Rapid earthquake vulnerability analysis method for deepwater bridge

Abstract

The invention discloses a rapid earthquake vulnerability analysis method for a deepwater bridge, which can rapidly generate artificial waves meeting the requirements of a standard response spectrum, can shorten the time for producing the artificial waves in a traditional earthquake-proof time history construction method to about 10 minutes, and greatly improves the construction efficiency of earthquake-proof time history waves. Meanwhile, the dynamic water additional mass of the deepwater bridge is determined by using a particle swarm optimization algorithm; and determining the optimal dynamic water additional mass of the deepwater bridge by checking the seismic response of the beam-column unit model corresponding to the bridge local pier entity finite element model under the dynamic water additional mass and the seismic response error of the fluid-structure interaction pier entity finite element model established on the local pier entity finite element model. Compared with a traditional numerical type deepwater bridge flowing water additional mass determination method, the method is small in calculation amount and high in calculation efficiency, and a foundation is laid for accurate earthquake vulnerability analysis of the deepwater bridge.

Description

Technical Field

[0001] The present invention relates to the field of seismic vulnerability analysis, and is particularly applicable to a rapid seismic vulnerability analysis method for deep-water bridges. Background Art

[0002] The occurrences of previous earthquakes have shown that compared with onshore bridges, deep-water high-pier bridges are more vulnerable to damage. When an earthquake disaster strikes, the damage of bridges in the earthquake-stricken area means the interruption of lifelines, directly hindering the progress of disaster relief operations, increasing life and property losses as well as indirect economic losses, and bringing great difficulties to post-disaster recovery and reconstruction. A systematic study on the structural response and seismic performance of deep-water high-pier bridges under earthquake action is of great significance and can effectively ensure the seismic safety of bridges.

[0003] Currently, the seismic time history method is mostly used in the design of deep-water high-pier bridges to evaluate the seismic performance of different bridge types. However, the seismic time history waves used in the seismic time history method need to correspond to the target response spectrum at different time periods, resulting in a long construction time for the seismic time history waves. For example, the time-consuming for constructing the seismic time history using the unconstrained optimization method is about 3 days, seriously affecting the engineering application of the seismic time history method.

[0004] At the same time, the hydrodynamic effect needs to be considered in the seismic analysis of deep-water bridges. However, currently, there are only hydrodynamic added mass calculation formulas for deep-water bridges with simple cross-sections such as circular cross-sections and rectangular cross-sections in domestic and foreign codes, and no hydrodynamic added mass calculation formula for piers with complex cross-sections is given. Even when using numerical analysis methods such as finite element, boundary element, and discrete element to analyze the water-structure interaction problem under earthquake action, due to the low calculation efficiency, it is not applicable to the seismic performance analysis of the entire bridge. Summary of the Invention

[0005] The purpose of the present invention is to provide a rapid seismic vulnerability analysis method for deep-water bridges to solve the problem of rapid seismic vulnerability analysis of deep-water bridges.

[0006] To achieve the above purpose, the present invention adopts the following technical solutions: The rapid seismic vulnerability analysis method for deep-water bridges according to the present invention includes the following steps: S1, constructing a seismic time history wave; S2, inputting the seismic time history wave into the fluid-structure interaction finite element model of the pier entity to obtain the first seismic response; S3, establishing a beam-column element model corresponding to the finite element model of the pier entity, and using the seismic time history wave in step S2 to obtain the second seismic response of the beam-column element model under different hydrodynamic added masses; S4, calculating the root mean square error value between the second seismic response and the first seismic response, and determining the hydrodynamic added mass corresponding to the second seismic response when the root mean square error value is the smallest; S5. Establish a full-bridge pier element model, apply the hydrodynamic added mass determined in step S3, determine the bridge seismic damage index, input the seismic time history wave, and obtain the third seismic response; S6. Establish a bridge seismic vulnerability curve based on the third seismic response to evaluate the seismic resistance capacity of the bridge.

[0007] Furthermore, the specific steps of constructing multiple seismic time history waves in step S1 are as follows. S1.1. Generate an artificial wave with a fixed number of steps and a fixed time interval based on the random number generation method; multiply the artificial wave by a coefficient that gradually increases with time to conform to the definition of the seismic time history method. S1.2. Perform wavelet denoising and scaling on the artificial wave generated in step S1.1 to make the response spectrum of the processed artificial wave fit the two-level target response spectrum, and calculate the root mean square error between the two. S1.3. Repeat steps S1.1 and S1.2, and use the artificial wave corresponding to the response spectrum of the artificial wave with the minimum root mean square error value as the initial artificial wave. S1.4. Segment and scale-optimize the initial artificial wave to obtain multiple seismic time history waves.

[0008] Furthermore, in step S1.1, the number of steps of the artificial wave is 4000 steps, and the time interval is 0.01 s.

[0009] Furthermore, in step S1.4, use the particle swarm optimization algorithm to perform scaling optimization on the initial artificial wave. First, segment the initial artificial wave; then initialize the parameters and population of the particle swarm optimization algorithm; calculate the fitness value of each particle, update the velocity and position of the particle, and perform iterative optimization until the termination condition is met, then output the optimal scaling coefficient, and perform scaling optimization on the segmented initial artificial wave according to the optimal scaling coefficient to obtain multiple seismic time history waves.

[0010] Furthermore, in step S2, the fluid-structure interaction finite element model of the bridge pier entity is composed of a bridge pier entity finite element model and potential fluid elements for simulating water bodies.

[0011] Furthermore, in step S3, use the particle swarm optimization algorithm multiple times for optimization to obtain different hydrodynamic added masses applied to the beam-column element model.

[0012] Furthermore, in step S5, the seismic damage index includes the curvature ductility coefficient of the top and bottom sections of the bridge pier in the beam-column element model and the displacement value of the bearing.

[0013] Furthermore, in step S6, calculate the damage exceedance probability of each component of the bridge according to the third seismic response, and establish the seismic vulnerability curve of each component of the bridge.

[0014] Further, in step S5, elastic beam-column elements are used for the main girder in the full bridge pier unit model, and fiber elements based on the flexibility method are used for the piers; the bearings are simulated by zero-length elements.

[0015] Further, the fluid-structure interaction finite element model of the bridge pier entity in step S2 and the beam-column element model corresponding to the finite element model of the bridge pier entity in step S3 adopt the local bridge pier entity finite element model.

[0016] The advantages of the present invention are that artificial waves meeting the requirements of the code response spectrum can be quickly generated, and the time for generating artificial waves in the traditional seismic time history construction method can be shortened to about 10 minutes, greatly improving the construction efficiency of seismic time history waves. At the same time, the present invention uses the particle swarm optimization algorithm to determine the hydrodynamic added mass of deep-water bridges, and determines the optimal hydrodynamic added mass of deep-water bridges by checking the error between the seismic responses of the beam-column element model corresponding to the local bridge pier entity finite element model of the deep-water bridge under the hydrodynamic added mass and the seismic responses of the fluid-structure interaction pier entity finite element model established on the local bridge pier entity finite element model. Compared with the traditional numerical method for determining the hydrodynamic added mass of deep-water bridges, the calculation amount is less and the calculation efficiency is high, laying a foundation for the accurate seismic vulnerability analysis of deep-water bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a flowchart of the method for rapid seismic vulnerability analysis of deep-water bridges according to the present invention.

[0018] Figure 2 is a flowchart of the method for constructing multiple seismic time history waves in the present invention.

[0019] Figure 3 is a schematic diagram of the seismic curve and response spectrum of the seismic time history wave constructed in the present invention.

[0020] Figure 4 is a schematic diagram of the beam-column element model of a certain deep-water high-pier long-span continuous rigid-frame bridge in the present invention.

[0021] Figure 5 is Figure 4 the probability seismic demand model schematic diagram of pier No. 5 based on spectral acceleration in

[0022] Figure 6 is a comparison chart of the bridge seismic vulnerability curves of the method of the present invention and the IDA method under four damage states.

[0023] Figure 7 is a flowchart of the method for determining the hydrodynamic added mass in the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0024] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all 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.

[0025] As Figure 1 shown, the method for rapid seismic vulnerability analysis of deep-water bridges according to the present invention includes the following steps: S1. Construct seismic-resistant time history waves. As Figure 2 shown, the specific steps are as follows: S1.1. Based on the random number generation method, generate an artificial wave with 4000 steps and a time interval of 0.01. For any moment, multiply it by a coefficient that gradually increases with time, so that the artificial wave conforms to the definition of the seismic-resistant time history method (the constructed seismic-resistant time history wave is the artificial wave).

[0026] S1.2. Perform wavelet denoising on the generated artificial wave, and then scale the wave so that its response spectrum can fit the two-level target response spectrum, and calculate the root mean square error value between the two.

[0027] S1.3. Repeat steps S1.1 and S1.2 multiple times to obtain the acceleration time history curve corresponding to the artificial wave response spectrum with the minimum root mean square error value, and use the artificial wave corresponding to this acceleration time history curve as the initial artificial wave.

[0028] S1.4. Segment the initial artificial wave obtained in S1.3. The scaling coefficient of the seismic wave within each segment is used as the independent variable of the objective function, and the root mean square error value between the overall response spectrum and the two-level target response spectrum is used as the objective function value. Based on the particle swarm optimization algorithm, first segment the initial artificial wave; then initialize the parameters and population of the particle swarm optimization algorithm; calculate the fitness value of each particle, update the velocity and position of the particle, and perform iterative optimization until the termination condition is met, then output the optimal scaling coefficient, and scale and optimize the segmented initial artificial wave according to the optimal scaling coefficient to obtain multiple seismic-resistant time history waves.

[0029] According to the above method, an artificial wave with a time interval of 0.01 s and a total time of 40 s can be generated. The time period from 0 to 30 s is fitted to the E1 seismic level, and the time period from 0 to 40 s is fitted to the E2 seismic level. Figure 3 A new artificial wave form suitable for two-level seismic design is given. As can be seen from Figure 3 Figure (a), the peak value of the seismic-resistant time history acceleration increases with time, which conforms to the basic principle of the seismic-resistant time history method. As can be seen from Figure 3(b) It can be seen that for the two-level seismic design, the response spectrum shape of the artificial wave generated by the present invention is similar to and highly consistent with the seismic time history response spectrum, and is consistent with the synthesis criterion of the seismic time history method, verifying the accuracy of the method for constructing the seismic time history wave of the present invention. Compared with the traditional method for constructing the seismic time history, which usually takes two or three days to generate the seismic time history wave, the method for constructing the seismic time history wave of the present invention can shorten the construction time of the seismic time history wave to about 10 minutes, greatly improving the construction efficiency of the seismic time history.

[0030] S2. Input the seismic time history wave into the fluid-structure interaction finite element model of the bridge pier entity to obtain the first seismic response. The fluid-structure interaction finite element model is composed of the finite element model of the bridge pier entity and the potential fluid element simulating the water body.

[0031] S3. Establish a beam-column element model corresponding to the finite element model of the bridge pier entity, and use the seismic time history wave in step S2 to obtain the second seismic response of the beam-column element model under different hydrodynamic added masses.

[0032] S4. Calculate the root mean square error value between the second seismic response and the first seismic response, and determine the hydrodynamic added mass corresponding to the second seismic response when the root mean square error value is the smallest. The hydrodynamic added mass is obtained through the particle swarm optimization algorithm. Taking the hydrodynamic added mass as the independent variable of the objective function and the root mean square error value between the second seismic response and the first seismic response as the objective function value, a solution with a smaller root mean square error value is obtained. Repeat this process multiple times to obtain multiple hydrodynamic added masses, and then compare them to find the optimal hydrodynamic added mass.

[0033] The purpose of steps S2 to S4 above is to determine the hydrodynamic added mass of the deep-water bridge. To more accurately determine the hydrodynamic added mass of the deep-water bridge, the hydrodynamic added mass of the deep-water bridge can be determined through the following specific steps, as Figure 7 shown: a. Establish a finite element model of the bridge pier entity, input the seismic time history wave into the finite element model of the bridge pier entity, and obtain the seismic response of the finite element model of the bridge pier entity.

[0034] b. Establish a beam-column element model corresponding to the finite element model of the bridge pier entity, and input the same seismic time history wave into the beam-column element model corresponding to the finite element model of the bridge pier entity to obtain the seismic response of the beam-column element model corresponding to the finite element model of the bridge pier entity.

[0035] c. Compare the error between the seismic responses of the pier solid finite element model and the beam-column element model corresponding to the pier solid finite element model. If the seismic responses of the two are quite different, adjust the beam-column element model corresponding to the pier solid finite element model to make the seismic response of the beam-column element model corresponding to the pier solid finite element model close to the seismic response of the pier solid finite element model. This step can determine that the established beam-column element model corresponding to the pier solid finite element model accurately reflects the seismic response of the pier solid finite element model, laying a good foundation for the accuracy of the subsequent steps.

[0036] d. On the basis that the beam-column element model corresponding to the pier solid finite element model accurately reflects the seismic response of the pier solid finite element model, add potential fluid elements simulating water bodies to the pier solid finite element model to construct a fluid-structure interaction finite element model.

[0037] e. Input the same seismic time history wave into the fluid-structure interaction finite element model to obtain the first seismic response, which has taken into account the influence of water body factors.

[0038] f. Take this first seismic response as a reference. Add hydrodynamic added mass to the beam-column element model corresponding to the pier solid finite element model, and input the same seismic time history wave into the beam-column element model corresponding to the pier solid finite element model with the added hydrodynamic added mass to obtain the second seismic response.

[0039] g. By calculating the root mean square error value between the second seismic response and the first seismic response, find the hydrodynamic added mass corresponding to the second seismic response when the root mean square error value is the smallest. This hydrodynamic added mass is the hydrodynamic added mass of the entire bridge.

[0040] In the process of finding the hydrodynamic added mass corresponding to the second seismic response when the root mean square error value is the smallest, the present invention adopts a particle swarm optimization algorithm. Taking the hydrodynamic added mass as the independent variable of the objective function and the root mean square error value between the second seismic response and the first seismic response as the objective function value. By initializing the parameters and population of the particle swarm optimization algorithm; calculating the fitness value of each particle, updating the velocity and position of the particle, and iteratively optimizing until the termination condition is met and then outputting the optimal hydrodynamic added mass. Repeat this process multiple times to obtain multiple optimal hydrodynamic added masses, add the multiple optimal hydrodynamic added masses to the beam-column element model corresponding to the pier solid finite element model respectively to obtain multiple second seismic responses. Compare each second seismic response with the first seismic response one by one to determine the hydrodynamic added mass corresponding to the second seismic response when the root mean square error value is the smallest as the hydrodynamic added mass of the entire bridge.

[0041] Taking the circular pier cross-section as an example, the applicant of the present invention uses the hydrodynamic added mass determination steps in Steps S2 to S4 and compares the calculation results with those of the current calculation formula for the hydrodynamic added mass of the circular pier cross-section. The calculation results of the two are close, proving that the hydrodynamic added mass determination steps in Steps S2 to S4 of the present invention have considerable accuracy.

[0042] In the present invention, the fluid-structure interaction finite element model is established using ADINA software, and the beam-column element model is established using OpenSees. The particle swarm optimization algorithm is implemented through a MATLAB program.

[0043] S5. Establish a full-bridge beam-column element model, apply the hydrodynamic added mass determined in Step S3, and determine the bridge seismic damage index. Input the seismic time history wave to obtain the third seismic response. In the full-bridge beam-column element model, the main beam uses elastic beam-column elements, and the piers use fiber elements based on the flexibility method; the bearings are simulated by zero-length elements.

[0044] As Figure 4 shown, it is the beam-column element model of a certain long-span continuous rigid-frame bridge with deep-water high piers. The beam-column element model is an OpenSees finite element model. In the beam-column element model, the main beam is simulated using elastic elements; the piers are simulated using fiber elements based on the flexibility method; the bearings are simulated by the zero-length element element zeroLength, and the cap and piles are considered as a mass point and located at the bottom of the cap. The piers and the main beam are rigidly connected by a rigid link beam rigidLink beam; the bearings and the main beam are also rigidly connected by a rigid link beam rigidLink beam; the piers and the cap are rigidly connected by a rigid link beam rigidLink beam; the pile-soil interaction is mainly considered through soil springs, that is, a zero-length element element zeroLength is connected to the mass point at the bottom of the cap, and an equivalent spring stiffness with 6 degrees of freedom is applied for simulation. The cover concrete and the core concrete both use Concrete01 material, and the steel bar material uses Steel02 material.

[0045] Four integration points are adopted for the nonlinear beam-column elements of the main girder to ensure the calculation accuracy. The pier cross-section is divided into several fiber elements to meet the calculation accuracy requirements and improve the calculation efficiency. For the double-column thin-wall pier, the core concrete is equally divided into 10 parts transversely and 10 parts longitudinally, and a total of 100 fiber cross-sections are divided; the protective layer concrete is equally divided into 1 part transversely and 10 parts longitudinally, and there are 4 pieces of protective layer concrete in total, which are divided into 40 fiber cross-sections, with a total of 140 fiber cross-sections. For the middle pier, the core concrete is equally divided into 10 parts transversely and 10 parts longitudinally, and there are 4 pieces of core concrete in total, which are divided into 400 fiber cross-sections. The protective layer concrete is equally divided into 10 parts transversely and 1 part longitudinally, and there are 8 pieces of protective layer concrete in total, which are divided into 80 fiber cross-sections, with a total of 480 fiber cross-sections. The bridge is composed of reinforced concrete, and a Rayleigh damping ratio of 5% is adopted in the nonlinear time-history analysis.

[0046] Under seismic action, the vulnerable components of the bridge are the piers and bearings. Therefore, the curvature ductility coefficients of the top and bottom sections of the piers in the beam-column element model and the displacement values of the bearings are selected as the seismic damage indices of the bridge.

[0047] S6. Calculate the damage exceedance probability of each component of the bridge according to the third seismic response, establish the seismic vulnerability curve of the bridge, and evaluate the seismic resistance of the bridge.

[0048] From Figure 4 Among the 3 piers shown, the curvature ductility coefficient of the top of Pier 5# is selected as the EDP (Engineering Demand Parameter, the structural seismic demand parameter), and the acceleration response spectrum is selected as the seismic ground motion intensity index (Intensity Measure, IM). The spectral acceleration with a period of 2.0 s and a damping ratio of 0.05 is used to construct the PSDM (Probabilistic Seismic Demand Model). The artificially generated wave constructed quickly is taken as the seismic ground motion input, and multiple seismic-resistant time-history waves are selected for section division, and the peak seismic responses are extracted. Based on the spectral acceleration to establish the PSDM. As Figure 5 shown, the abscissa is ln( ), representing the value of the spectral acceleration after taking the natural logarithm. The ordinate is ln(Column density factor), representing the value of the column density factor after taking the natural logarithm. The red circles represent the specific data points of the probabilistic seismic demand model based on the spectral acceleration . The blue straight line is the regression line obtained by fitting these data points, revealing the linear relationship between the spectral acceleration and the column density factor in the probabilistic seismic demand model. From Figure 5As can be seen, when using spectral acceleration it can well fit the logarithmic linear relationship between seismic response and ground motion intensity, and smoothly establish the bridge seismic vulnerability curve.

[0049] Figure 6 The seismic vulnerability curves of the method of the present invention and the IDA method for the curvature ductility coefficient at the top of Pier 5 under four damage states are given. From Figure 6 the comparison of the bridge seismic vulnerability curves under the four damage states, it can be seen that in the four damage states, the trends of the vulnerability curves obtained by using the method of the present invention and the IDA method are basically the same, and the difference is very small. In the slight damage state as Figure 6 shown in a, the vulnerability of the method of the present invention is slightly higher than that of the IDA method, but the difference is very small; in the moderate damage as Figure 6 shown in b, severe damage as Figure 6 shown in c, and complete failure state as Figure 6 shown in d, the vulnerability curves of the two are very close, verifying the accuracy of the method of the present invention.

Claims

1. A rapid seismic vulnerability analysis method for deep-water bridges, characterized in that: The following steps are involved: S1, structural seismic time-history wave; S2, inputting the seismic time-history wave into a fluid-solid coupling finite element model of the bridge pier entity to obtain a first seismic response; S3, establishing a beam-column unit model corresponding to the finite element model of the bridge pier entity, and using the seismic time history wave described in step S2 to obtain the second seismic response of the beam-column unit model under different dynamic water added masses; S4, calculating the root mean square error between the second seismic response and the first seismic response, and determining the dynamic water added mass corresponding to the second seismic response when the root mean square error is minimum; S5, establishing a full bridge column unit model, applying the dynamic water additional mass determined in step S3, determining the bridge seismic damage index, inputting the seismic time history wave, and obtaining a third seismic response; S6. Establish the seismic vulnerability curve of the bridge based on the third earthquake response and evaluate the seismic resistance of the bridge.

2. The rapid seismic vulnerability analysis method for deepwater bridges according to claim 1 is characterized in that: The construction of multiple seismic time-history waves in step S1 specifically includes the following steps: S1.1, based on a random number generation method, an artificial wave with a fixed number of steps and a fixed time interval is generated; the artificial wave is multiplied by a coefficient that gradually increases over time to meet the definition of the seismic time history method; S1.2, performing wavelet denoising and scaling on the artificial wave generated in step S1.1, so that the processed artificial wave response spectrum fits the two-level target response spectrum, and calculating the root mean square error between the two; S1.3, repeat steps S1.1 and S1.2, and take the artificial wave corresponding to the artificial wave response spectrum with the smallest RMS error value as the initial artificial wave; S1.4, segmenting, scaling and optimizing the initial artificial wave to obtain a plurality of seismic time-history waves.

3. The rapid seismic vulnerability analysis method for deepwater bridges according to claim 2 is characterized in that: The number of steps of the artificial wave in step S1.1 is 4000, and the time interval is 0.01S.

4. The rapid seismic vulnerability analysis method for deepwater bridges according to claim 2 is characterized in that: In step S1.4, the particle swarm optimization algorithm is used to optimize the scaling of the initial artificial wave. The initial artificial wave is first segmented; then the particle swarm optimization algorithm parameters and population are initialized; the fitness value of each particle is calculated, the speed and position of the particle are updated, and the optimization is iteratively optimized until the termination condition is met and the optimal scaling coefficient is output. The segmented initial artificial wave is scaled and optimized according to the optimal scaling coefficient to obtain multiple seismic time-history waves.

5. The rapid seismic vulnerability analysis method for deepwater bridges according to claim 1 is characterized in that: The fluid-solid coupling finite element model of the pier entity described in step S2 is composed of a finite member model of the pier entity and a potential fluid unit simulating a water body.

6. The rapid seismic vulnerability analysis method for deep-water bridges according to claim 1 is characterized by: In step S3, the particle swarm optimization algorithm is used multiple times to obtain different dynamic water added masses imposed on the beam-column unit model.

7. The rapid seismic vulnerability analysis method for deep-water bridges according to claim 1 is characterized in that: The earthquake damage index in step S5 includes the curvature ductility coefficient of the cross section of the pier top and the pier bottom in the beam-column unit model and the displacement value of the support.

8. The rapid seismic vulnerability analysis method for deepwater bridges according to claim 1 is characterized by: In step S6, the damage exceedance probability of each bridge component is calculated according to the third earthquake response, and the seismic fragility curve of each bridge component is established.

9. The rapid seismic vulnerability analysis method for deepwater bridges according to claim 1 is characterized by: In step S5, the main beam in the full bridge column unit model uses elastic beam-column units, the pier uses fiber units based on the flexibility method, and the support is simulated by zero-length units.

10. The rapid seismic vulnerability analysis method for deep-water bridges according to claim 1 is characterized in that: The fluid-solid coupling finite element model of the pier entity described in step S2 and the beam-column unit model corresponding to the pier entity finite element model described in step S3 adopt the local pier entity finite element model of the bridge.

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