A seismic wave selection method for bridge seismic analysis based on equilibrium dispersion theory

Abstract

A seismic wave selection method for bridge seismic analysis based on balanced dispersion theory, which relates to the technical field of bridge structure engineering seismic research, includes step A, establishing a seismic wave selection method model based on orthogonal experimental design combined with balanced dispersion theory; step B, performing seismic wave selection analysis on engineering bridges based on the seismic wave selection method model; step C, evaluating the reliability of seismic wave selection through residual analysis. Based on the balanced dispersion theory, the present invention selects representative seismic motion records for nonlinear dynamic time history analysis of bridge structures, significantly reduces the amount of calculation of structural seismic time history analysis, and can more completely reflect the seismic probability requirements of the structure.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge structure engineering seismic research, and in particular to a method for selecting seismic waves for bridge seismic analysis based on equilibrium dispersion theory. Background Art

[0002] Earthquakes, as sudden and destructive natural disasters, pose a serious threat to life and property. As an earthquake-prone country, my country requires seismic design for engineering structures, especially major ones. Bridges, as integral lifeline structures, play a vital role in earthquake relief and post-disaster recovery, making improved seismic design even more crucial.

[0003] Due to the complexity and randomness of seismic motion, its amplitude, spectrum, and duration have a significant impact on the seismic response of bridge structures. Affected by the propagation process and site conditions, even seismic motion recorded in different locations under the same earthquake can exhibit certain differences. Due to the randomness and discreteness of measured seismic waves, the number of seismic waves that fully meet code requirements is relatively small. To identify the seismic wave suitable for a specific project among the numerous seismic motion records, structural engineers must undergo a tedious trial-and-error process. The unpredictable nature of this process can make nonlinear dynamic time-history analysis of structures time-consuming, thereby extending the design and calculation cycle of the entire project. Furthermore, the significant differences in structural seismic response due to different seismic wave selections pose significant challenges to structural designers. Therefore, selecting the appropriate seismic wave to quantitatively describe the magnitude of an earthquake and, subsequently, analyze its destructive effects on bridges is crucial for seismic analysis of bridge structures. Scholars from various countries have conducted extensive research on methods for selecting seismic waves for seismic analysis of bridge structures. For example, seismic waves are selected through segmentation, seismic waves are selected based on earthquake safety evaluation, and seismic waves are selected based on magnitude, epicentral distance, focal mechanism, site category, acceleration peak, and spectral characteristics. These seismic wave selection methods have problems such as large discreteness and unstable results.

[0004] To address the impact of the randomness of seismic motion, the introduction of probabilistic analysis methods into the analysis and assessment of bridge seismic performance has gradually become a research hotspot. Probabilistic analysis of structural seismic demand involves selecting a certain number of seismic motion records and combining them with the Latin hypercube sampling method to establish sample pairs for structural seismic demand analysis. The randomness of seismic waves is accounted for by increasing the number of seismic waves and the number of structural dynamic time-history analyses, but this is computationally intensive and time-consuming. Even so, finding a sufficient number of seismic waves that can comprehensively reflect the magnitude of seismic motion for probabilistic structural seismic demand analysis remains a challenge in the field of structural engineering seismic resistance, and it is a fundamental issue that urgently needs to be addressed in performance-based seismic design. Summary of the Invention

[0005] The present invention provides a seismic wave selection method for bridge seismic analysis based on the equilibrium dispersion theory. The purpose is to make the results of nonlinear dynamic analysis in the structural seismic design process more reliable, and fully consider the randomness of seismic motion to avoid the problem of large differences in structural seismic analysis due to different seismic wave selection.

[0006] In order to achieve the above object, the technical solution of the present invention is:

[0007] A seismic wave selection method for bridge seismic analysis based on balanced dispersion theory comprises the following steps: A. establishing a seismic wave selection method model based on orthogonal experimental design combined with balanced dispersion theory; B. performing seismic wave selection analysis on engineering bridges based on the seismic wave selection method model; and C. evaluating the reliability of the seismic wave selection through residual analysis.

[0008] Preferably, the step A includes the following specific steps: A1, determining earthquake motion parameter indicators; A2, formulating an orthogonal table and performing balanced dispersion analysis using balanced dispersion theory.

[0009] Preferably, the specific step A1 includes: collating and summarizing existing earthquake intensity indices, performing correlation analysis on them, selecting earthquake parameters with weaker correlation, reducing cross-information between different earthquake parameters, and selecting representative indicators among acceleration-type, velocity-type, and displacement-type earthquake parameters as earthquake parameters based on the physical meaning of the earthquake parameters and the correlation analysis results;

[0010] The specific step A2 includes:

[0011] A21. Determine the intensity level of each indicator based on the selected seismic parameters, and then develop the corresponding orthogonal table;

[0012] A22. Using the balanced dispersion theory, actual ground motion records are selected based on the orthogonal table for balanced dispersion analysis.

[0013] A23. Through balanced dispersion analysis, ensure that each seismic motion record is representative and can reflect the actual situation of the seismic motion.

[0014] Preferably, the step B includes the following specific steps: B1. Collecting and organizing the actual situation of the bridge project to determine the structural form and site type of the bridge; B2. Preliminary selection of seismic motion records; B3. Selecting seismic motion records based on the equilibrium dispersion theory; B4. Establishing a finite element model of a common bridge structure; B5. Conducting seismic demand analysis.

[0015] Preferably, in step B1, a small or medium span reinforced concrete continuous beam bridge is used, the main beam of each span is composed of 4 T-beams, the piers are solid circular double-column piers, the cap beam is a rectangular cross-section, the foundation adopts a single row of cast-in-place piles, and the geological conditions of the bridge are Class II sites.

[0016] Preferably, in step B2, according to the site type and structural form of the bridge structure, N seismic motion parameters are determined according to the seismic wave selection method model, each seismic motion parameter is divided into T intensity levels, and a certain number of seismic motion records are preliminarily selected based on the seismic parameters and intensity levels of each location; the preliminarily selected seismic motion records are records under different earthquakes, and the number of the preliminarily selected seismic motion records is greater than N. T .

[0017] Preferably, in step B2, peak ground acceleration (PGA), peak ground velocity (PGV), and peak ground displacement (PGD) are selected as ground motion parameters, and there are three intensity levels.

[0018] Preferably, in the step B3, 9 earthquake motion records, 27 earthquake motion records, and 100 earthquake motion records are respectively selected as three groups of preferred earthquake records based on the balanced dispersion theory.

[0019] Preferably, in step B4, the main beam of the finite element model is simulated using elastic beam-column units; the bridge piers are simulated using nonlinear fiber beam-column units; the supports are simulated using zero-length units, and the constitutive relationship of the supports adopts an ideal elastic-plastic model; a simplified model is used for simulation based on the foundation type of the abutment and the backfill behind the abutment; and the bridge pier foundation is simulated using linear springs.

[0020] Preferably, in the step B4, seismic demand analysis is performed based on each group of preferred vibration records by a nonlinear time history analysis method.

[0021] Preferably, in the step C, residual analysis is performed on the nonlinear time history analysis results of 9, 27 and 100 earthquake motion records.

[0022] Beneficial effects of the seismic wave selection method for bridge seismic analysis based on the balanced dispersion theory of the present invention:

[0023] 1. Based on the theory of equilibrium dispersion, the present invention selects representative earthquake motion records for nonlinear dynamic time-history analysis of bridge structures, significantly reducing the computational complexity of structural earthquake time-history analysis and being able to more completely reflect the earthquake probability requirements of the structure.

[0024] 2. The present invention is based on the theory of balanced dispersion. The selected representative seismic motion records are evenly dispersed in the actual seismic motion records that meet the site conditions of the bridge structure. The randomness can be well taken into account, and the obtained calculation results are stable.

[0025] 3. The present invention is based on the theory of balanced dispersion and utilizes orthogonal experimental design, and has wide applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 , a flow chart of the implementation of the present invention;

[0027] Figure 2 , schematic diagram of equilibrium dispersion theory;

[0028] Figure 3 , bridge structure layout drawing;

[0029] Figure 4 , acceleration response spectrum;

[0030] Figure 5 , finite element model diagram of the bridge structure;

[0031] Figure 6 , nonlinear time history analysis results of bridge piers;

[0032] Figure 7 , residual analysis diagram of nonlinear time history analysis of bridge piers;

[0033] 1. Ground line; 2. Slightly weathered granite; 3. Moderately weathered granite; 4. Completely weathered mixed rock; 5. Residual slope rock; 6. Bridge pier. DETAILED DESCRIPTION

[0034] The following describes in detail the implementation methods of the present invention in a step-by-step manner. This description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

[0035] In the description of the present invention, it should be noted that the terms "up", "down", "left", "right", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings. They are only for describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, and a specific orientation structure and operation. Therefore, they cannot be understood as limiting the present invention.

[0036] Example 1:

[0037] A seismic wave selection method for bridge seismic analysis based on equilibrium dispersion theory, such as Figure 1 As shown, the method includes step A, establishing a seismic wave selection method model based on orthogonal experimental design combined with equilibrium dispersion theory; step B, performing seismic wave selection analysis on engineering bridges based on the seismic wave selection method model; and step C, evaluating the reliability of seismic wave selection through residual analysis.

[0038] like Figure 1 As shown, the step A includes the following specific steps: A1, determining the earthquake parameter index; A2, formulating an orthogonal table, and performing balanced dispersion analysis using the balanced dispersion theory.

[0039] The specific step A1 includes: collating and summarizing existing earthquake intensity indices, performing correlation analysis on them, selecting earthquake parameters with weaker correlation, reducing cross-information between different earthquake parameters, and selecting representative indicators among acceleration-type, velocity-type, and displacement-type earthquake parameters as earthquake parameters based on the physical meaning of the earthquake parameters and the correlation analysis results;

[0040] The specific step A2 includes:

[0041] A21. Determine the intensity level of each indicator based on the selected seismic parameters, and then develop the corresponding orthogonal table;

[0042] A22. Using the balanced dispersion theory, select actual ground motion records based on the orthogonal table and perform balanced dispersion analysis.

[0043] A23. Through balanced dispersion analysis, ensure that each seismic motion record is representative and can reflect the actual situation of the seismic motion.

[0044] As shown in Table 1: If the selected seismic parameters are 4 and the number of levels is 3, then an orthogonal table L9(34) can be formulated, where L is the orthogonal table code, 9 is the number of required seismic waves (seismic records), 4 is the maximum number of factors (i.e., seismic parameters) that can be considered, and 3 is the number of intensity levels for each factor. Among them, factor A is PGA, factor B is PGV, and factor C is PGD.

[0045] The following is an explanation of the equilibrium dispersion theory:

[0046] For the sake of illustration, draw a cube with a side length of 2, such as Figure 2 As shown, the length, width and height of the cube have three factors respectively, and the coordinate values ​​represent the level of the factors. The cube has 9 faces (including cross sections), of which A1, A2 and A3 correspond to the left, middle and right faces; B1, B2 and B3 correspond to the front, middle and back faces; C1, C2 and C3 correspond to the bottom, middle and top faces; the 27 nodes on the cube represent the 27 seismic records required for structural earthquake analysis in theory. The 9 seismic records selected using the orthogonal table L9 (34) correspond to Figure 2 There are 9 nodes marked as 1, 2, 3, 4, 5, 6, 7, 8, and 9.

[0047] from Figure 2 You can see:

[0048] (1) These nine earthquake motion records are evenly distributed on the nine faces of the cube, and there are exactly three earthquake motion records on each face;

[0049] (2) Although there are only 9 seismic motion records, there is exactly one seismic motion record on each axis of the cube where the 27 seismic motion records are located.

[0050] This shows that the 9 seismic motion records are evenly distributed in the entire cube, indicating that the seismic motion records, i.e., the seismic waves, selected by the seismic wave selection method model of the present invention have "balanced dispersion", which means that each seismic motion record is representative and can reflect the actual situation of the seismic motion.

[0051]

[0052] Table 1

[0053] Example 2:

[0054] Based on Example 1, this example further discloses:

[0055] The step B includes the following specific steps: B1. Collecting and organizing the actual situation of the bridge project to determine the structural form and site type of the bridge; B2. Preliminary selection of seismic motion records; B3. Selecting seismic motion records based on the equilibrium dispersion theory; B4. Establishing a finite element model of a common bridge structure; B5. Conducting seismic demand analysis.

[0056] In step B1, a small-to-medium span reinforced concrete continuous beam bridge commonly seen in actual engineering is used. The main beam of each span is composed of four T-beams, the piers are solid circular double-column piers, the cap beam is of rectangular cross-section, and the foundation is a single row of cast-in-place piles. The geological conditions of the bridge are Class II sites, and the bridge structure is arranged as follows: Figure 3 shown.

[0057] In step B2, according to the site type and structural form of the bridge structure, N seismic motion parameters are determined according to the seismic wave selection method model, each seismic motion parameter is divided into T intensity levels, and a certain number of seismic motion records are preliminarily selected based on the seismic parameters and intensity levels of each location, and an orthogonal test table is designed. The preliminarily selected seismic motion records are records under different earthquakes, and the number of the preliminarily selected seismic motion records is greater than N. T .

[0058] In step B2, peak ground acceleration (PGA), peak ground velocity (PGV), and peak ground displacement (PGD) are selected as ground motion parameters, and there are three intensity levels.

[0059] In step B3, based on the balanced dispersion theory, 9, 27, and 100 earthquake records are selected as three groups of preferred earthquake records. Referring to Table 1, the acceleration response spectra of 9, 27, and 100 earthquake records are: Figure 4 .

[0060] In step B4, the main beam of the finite element model is basically in an elastic state under the action of an earthquake, and is simulated using elastic beam-column elements; the bridge piers may form plastic hinges and undergo plastic failure, and are simulated using nonlinear fiber beam-column elements; the supports are simulated using zero-length elements, and the constitutive relationship of the supports adopts an ideal elastic-plastic model; based on the foundation type of the abutment and the backfill, a simplified model is used for simulation; the bridge pier foundation is simulated using linear springs, and the finite element model of the bridge structure is as follows: Figure 5 shown.

[0061] In step B4, seismic demand analysis is performed based on each set of preferred vibration records using a nonlinear time history analysis method. The results of the nonlinear time history analysis are as follows: Figure 6 As shown in the figure, by comparing the effects of 9, 27 and 100 earthquake motion records on the seismic response of bridge structural components, it can be seen that in the logarithmic space, when the corresponding PGA, PGV and PGD are used as earthquake motion parameters, the linear regression analysis results are better.

[0062] In step C, residual analysis is performed on the nonlinear time history analysis results of 9, 27 and 100 earthquake records. The results are as follows: Figure 7 As shown, lighter circles represent residual values, vertical lines represent the 95% confidence interval for each residual value, and darker circles indicate outliers. It can be seen that the residual values ​​are symmetrical and evenly distributed on both sides of the zero axis, indicating that the nonlinear time history analysis results are valid. Although there are four outliers in the residual analysis of 100 ground motion records (the darker circles on the bold vertical line), the overall distribution of residual values ​​does not show significant heteroskedasticity.

[0063] Principle of the present invention:

[0064] This method utilizes the theory of balanced dispersion to select the required seismic records for bridge seismic analysis through orthogonal design. This ensures that the required seismic records are evenly dispersed among the actual seismic records that meet the bridge structure's site conditions. Each seismic record is highly representative, and nonlinear dynamic time-history analysis of the bridge structure using only the required seismic records can provide a relatively complete reflection of the bridge structure's probabilistic seismic requirements.

[0065] Based on the theory of balanced dispersion, this paper selects nine highly representative ground motion records. The seismic demand analysis of these nine records more fully reflects the seismic demand analysis of the 27 ground motion records from the comprehensive test. Furthermore, 27 more highly representative ground motion records are selected, and the seismic demand analysis of these 27 records more fully reflects the seismic demand analysis of the selected 100 ground motion records.

[0066] It should be noted that:

[0067] 1. According to the balanced dispersion theory, the orthogonal test table selected in this invention is L9(3 4 ), other orthogonal test tables can be selected according to specific circumstances.

[0068] 2. In the orthogonal test table L9(3 4 ), the selected factors are PGA, PGV, and PGD. Factor 4 is optional and can be selected based on the specific experimental conditions. Furthermore, the selected factors are PGA, PGV, and PGD, but are not limited to these. The number of factor levels and their values ​​can be determined based on the specific circumstances.

Claims

1. A seismic wave selection method for bridge seismic analysis based on equilibrium dispersion theory, characterized by: The method comprises the steps of: A, establishing a seismic wave selection method model based on orthogonal experimental design combined with balanced dispersion theory; B, performing seismic wave selection analysis on engineering bridges based on the seismic wave selection method model; and C, evaluating the reliability of seismic wave selection through residual analysis. The step A comprises the following specific steps: A1, determining the earthquake motion parameter index; A2, formulating an orthogonal table and performing a balanced dispersion analysis using the balanced dispersion theory; The specific step A1 includes: collating and summarizing existing earthquake intensity indices, performing correlation analysis on them, selecting earthquake parameters with weak correlation, reducing cross information between different earthquake parameters, and selecting representative indices among acceleration-type, velocity-type and displacement-type earthquake parameters as earthquake parameters according to the physical meaning of earthquake parameters and the results of correlation analysis; The specific step A2 comprises: A21. According to the selected seismic parameters, determine the intensity level of each index and then formulate the corresponding orthogonal table; A22. Using the balanced dispersion theory, actual ground motion records are selected based on the orthogonal table for balanced dispersion analysis. A23. Through balanced dispersion analysis, ensure that each seismic motion record is representative and can reflect the actual situation of the seismic motion.

2. A method for selecting seismic waves for seismic analysis of bridges based on the balanced dispersion theory as described in claim 1, characterized in that: the step B comprises the following specific steps: B1, collecting and arranging the actual situation of the bridge project, and determining the structural form and site type of the bridge; B2, preliminarily selecting seismic motion records; B3, selecting seismic motion records based on the balanced dispersion theory; B4, establishing a finite element model of a common bridge structure; B5, conducting an earthquake demand analysis.

3. A seismic wave selection method for bridge seismic analysis based on balanced dispersion theory as claimed in claim 2, characterized in that: In the step B1, a small-to-medium span reinforced concrete continuous beam bridge is used. The main beam of each span is composed of 4 T-beams. The piers are solid circular double-column piers. The cap beam is of rectangular cross-section. The foundation adopts a single row of cast-in-place piles. The geological conditions of the bridge are Class II sites.

4. A seismic wave selection method for bridge seismic analysis based on balanced dispersion theory as claimed in claim 3, characterized in that: In the step B2, according to the site type and structural form of the bridge structure, N seismic motion parameters are determined according to the seismic wave selection method model, each seismic motion parameter is divided into T intensity levels, and a certain number of seismic motion records are preliminarily selected based on the seismic parameters and intensity levels of each location; the preliminarily selected seismic motion records are records under different earthquakes, and their number is greater than N T .

5. The method for selecting seismic waves for bridge seismic analysis based on balanced dispersion theory as claimed in claim 4, characterized in that: In the step B2, the ground motion peak acceleration (PGA), the ground motion peak velocity (PGV), and the ground motion peak displacement (PGD) are selected as ground motion parameters, and there are three intensity levels.

6. A seismic wave selection method for bridge seismic analysis based on balanced dispersion theory as claimed in claim 5, characterized in that: In the step B3, 9 earthquake records, 27 earthquake records, and 100 earthquake records are selected as three groups of earthquake records based on the balanced dispersion theory.

7. A method for selecting seismic waves for bridge seismic analysis based on balanced dispersion theory as claimed in claim 6, characterized in that: In the step B4, the main beam of the finite element model is simulated by elastic beam-column units; the bridge pier is simulated by nonlinear fiber beam-column units; the support is simulated by zero-length units, and the constitutive relationship of the support adopts an ideal elastic-plastic model; according to the foundation type of the abutment and the backfill of the abutment, a simplified model is used for simulation; the bridge pier foundation is simulated by linear springs.

8. The method for selecting seismic waves for bridge seismic analysis based on the balanced dispersion theory as claimed in claim 7, characterized in that: In the step B4, seismic demand analysis is performed based on each group of vibration records by using a nonlinear time history analysis method.

9. A method for selecting seismic waves for bridge seismic analysis based on balanced dispersion theory as claimed in claim 8, characterized in that: In the step C, residual analysis is performed on the nonlinear time history analysis results of 9, 27 and 100 earthquake records.

Images