Method for predicting fatigue life of steel box girder by considering time-varying vehicle load and bridge model

Abstract

The invention belongs to the field of bridge structure health monitoring, and discloses a steel box girder fatigue life prediction method considering a time-varying vehicle load and a bridge model, and the method comprises the following steps: carrying out the modeling of the time-varying fatigue vehicle load considering time-space distribution, including a random traffic flow feature model and a traffic flow long-term trend model; multi-scale model correction and calibration based on random vehicle-induced response, including modeling based on substructure-fine unit combination and bridge input and output relation reconstruction based on random vehicle-induced response probability characteristics; and loading a load on the calibrated bridge model to obtain a fatigue load effect, and dynamically predicting the fatigue life of the steel box girder based on the time-varying reliability. According to the method, fatigue accumulated damage in the service period can be considered, long-term dynamic evaluation of the fatigue performance of the steel box girder becomes possible based on the long-term monitoring calibration load model and the bridge loading model, and the method is easy to operate and has high engineering use value.

Description

Technical Field

[0001] The invention belongs to the field of bridge structure health monitoring and relates to a steel box girder fatigue life prediction method considering time-varying vehicle loads and bridge models. Background Art

[0002] Steel box girders are subjected to repeated variable amplitude random vehicle loads and corrosive environments for a long time during their service life, and structures such as steel bridge decks are prone to high-cycle fatigue damage. The extension of fatigue cracks is difficult to determine in the initial stage and develops rapidly. Severe fatigue problems may lead to a decrease in the bearing capacity of the bridge, a shortened service life of the bridge, and even catastrophic damage such as the collapse of the bridge structure. Therefore, fatigue life prediction that fully considers the fatigue load and resistance changes during the life cycle of the bridge is of great significance to the maintenance, reinforcement and safe use of bridge structures.

[0003] The focus of fatigue assessment based on fatigue accumulation criteria is on obtaining fatigue load effects (fatigue stress time history). At present, there are two main methods for obtaining fatigue effects: directly based on monitoring strain time history and by establishing a fatigue load model to load the bridge model. For example, publication numbers CN114117622B and CN113868749A use finite element models and influence line models as bridge loading models, respectively. However, directly using monitoring data can only evaluate the fatigue performance during the monitored period, and cannot consider the load and resistance changes during the long-term operation of the bridge. At the same time, the vehicle load model used often fails to fully consider its short-term characteristics and the time-varying characteristics of long-term traffic. The finite element model used as a loading model often differs from the actual structure due to modeling simplification, and the acquisition of the modified model and influence line model requires closed traffic load tests, which are costly and have poor timeliness, making it difficult to achieve long-term dynamic prediction of fatigue life.

[0004] To this end, the present invention proposes a method for predicting the fatigue life of a steel box girder that takes into account time-varying vehicle loads and bridge models. Based on long-term monitoring data, a vehicle load model that takes into account temporal and spatial distribution is established, and the correction and long-term calibration of the multi-scale model are realized based on the monitoring of random vehicle-induced responses. Finally, a dynamic prediction of fatigue life is realized based on the time-varying reliability assessment theory. The present invention can take into account the cumulative fatigue damage during the service period, and based on the long-term monitoring calibration load model and bridge loading model, it makes it possible to perform a long-term dynamic evaluation of the fatigue performance of steel box girders. Summary of the invention

[0005] The purpose of the present invention is to provide a steel box girder fatigue life prediction method taking into account time-varying vehicle loads and bridge models, so as to achieve long-term dynamic evaluation of the fatigue life of the steel box girder.

[0006] The technical solution of the present invention:

[0007] A fatigue life prediction method for steel box girders considering time-varying vehicle loads and bridge models is proposed. The steps are as follows:

[0008] Step 1. Modeling of time-varying fatigue vehicle loads considering temporal and spatial distribution

[0009] (1.1) Vehicle load characteristic modeling;

[0010] The vehicle load characteristic parameters include the vehicle weight, speed and distance between vehicles of each vehicle model; the traffic flow proportion of each vehicle model in each quarter of the year, the traffic flow proportion in 24 time periods of the day and the distribution proportion in each lane are counted; the vehicle load characteristic parameters of each vehicle model are subjected to probability fitting to determine their probability distribution, which is the vehicle load characteristic model;

[0011] (1.2) Random traffic flow simulation;

[0012] Calculate the average daily traffic volume based on the annual traffic volume; determine the traffic volume and vehicle type ratio of each lane in 24 time periods based on the average daily traffic volume; based on the vehicle load characteristic model established in step (1.1), use Monte Carlo sampling to extract the vehicle load parameters of 24 time periods according to the average daily traffic volume to generate a random traffic flow model;

[0013] (1.3) Traffic flow trend modeling;

[0014] The long-term traffic volume change is mainly caused by the trend traffic volume. The decisive factor of the trend traffic volume is economic development. The Logit model is introduced to describe it, as shown in formula (1):

[0015]

[0016] Among them, y is the predicted traffic volume in the tth year; when the annual traffic volume of the bridge operation time can be obtained through monitoring, the parameters a, b and c are determined by fitting; when the annual traffic volume of the bridge operation time cannot be obtained through monitoring, the parameters a, b and c are the traffic volume saturation growth coefficients related to the regional economic development level, which are selected through actual investigation;

[0017] Step 2. Multiscale model correction and calibration based on random vehicle-induced response

[0018] (2.1) Multiscale modeling;

[0019] The multi-scale model has the advantage of satisfying both efficiency and accuracy by finely modeling key local components and retaining the global simplified model of other parts, making it more suitable for fatigue analysis.

[0020] Firstly, a local refined model that satisfies the Saint-Venant principle is established in vulnerable parts or parts with large load effects (such as the mid-span steel box girder section), and a simplified beam-bar model is used to establish a global model in other parts; secondly, the local refined model is divided into three parts, the part containing the analysis section is retained as a local refined unit, and the remaining two symmetrical parts are reduced to a super unit using the substructure method; finally, the super unit, the local refined unit and the global model are coupled based on the multi-point constraint method of deformation coordination to establish a multi-scale model;

[0021] (2.2) Multi-scale model modification and long-term dynamic correction based on monitoring data;

[0022] First, the time period that needs to be modified and corrected for the multi-scale model is determined, and the quasi-static vehicle-induced responses of the strain sensors and the deflection sensors of the main beam control section arranged at the fatigue-prone detail positions (such as the welds between the U-rib and the top plate, and the butt welds of the U-rib) during this period are extracted, and random traffic with the same probability characteristics as the actual traffic is simulated as a known load; secondly, the objective function is established, and the structural parameters to be updated are determined through experience and sensitivity analysis. The objective function is as follows:

[0023]

[0024] Among them, θ is the correction parameter, FEM p (Traffic,θ) and SHM p (Traffic,θ) are the finite element response probability characteristics and monitoring response probability characteristics under random traffic flow; DSF k (θ) and SSF j (θ) are the sub-objective functions of random vehicle-induced deflection and strain response; m1 and m2 are the number of deflection and strain sensors, respectively; α1 and α2 are the weight coefficients of the subjective functions of deflection and strain, respectively, and the sum of the weight coefficients is 1;

[0025] The sub-objective function of the random vehicle-induced deflection and strain response described by mixed Gaussian distribution is as follows:

[0026]

[0027] Where K is the number of Gaussian components in the mixed Gaussian distribution; and are the i-th Gaussian mixture component of the random vehicle induced response distributions from monitoring and finite element calculations, respectively; and are the average values ​​of the i-th Gaussian mixture components of the random vehicle-induced responses obtained by monitoring and finite element calculation, respectively; and The standard deviation of the ith Gaussian mixture component of the random vehicle-induced response from monitoring and finite element calculation, respectively;

[0028] Finally, the optimal solution of the optimization problem is obtained through the particle swarm optimization algorithm; the optimal solution is introduced into the multi-scale model, that is, the updated multi-scale finite element model is obtained;

[0029] Step 3. Prediction of fatigue life of steel box girder based on time-varying reliability

[0030] (3.1) Obtaining fatigue load effects;

[0031] The random traffic flow simulated in step (2.2) is converted into load position information and load amplitude information at each moment, and then loaded onto the corrected and calibrated multi-scale finite element model through virtual loading based on matrix operation to obtain the fatigue load effect;

[0032] (3.2) Establishment of fatigue limit state equation;

[0033] After obtaining the fatigue load effect, the rain flow counting method is used to solve the equivalent stress amplitude and the number of cycles as follows:

[0034]

[0035] Among them, S i and S j are the stress amplitudes greater than and less than the constant amplitude fatigue limit in the stress spectrum caused by random vehicle loads; n i and n j is the corresponding stress cycle number; S eq is the hourly equivalent stress amplitude of random traffic flow; N d K is the number of hourly cycles corresponding to the equivalent stress amplitude of random traffic flow; C and K D are and are the fatigue strength coefficients of the bridge structure details respectively;

[0036] In order to ensure the safety of the bridge structure, the fatigue resistance of each fatigue detail (such as the weld between the U-rib and the top plate of the steel box girder, the U-rib butt weld, etc.) must be greater than the load effect during long-term use; the state functions of the linear fatigue damage accumulation limit based on probability are expressed as follows:

[0037]

[0038] Among them, D f is the critical fatigue damage of bridge details; D(t) and D(t-1) are the linear cumulative damages of the current and previous service years, respectively. When t=1, D1(t-1)=0; γ(t) is the annual change rate of traffic flow;

[0039] (3.2) Fatigue life prediction;

[0040] Taking into account the uncertainty of variables, the Monte Carlo method is used to analyze the reliability of fatigue details; when g(t) < 0, the bridge structure fails due to fatigue, and the time-varying fatigue reliability is expressed as follows:

[0041] β(t)=-Φ -1 (P(g(t)<0)) (7)

[0042] Among them, P f =P(g(t)<0) is the failure probability; Φ -1 (·) is the inverse function of the standard normal cumulative distribution;

[0043] When the fatigue reliability is less than the target reliability limit, the fatigue bearing capacity of the bridge does not meet the requirements. At this time, the total number of stress cycles borne is the fatigue life of the bridge, as shown in the following formula:

[0044] T Life =find{β(t)<β target} (8)

[0045] Among them, T Life is fatigue service life, β target It is a reliability indicator.

[0046] Beneficial effects of the present invention:

[0047] 1. The fatigue life prediction method of steel box girder based on time-varying reliability of the present invention can fully consider the changes of load effect and fatigue resistance with the service time of the bridge, and give maintenance and reinforcement suggestions according to different regulations and owner needs, which has high engineering practical value;

[0048] 2. The stress amplitude range obtained by the load modeling method considering the temporal and spatial distribution of the present invention is closer to the actual value. The proposed Logit model can more reasonably predict the long-term traffic flow growth than the linear model;

[0049] 3. The multi-scale model correction and calibration method based on random vehicle-induced response can overcome the limitation of measuring points and realize fatigue assessment at any position. The model is calibrated using monitoring data, avoiding the influence of closed traffic in load test, making the bridge model more representative of the real bridge structure and reducing fatigue assessment error;

[0050] 4. The present invention can take into account the fatigue cumulative damage during the service period and calibrate the load model and bridge loading model based on long-term monitoring, making long-term dynamic evaluation of the fatigue performance of steel box girders possible. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a flow chart of the present invention.

[0052] Figure 2The long-term vehicle load statistical characteristics obtained by implementing the method of the present invention; wherein, (a) the traffic volume distribution in each time period, (b) the distribution proportion of each vehicle type in each time period, (c) the probability distribution of the weight of a five-axle vehicle, and (d) the long-term traffic volume prediction model.

[0053] Figure 3 Comparison of multi-scale model correction results obtained by implementing the method of the present invention; wherein, (a) is a comparison of the probability models of random vehicle-induced responses before and after correction, and (b) is a comparison of influence lines before and after correction.

[0054] Figure 4 Comparison of fatigue load effect curves obtained by implementing the method of the present invention;

[0055] Figure 5 The figures are a comparison of fatigue reliability and life prediction results using the method of the present invention; wherein (a) is a comparison of calculation results using different traffic volume prediction models, and (b) is a comparison of calculation results using different bridge loading models. DETAILED DESCRIPTION

[0056] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0057] A steel box girder fatigue life prediction method considering time-varying vehicle loads and bridge models is divided into three steps: "time-varying fatigue vehicle load modeling considering temporal and spatial distribution", "multi-scale model correction and calibration based on random vehicle-induced response", and "fatigue life prediction of steel box girders based on time-varying reliability".

[0058] Example

[0059] The actual monitoring data of a 1,280-meter-long, six-lane, large-span steel box girder suspension bridge was used for verification. First, the vehicle weight, vehicle spacing, and vehicle speed data of the random traffic flow in each lane were obtained through the dynamic weighing data installed on the bridge. The random traffic flow was divided into 24 time periods, and the average hourly traffic flow ratio and vehicle type ratio characteristics that affect fatigue analysis were statistically analyzed for each lane, such as Figure 2 (a) and Figure 2 (b) is shown. It can be seen that the traffic volume increases during the day and decreases at night. The proportion of small cars increases during the day and the proportion of heavy cars increases at night, which is closely related to the driving habits of drivers. Therefore, in order to better interpret the spatiotemporal distribution of bridge vehicle loads and reasonably calculate the stress amplitude and the number of cycles, it is necessary to fully consider the distribution of vehicle type ratio and traffic volume. The weight, speed and vehicle spacing distribution of each vehicle type are determined by probability fitting, and the vehicle load parameters are modeled. Figure 2 (c) Take the weight of a 5-axle vehicle as an example. Based on the average daily traffic volume data for three years during the operation period, the Logit model is used to predict the long-term traffic volume growth model, such as Figure 2 (d) as shown.

[0060] Secondly, a multi-scale model correction method based on the probability characteristics of random vehicle-induced response is proposed for long-term fatigue assessment of steel box girders. The global model uses beam-bar elements, and the mid-span local steel box girder uses plate-shell elements. Taking the U-rib measurement point on the top plate of the steel box girder as an example, the correction results are as follows: Figure 3 It can be seen that the simplified model cannot reflect the local stress, and the stress amplitudes before and after the model correction are different. It will cause large errors when used for fatigue analysis, which shows the necessity of multi-scale model correction.

[0061] After the model is modified, the random vehicle load is loaded by extracting the influence surface of key details to increase the loading speed and obtain the stress history caused by the vehicle load. The stress history curve under the random vehicle load is analyzed by the rain flow counting method to obtain the fitting probability distribution of the equivalent stress amplitude and the number of cycles in each period. Figure 4 As shown, it can be seen that the equivalent stress and stress cycle from 9:00 to 17:00 are significantly greater than those at other times of the day. If the temporal and spatial distribution of the load is not considered, large errors in fatigue damage will occur.

[0062] Finally, the fatigue life prediction of steel box beams based on time-varying reliability is realized. In this implementation, the Monte Carlo method is used to perform 100,000 simulations. The time-varying reliability evaluation results considering different influencing factors are as follows: Figure 5 As shown. It can be seen that the load model determined by the fatigue load effect needs to consider the temporal and spatial distribution of random vehicle loads and the reasonable prediction of long-term traffic flow, and whether the bridge load model is corrected by a multi-scale model and the evaluation results of long-term calibration are quite different, which will have a great impact on the project operation and maintenance, verifying the effectiveness of the steel box girder fatigue life prediction method considering time-varying vehicle loads and bridge models of the present invention.

Claims

1. A method for predicting fatigue life of steel box girders considering time-varying vehicle loads and bridge models, characterized in that: Here are the steps: Step 1. Modeling of time-varying fatigue vehicle loads considering temporal and spatial distribution (1.1) Vehicle load characteristics modeling; The vehicle load characteristic parameters include the vehicle weight, speed and distance between vehicles of each vehicle model; the traffic flow proportion of each vehicle model in each quarter of the year, the traffic flow proportion in 24 time periods of the day and the distribution proportion in each lane are counted; the vehicle load characteristic parameters of each vehicle model are subjected to probability fitting to determine their probability distribution, which is the vehicle load characteristic model; (1.2) Random traffic flow simulation; Calculate the average daily traffic volume based on the annual traffic volume; determine the traffic volume and vehicle type ratio of each lane in 24 time periods based on the average daily traffic volume; based on the vehicle load characteristic model established in step (1.1), use Monte Carlo sampling to extract the vehicle load parameters of 24 time periods according to the average daily traffic volume to generate a random traffic flow model; (1.3) Traffic flow trend modeling; The long-term traffic volume change is mainly caused by the trend traffic volume. The decisive factor of the trend traffic volume is economic development. The Logit model is introduced to describe it, as shown in formula (1): Among them, y is the predicted traffic volume in the tth year; when the annual traffic volume of the bridge operation time can be obtained through monitoring, the parameters a, b and c are determined by fitting; when the annual traffic volume of the bridge operation time cannot be obtained through monitoring, the parameters a, b and c are the traffic volume saturation growth coefficients related to the regional economic development level, which are selected through actual investigation; Step 2. Multiscale model correction and calibration based on random vehicle-induced response (2.1) Multiscale modeling; Firstly, a local refined model that satisfies the Saint-Venant principle is established in the vulnerable parts or the parts with large load effects, and a simplified beam-bar model is used to establish a global model in other parts; secondly, the local refined model is divided into three parts, the part containing the analysis section is retained as a local refined unit, and the remaining two symmetrical parts are reduced to super units by the substructure method; finally, the super units, local refined units and global models are coupled based on the multi-point constraint method of deformation coordination to establish a multi-scale model; (2.2) Multi-scale model modification and long-term dynamic correction based on monitoring data; First, the time period that needs to be modified and corrected for the multi-scale model is determined, and the quasi-static vehicle-induced responses of the strain sensors arranged at the fatigue-prone detail positions and the deflection sensors of the main beam control section during this period are extracted, and random traffic with the same probability characteristics as the actual traffic is simulated as a known load; secondly, the objective function is established, and the structural parameters to be updated are determined through experience and sensitivity analysis. The objective function is as follows: Among them, θ is the correction parameter, FEM p (Traffic,θ) and SHM p (Traffic,θ) are the finite element response probability characteristics and monitoring response probability characteristics under random traffic flow; DSF k (θ) and SSF j (θ) are the sub-objective functions of random vehicle-induced deflection and strain response; m1 and m2 are the number of deflection and strain sensors, respectively; α1 and α2 are the weight coefficients of the subjective functions of deflection and strain, respectively, and the sum of the weight coefficients is 1; The sub-objective function of the random vehicle-induced deflection and strain response described by mixed Gaussian distribution is as follows: Where K is the number of Gaussian components in the mixed Gaussian distribution; and are the i-th Gaussian mixture component of the random vehicle induced response distributions from monitoring and finite element calculations, respectively; and are the average values ​​of the i-th Gaussian mixture components of the random vehicle-induced responses obtained by monitoring and finite element calculation, respectively; and The standard deviation of the ith Gaussian mixture component of the random vehicle-induced response from monitoring and finite element calculation, respectively; Finally, the optimal solution of the optimization problem is obtained through the particle swarm optimization algorithm; the optimal solution is introduced into the multi-scale model, that is, the updated multi-scale finite element model is obtained; Step 3. Prediction of fatigue life of steel box girder based on time-varying reliability (3.1) Obtaining fatigue load effects; The random traffic flow simulated in step (2.2) is converted into load position information and load amplitude information at each moment, and then loaded onto the corrected and calibrated multi-scale finite element model through virtual loading based on matrix operation to obtain the fatigue load effect; (3.2) Establishment of fatigue limit state equation; After obtaining the fatigue load effect, the rain flow counting method is used to solve the equivalent stress amplitude and the number of cycles as follows: Among them, S i and S j are the stress amplitudes greater than and less than the constant amplitude fatigue limit in the stress spectrum caused by random vehicle loads; n i and n j is the corresponding stress cycle number; S eq is the hourly equivalent stress amplitude of random traffic flow; N d K is the number of hourly cycles corresponding to the equivalent stress amplitude of random traffic flow; C and K D are and are the fatigue strength coefficients of the bridge structure details respectively; In order to ensure the safety of the bridge structure, the fatigue resistance of each fatigue detail must be greater than the load effect during long-term use; the state functions of the linear fatigue damage accumulation limit based on probability are expressed as follows: Among them, D f is the critical fatigue damage of bridge details; D(t) and D(t-1) are the linear cumulative damages of the current and previous service years, respectively. When t=1, D1(t-1)=0; γ(t) is the annual change rate of traffic flow; (3.2) Fatigue life prediction; Taking into account the uncertainty of variables, the Monte Carlo method is used to analyze the reliability of fatigue details; when g(t) < 0, the bridge structure fails due to fatigue, and the time-varying fatigue reliability is expressed as follows: β(t)=-Φ -1 (P(g(t)<0)) (7) Among them, P f =P(g(t)<0) is the failure probability; Φ -1 (·) is the inverse function of the standard normal cumulative distribution; When the fatigue reliability is less than the target reliability limit, the fatigue bearing capacity of the bridge does not meet the requirements. At this time, the total number of stress cycles borne is the fatigue life of the bridge, as shown in the following formula: T Life =find{β(t)<β target } (8) Among them, T Life is fatigue service life, β target It is a reliability indicator.

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