A method for evaluating the seismic vulnerability of bridges based on an influence line correction model

Abstract

The present invention discloses a bridge seismic vulnerability assessment method based on an influence line correction model, belonging to the technical field of bridge seismic vulnerability assessment, and comprising the following steps: S1: finite element model correction; S2: seismic vulnerability assessment. The present invention uses the measured bridge structure strain influence line as the target parameter and utilizes an artificial neural network to correct the bridge finite element model; performs seismic vulnerability analysis on the optimized model of the corrected bridge finite element model, imports 20 seismic motion records and 1 artificial seismic wave, extracts the displacement response of the bridge structure under different peak ground accelerations, plots the structural exceedance probability, and calculates the vulnerability matrix. Furthermore, an expression for the structural seismic damage index is constructed based on the β probability distribution, and a seismic damage comparison curve is plotted using the expected value of the seismic damage index, thereby achieving an accurate evaluation of the seismic resistance of existing bridge structures.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge seismic vulnerability assessment, and in particular to a bridge seismic vulnerability assessment method based on an influence line correction model. Background Art

[0002] The bridge seismic fortification verification calculation can only relatively simply reflect the ductility seismic resistance requirements of reinforced concrete structures, but cannot accurately assess the possibility of various types of damage to the bridge structure under different earthquake motion intensities.

[0003] Bridge seismic vulnerability studies are often based on finite element model calculations. However, modeling based on design drawings often fails to account for model simplification or geometric material uncertainties. These issues can result in the initial finite element model failing to accurately represent the actual bridge's structural characteristics. To address this issue, a bridge seismic vulnerability assessment method based on an influence line modified model is proposed. Summary of the Invention

[0004] The technical problem to be solved by the present invention is: how to comprehensively carry out a systematic study on the seismic damage expression relationship of bridge structures under different performance levels, so that the constructed model can better consider the strength deviation of structural materials, actual construction errors and non-ideal characteristics of actual structural boundaries, improve the accuracy and true structural characteristics of the initial finite element model established by structural design and design drawings, and thus achieve a more accurate bridge seismic vulnerability assessment, and provide a bridge seismic vulnerability assessment method based on the influence line correction model.

[0005] The present invention solves the above technical problems through the following technical solutions, which include the following steps:

[0006] S1: Finite element model modification

[0007] Obtain the measured influence lines and calculated influence lines of the bridge, construct a BP neural network, and modify the initial finite element model based on the BP neural network to obtain a modified finite element model;

[0008] S2: Seismic Vulnerability Assessment

[0009] Seismic wave data were selected and imported into the modified finite element model. Damage indicators were defined, the displacement responses of the bridge structure under different peak ground accelerations were extracted, the structural exceedance probability was calculated, and a vulnerability matrix was constructed based on the structural exceedance probability. The continuous β probability density function of the bridge structure was then obtained. An expression for the structural seismic damage index was constructed based on the β probability density function, and a seismic damage comparison curve was plotted using the expected value of the seismic damage index to evaluate the seismic vulnerability of the bridge.

[0010] Furthermore, in step S1, the measured influence line is obtained by loading the vehicle's quasi-static influence line, installing a surface strain gauge at the bottom of the mid-span beam, setting a loading route, controlling the test vehicle to move along the loading route, measuring the strain response data of the bridge structure under the quasi-static influence line loading test, and then identifying the strain influence line of the structure under the unit load of the bridge, that is, obtaining the measured influence line; the calculated influence line is obtained by calculating the initial finite element model.

[0011] Furthermore, in step S1, the process of modifying the initial finite element model includes the following steps:

[0012] S11: Constructing BP neural network

[0013] The input layer of the BP neural network selects 5 nodes, corresponding to the 5 shape control points of the bridge, and the output layer selects 4 nodes, corresponding to the 4 correction parameters. The number of hidden layer nodes is calculated by the following formula:

[0014]

[0015] Where m is the number of input layer nodes; n is the number of output layer nodes; a is a constant between 1 and 10;

[0016] S12: Select the objective function

[0017] The measured influence line is selected as the model correction target, and four types of errors between the measured influence line and the calculated influence line are constructed as the objective function. The absolute error, percentage error, relative error, and correlation coefficient are used to comprehensively evaluate the consistency between the actual bridge structure and the finite element model. The calculation formulas for absolute error, percentage error, relative error, and correlation coefficient are as follows:

[0018] Absolute error: ∑|ε a -ε m |

[0019] Percent error: ∑(ε a -ε m ) 2 / ∑(ε m ) 2

[0020] Relative error: ∑|ε a -ε m | / ∑|ε m |

[0021] Correlation coefficient:

[0022] Among them, ε a Indicates the calculated influence line strain value, ε m Indicates the measured influence line strain value;

[0023] S13: Select correction parameters

[0024] Through sensitivity analysis, four physical parameters of the finite element model material are selected as correction parameters, namely the main beam elastic modulus E, the main beam top plate thickness T1, the main beam bottom plate thickness T2, and the main beam web thickness Tw;

[0025] S14: Training BP neural network

[0026] Import the sample data into the established BP neural network, train, verify and test the BP neural network, and save the trained BP neural network after it meets the calculation error requirements after training;

[0027] S15: Finite element model modification

[0028] The five shape control points in the measured influence line are imported into the trained BP neural network as input parameters, and the correction parameters of the finite element model are predicted to obtain the corrected physical parameters. The corrected physical parameters are then substituted back into the initial finite element model to obtain the corrected finite element model.

[0029] Furthermore, in step S2, when selecting seismic wave data, a local code response spectrum is drawn according to the seismic fortification level of the bridge location, multiple natural seismic motion records are selected from the existing database, and at least one artificial seismic wave is generated based on the code response spectrum. The natural seismic motion records and the artificial seismic waves are the selected seismic waves.

[0030] Furthermore, in step S2, whether the selected seismic wave meets the seismic analysis requirements is evaluated by the area enclosed by the seismic wave response spectrum curve and the periodic coordinates, and the area enclosed by the code response spectrum curve and the periodic coordinates. The specific calculation formula is as follows:

[0031]

[0032] K T =S T1 / S T2

[0033] K N =S N1 / S N2

[0034] Among them, S T1 The area from 0.1s to the characteristic period of the seismic wave response spectrum; S T2 The area enclosed by 0.7 to 1.3 times the characteristic period of the seismic wave response spectrum; S N1 The area from 0.1s to the characteristic period of the standard response spectrum; S N2It is the area enclosed by 0.7 times to 1.3 times the characteristic period of the standard response spectrum;

[0035] When K T / K N When the value is between 0.8 and 1.2, that is, the difference between the ratio of the area enclosed by the high-frequency band of the selected seismic wave response spectrum and the area enclosed by the low-frequency band of the code response spectrum is within ±20%, which means that the selected seismic wave meets the requirements of seismic analysis.

[0036] Furthermore, in step S2, when defining the damage index, the pier is set as a vulnerable component, and the yield curvature φ corresponding to the structural damage state is used as the basis for pier damage evaluation, which is converted by the following formula:

[0037]

[0038] θ u =l p (φ u -φ y ) / K

[0039] l p =0.08l+0.022d s f y

[0040] Among them, Δ cy1 is the maximum displacement of the pier top when the reinforcement yields for the first time; Δ y is the elastic displacement of the pier top; Δ u is the maximum displacement of the pier top when a plastic hinge appears at the pier bottom; φ y ' is the initial yield curvature of the pier column; φ y is the equivalent yield curvature of the pier column; φ u is the ultimate yield curvature of the pier column; θ u is the plastic rotation angle of the pier top when a plastic hinge appears on the pier top; l is the pier height; l p is the equivalent plastic hinge length; d s is the diameter of the longitudinal reinforcement in the pier; f y is the yield stress of steel bar; K is the safety factor;

[0041] Based on the above conversion, the displacement ductility ratio μ of the pier column is selected d As the damage index, the bridge damage level μ c Defined as 5 performance levels:

[0042] Basically intact: μ d ≤μ cy1 ;

[0043] Slight damage: μ cy1 <μ d ≤μ cy ;

[0044] Moderate damage: μ cy <μ d ≤μ c4 ;

[0045] Severe damage: μ c4 <μ d ≤μ cmax ;

[0046] Collapse: μ d >μ cmax ;

[0047] Among them, the bridge damage level μ c That is, the damage index, μ d is the displacement ductility ratio of the pier column; μ cy1 is the displacement ductility ratio of the pier when the reinforcement yields for the first time, which is 1; μ cy is the displacement ductility ratio of the pier at the equivalent yield point; μ c4 is the displacement ductility ratio of the pier when the compressive strain of the concrete in the pier cover reaches 0.004; μ cmax is the ductility ratio of the ultimate displacement of the pier; μ cy1 、μ cy 、μ c4 、μ cmax The calculation formula is as follows:

[0048]

[0049] μ cmax =μ c4 +3

[0050] Where, Δ is the maximum displacement of the pier top;

[0051] The bending moment curvature curve was converted into a double-broken line model using the XTRACT program, and the initial, equivalent and ultimate yield curvatures of the pier were extracted to calculate the damage index of the bridge structure.

[0052] Furthermore, in step S2, the bridge pier ductility ratio μ is set to d and damage index μ c Obeying the log-normal distribution, the relationship between the mean λ and the peak ground acceleration PGA is obtained through regression analysis:

[0053] λ=qln(PGA)+p

[0054] Among them, the peak ground acceleration PGA is the earthquake intensity index, q is the regression slope, p is the regression slope distance, and ln(μ d / μ c ) is:

[0055]

[0056] Among them, S r is the residual sum of squares; n is the number of samples.

[0057] Furthermore, in step S2, the structural exceedance probability is:

[0058]

[0059] Where Φ is the standard normal distribution probability function.

[0060] Furthermore, in step S2, the process of obtaining the continuous β probability density function of the bridge structure is as follows:

[0061] S301: Define the beta probability density of the random variable x:

[0062]

[0063] Where a and b are the shape parameters of the beta distribution function, a>0, b>0, and its expectation and variance are:

[0064]

[0065] S302: Fit the structural vulnerability matrix under the given PGA conditions, and let the structural damage level in the vulnerability matrix be represented by the earthquake damage level D r Indicates that the probability density value of the structural damage level is:

[0066]

[0067] Where: i is the earthquake intensity level; j is the structural damage level; ΔD r ij These are the probability density, probability value and interval of the occurrence of level j damage under earthquake intensity level i. The five performance levels correspond to the following intervals: 0-0.1, 0.1-0.3, 0.3-0.5, 0.5-0.7, 0.7-1.0;

[0068] The expected damage level E under the earthquake intensity level i at this time i , variance σ i 2 They are:

[0069]

[0070] S303: Calculate the shape parameter a of the β distribution function under the earthquake intensity i i 、b i They are:

[0071]

[0072] The shape parameter a i 、b i Substituting into step S301, the continuous β probability density function of the bridge structure under the earthquake intensity i is obtained.

[0073] Furthermore, in step S2, the specific process of evaluating the seismic vulnerability of the existing bridge is as follows:

[0074] S31: importing the selected seismic wave data into the modified finite element model to perform nonlinear time history analysis;

[0075] S32: Extract the maximum displacement Δ of the bridge pier top and draw the IDA curve cluster;

[0076] S33: Calculate the displacement ductility ratio μ of the pier column under each working condition d ;

[0077] S34: Combine the ground motion intensity index PGA and μ d / μ c Take the logarithm, draw a scatter plot and calculate the regression relationship;

[0078] S35: Calculate the probability of exceedance for each performance level of the structure;

[0079] S36: Extract the vulnerability matrix based on the structural exceedance probability, calculate the probability density value of a certain damage level of the structure, and then obtain the expected value and variance of the earthquake damage index, and then obtain the shape parameters of the β function and draw the β probability density curve;

[0080] S37: Using expectation as the earthquake damage index and combining it with the β probability density curve, a earthquake damage comparison curve is constructed to evaluate the seismic capacity of bridge structures before and after the finite model modification.

[0081] Compared with the existing technology, the present invention has the following advantages: the bridge seismic vulnerability assessment method based on the influence line correction model uses the measured bridge structure strain influence line as the target parameter and utilizes the artificial neural network to correct the bridge finite element model; the seismic vulnerability analysis is carried out on the optimized model after the correction of the bridge finite element model, 20 seismic motion records and 1 artificial seismic wave are imported, the displacement response of the bridge structure under different peak ground accelerations is extracted, the structural exceedance probability is plotted and the vulnerability matrix is calculated, and then the structural seismic damage index expression is constructed based on the β probability distribution, and the seismic damage comparison curve is plotted with the expected value of the seismic damage index, thereby achieving an accurate evaluation of the seismic resistance of the existing bridge structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 1 is a flow chart of a bridge seismic vulnerability assessment method based on an influence line correction model in an embodiment of the present invention;

[0083] FIG2( a ) is a diagram of a bridge model in an embodiment of the present invention (unit: mm);

[0084] FIG2( b ) is a cross-sectional view of a bridge in an embodiment of the present invention (unit: mm);

[0085] Figure 3 Schematic diagram of the arrangement of measuring points in an embodiment of the present invention (unit: mm);

[0086] Figure 4 BP neural network topology diagram in an embodiment of the present invention;

[0087] Figure 5 1 is a schematic diagram of BP neural network iteration in an embodiment of the present invention;

[0088] FIG6( a ) is a comparison diagram of the influence lines of the uncorrected model according to an embodiment of the present invention;

[0089] FIG6( b ) is a comparison diagram of the influence lines of the modified model in an embodiment of the present invention;

[0090] Figure 7 is a comparison diagram of the mean response spectrum and the standard response spectrum in an embodiment of the present invention;

[0091] Figure 8 is a pier column bending moment curvature curve in an embodiment of the present invention;

[0092] Figure 9 is the time history curve of pier top displacement in the embodiment of the present invention;

[0093] FIG10( a ) is an IDA curve cluster under the initial model in an embodiment of the present invention;

[0094] FIG10( b ) is an IDA curve cluster under the optimization model according to an embodiment of the present invention;

[0095] FIG11( a ) is a graph showing the collapse performance regression analysis results of the initial model according to an embodiment of the present invention;

[0096] FIG11( b ) is a graph showing the collapse performance regression analysis results of the optimized model according to an embodiment of the present invention;

[0097] FIG12( a ) is a comparison diagram of the fragility curves before and after model modification in an embodiment of the present invention;

[0098] FIG12( b ) is a partial detail view of FIG12( a );

[0099] FIG13( a ) is a β probability density curve diagram according to an embodiment of the present invention;

[0100] FIG13( b ) is a β probability density waterfall diagram according to an embodiment of the present invention;

[0101] Figure 142 is a comparison curve diagram of earthquake damage in an embodiment of the present invention. DETAILED DESCRIPTION

[0102] The following is a detailed description of an embodiment of the present invention. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process. However, the protection scope of the present invention is not limited to the following embodiment.

[0103] like Figure 1 As shown, this embodiment provides a technical solution: a bridge seismic vulnerability assessment method based on an influence line correction model, comprising the following steps:

[0104] S1: Finite element model modification

[0105] Obtain the measured influence lines and calculated influence lines of the bridge, construct a BP neural network, and modify the initial finite element model based on the BP neural network to obtain a modified finite element model;

[0106] S2: Seismic Vulnerability Assessment

[0107] Seismic waves are selected and imported into the modified finite element model. Damage indicators are defined, the displacement response of the bridge structure under different peak ground accelerations is extracted, the structural exceedance probability is calculated, and a vulnerability matrix is constructed based on the structural exceedance probability, thereby obtaining a continuous β probability density function of the bridge structure. An expression for the structural seismic damage index is constructed based on the β probability density function, and a seismic damage comparison curve is then plotted using the expected value of the seismic damage index to evaluate the seismic vulnerability of the bridge.

[0108] The main contents of step S1 are described below:

[0109] (1) Measured influence line identification

[0110] In order to measure the strain influence line response of the bridge structure, the test was carried out by quasi-static vehicle influence line loading. The surface strain gauge was installed at the bottom of the mid-span beam. The loading route was selected to be 6.375m away from the centerline of the bridge. The test vehicle with a full load of 37T was made to move along the loading route. The strain response data of the bridge structure under the quasi-static influence line loading test was measured, and then the strain influence line of the structure under the unit load of the bridge was identified, that is, the measured influence line was obtained. The measurement point layout diagram is shown in Figure 3 .

[0111] (2) Model modification theory

[0112] Model modification constructs the error between theoretical and experimental results as the objective function, and continuously changes the physical parameters of the finite element model in order to obtain the optimal solution of the objective function. It mainly consists of the following three parts:

[0113] Correction method: Artificial neural networks have excellent nonlinear mapping capabilities and can effectively convert the inverse problem of model correction into a forward problem. A two-layer feedforward BP neural network is constructed using MATLAB. 5 nodes are selected for the input layer and 4 nodes are selected for the output layer. The number of nodes in the hidden layer is obtained by the empirical formula:

[0114]

[0115] Wherein, m is the number of input layer nodes; n is the number of output layer nodes; a is a constant between 1 and 10, and the number of hidden layer nodes P in the present invention is 12.

[0116] According to the number of nodes in each layer, a 5-12-4-4 two-layer feedforward BP neural network is constructed. There is no self-feedback between the nodes in each layer. The transfer function uses the Tansig function and the Pureline function. The back propagation algorithm uses the LM (Levenberg-Marquardt) optimization algorithm. The topological network structure is shown in Figure 4

[0117] Objective function: The measured strain influence line is selected as the model correction target, and four types of errors between the measured influence line and the finite element calculation influence line are constructed as the objective function. That is, the absolute error, percentage error, relative error, and correlation coefficient are used to comprehensively evaluate the consistency between the actual bridge structure and the finite element model. The relevant formulas are shown in Table 1.

[0118] Table 1 Error calculation formula

[0119]

[0120] Among them, ε a Indicates the calculated influence line strain value, ε m Indicates the measured influence line strain value;

[0121] Correction parameters: To avoid inaccurate physical meaning caused by directly modifying the bridge substructure, this paper conducts sensitivity analysis and selects four physical parameters in the finite element model material as correction parameters to carry out model correction research, namely, the main beam elastic modulus E; the main beam top plate thickness T1; the main beam bottom plate thickness T2; and the main beam web thickness Tw.

[0122] (3) Modification of bridge strain influence line model based on BP neural network

[0123] BP neural network training results

[0124] The constructed 5-12-4-4 two-layer feedforward BP neural network was imported with 30 bridge strain influence line data samples under different correction parameters, and sample training, verification and testing were carried out. After 34 repeated iterations, the sample mean square error reached the expected value. The sample test was carried out based on the trained BP neural network. The BP neural network training results are as follows: Figure 5 The sample fitting results are shown in Table 2.

[0125] Table 2 Sample fitting results

[0126] category training set Validation set Test set overall Regression coefficient R 0.9673 0.9502 0.9315 0.9559

[0127] Depend on Figure 5 As shown in Table 2, the BP neural network iteration is the best at the 28th time, with a mean square error of 4.69×10-4, and the sample fitting regression coefficients of the training set, validation set and test set are all above 0.93, and the overall regression fitting evaluation reaches 0.9559. It is easy to see that the neural network has good mapping ability, and the model parameters can be modified based on the trained BP neural network.

[0128] Finite element model update results

[0129] The measured influence line data were imported into the trained BP neural network to predict the finite element model correction parameters and obtain the corrected physical parameters. The corrected physical parameters were then substituted back into the finite element model to calculate the bridge structure strain influence line and compare it with the measured influence line. The results before and after correction are shown in Table 3 and Figures 6(a) and (b).

[0130] Table 3 Error comparison

[0131] Error category unit Before correction After correction Absolute error με 3.34 0.83 Percent error ％ 16.49 0.89 Relative error ％ 38.00 9.43 Correlation coefficient / 0.99669 0.99671

[0132] Table 3 and Figures 6(a) and (b) show that the revised optimized model fits the actual bridge structure better than the initial model. The absolute error is reduced from 3.34με to 0.83με, and both the percentage error and relative error are less than 10%, with the percentage error being less than 1%. The correlation coefficient increases from 0.99669 to 0.99671. These results demonstrate that the BP neural network-based model revision method can accurately and rapidly approximate the model to the actual bridge structure, making vulnerability analysis of the revised optimized model more scientific and rigorous.

[0133] This example uses a real-world three-span steel-plate composite beam bridge as the research object, conducting finite element model modification and seismic vulnerability research as a further illustration of step S2. This bridge is a double-span bridge with identical structural parameters on both the left and right spans. In this example, the right span was selected for experimental testing and model modification. The total length of the bridge structure is 105m, the span of each span is 35m, and the width of each span is 12m. The superstructure utilizes I-shaped steel and concrete deck composite beams. The main span is constructed of Q345 steel. The substructure utilizes circular pier-type piers constructed with C40 sulfur-resistant concrete. The design seismic fortification level is 8 degrees 0.2g, and the site category is Class II. Bridge information and dimensions are shown in Figures 2(a) and (b). To simulate the nonlinear characteristics of the bridge structure under earthquake action, the finite element model uses the Mander constitutive model for concrete, the bimodal constitutive model for steel, and the fiber-section segmented and distributed plastic hinges for the piers.

[0134] Bridge seismic vulnerability analysis is typically expressed using fragility curves, which reflect the conditional probability of an existing bridge structure exceeding its ultimate limit state under a given seismic motion intensity. Seismic fragility analysis methods are also important decision-making support tools in performance-based seismic fortification. Therefore, in practical projects, seismic fragility curves can be used to promptly identify deficiencies in the seismic performance of structures or components, allowing for optimized structural design and achieving the seismic resistance goal of "sustaining damage in minor earthquakes, repairable in moderate earthquakes, and resistant to collapse in major earthquakes."

[0135] The main contents of step S1 are described below:

[0136] (1) Seismic wave selection

[0137] Selecting appropriate seismic waves is a crucial step in seismic vulnerability analysis. The selected seismic motion records must be able to fully reflect the uncertainty of seismic hazards in the area where the bridge is located. To ensure that the selected seismic wave response spectrum is consistent with the code response spectrum, the degree of response spectrum agreement can be evaluated using the area enclosed by the seismic wave response spectrum curve and the periodic coordinates, and the area enclosed by the code response spectrum curve and the periodic coordinates:

[0138]

[0139] K T =S T1 / S T2 (3)

[0140] K N =S N1 / S N2 (4)

[0141] Among them, S T1 The area from 0.1s to the characteristic period of the seismic wave response spectrum; S T2The area enclosed by 0.7 to 1.3 times the characteristic period of the seismic wave response spectrum; S N1 The area from 0.1s to the characteristic period of the standard response spectrum; S N2 It is the area enclosed by 0.7 times to 1.3 times the characteristic period of the standard response spectrum.

[0142] According to the seismic fortification level of the steel plate composite beam bridge, the local code response spectrum is drawn, 20 natural earthquake motion records are selected from the Pacific Earthquake Engineering Research Center database, and an artificial seismic wave is generated based on the code response spectrum. The degree of fit of the 21 seismic waves is calculated according to formulas (2)-(4), and the results are as follows: Figure 7 , as shown in Table 4.

[0143] Table 4 Detailed information of 21 seismic waves

[0144]

[0145]

[0146] Depend on Figure 7 , Table 4 shows that K T / K N The value is between 0.8 and 1.2, that is, the difference between the ratio of the area enclosed by the high-frequency band of the selected seismic wave response spectrum and the area enclosed by the low-frequency band of the code response spectrum is within ±20%. Therefore, the selection of 21 seismic waves meets the requirements of seismic analysis.

[0147] (2) Definition of damage indicators

[0148] Under earthquake action, the main bridge tends to be elastic, but the bridge piers are prone to plastic deformation, leading to structural collapse. Therefore, the piers are set as vulnerable components, and the yield curvature φ corresponding to the structural damage state is used as the basis for pier damage evaluation, which is converted by the following formula:

[0149]

[0150] θ u =l p (φ u -φ y ) / K (8)

[0151] l p =0.08l+0.022d s f y (9)

[0152] Among them, Δ c y1 is the maximum displacement of the pier top when the reinforcement yields for the first time; Δ y is the elastic displacement of the pier top; Δ u is the maximum displacement of the pier top when a plastic hinge appears at the pier bottom; φ y' is the initial yield curvature of the pier column; φ y is the equivalent yield curvature of the pier column; φ u is the ultimate yield curvature of the pier column; θ u is the plastic rotation angle of the pier top when a plastic hinge appears on the pier top; l is the pier height; l p is the equivalent plastic hinge length; d s is the diameter of the longitudinal reinforcement in the pier; f y is the yield stress of the steel bar; K is the safety factor, which is 2.

[0153] Based on the above conversion, the displacement ductility ratio μ of the pier column is selected d As the damage index, the bridge damage level μ c (μ cy1 、μ cy 、μ c4 、μ cmax ) is defined as 5 states:

[0154] Table 5 Performance levels and limits

[0155] Performance level Limit Basically intact <![CDATA[μ d ≤μ cy1 ]]> Minor damage <![CDATA[μ cy1 <m d ≤μ cy ]]> Moderate damage <![CDATA[μ cy <m d ≤μ c4 ]]> severe damage <![CDATA[μ c4 <m d ≤μ cmax ]]> collapse <![CDATA[μ d >m cmax ]]>

[0156] Among them, μ d is the displacement ductility ratio of the pier column; μ cy1 is the displacement ductility ratio of the pier when the reinforcement yields for the first time, which is 1; μ cy is the displacement ductility ratio of the pier at the equivalent yield point; μ c4 is the displacement ductility ratio of the pier when the compressive strain of the concrete in the pier cover reaches 0.004; μ cmax is the ductility ratio of the ultimate displacement of the pier. The above parameters are calculated by equations (10)-(13):

[0157]

[0158] μ cmax =μ c4 +3 (13)

[0159] Where, Δ is the maximum displacement of the pier top;

[0160] The bending moment curvature curve is equivalent to a double broken line model through the XTRACT program, see Figure 8 , extract the initial, equivalent and ultimate yield curvatures of the pier column, see Table 6, substitute them into equations (5)-(13) to calculate the structural damage index, see Table 7.

[0161] Table 6 Pier column bending moment curvature results

[0162] parameter Numerical <![CDATA[Initial yield curvature φ y ']]> 0.002328(1 / m) <![CDATA[Equivalent yield curvature φ y > 0.003186(1 / m) <![CDATA[Ultimate yield curvature φ u > 0.04400(1 / m)

[0163] Table 7 Damage Index

[0164] Damage level Ductility ratio <![CDATA[μ cy1 ]]> 1.0000 <![CDATA[μ cy ]]> 1.3686 <![CDATA[μ c4 ]]> 4.4273 <![CDATA[μ cmax ]]> 7.4273

[0165] (3) Earthquake vulnerability theory based on β distribution

[0166] Performance-based seismic vulnerability analysis converts the structural response to earthquake motion into a damage index. This damage index is then compared to the damage index threshold at each performance level, and the probability of the structure exceeding a certain performance level is determined through linear regression analysis. Based on the β probability density distribution, the exceedance probability for each performance level is converted into an expression for the overall structural damage. Seismic vulnerability analysis of a steel-plate composite beam bridge using a modified model is then conducted.

[0167] Assuming that the ductility ratio of bridge pier is μ d and damage index μ c Obeying the log-normal distribution, the relationship between the mean λ and the peak ground acceleration PGA is obtained through regression analysis:

[0168] λ=qln(PGA)+p (14)

[0169] Among them, q is the regression slope; p is the regression slope distance, ln(μ d / μ c ) is:

[0170]

[0171] Among them, S r is the residual sum of squares; n is the number of samples.

[0172] The structural exceedance probability is:

[0173]

[0174] Where: Φ is the standard normal distribution probability function.

[0175] A structural vulnerability matrix is constructed based on the exceedance probability, and then converted into an expression of seismic damage index-peak ground acceleration based on the β probability distribution, thereby comprehensively and systematically evaluating the seismic vulnerability of bridge structures.

[0176] Now define the beta probability density of the random variable x:

[0177]

[0178] Where a and b are the shape parameters of the beta distribution function, a>0, b>0, and its expectation and variance are:

[0179]

[0180] Based on the above analysis, the structural vulnerability matrix under the given PGA conditions is fitted, and the structural damage level in the vulnerability matrix is expressed as the earthquake damage level D. r Indicates that the probability density value of the structural damage level is:

[0181]

[0182] Where: i is the earthquake intensity level; j is the structural damage level; ΔD r ij These are the probability density, probability value and interval of level j damage occurring under seismic intensity level i. The five performance levels (basically intact, slightly damaged, moderately damaged, severely damaged and collapsed) correspond to the intervals of 0-0.1, 0.1-0.3, 0.3-0.5, 0.5-0.7 and 0.7-1.0.

[0183] The expected damage level E under the earthquake intensity level i at this time i , variance σ i 2 They are:

[0184]

[0185] Combining equations (19)-(23), we can obtain the shape parameter a of the β distribution function under ground motion intensity i: i 、b i They are:

[0186]

[0187] Substituting into equations (17) and (18) we can obtain the continuous β probability density function of the bridge structure under earthquake intensity i.

[0188] (4) Bridge seismic vulnerability analysis

[0189] As a parameter analysis method, IDA has been widely used in the evaluation of seismic performance of structures in recent years. This method adjusts the amplitude of the selected seismic wave according to a specific ratio, and imports the modulated seismic wave into the structure as input to carry out nonlinear time history analysis. The present invention adopts equal-step amplitude modulation, that is, setting a fixed step size of 0.1g, and modulating the peak ground acceleration from 0.1g to 1.0g in equal steps. The 21 amplitude-modulated seismic records and 10 amplitude-modulated seismic wave samples, a total of 210 seismic wave samples, are imported into the modified finite element model for nonlinear time history analysis. The maximum displacement Δ of the bridge pier top is extracted, see Figure 9 , draw the IDA curve cluster, see Figure 10 (a), (b). According to formula (10), the displacement ductility ratio μ of the pier column under each working condition is calculated d , the earthquake intensity index PGA and μ d / μ cTake the logarithm, draw a scatter plot and substitute it into formula (14) to calculate the regression relationship, see Figure 11 (a) and (b), and calculate the exceedance probability of each performance level of the structure according to formula (15) and (16), see Figure 12 (a) and (b).

[0190] The vulnerability matrix is extracted based on the structural exceedance probability, see Table 8. The probability density value of a certain damage level of the structure is calculated according to formula (21), see Table 9. Substituting it into formulas (22) and (23) to obtain the expected value and variance of the earthquake damage index, the shape parameters of the β distribution function are obtained according to formulas (17), (18), (24) and (25), see Table 10, and the probability density diagram is drawn, see Figures 13(a) and (b).

[0191] Using the expectation as the earthquake damage index, the β probability density curve is combined to construct the earthquake damage comparison curve (SDCC), see Figure 14 , in order to evaluate the seismic capacity of the bridge structure before and after the model modification.

[0192] Table 8 Vulnerability probability of optimized model

[0193]

[0194]

[0195] Table 9 Probability density of optimized model

[0196]

[0197] Table 10 β distribution function parameters

[0198]

[0199] As shown in Figures 10(a) and (b), the displacement of the bridge pier top increases with the increase of PGA. When PGA reaches 0.3g, the structure goes beyond the elastic stage and enters the plastic stage, generating a plastic hinge. Therefore, the rate of increase of the pier top displacement also increases. As shown in Figures 11(a) and (b), ln(PGA) and ln(μ d / μ c ) provides a good linear fit and can be used to calculate the exceedance probability of existing bridges. Analysis of Figures 12(a) and (b) shows that the exceedance probability of the optimized model increases with increasing PGA. As the PGA increases to 0.4g, the probability of the structure exceeding the minor damage level reaches approximately 100%. When the PGA reaches 0.5g, the bridge structure primarily exhibits moderate damage. When the PGA reaches 0.6g, the probability of collapse begins to appear for the first time. When the PGA reaches 1.0g, the probability of structural collapse reaches 65%.

[0200] Compared to the initial model without model correction, the exceedance probabilities for minor, moderate, and severe damage were similar. However, when the PGA reached 0.6g or above, the optimized model's collapse probability increased more slowly than the initial model, resulting in better seismic performance. At a PGA of 1.0g, the optimized model's exceedance probability for collapse was 5% lower than that of the initial model. The initial model based on the design drawings exhibited poor structural seismic performance. Model correction resulted in more accurate seismic vulnerability assessments for existing bridge structures, and the actual seismic performance of existing bridges surpassed that of the initial design model.

[0201] As shown in Figures 13(a) and (b), the method of converting the vulnerability matrix into a seismic damage index based on β distribution is effective and reliable, and the structural β distribution probability density curve is feasible and reasonable. With the increase of PGA, the peak point of the probability density curve shifts to the right, and the bridge enters the high damage level stage. Figure 14 It is known that with the increase of PGA, the seismic damage index of the bridge increases, and the increasing trend accelerates. When the PGA reaches above 0.6g, the seismic damage index of the initial model (initial finite element model) increases faster and the seismic damage performance is more obvious. When the PGA is 1.0g, the seismic damage index of the optimized model (corrected finite element model) is 0.62, which is 2.5% larger than that of the initial model.

[0202] In summary, the bridge seismic vulnerability assessment method based on the influence line correction model of the above embodiment uses the measured bridge structure strain influence line as the target parameter and utilizes an artificial neural network to correct the bridge finite element model. A seismic vulnerability analysis is performed on the optimized model of the corrected bridge finite element model. Twenty seismic motion records and one artificial seismic wave are imported to extract the displacement response of the bridge structure under different peak ground accelerations (PGA). The structural exceedance probability is plotted and the vulnerability matrix is calculated. Then, an expression for the structural seismic damage index is constructed based on the β probability distribution. A seismic damage comparison curve (SDCC) is plotted using the expected value of the seismic damage index to accurately evaluate the seismic resistance of existing bridge structures.

[0203] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A bridge seismic vulnerability assessment method based on an influence line correction model, characterized in that: The following steps are involved: S1: Finite element model modification Obtain the measured influence lines and calculated influence lines of the bridge, construct a BP neural network, and modify the initial finite element model based on the BP neural network to obtain a modified finite element model; In step S1, the process of modifying the initial finite element model includes the following steps: S11: Construct BP neural network; S12: Select the objective function The measured influence line is selected as the model correction target, and four types of errors between the measured influence line and the calculated influence line are constructed as the objective function. The absolute error, percentage error, relative error, and correlation coefficient are used to comprehensively evaluate the consistency between the actual bridge structure and the finite element model. The calculation formulas for absolute error, percentage error, relative error, and correlation coefficient are as follows: Absolute error: ∑|ε a -ε m | Percent error: ∑(ε a -ε m ) 2 / ∑(ε m ) 2 Relative error: ∑|ε a -ε m | / ∑|ε m | Correlation coefficient: Among them, ε a Indicates the calculated influence line strain value, ε m Indicates the measured influence line strain value; S13: Select correction parameters Through sensitivity analysis, four physical parameters of the finite element model material are selected as correction parameters, namely the main beam elastic modulus E, the main beam top plate thickness T1, the main beam bottom plate thickness T2, and the main beam web thickness Tw; S14: training BP neural network; S15: Finite element model modification The five shape control points in the measured influence line are imported into the trained BP neural network as input parameters to predict the correction parameters of the finite element model to obtain the corrected physical parameters. The corrected physical parameters are then substituted back into the initial finite element model to obtain the corrected finite element model. S2: Seismic Vulnerability Assessment Seismic wave data were selected and imported into the modified finite element model. Damage indicators were defined, the displacement responses of the bridge structure under different peak ground accelerations were extracted, the structural exceedance probability was calculated, and a vulnerability matrix was constructed based on the structural exceedance probability. The continuous β probability density function of the bridge structure was then obtained. An expression for the structural seismic damage index was constructed based on the β probability density function, and a seismic damage comparison curve was plotted using the expected value of the seismic damage index to evaluate the seismic vulnerability of the bridge.

2. The bridge seismic vulnerability assessment method based on the influence line correction model according to claim 1 is characterized by: In step S1, the measured influence line is obtained by: using a quasi-static influence line loading method of a vehicle, installing a surface strain gauge at the bottom of the mid-span beam, setting a loading route, controlling the test vehicle to move along the loading route, measuring the strain response data of the bridge structure under the quasi-static influence line loading test, and then identifying the strain influence line of the structure under the unit load of the bridge, that is, obtaining the measured influence line; The influence lines are calculated from the initial finite element model.

3. The bridge seismic vulnerability assessment method based on the influence line correction model according to claim 2 is characterized by: In step S1, the specific process of constructing the BP neural network in step S11 is: The input layer of the BP neural network selects 5 nodes, corresponding to the 5 shape control points of the bridge, and the output layer selects 4 nodes, corresponding to the 4 correction parameters. The number of hidden layer nodes is calculated by the following formula: Where m is the number of input layer nodes; n is the number of output layer nodes; a is a constant between 1 and 10; The specific process of training the BP neural network in step S14 is as follows: The sample data is imported into the established BP neural network, and the BP neural network is trained, verified and tested. When the BP neural network meets the calculation error requirements after training, the trained BP neural network is saved.

4. The bridge seismic vulnerability assessment method based on the influence line correction model according to claim 1 is characterized by: In step S2, when selecting seismic wave data, a local code response spectrum is drawn according to the seismic fortification level of the bridge location, multiple natural seismic motion records are selected from the existing database, and at least one artificial seismic wave is generated based on the code response spectrum. The natural seismic motion records and the artificial seismic waves are the selected seismic waves.

5. The bridge seismic vulnerability assessment method based on the influence line correction model according to claim 4 is characterized by: In step S2, whether the selected seismic wave meets the seismic analysis requirements is evaluated by the area enclosed by the seismic wave response spectrum curve and the periodic coordinates, and the area enclosed by the standard response spectrum curve and the periodic coordinates. The specific calculation formula is as follows: K T =S T1 / S T2 K N =S N1 / S N2 Among them, S T1 The area from 0.1s to the characteristic period of the seismic wave response spectrum; S T2 The area enclosed by 0.7 to 1.3 times the characteristic period of the seismic wave response spectrum; S N1 The area from 0.1s to the characteristic period of the standard response spectrum; S N2 It is the area enclosed by 0.7 times to 1.3 times the characteristic period of the standard response spectrum; When K T / K N When the value is between 0.8 and 1.2, that is, the difference between the ratio of the area enclosed by the high-frequency band of the selected seismic wave response spectrum and the area enclosed by the low-frequency band of the code response spectrum is within ±20%, which means that the selected seismic wave meets the requirements of seismic analysis.

6. The bridge seismic vulnerability assessment method based on the influence line correction model according to claim 4 is characterized by: In step S2, when defining the damage index, the pier is set as a vulnerable component, and the yield curvature φ corresponding to the structural damage state is used as the basis for pier damage evaluation, which is converted by the following formula: i u =l p (f u -f y ) / K the p =0.08l+0.022d s in y Among them, Δ cy1 is the maximum displacement of the pier top when the reinforcement yields for the first time; Δ y is the elastic displacement of the pier top; Δ u is the maximum displacement of the pier top when a plastic hinge appears at the pier bottom; φ y ' is the initial yield curvature of the pier column; φ y is the equivalent yield curvature of the pier column; φ u is the ultimate yield curvature of the pier column; θ u is the plastic rotation angle of the pier top when a plastic hinge appears on the pier top; l is the pier height; l p is the equivalent plastic hinge length; d s is the diameter of the longitudinal reinforcement in the pier; f y is the yield stress of steel bar; K is the safety factor; Based on the above conversion, the displacement ductility ratio μ of the pier column is selected d As the damage index, the bridge damage level μ c Defined as 5 performance levels: Basically intact: μ d ≤μ cy1 ; Slight damage: μ cy1 <μ d ≤μ cy ; Moderate damage: μ cy <μ d ≤μ c4 ; Severe damage: μ c4 <μ d ≤μ cmax ; Collapse: μ d >μ cmax ; Among them, the bridge damage level μ c That is, the damage index, μ d is the displacement ductility ratio of the pier column; μ cy1 is the displacement ductility ratio of the pier when the reinforcement yields for the first time, which is 1; μ cy is the displacement ductility ratio of the pier at the equivalent yield point; μ c4 is the displacement ductility ratio of the pier when the compressive strain of the concrete in the pier cover reaches 0.004; μ cmax is the ductility ratio of the ultimate displacement of the pier; μ cy1 、μ cy 、μ c4 、μ cmax The calculation formula is as follows: m cmax =μ c4 +3 Where, Δ is the maximum displacement of the pier top; The bending moment curvature curve was converted into a double-broken line model using the XTRACT program, and the initial, equivalent and ultimate yield curvatures of the pier were extracted to calculate the damage index of the bridge structure.

7. The bridge seismic vulnerability assessment method based on the influence line correction model according to claim 6, characterized in that: In step S2, let the bridge pier ductility ratio μ d and damage index μ c Obeying the log-normal distribution, the relationship between the mean λ and the peak ground acceleration PGA is obtained through regression analysis: λ=qln(PGA)+p Among them, the peak ground acceleration PGA is the earthquake intensity index, q is the regression slope, p is the regression slope distance, and ln(μ d / μ c ) is: Among them, S r is the residual sum of squares; n is the number of samples.

8. The bridge seismic vulnerability assessment method based on the influence line correction model according to claim 7 is characterized by: In step S2, the structural exceedance probability is: Where Φ is the standard normal distribution probability function.

9. The bridge seismic vulnerability assessment method based on the influence line correction model according to claim 8, characterized in that: In step S2, the process of obtaining the continuous β probability density function of the bridge structure is as follows: S301: Define the beta probability density of the random variable x: Where a and b are the shape parameters of the beta distribution function, a>0, b>0, and its expectation and variance are: S302: Fit the structural vulnerability matrix under the given PGA conditions, and let the structural damage level in the vulnerability matrix be represented by the earthquake damage level D r Indicates that the probability density value of the structural damage level is: Where: i is the earthquake intensity level; j is the structural damage level; ΔD r ij These are the probability density, probability value and interval of the occurrence of level j damage under earthquake intensity level i. The five performance levels correspond to the following intervals: 0-0.1, 0.1-0.3, 0.3-0.5, 0.5-0.7, 0.7-1.0; The expected damage level E under the earthquake intensity level i at this time i , variance σ i 2 They are: S303: Calculate the shape parameter a of the β distribution function under the earthquake intensity i i 、b i They are: The shape parameter a i 、b i Substituting into step S301, the continuous β probability density function of the bridge structure under the earthquake intensity i is obtained.

10. The bridge seismic vulnerability assessment method based on the influence line correction model according to claim 9, characterized in that: In step S2, the specific process of evaluating the seismic vulnerability of an existing bridge is as follows: S31: importing the selected seismic wave data into the modified finite element model to perform nonlinear time history analysis; S32: Extract the maximum displacement Δ of the bridge pier top and draw the IDA curve cluster; S33: Calculate the displacement ductility ratio μ of the pier column under each working condition d ; S34: Combine the ground motion intensity index PGA and μ d / μ c Take the logarithm, draw a scatter plot and calculate the regression relationship; S35: Calculate the probability of exceedance for each performance level of the structure; S36: Extract the vulnerability matrix based on the structural exceedance probability, calculate the probability density value of a certain damage level of the structure, and then obtain the expected value and variance of the earthquake damage index, and then obtain the shape parameters of the β function and draw the β probability density curve; S37: Using expectation as the earthquake damage index and combining it with the β probability density curve, a earthquake damage comparison curve is constructed to evaluate the seismic capacity of bridge structures before and after the finite model modification.

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