Method for comprehensively evaluating anti-seismic performance of suspension bridge based on seismic oscillation intensity index

Abstract

The invention relates to the technical field of suspension bridge anti-seismic performance evaluation, in particular to a method for comprehensively evaluating the anti-seismic performance of a suspension bridge based on a seismic oscillation intensity index. Seismic oscillation intensity indexes are selected as many as possible to comprehensively reflect the amplitude, frequency spectrum, duration and other characteristics of seismic oscillation, and corresponding structural response indexes are determined for different structural members and sections of the suspension bridge; effectiveness, sufficiency and practicability analysis is carried out, and an optimal seismic oscillation intensity index for predicting response of different structural members of the suspension bridge is determined, so that the method is different from a method based on a single Sa (T) value in a traditional method; establishing seismic vulnerability curves of different structural members and sections based on the optimal seismic oscillation intensity index, giving a general fitting expression, and determining dangerous members and sections; meanwhile, the influence of different seismic oscillation input angles on the anti-seismic performance of the bridge is considered, so that the anti-seismic performance of the suspension bridge is comprehensively evaluated.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic performance evaluation of suspension bridges, and particularly to a method for comprehensively evaluating the seismic performance of suspension bridges based on ground motion intensity indices. Background Art

[0002] A suspension bridge is a flexible structure with good seismic performance, and its seismic performance is an important index to measure its overall performance. However, the traditional methods for evaluating the seismic performance of suspension bridges have certain limitations.

[0003] Firstly, PGA and Sa are often selected when establishing the seismic vulnerability curves of different structural components of suspension bridges. However, various studies in recent years have shown that the commonly used PGA and Sa have poor prediction effects and low correlations for predicting the responses of flexible structures such as long-span suspension bridges. Secondly, the pulse effect of ground motion is not considered during the seismic check calculation of suspension bridges, greatly underestimating the damage ability of earthquakes to the suspension bridge structure. Most importantly, during the dynamic time history analysis process, earthquake ground motion records are mostly input in the longitudinal or transverse direction of the bridge, and experimental studies from other input angles are rare. However, in actual earthquakes, the direction of ground motion acting on the bridge often has a certain angle.

[0004] Therefore, in view of the deficiencies of the existing methods for evaluating the seismic performance of suspension bridges, a new method for comprehensively evaluating the seismic performance of suspension bridges is urgently needed. Summary of the Invention

[0005] The purpose of this application is to provide a method for comprehensively evaluating the seismic performance of suspension bridges based on ground motion intensity indices, aiming to solve the problems in the above-mentioned existing technologies.

[0006] This application provides a method for comprehensively evaluating the seismic performance of suspension bridges based on ground motion intensity indices, including the following steps:

[0007] Step S1, determining the initial ground motion records and intensity indices;

[0008] Step S2, determining the response indices of different structural components and sections of the suspension bridge;

[0009] Step S3, analyzing the initial ground motion intensity indices and the response indices with three evaluation indices to determine the optimal ground motion intensity indices characterizing the responses of different structural components and sections of the suspension bridge;

[0010] Step S4, establishing a vulnerability curve for the optimal ground motion intensity index and the cumulative probability of structural component damage, giving a general fitting expression, and determining the critical components and sections;

[0011] Step S5: Calculate the structural responses by inputting ground motions from different angles respectively, establish the fragility curve, determine the most unfavorable ground motion input angle for the suspension bridge, and comprehensively evaluate the seismic performance of the suspension bridge.

[0012] Further, based on Step S1, first select ordinary ground motion records and pulse ground motion records simultaneously, then select multiple ground motion intensity indices characterizing the damage degrees of different structures by ground motions, and finally conduct principal component analysis on the ground motion intensity indices, and select relatively independent ground motion intensity indices as the initial ground motion intensity indices.

[0013] Further, based on the seismic action, select the damaged structural members and sections of the long-span suspension bridge, and then select appropriate response indices according to different structural members and sections.

[0014] Further, the three evaluation indices include effectiveness, sufficiency, and practicality. Comprehensively analyze the results of the above three evaluation indices, and select the ground motion intensity index with the best performance.

[0015] Further, the effectiveness is an evaluation criterion for measuring the correlation between the ground motion intensity index and the structural response index. Usually, the conditional logarithmic standard deviation β is used for measurement. The smaller the β value, the better the correlation between the two. Specifically, as shown in Formula 1:

[0016]

[0017] In the formula: DM is the true structural response, IM is the ground motion intensity index, a and b are the parameters in the functional relationship between the structural response and the intensity index ln(DM) = bln(IM) + lna, a is a constant, and b is the slope.

[0018] The sufficiency is the independence of the intensity index relative to other ground motion characteristic parameters when predicting the structural response index. It is measured by the simplified relative sufficiency method, that is, establish a linear functional relationship between the residual (the difference between the true response and the predicted response, y) and the seismic information parameters (magnitude, epicentral distance, x). The smaller the slope, the more sufficient the intensity index.

[0019] The practicality describes the dependence degree of the structural response index on the ground motion intensity index, that is, the sensitivity of the response index to the change of the intensity index. It is represented by the slope b. Specifically, as shown in Formula 2:

[0020]

[0021] Furthermore, determine the thresholds for different components and cross-section failures, determine the cumulative probabilities of component and cross-section failures under given strength indices, establish the vulnerability curves of structural components with the optimal strength index on the abscissa, then give the general expression through the fitting method to reduce the discreteness in the traditional fitting based on PGA and Sa, and determine the critical components and cross-sections of the suspension bridge.

[0022] The beneficial effects of the present invention are as follows: In the present invention, pulse-type ground motions and ordinary ground motions are respectively selected for analysis, and as many ground motion intensity indices as possible are selected to comprehensively reflect the characteristics of the amplitude, frequency spectrum, and duration of ground motions. For different structural components and cross-sections of the suspension bridge, the corresponding structural response indices are determined; effectiveness, sufficiency, and practicality analyses are carried out to determine the optimal ground motion intensity indices for predicting the responses of different structural components of the suspension bridge, thus differing from the traditional method based on a single Sa(T) value; based on the optimal ground motion intensity indices, the seismic vulnerability curves of different structural components and cross-sections are established, the general fitting expression is given, and the critical components and cross-sections are determined; at the same time, the influence of different ground motion input angles on the seismic performance of the bridge is considered to comprehensively evaluate the seismic performance of the suspension bridge. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a flowchart of the present invention.

[0024] Figure 2 It is a schematic diagram of the effectiveness results of the responses and strength indices of different structural components and cross-sections of the suspension bridge according to the present invention.

[0025] Figure 3 It is a schematic diagram of the sufficiency results of the responses and strength indices of different structural components and cross-sections of the suspension bridge according to the present invention.

[0026] Figure 4 It is a schematic diagram of the practicality results of the responses and strength indices of different structural components and cross-sections of the suspension bridge according to the present invention.

[0027] Figure 5 It is a schematic diagram of the vulnerability cloud map of the seismic ground motion records acting on different structural components and cross-sections of the suspension bridge from different angles according to the present invention.

[0028] Figure 6 It is a schematic diagram of the vulnerability curves of different input angles at the critical cross-section of the suspension bridge according to the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0029] 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 only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0030] As Figure 1 shown, a method for comprehensively evaluating the seismic performance of a suspension bridge based on ground motion intensity indexes includes the following steps:

[0031] Step S1: Determine the initial ground motion records and intensity indexes;

[0032] Step S2: Determine the response indexes of different structural components and sections of the suspension bridge;

[0033] Step S3: Analyze the initial ground motion intensity indexes and the response indexes with three evaluation indexes to determine the optimal ground motion intensity indexes representing the responses of different structural components and sections of the suspension bridge;

[0034] Step S4: Establish a vulnerability curve for the optimal ground motion intensity index and the cumulative probability of structural component damage, give a general fitting expression, and determine the critical components and sections;

[0035] Step S5: Input ground motions from different angles to calculate the structural responses respectively, establish a vulnerability curve, determine the most unfavorable ground motion input angle for the suspension bridge, and comprehensively evaluate the seismic performance of the suspension bridge.

[0036] Based on Step S1, first select ordinary ground motion records and pulse ground motion records simultaneously, then select multiple ground motion intensity indexes characterizing the damage degrees of different structures by ground motions, and finally perform principal component analysis on the ground motion intensity indexes to select relatively independent ground motion intensity indexes as the initial ground motion intensity indexes.

[0037] In terms of ground motion records, ordinary ground motions are usually mainly considered in existing seismic checks, and less research is conducted on near-field pulse ground motions. In terms of ground motion parameters, the characteristics of ground motions are mainly reflected by ground motion parameters such as amplitude, duration, and frequency spectrum in existing methods. Specifically, it is impossible to determine which ground motion parameters can characterize the damage ability of ground motions to structures. Therefore, ground motion intensity indexes are widely selected first, and the initial ground motion intensity indexes are determined through principal component analysis of ground motion parameters. Pulse ground motion records and non-pulse ground motion records containing pulses are screened out from more than 60,000 ground motion records globally, and the ground motion intensity indexes are calculated based on the selected records. Six relatively independent ground motion intensity indexes are selected as the preliminary selected ground motion intensity indexes by the principal component analysis method, as shown in Table 1:

[0038] Table 1 Initial Selection of Ground Motion Intensity Indexes

[0039]

[0040] Note: In the formula, ξ is the damping ratio, S v is the velocity response spectrum, and Td is the duration.

[0041] Based on the seismic action, the damaged structural components and sections of the long-span suspension bridge are selected, and then appropriate response indexes are selected according to different structural components and sections.

[0042] From the aspect of the damage of the suspension bridge structure, according to the different degrees of damage of the bridge, the damage of the bridge can be divided into five different levels in turn: no damage, slight damage, moderate damage, severe damage and complete destruction. The structural damage index parameters are used to represent the structural damage caused by the earthquake, such as the curvature ductility index, displacement ductility index, and stress ratio index. For example, the curvature ductility index is used at the bottom of the bridge tower, the displacement ductility index is used at the top of the tower and the main girder, and the stress ratio index is used for the main cable and the suspender. For different structural components and sections, the response indexes for measuring the structure under ground motion are also different. For example, for the main girder and the top of the tower, displacement is generally used for measurement, for the bottom of the tower, curvature and moment indexes are generally selected for measurement, and for the main cable and the suspender, axial force and stress are generally used for measurement. Therefore, it is also important to determine the response indexes of different structural components and sections of the suspension bridge.

[0043] As Figures 2-4 shown, through the dynamic time history analysis using finite element analysis software, three evaluation indexes for predicting the response of ground motion intensity indexes will be analyzed. The best intensity index for the bridge tower is EPV, and the best intensity indexes for the main cable and the suspender are Sa(T1). The three evaluation indexes include effectiveness, sufficiency and practicability. By comprehensively analyzing the results of the above three evaluation indexes, the best-performing ground motion intensity index is selected.

[0044] The so-called effectiveness is an evaluation criterion for measuring the correlation between the ground motion intensity index and the structural response index. Usually, the conditional logarithmic standard deviation β is used for measurement. The smaller the β value, the better the correlation between the two. Specifically, as shown in Formula 1:

[0045]

[0046] In the formula: DM is the true structural response, IM is the ground motion intensity index, a and b are the parameters in the functional relationship ln(DM) = bln(IM) + lna between the structural response and the intensity index, a is a constant, and b is the slope.

[0047] The sufficiency is the independence of the intensity index relative to other ground motion characteristic parameters when predicting the structural response index, which is measured by a simplified relative sufficiency method, that is, a linear functional relationship between the residual (the difference between the true response and the predicted response, y) and the seismic information parameters (magnitude, epicentral distance, x) is established. The smaller the slope, the more sufficient the intensity index.

[0048] The practicability described the degree of dependence of the structural response index on the ground motion intensity index, that is, the sensitivity of the response index to the change of the intensity index, which is represented by the slope b, as specifically shown in Equation 2:

[0049]

[0050] Determine the thresholds for the failure of different components and sections, determine the cumulative probability of the failure of components and sections under given intensity index conditions, establish the seismic vulnerability curves of different components and sections, and establish the vulnerability curves of structural components with the best intensity index as the abscissa. In previous studies, the vulnerability curves of bridge structures were often obtained through PGA or Sa. However, for suspension bridges, the discreteness between PGA and Sa and the bridge response is relatively large, resulting in the inaccuracy of PGA and Sa in predicting the bridge response. Therefore, in this study, the vulnerability curves of structural components with the best intensity index as the abscissa are established. The general expression is given by the fitting method to reduce the discreteness during the traditional fitting based on PGA and Sa, and determine the dangerous components and sections of the suspension bridge. Taking the bridge tower of the suspension bridge as an example, its dangerous components and sections are determined as shown in Equation 3:

[0051]

[0052] In the formula: P f is the failure probability, S d and S c are the structural demand and the structural capacity respectively, S r is the sum of the squares of the residuals of each discrete point relative to the regression curve, Φ is the cumulative distribution function of the standard normal distribution, a, b, and c are the statistical parameters obtained from the regression analysis, and n is the number of times of the nonlinear dynamic time history analysis.

[0053] When studying the seismic performance of bridges based on numerical simulation methods, the ground motion records are mostly input longitudinally or transversely to the bridge. However, in real earthquake scenarios, the ground motion records act on the bridge from different angles. Such as Figure 5 and 6As shown, the seismic responses of the structure are calculated by inputting ground motions from different angles, and the fragility curves are established. By comparing the fragility curves obtained from different input angles, it is determined that the most unfavorable input angles of ground motions for the suspension bridge are 0° or 180°. When the tower heights are different, generally, the most unfavorable input direction is from the side of the higher tower along the bridge axis. Then, the failure probabilities of each section in the most unfavorable direction are analyzed, and finally, the seismic performance of the suspension bridge is comprehensively evaluated.

[0054] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be encompassed by the present invention. Any reference signs in the claims should not be regarded as limiting the claims involved.

Claims

1. A method for comprehensively evaluating the seismic performance of a suspension bridge based on earthquake intensity index, characterized in that: The following steps are involved: Step S1, determining the initial ground motion record and intensity index; Step S2, determining the response indexes of different structural components and sections of the suspension bridge; Step S3, performing three evaluation index analyses on the initial earthquake intensity index and the response index to determine the best earthquake intensity index that characterizes the responses of different structural components and sections of the suspension bridge; Step S4, establishing a fragility curve for the optimal earthquake intensity index and the cumulative probability of structural component damage, providing a general fitting expression, and determining dangerous components and sections; Step S5, inputting earthquake motions from different angles to calculate the structural response, and establishing a fragility curve, determining the most unfavorable earthquake motion input angle for the suspension bridge, and comprehensively evaluating the seismic performance of the suspension bridge.

2. The method for comprehensively evaluating the seismic performance of a suspension bridge based on earthquake intensity index according to claim 1 is characterized in that: Based on step S1, first, ordinary earthquake motion and pulse earthquake motion records are selected simultaneously, then multiple earthquake motion intensity indices that characterize the degree of earthquake motion damage to different structures are selected, and finally, principal component analysis is performed on the earthquake motion intensity indices, and relatively independent earthquake motion intensity indicators are selected as the initial earthquake motion intensity indicators.

3. The method for comprehensively evaluating the seismic performance of a suspension bridge based on earthquake intensity index according to claim 1 is characterized in that: Based on the earthquake action, the damaged structural components and sections of the long-span suspension bridge are selected, and then the appropriate response indicators are selected according to the different structural components and sections.

4. The method for comprehensively evaluating the seismic performance of a suspension bridge based on earthquake intensity index according to claim 1 is characterized in that: The three evaluation indicators include effectiveness, sufficiency and practicality. The results of the above three evaluation indicators are comprehensively analyzed to select the best performing seismic intensity indicator.

5. The method for comprehensively evaluating the seismic performance of a suspension bridge based on earthquake intensity index according to claim 4 is characterized in that: The effectiveness is an evaluation criterion for measuring the correlation between the earthquake intensity index and the structural response index. It is usually measured by the conditional logarithmic standard deviation β. The smaller the β value, the better the correlation between the two. Specifically, as shown in Formula 1: Where: DM is the real structural response, IM is the seismic intensity index, a and b are the parameters in the functional relationship between structural response and intensity index ln(DM)=bln(IM)+lna, a is a constant, b is the slope; The sufficiency is the independence of the strength index relative to other earthquake motion characteristic parameters when predicting the structural response index, and is measured by a simplified relative sufficiency method, that is, a linear function relationship between the residual and the earthquake information parameter is established. The smaller the slope, the more sufficient the strength index is. The practicality describes the dependence of the structural response index on the seismic intensity index, that is, the sensitivity of the response index to the change of the intensity index, which is expressed by the slope b, as shown in Formula 2:

6. The method for comprehensively evaluating the seismic performance of a suspension bridge based on earthquake intensity index according to claim 1 is characterized in that: Determine the failure thresholds of different components and sections, determine the cumulative probability of failure of components and sections under given strength index conditions, establish a structural component fragility curve with the horizontal axis as the optimal strength index, and then give a general expression through fitting method to reduce the discreteness of traditional PGA and Sa fitting, and determine the dangerous components and sections of the suspension bridge.

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