of the crack tip and crack edge as the number of loading cycles changes.

[0177] Based on formula (5) and formula (6), the crack semi-major axis length and the increment of the number of load cycles are solved for a given crack depth expansion increment. The specific formula is:

[0178]

[0179] Where Δa represents the crack depth increment, Δc represents the crack semi-major axis increment, and ΔN represents the load cycle increment. Substitute the defined crack depth increment, the material parameters of the fifth sample, and the equivalent stress intensity factor range of the crack tip under actual traffic flow into formula (7) to calculate the load cycle increment. Substitute the load cycle increment, the material parameters of the fifth sample, and the equivalent stress intensity factor range of the crack edge under actual traffic flow into formula (8) to calculate the crack semi-major axis increment.

[0180] Step 6.5: Crack expansion is performed according to the crack depth expansion increment, the crack semi-major axis expansion increment, and the corresponding load cycle number increment to obtain the current crack depth, the current crack semi-major axis length, and the current load cycle number.

[0181] The random crack growth process is discretized into a gradual superposition of crack depth and semi-major axis length. The current crack depth, crack semi-major axis length, and number of load cycles are calculated based on the crack depth growth increment, crack semi-major axis length growth increment, and the corresponding load cycle increment. To ensure calculation accuracy, the crack depth growth increment is set to 1% of the initial crack depth.

[0182] Step 6.6: Determine whether to terminate crack growth based on the current crack depth and the critical crack depth. If so, obtain the distribution characteristics of the sensitivity parameters during the random crack growth process. If not, proceed to step 6.2 based on the current crack depth, the current crack semi-major axis length, and the current number of load cycles.

[0183] When the current crack depth is less than or equal to the critical crack depth, crack propagation continues, that is, based on the current crack depth, the current crack semi-major axis length, and the current number of load cycles, the process proceeds to step 6.2. When the current crack depth is greater than the critical crack depth, crack propagation is terminated, and the sensitivity parameters of the crack during its propagation process are obtained.

[0184] According to steps 6.2 to 6.6, a crack random propagation analysis is performed on the crack corresponding to each fifth sample to obtain the distribution characteristics of the sensitivity parameters during the random propagation process of each crack.

[0185] The present invention introduces the RF model to predict the equivalent stress range and the equivalent stress intensity factor range. There is no need to use a finite element model for crack propagation, and there is no need to perform cycle-by-cycle growth analysis and stress intensity factor calculation on each sample when evaluating fatigue crack propagation. This reduces time consumption and improves crack propagation efficiency while ensuring propagation accuracy.

[0186] Compared to relying solely on finite element models or conducting random fatigue crack growth analysis based on analytical solutions or interpolation of deterministic finite element results, this invention introduces an RF model for random crack growth, significantly improving computational efficiency. Under the same hardware configuration, this invention achieves a computational efficiency improvement of over 1,400 times.

[0187] Step 7: Perform probabilistic evolution analysis and steel bridge deck reliability assessment based on the distribution characteristics of sensitivity parameters during random crack propagation.

[0188] In a specific embodiment of the present invention, the sensitivity parameters during the random crack propagation process include the crack semi-major axis length at each crack depth, the aspect ratio, the number of load cycles, and the equivalent stress intensity factor range at the crack tip and crack edge.

[0189] Probabilistic evolution analysis includes equivalent stress intensity factor range evolution analysis, crack morphology evolution analysis, load cycle number evolution analysis and residual fatigue life evolution analysis.

[0190] In order to evaluate the reliability of steel bridge decks, the critical crack depth is used as the structural failure criterion and the limit state function is established:

[0191] G(t)=a(t)-a f (9)

[0192] Among them, a f represents the critical crack depth, t represents the service life of the steel bridge deck, G represents the limit state function of fatigue failure of the steel bridge deck weld, and a represents the crack depth. Based on formula (9), the failure probability of the steel bridge deck can be derived as:

[0193] P f =P[G(t)≥0]=P[a(t)-a f ≥0] (10)

[0194] Among them, P f represents the failure probability of the steel bridge deck.

[0195] According to the random crack growth results of the fifth sample and combined with the average daily traffic volume probability model, the P corresponding to each service time point of the steel bridge deck is solved. f :

[0196]

[0197] Among them, I[] i Indicates the true or false indicator of the fifth i-th sample, n MCS Indicates the number of the fifth sample.

[0198] The ability of a structure to perform its intended functions within its specified operational service life and operating conditions can be evaluated using reliability indices. Based on the geometric meaning of the reliability index, the relationship between the failure probability of a steel bridge deck and the reliability index is:

[0199] β=norminv(1-P f ) (12)

[0200] Where β represents the fatigue reliability index, and norminv represents the inverse function of the normal distribution function.

[0201] The equivalent stress intensity factor range of the crack tip corresponding to each crack depth is statistically analyzed and fitted to obtain the probability evolution model of the equivalent stress intensity factor range of the crack tip point (only four crack depths of 2mm, 4mm, 6mm and 8mm are selected in this example), as shown in Figure 2. Figure 13 As shown, where Kp represents the crack tip, a i represents the crack depth of the i-th expansion, c i Represents the semi-major axis length of the crack at the i-th extension. The equivalent stress intensity factor range of each crack edge under the measured traffic flow at each crack depth is statistically analyzed and fitted to obtain the probability evolution model of the equivalent stress intensity factor range at the crack tip edge, as shown in Figure 14 As shown, where Ke represents the crack edge.

[0202] according to Figures 13 and 14 It can be seen that the lognormal distribution can accurately fit the probability evolution model of the equivalent SIF range. The mean value of the equivalent SIF range at the crack edge is always higher than that at the crack tip. When fatigue failure occurs, the mean value of the equivalent SIF range at the crack edge is 124.52 MPa·mm 1 / 2 , which is 52.21% higher than the crack tip.

[0203] The crack semi-major axis length corresponding to each crack depth is fitted to obtain the crack semi-major axis evolution process, such as Figure 15 As shown; the morphological ratio of each crack at each crack depth is fitted to obtain the crack morphological evolution process, as shown in Figure 16 As shown, in this example, only eight crack depths ranging from 1 mm to 8 mm are selected.

[0204] according to Figure 15 and Figure 16 It can be seen that as the crack expands, the dispersion and average value of the crack semi-major axis will increase, and its growth rate will continue to accelerate even after fatigue failure; the crack morphology ratio has the opposite trend. Once the crack depth exceeds the critical value, the crack morphology ratio will stabilize within a very small range.

[0205] The load cycle number corresponding to each crack depth is statistically analyzed and fitted to obtain the load cycle number probability evolution model, such as Figure 17 As shown; the remaining fatigue life of each crack depth is statistically analyzed and fitted to obtain the remaining fatigue life probability evolution model, as shown in Figure 18 shown.

[0206] according to Figure 17 and Figure 18 It can be seen that the probability evolution model of the number of load cycles can be well described by the lognormal distribution, while the remaining fatigue life follows a mixed distribution of lognormal and exponential distributions. It is worth noting that this distribution transition occurs at a crack depth of 5 mm, at which point the degradation rate of the weld joint is significantly accelerated.

[0207] according to Figure 19 and Figure 20 It can be seen that the reliability index decreases with increasing traffic volume and gross vehicle weight, with the impact of gross vehicle weight being more significant. Specifically, a 40% increase in traffic volume reduces the reliability index from 2.46 to 1.87 in the 100th year, while a 20% increase in gross vehicle weight reduces the reliability index from 2.46 to 1.68 in the 100th year. For a steel bridge with an expected design life of 100 years, a 40% increase in traffic volume shortens the fatigue life to 99 years, while a 20% increase in gross vehicle weight shortens it to 82 years.

[0208] During the random expansion of fatigue cracks, the present invention fully considers the uncertainties in the crack structure material properties, load, crack size, etc., obtains the statistical characteristics of the crack expansion sensitivity parameters of steel bridge decks under measured traffic flow, and conducts a probabilistic evolution analysis based on this. The critical crack depth is used as the structural failure criterion to establish the limit state function, thereby more reasonably evaluating the structural reliability.

[0209] Example 2

[0210] An embodiment of the present invention also provides an electronic device, which includes: a memory, a processor, and a computer program / instructions stored in the memory, and the processor executes the computer program / instructions to implement the steel bridge deck fatigue crack propagation assessment method in the embodiment of the present application.

[0211] Although not shown, the electronic device includes a processor that can perform various appropriate operations and processes based on the programs and / or data stored in the read-only memory (ROM) or the programs and / or data loaded from the storage portion into the random access memory (RAM). The processor can be a multi-core processor or can include multiple processors. In some embodiments, the processor can include a general-purpose main processor and one or more special coprocessors, such as a central processing unit, a graphics processing unit (GPU), a neural network processor (NPU), a digital signal processor (DSP), etc. In the RAM, there is also stored

[0212] Stores various programs and data required for device operation. The processor, ROM, and RAM are connected to each other via a bus. The input / output (I / O) interface is also connected to the bus.

[0213] The processor and memory are used together to execute the program / instructions stored in the memory. When the program / instructions are executed by the computer, the methods, steps or functions described in the above embodiments can be implemented.

[0214] Although not shown, an embodiment of the present invention further provides a computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the steel bridge deck fatigue crack propagation assessment method in an embodiment of the present application.

[0215] Storage media in embodiments of the present invention include permanent and non-permanent, removable and non-removable items that can be used to store information using any method or technology. Examples of storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device.

[0216] Computer-readable storage media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. The information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices, or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media does not include transitory media such as modulated data signals and carrier waves.

[0217] Although not shown, an embodiment of the present invention further provides a computer program product, including: a computer program / instruction, which, when executed by a processor, implements the steel bridge deck fatigue crack growth assessment method in the embodiment of the present application.

[0218] The above disclosure is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field can easily think of changes or modifications within the technical scope disclosed in the present invention, and they should all be covered by the scope of protection of the present invention.

Claims

1. A method for evaluating fatigue crack growth in steel bridge decks, characterized in that: The evaluation method includes: Obtaining measured traffic flow data, performing statistical analysis and fitting on the measured traffic flow data, and obtaining a probability model of the measured traffic load; Constructing an equivalent stress range prediction model for different vehicle types based on the probability model of the measured traffic load; Constructing a fatigue stress spectrum probability model for steel bridge deck welds based on the probability model of the measured traffic load and the equivalent stress range prediction model for different vehicle types; Construct a prediction model for the equivalent stress intensity factor range at the crack tip and crack edge; Probabilistic models for obtaining initial crack depth, morphology ratio, and material-related parameters; Based on the probability model of initial crack depth, morphology ratio and material-related parameters, the probability model of fatigue stress spectrum of steel bridge deck welds, and the equivalent stress intensity factor range prediction model at the crack tip and crack edge, a random crack growth analysis was performed to obtain the distribution characteristics of sensitivity parameters during the random crack growth process. Based on the distribution characteristics of sensitivity parameters during random crack propagation, the probability evolution analysis of different sensitivity parameters and the reliability evaluation of steel bridge deck are carried out; Based on the probability model of initial crack depth, morphology ratio and material parameters, the probability model of fatigue stress spectrum of steel bridge deck welds, and the equivalent stress intensity factor range prediction model at the crack tip and crack edge, a random crack growth analysis is conducted, specifically including: Step 6.1: Extract multiple fifth samples from the probability model of initial crack depth, shape ratio, and material-related parameters, and the probability model of fatigue stress spectrum of steel bridge deck welds; each fifth sample corresponds to a crack, and each fifth sample includes the initial crack depth, crack semi-major axis length, material-related parameters, and equivalent stress range; the crack semi-major axis length is calculated based on the initial crack depth and shape ratio; Step 6.2: For each fifth sample, predict the initial crack depth and crack semi-major axis length of the fifth sample using the equivalent stress intensity factor range prediction model at the crack tip and crack edge to obtain the equivalent stress intensity factor range at the crack tip and crack edge under the deterministic load; Step 6.3: Obtain the equivalent stress range under the deterministic load; calculate the equivalent stress intensity factor range of the crack tip and crack edge under the measured traffic flow based on the equivalent stress range under the deterministic load, the equivalent stress range of the fifth sample, and the equivalent stress intensity factor range of the crack tip and crack edge under the deterministic load; Step 6.4: Define a crack depth growth increment, and calculate a crack semi-major axis length growth increment and a corresponding load cycle increment for the fifth sample based on the crack depth growth increment, material parameters of the fifth sample, and the equivalent stress intensity factor range of the crack tip and crack edge under actual traffic flow. Step 6.5: Crack extension is performed according to the crack depth extension increment, the crack semi-major axis extension increment, and the corresponding load cycle number increment to obtain the current crack depth, the current crack semi-major axis length, and the current load cycle number; Step 6.6: Determine whether to terminate crack growth based on the current crack depth and the critical crack depth. If so, obtain the distribution characteristics of the sensitivity parameters corresponding to the random crack growth process. If not, proceed to step 6.2 based on the current crack depth, the current crack semi-major axis length, and the current number of load cycles. The calculation formula for the equivalent stress intensity factor range of the crack tip or crack edge under the measured traffic flow is: ； Where p represents the crack tip and e represents the crack edge; Indicates the range of equivalent stress intensity factors at the crack tip or crack edge under measured traffic flow; Indicates the range of equivalent stress intensity factors at the crack tip or crack edge under deterministic load, represents the equivalent stress range of the fifth sample, Indicates the equivalent stress range under deterministic load.

2. The steel bridge deck fatigue crack growth assessment method according to claim 1, characterized in that: Based on the probability model of the measured traffic load, a prediction model for the equivalent stress range of different vehicle models is constructed, including: Designing a plurality of first subsamples based on the probability model of the measured traffic load, and constructing a first subsample data set based on the plurality of first subsamples; wherein each vehicle type corresponds to a first subsample data set, and each first subsample in each first subsample data set includes the vehicle load and wheel track lateral offset distance of the corresponding vehicle type; Construct a finite element model of a steel bridge deck; For each first subsample data set, simulate the operation of a vehicle on a steel bridge deck finite element model based on each first subsample of the first subsample data set to generate a stress history curve corresponding to the first subsample; use a rain flow counting method to convert the stress history curve into multiple stress ranges and their corresponding number of cyclic actions; calculate the equivalent stress range based on the multiple stress ranges and their corresponding number of cyclic actions for each first subsample; construct a first sample data set corresponding to the vehicle type based on each first subsample of the first subsample data set and its equivalent stress range; wherein each first sample of the first sample data set includes the vehicle load, wheel track lateral offset distance, and equivalent stress range of the corresponding vehicle type; Constructing a first prediction model; For each first sample data set, the first prediction model is trained and verified using the first sample data set to obtain an equivalent stress range prediction model for the corresponding vehicle model; The equivalent stress range is calculated based on the multiple stress ranges of each first sub-sample and its corresponding number of cycles. The specific formula is: ； in, represents the equivalent stress range, represents the i-th stress range, Represents the number of cycles, and m represents material-related parameters.

3. The steel bridge deck fatigue crack growth assessment method according to claim 1, characterized in that: Based on the probability model of the measured traffic load and the equivalent stress range prediction model of different vehicle models, a probability model of fatigue stress spectrum of steel bridge deck welds is constructed, including: Extracting a plurality of second samples from the probability model of the measured traffic load; wherein each second sample includes vehicle loads and lateral wheel track offset distances of different vehicle types; Using the equivalent stress range prediction model of different vehicle models to predict the second sample of the corresponding vehicle model, the equivalent stress range of the corresponding second sample is obtained; Statistical analysis and fitting are performed on multiple equivalent stress ranges to obtain a probabilistic model of fatigue stress spectrum of steel bridge deck welds.

4. The steel bridge deck fatigue crack growth assessment method according to claim 1, characterized in that: Construct a prediction model for the equivalent stress intensity factor range at the crack tip and crack edge, including: Step 4.1: Constructing a third sample data set and a fourth sample data set; wherein each third sample in the third sample data set includes a crack parameter and an equivalent stress intensity factor range at the crack tip; and each fourth sample in the fourth sample data set includes a crack parameter and an equivalent stress intensity factor range at the crack edge; Step 4.2: Construct a second prediction model, and use the third sample data set and the fourth sample data set to train and verify the second prediction model respectively to obtain the equivalent stress intensity factor range prediction model of the crack tip and the crack edge.

5. The steel bridge deck fatigue crack growth assessment method according to claim 4, characterized in that: Constructing the third sample data set and the fourth sample data set includes: Step 4.11: Import the steel bridge deck finite element model into FRANC3D software, embed fatigue cracks at the welds between the steel bridge deck top plate and the longitudinal ribs, and construct a solid sub-model containing fatigue cracks; Step 4.12: Apply a deterministic load to the solid sub-model containing the fatigue crack and perform simulation calculations to obtain the stress intensity factor history curves at the crack tip and crack edge; Step 4.13: Using a rain flow counting method, convert the stress intensity factor history curve at the crack tip into multiple stress intensity factor ranges at the crack tip and their corresponding number of cycles; The stress intensity factor history curve of the crack edge is converted into multiple stress intensity factor ranges of the crack edge and their corresponding cyclic action times by using a rain flow counting method; Step 4.14: Calculate the equivalent stress intensity factor range at the crack tip based on the multiple stress intensity factor ranges at the crack tip and their corresponding number of cycles; Calculate the equivalent stress intensity factor range of the crack edge based on multiple stress intensity factor ranges at the crack edge and their corresponding cyclic action times; Step 4.15: Repeat steps 4.11 to 4.14 to obtain the equivalent stress intensity factor range for each fatigue crack and its crack tip and crack edge; Step 4.16: Construct a third sample data set based on the range of equivalent stress intensity factors of all fatigue cracks and their crack tips; construct a fourth sample data set based on the range of equivalent stress intensity factors of all fatigue cracks and their crack edges; The equivalent stress intensity factor range at the crack tip or crack edge is calculated based on the multiple stress intensity factor ranges at the crack tip or crack edge and their corresponding number of cycles. The specific formula is: ； in, Indicates the range of equivalent stress intensity factors at the crack tip or crack edge, represents the range of the i-th stress intensity factor at the crack tip or crack edge, represents the number of cycles of action at the crack tip or crack edge, and m represents the material-related parameters.

6. The method for evaluating fatigue crack growth of a steel bridge deck according to any one of claims 1 to 5, wherein: The sensitivity parameters during the random crack propagation process include the crack semi-major axis length, shape ratio, number of load cycles, and equivalent stress intensity factor ranges at the crack tip and crack edge for each crack depth; the probabilistic evolution analysis includes an analysis of the evolution of the equivalent stress intensity factor range, the evolution of the crack shape, the evolution of the number of load cycles, and the evolution of the remaining fatigue life; The analysis of the evolution of the equivalent stress intensity factor range includes: The equivalent stress intensity factor ranges of each crack at the crack tip and crack edge at each crack depth were statistically analyzed and fitted, and the probability evolution models of the equivalent stress intensity factor ranges at the crack tip and crack edge were obtained respectively. The crack morphology evolution analysis includes: The crack semi-major axis length and morphology ratio of each crack at each crack depth are statistically analyzed to obtain the crack semi-major axis evolution and crack morphology evolution respectively; The load cycle evolution analysis includes: The load cycle number of each crack at each crack depth is statistically analyzed and fitted to obtain a load cycle number probability evolution model; The remaining fatigue life evolution analysis includes: The residual fatigue life of each crack at each crack depth is statistically analyzed and fitted to obtain the residual fatigue life probability evolution model; The calculation formula for the steel bridge deck reliability is: ； ； in, represents the fatigue reliability index, represents the inverse function of the normal distribution function, represents the failure probability of steel bridge deck, represents the crack depth of the steel bridge deck at service time t, represents the critical crack depth, Indicates the true or false indicator of the fifth i-th sample, Indicates the number of the fifth sample.

7. An electronic device comprising a memory, a processor, and a computer program or instruction stored in the memory, characterized in that: The processor executes the computer program or instruction to implement the steel bridge deck fatigue crack growth assessment method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program or instruction stored thereon, characterized in that: When the computer program or instruction is executed by a processor, the method for evaluating fatigue crack growth of a steel bridge deck according to any one of claims 1 to 6 is implemented.

9. A computer program product comprising a computer program or instructions, characterized in that When the computer program or instruction is executed by a processor, the method for evaluating fatigue crack growth of a steel bridge deck according to any one of claims 1 to 6 is implemented.

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