Arch bridge toughness evaluation method based on disturbance theory

Abstract

The invention discloses an arch bridge toughness evaluation method based on a disturbance theory and belongs to the technical field of arch bridge engineering. The method comprises the following specific steps: step 1, for a selected arch bridge, establishing a finite element model, obtaining calculation parameters and working conditions, and analyzing the structural performance of the arch bridge to obtain structural parameters; step 2, calculating a toughness index R of the arch bridge after the earthquake by using a toughness evaluation method of an anti-seismic toughness community in combination with the content in the step 1; 3, repairing the arch bridge, obtaining the state change of the arch bridge in the repairing process, obtaining the secondary related parameters of the second earthquake, and correspondingly calculating the sensitivity delta; and 4, calculating by using the primary related parameters and the secondary related parameters to obtain a result, and evaluating a repair strategy of the arch bridge by using the result. According to the method, an arch bridge toughness adaptability cycle evaluation model is established by using the only-disturbance adaptability cycle theory, so that the effect of arch bridge repair work is evaluated in multiple aspects.

Description

Technical Field

[0001] The present invention relates to the technical field of arch bridge engineering, and particularly relates to a method for evaluating the resilience of arch bridges based on chaos theory. Background Art

[0002] There are various structural types of arch bridges, and their force-bearing conditions are different. In the formulation and calculation process of the resilience evaluation method, it is necessary to conduct targeted research on the structural characteristics of different engineering structures. In addition, even for arch bridges of the same structural type, due to the increase in the span or the width of the bridge deck of the arch bridge, the structural performance of the arch bridge will change, and it is necessary to conduct targeted safety research on such arch bridges. At the same time, arch bridges can be divided into highway arch bridges, railway arch bridges, freight arch bridges, etc. according to their usage functions. Due to different usage functions, their safety evaluation criteria will also be different. It is necessary to adopt reasonable indicators relative to their usage functions for their safety evaluation. In the process of safety evaluation, the specification evaluation method is used to check the strength, stiffness, stability and dynamic performance of the arch bridge structure, and a qualified or unqualified evaluation can be given to the arch bridge components. To a certain extent, the structural performance and vulnerable components of long-span arch bridges can also be analyzed. However, it is found in the evaluation process that this method still has deficiencies such as a single repair plan and difficulty in quantitatively evaluating strategies. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for evaluating the resilience of arch bridges based on chaos theory, using the chaos adaptability cycle theory to establish an arch bridge resilience adaptability cycle evaluation model to evaluate the effect of the arch bridge repair work and provide guiding suggestions for the repair work.

[0004] To achieve the above purpose, the present invention provides a method for evaluating the resilience of arch bridges based on chaos theory, including the following steps:

[0005] Step 1: For the selected arch bridge, obtain the working conditions and combination coefficients, analyze the structural performance of the arch bridge to obtain structural parameters, and accordingly establish a finite element model;

[0006] Step 2: Use the resilience evaluation method of the seismic resilience community to calculate the resilience index R1 of the arch bridge after the first earthquake;

[0007] Step 3: Repair the arch bridge, obtain the state change during the repair process of the arch bridge, and obtain the resilience index R2 of the second earthquake, and accordingly calculate the sensitivity δ;

[0008] Step 4: Calculate the result using the primary relevant parameters and the secondary relevant parameters, and use the result to evaluate the repair strategy of the arch bridge.

[0009] Preferably, the content in Step 1 is as follows. The structural parameters include reaction force, arch rib stiffness, main girder stiffness, hanger strength, arch rib strength, main girder strength, cross beam strength, and elastic stability safety factor.

[0010] Preferably, in Step 2, the calculation process is as follows:

[0011] Obtain the seismic parameters for the first time. The seismic parameters include seismic intensity parameters, corresponding parameters, and behavior parameters. According to the seismic resistance grade of the arch bridge, obtain the seismic response spectrum accordingly. According to the seismic response spectrum, use the finite element model to analyze the structural strain and displacement of the arch bridge under different seismic intensities; based on the structural strain and displacement and according to the design requirements and specifications of the arch bridge, divide the vulnerability of the arch bridge to obtain a vulnerability evaluation table. Input the model and seismic parameters into the finite element to obtain the time history analysis results, and refer to the vulnerability evaluation table to fit the seismic loss function ΔQ(I) that conforms to the actual situation accordingly. The fitting methods include linear or polynomial curve fitting, piecewise function fitting, and complex function curve fitting;

[0012] Use the fitted seismic loss function ΔQ(I) to obtain the recovery function Q(t). The formula is as follows:

[0013]

[0014] In the above formula, Q'0 represents the structural function value after repair. Complete repair to the original level is 100%. t represents the independent variable time, t0 represents the time before the start of the repair work after the first earthquake occurs, and T represents the time taken for the repair.

[0015] Use the recovery function Q(t) to calculate the toughness index R1 after the first earthquake. The formula is as follows:

[0016]

[0017] In the above formula, R1 represents the rapidity evaluation index in the toughness index after an earthquake. Q(t) is the structural function of the arch bridge, t OE1 is the occurrence time of the earthquake disaster, and T CL1 is the total time from the response to the completion of the repair by the emergency department after the earthquake occurs.

[0018] Preferably, the specific content in Step 3 is as follows:

[0019] Formulate a repair strategy based on the damaged state of the arch bridge, establish a finite element model of the repaired arch bridge, use the finite element model of the repaired arch bridge to conduct the second seismic resilience analysis calculation, perform the calculation using the same method as in step two, analyze through the finite element model, and conduct vulnerability assessment on the obtained results and correspondingly fit to obtain the secondary seismic loss function Q”0. Use the secondary seismic function to construct the secondary recovery function Q'(t), and the formula is as follows:

[0020]

[0021] Obtain the recovery time T after the secondary earthquake CL2 , and correspondingly calculate the secondary resilience index R2, and the formula is as follows:

[0022]

[0023] Use the resilience index and the secondary resilience index to conduct sensitivity calculation, and the formula is as follows:

[0024]

[0025] In the above formula, R i represents the resilience shown by the damage and repair of the arch bridge after each earthquake, n represents the number of earthquakes involved in the calculation, and the sensitivity approaching 0 indicates that the system has stronger adaptability to impacts.

[0026] Preferably, calculate the resilience index and sensitivity δ for different repair strategies respectively according to the above calculation method, and evaluate the impact of the repair strategy on resilience.

[0027] Therefore, the present invention adopts the above-mentioned method for evaluating the resilience of an arch bridge based on the chaos theory, which has the following advantages:

[0028] In the present invention, the resilience evaluation method based on the chaos theory is applicable to evaluating the resilience of long-span arch bridges. The combination of different repair strategies greatly affects the resilience sensitivity index. A reasonable combination of repair strategies is of great help in providing the resilience of the arch bridge and improving the evaluation of the arch bridge operation and maintenance system;

[0029] Next, through the drawings and embodiments, the technical solutions of the present invention will be further described in detail. Brief Description of the Drawings

[0030] Figure 1 is the flow step of a method for evaluating the resilience of an arch bridge based on the chaos theory of the present invention;

[0031] Figure 2 is the community evaluation process diagram in a method for evaluating the resilience of an arch bridge based on the chaos theory of the present invention;

[0032] Figure 3This is the evaluation process diagram of a method for evaluating the resilience of arch bridges based on chaos theory of the present invention. Detailed implementation mode

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Usually, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations. The specific model specifications need to be selected according to the actual specifications of the device, etc. The specific selection calculation method adopts the existing technology in the art, so it will not be described in detail here.

[0034] Embodiment

[0035] As Figures 1 - 3 shown, the present invention provides a method for evaluating the resilience of arch bridges based on chaos theory, including the following steps:

[0036] Step 1: For the selected arch bridge, obtain the working conditions and combination coefficients, analyze the structural performance of the arch bridge to obtain the structural parameters, and accordingly establish a finite element model; the specific contents of the working conditions and combination coefficients are shown in Table 1 below:

[0037] Table 1

[0038]

[0039] The structural parameters include support reactions, arch rib stiffness, main longitudinal beam stiffness, hanger strength, arch rib strength, main longitudinal beam strength, middle crossbeam strength, and elastic stability safety factor;

[0040] Step 2: Use the resilience evaluation method of the seismic resilience community to calculate the resilience index R1 of the arch bridge after the first earthquake; the calculation process is as follows:

[0041] Obtain the earthquake parameters of the first time. The earthquake parameters include earthquake intensity parameters, corresponding parameters, and behavior parameters. According to the seismic grade of the arch bridge, obtain the seismic response spectrum accordingly. According to the seismic response spectrum, use the finite element model to analyze the structural strain and displacement of the arch bridge under different earthquake intensities; based on the structural strain and displacement, divide the vulnerability of the arch bridge, and the division criteria are as follows:

[0042] Table 2

[0043]

[0044] According to the damage state classification in Table 2, combined with the constitutive relations of steel structures and concrete and the design drawings of the arch bridge, the damage grades of the vulnerable components or vulnerable parts of the arch bridge are divided. The damage indicators are divided into strain and displacement, and the damage states are divided into five levels, namely basically intact (level 0), slightly damaged (level 1), moderately damaged (level 2), severely damaged (level 3), and completely destroyed (level 4). The specific vulnerability indicators are as follows:

[0045] Table 3:

[0046]

[0047] Based on the vulnerability evaluation table of the above process; input the model and seismic parameters in the finite element to obtain the time history analysis results, and refer to the vulnerability evaluation table to fit the seismic loss function ΔQ(I) that conforms to the actual situation, that is, the correlation function between the degree of structural function loss caused by the earthquake and the peak acceleration of the ground motion response. The fitting methods include linear or polynomial curve fitting, piecewise function fitting, and complex function curve fitting, which can be implemented through MATLAB code. Among them, the polynomial curve uses the poly function, and the complex function curve uses the curvefit function. Here, linear fitting is selected, and the formula is as follows:

[0048]

[0049] In this embodiment, the above formula is transformed to obtain the following formula:

[0050]

[0051] In the above formula, a, b, and u are all calculation constants, ΔQ(I) represents the seismic loss function, and I represents the peak acceleration of the earthquake; use the fitted seismic loss function ΔQ(I) to obtain the recovery function Q(t), and the formula is as follows:

[0052]

[0053] In the above formula, Q'0 represents the structural function value after repair, and complete repair to the original level is 100%. t represents the independent variable time, t0 represents the time before the repair work starts after the first earthquake occurs, and T represents the time used for repair;

[0054] Use the recovery function Q(t) to calculate the toughness index R1 after the first earthquake, and the formula is as follows:

[0055]

[0056] In the above formula, R1 represents the rapidity evaluation index in the toughness index after one earthquake, Q(t) is the structural function function of the arch bridge, t OE1 is the occurrence time of the earthquake disaster, T CL1It is the total time from the response of the emergency department to the completion of the repair after an earthquake occurs.

[0057] Step 3: Repair the arch bridge, obtain the state changes during the repair process of the arch bridge, obtain the secondary relevant parameters of the second earthquake, and calculate the sensitivity δ accordingly; the specific content in Step 3 is as follows:

[0058] Formulate a repair strategy according to the damaged state of the arch bridge, establish a finite element model of the repaired arch bridge, use the finite element model of the repaired arch bridge to conduct a second seismic resilience analysis calculation, use the same method as in Step 2 for calculation, analyze through the finite element model, and conduct vulnerability assessment on the obtained results and fit accordingly to obtain the secondary earthquake loss function Q”0. Use the secondary earthquake function to construct the secondary recovery function Q'(t), and the formula is as follows:

[0059]

[0060] Obtain the recovery time T after the second earthquake CL2 , and calculate the secondary resilience index R2 accordingly. The formula is as follows:

[0061]

[0062] Use the resilience index and the secondary resilience index to calculate the sensitivity. The formula is as follows:

[0063]

[0064] In the above formula, R i represents the resilience shown by the damage and repair of the arch bridge after each earthquake, n represents the number of earthquakes involved in the calculation, and the sensitivity approaching 0 indicates that the system has stronger adaptability to shocks.

[0065] Step 4: Use the results calculated from the primary relevant parameters and the secondary relevant parameters, calculate the resilience index and the sensitivity δ for different repair strategies respectively according to the above calculation method, evaluate the impact of the repair strategy on the resilience to guide the implementation of the repair, and use the results to evaluate the repair strategy of the arch bridge. The specific selection criteria can be given specific values by experts.

[0066] Therefore, the present invention adopts a method for evaluating the resilience of an arch bridge based on the chaos theory, uses the chaos adaptability cycle theory to establish a chaos resilience adaptability cycle evaluation model for the arch bridge, evaluates the effect of the arch bridge repair work, and can give guiding suggestions for the repair work.

[0067] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions of the present invention or make equivalent replacements, and these modifications or equivalent replacements do not enable the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An arch bridge ductility evaluation method based on chaos theory, characterized in that: It includes the following steps: Step 1: For the selected arch bridge, obtain the working conditions and combination coefficients, analyze the structural performance of the arch bridge to obtain structural parameters, and accordingly establish a finite element model; Step 2: Use the resilience evaluation method of the seismic resilience community to calculate the resilience index R1 of the arch bridge after the first earthquake; Step 3: Repair the arch bridge, obtain the state changes during the repair process of the arch bridge, and obtain the resilience index R2 of the second earthquake, and accordingly calculate the sensitivity δ; Step 4: Use the primary relevant parameters and secondary relevant parameters to calculate the results, and use the results to evaluate the repair strategy of the arch bridge.

2. The method for evaluating the toughness of an arch bridge based on chaos theory according to claim 1, characterized in that: The content in Step 1 is as follows. The structural parameters include reaction forces, arch rib stiffness, main longitudinal beam stiffness, hanger strength, arch rib strength, main longitudinal beam strength, middle cross beam strength, and elastic stability safety factor.

3. The method for evaluating the ductility of an arch bridge based on chaos theory according to claim 2, characterized in that: In Step 2, the calculation process is as follows: Obtain the seismic parameters of the first time. The seismic parameters include seismic intensity parameters, corresponding parameters, and performance parameters. According to the seismic grade of the arch bridge, accordingly obtain the seismic response spectrum. According to the seismic response spectrum, use the finite element model to analyze the structural strain and displacement of the arch bridge under different seismic intensities; Based on the structural strain and displacement and according to the design requirements and specifications of the arch bridge, divide the vulnerability of the arch bridge to obtain a vulnerability evaluation table. Input the model and seismic parameters in the finite element to obtain the time history analysis results, and refer to the vulnerability evaluation table to accordingly fit a seismic loss function ΔQ(I) that conforms to the actual situation. The fitting methods include linear or polynomial curve fitting, piecewise function fitting, and complex function curve fitting; Use the fitted seismic loss function ΔQ(I) to obtain the recovery function Q(t), and the formula is as follows: In the above formula, Q'0 represents the structural function value after repair, and complete repair to the original level is 100%. t represents the independent variable time, t0 represents the time before the start of the repair work after the first earthquake, and t represents the time taken for the repair; Use the recovery function Q(t) to calculate the resilience index R1 after the first earthquake, and the formula is as follows: In the above formula, R1 represents the rapidity evaluation index in the ductility index after an earthquake, Q(t) is the arch bridge structure function, t OE1 is the occurrence time of the earthquake disaster, T CL1 is the total time from the response of the emergency department to the completion of the repair after the earthquake occurs.

4. The method for evaluating the toughness of an arch bridge based on chaos theory according to claim 3, characterized in that: In Step 3, the specific content is as follows: Formulate a repair strategy according to the damaged state of the arch bridge, establish a finite element model of the repaired arch bridge, use the finite element model of the repaired arch bridge to conduct a second earthquake resilience analysis calculation, and adopt the same method as in Step 2 for calculation. Analyze through the finite element model, and the obtained results are also subjected to vulnerability assessment and accordingly fit to obtain the secondary earthquake loss function Q″0. Use the secondary earthquake function to construct the secondary recovery function Q'(t), and the formula is as follows: Obtain the recovery time T after the secondary earthquake CL2 , and calculate the secondary ductility index R2 accordingly. The formula is as follows: Use the resilience index and the secondary resilience index to conduct sensitivity calculation, and the formula is as follows: In the above formula, R i represents the toughness shown by the damage and repair of the arch bridge after each earthquake, n represents the number of earthquakes involved in the calculation, and the sensitivity approaches 0, indicating that the system has stronger adaptability to impacts.

5. A method for evaluating the ductility of an arch bridge based on chaos theory according to claim 4, characterized in that: Calculate the resilience index and sensitivity δ for different repair strategies respectively according to the above calculation method, and evaluate the impact of the repair strategy on resilience.

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