A seismic vulnerability assessment method for asymmetric long-span special-shaped steel arch bridges

Abstract

The present invention provides a method for assessing the seismic vulnerability of an asymmetric large-span special-shaped steel arch bridge, comprising the following steps: S1: conducting a dynamic test of a large-span asymmetric special-shaped steel arch bridge; S2: establishing a full-bridge numerical analysis model and comparing and verifying it with the dynamic test results; S3: conducting a seismic response analysis of a large-span asymmetric special-shaped steel arch bridge; S4: conducting a vulnerability analysis of typical components of a large-span asymmetric special-shaped steel arch bridge; S5: conducting a system vulnerability analysis of a large-span asymmetric special-shaped steel arch bridge. The present invention conducts a seismic performance analysis method applicable to a finite element model of a large-span asymmetric special-shaped steel arch bridge on the basis that the finite element model of a large-span asymmetric special-shaped steel arch bridge can better reflect the dynamic response of the bridge through a full-bridge numerical analysis model and comparing and verifying it with the dynamic test results, thereby improving the accuracy and credibility of the seismic vulnerability assessment of the asymmetric large-span special-shaped steel arch bridge.

Description

Technical Field

[0001] The invention relates to the technical field of seismic vulnerability assessment, and in particular to a seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge. Background Art

[0002] With the increasing application of long-span special-shaped arch bridges in urban landscape bridge design, the impact of their unique and complex structures on the seismic resistance of bridges has become an important issue that needs to be studied urgently.

[0003] The large-span asymmetric special-shaped steel arch bridge has a complex structure, integrating the characteristics of various special-shaped arch bridge structures, and exhibits strong asymmetry in seismic response. At the same time, there are many types of bridge components of this type, and the damage area and degree of the structure under earthquake action are unclear. Therefore, it is of great significance to study the damage area of ​​the bridge structure under earthquake action and then study the vulnerability of the components in the damage area. As a probabilistic risk analysis method, seismic vulnerability analysis can provide a more reasonable evaluation basis for the seismic optimization design of bridges.

[0004] At present, the research on the relatively new types of special-shaped arch bridges is still limited. First, the morphology of asymmetric special-shaped arch bridges varies greatly, and the seismic performance and seismic response laws of this type of special-shaped arch bridges need further in-depth research. Second, the seismic vulnerability research of special-shaped arch bridges is still uncommon, and there has been no research on the damage mechanism of this type of special-shaped arch bridge under earthquake action. Summary of the invention

[0005] To solve the above problems, the present invention aims to propose a method for seismic vulnerability assessment of asymmetric large-span special-shaped steel arch bridges. Through the numerical analysis model of the whole bridge and comparison and verification with the dynamic test results, on the basis that the finite element model of the large-span asymmetric special-shaped steel arch bridge can better reflect the dynamic response of the bridge, a seismic performance analysis method suitable for the finite element model of the large-span asymmetric special-shaped steel arch bridge is developed to improve the accuracy and credibility of the seismic vulnerability assessment of the asymmetric large-span special-shaped steel arch bridge.

[0006] To achieve the above object, the technical solution of the present invention is achieved as follows:

[0007] A seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge includes the following steps:

[0008] S1: Conduct dynamic testing of large-span asymmetric special-shaped steel arch bridges;

[0009] S2: Establish a full-bridge numerical analysis model and compare and verify it with the dynamic test results;

[0010] S3: Conduct seismic response analysis of large-span asymmetric special-shaped steel arch bridges;

[0011] S4: Conduct vulnerability analysis of typical components of large-span asymmetric special-shaped steel arch bridges;

[0012] S5: Conduct vulnerability analysis of large-span asymmetric special-shaped steel arch bridge systems.

[0013] Furthermore, the step S1 of carrying out the dynamic test of the large-span asymmetric special-shaped steel arch bridge includes the following steps:

[0014] S11. Arrange a vehicle with a counterweight on each of the two lanes of the bridge, taking into account the three parameters of vehicle speed, vehicle direction and vehicle spacing;

[0015] S12. According to the structural characteristics of the large-span asymmetric special-shaped steel arch bridge, the acceleration sensor is arranged above the outer longitudinal beam, and the measuring points are arranged asymmetrically on the north and south sides accordingly. On one side, the measuring point B is arranged at the mid-span, and on the other side, the measuring points A, C, and D are arranged at the mid-span, 1 / 4 span, and 3 / 4 span positions respectively to carry out bridge dynamic testing.

[0016] Furthermore, the step S2 of establishing a full-bridge numerical analysis model and comparing and verifying it with the power test results includes the following steps:

[0017] S21: Based on the finite element calculation software Midas Civil, a spatial finite element model of a large-span asymmetric special-shaped steel arch bridge is established. The arch bridge structure is discretized into spatial bar system units. According to the stress characteristics of the arch bridge, the tension unit is simulated by truss unit, and the bridge deck system, arch ribs, wind bracing, hangers, diagonal braces, and tie rods are simulated by beam units.

[0018] S22: Obtain the dynamic response results of the bridge dynamic test and compare them with the time history analysis results of the finite element simulation to verify that the dynamic response results of the bridge are in good agreement, so as to carry out seismic performance research.

[0019] Furthermore, the step S3 of carrying out seismic response analysis of a large-span asymmetric special-shaped steel arch bridge comprises the following steps:

[0020] S31: seismic wave selection and input;

[0021] S32: One-dimensional earthquake response analysis;

[0022] S33: Multidimensional seismic response analysis.

[0023] Furthermore, the S31 seismic wave selection and input includes the following steps:

[0024] S311. Use the analog seismic wave method to select the seismic acceleration time history, that is, select strong earthquake records with similar geological environment, magnitude and spectrum characteristics to the site of the bridge to be built as input, refer to the engineering geological report and the "Evaluation Rules for Seismic Performance of Highway Bridges" (JTG / T 2231-02), and use Taft seismic wave correction to perform time history analysis;

[0025] S312. When conducting time-history analysis on the special-shaped arch bridge structure, the Rayleigh damping in proportional damping is used to calculate the damping ratio, and the frequencies of the first and ninth modes with larger participating masses in the X and Y directions of the first ten vibration modes are selected as typical frequencies, and the damping ratio ξ=0.0444 is obtained; the direct integration method is used for both E1 and E2 time-history analyses, with an analysis time of 20s and an analysis step of 0.02s. The vertical seismic action is taken as 65% of the acceleration of the horizontal seismic action.

[0026] Furthermore, the S32 one-dimensional earthquake response analysis includes the following steps:

[0027] S321. Using the method of inputting seismic waves separately from three orthogonal directions, namely longitudinal, transverse and vertical, a consistent excitation E1 and E2 time history analysis is performed on the model considering pile-soil interaction to analyze the displacement response and internal force response of the main control section of the special-shaped arch bridge under one-dimensional earthquake action.

[0028] S322. In view of the asymmetric structural characteristics of the special-shaped arch bridge, the 1 / 4 arch rib, 1 / 2 arch rib, 3 / 4 arch rib, arch feet on the north and south banks, and the top of the diagonal brace and tie rod of the side arch and the middle arch are selected as control points; among them, the side arch, diagonal brace and tie rod use the structural data of the east side of the bridge;

[0029] S323. Conduct one-dimensional earthquake dynamic response analysis, and obtain the displacement and internal force time history curves of the longitudinal, transverse, vertical side arch and middle arch control sections.

[0030] Further, in S3, the S33 multi-dimensional earthquake action response analysis includes:

[0031] S331. According to the Code for Seismic Design of Buildings (GB 50011), the ground motions in three orthogonal directions are combined in a ratio of 1:0.85:0.65;

[0032] S332, perform consistent excitation E1 time history analysis to extract the displacement response and internal force response of some control sections of the large-span asymmetric special-shaped steel arch bridge under multi-dimensional earthquake action;

[0033] S333, conduct time history analysis considering the effect of dead load, that is, the load combination is the addition of Taft seismic wave and dead load; the seismic wave adopts the three-way combination input reflecting the most unfavorable state of the structure, and the dead load adopts the time-varying static load mode;

[0034] S334. Perform consistent excitation E1 and E2 time history analysis to extract the dynamic response results of some control sections of the large-span asymmetric special-shaped steel arch bridge under multi-dimensional seismic action considering the action of constant load.

[0035] Furthermore, the step S4 of carrying out the vulnerability analysis of typical components of the large-span asymmetric special-shaped steel arch bridge specifically refers to: comprehensively comparing the seismic performance of the asymmetric large-span special-shaped steel arch bridge under one-dimensional earthquake action, multi-dimensional earthquake action and multi-dimensional earthquake action considering the action of dead load; and in order to explore the application possibility and prospect of the large-span asymmetric special-shaped steel arch bridge structure in higher defense areas, the characteristics of the complex structure of the special-shaped arch bridge are disassembled, and the influencing factors of the seismic performance of the special-shaped arch bridge are analyzed from the perspective of structural design, and the key control factors of the seismic performance of the special-shaped arch bridge are found;

[0036] The key control factors for finding seismic performance include:

[0037] S41. Based on the original design of unequal heights between the middle arch and the side arch, the rise heights of the side arch and the middle arch are increased and decreased synchronously. The modified Taft wave under the strong earthquake level is selected in the previous article. The dynamic response results of each key control section are analyzed under the multi-dimensional earthquake action response considering the effect of the dead load.

[0038] S42. By reducing the mid-arch rise height and establishing the arch rib height difference, the dynamic response results of each key control section are extracted under the same earthquake action response;

[0039] S43. Reasonable arch rib inclination angle can reasonably improve the dynamic characteristics of the arch bridge and enhance the overall stability. By adjusting the arch rib inclination design angle, other design parameters are kept unchanged on the basis of reasonable structural stress, and the dynamic response results of each arch rib control section under different arch rib inclination angles are extracted;

[0040] S44, arch foot area offset, adjust the asymmetry of the arch rib curve in the xy and xx planes, and extract the dynamic response results of each arch rib control section under different arch foot outward displacements;

[0041] S45. The arch crown position is adjusted, the axis of the arch rib curve in the XZ plane is adjusted, and the dynamic response results of each arch rib control section under different arch crown positions are extracted.

[0042] Furthermore, the step S5 of conducting system vulnerability analysis of large-span asymmetric special-shaped steel arch bridges specifically refers to: seismic vulnerability analysis of three-dimensional special-shaped steel arch bridges. As a probabilistic risk analysis method, seismic vulnerability analysis can provide a more reasonable evaluation basis for seismic optimization design of bridges. 15 time-history waves are selected from the PEER database based on the site characteristics of the bridge location, and the average strain is used as the performance indicator. The time-history analysis of the asymmetric special-shaped arch bridge is performed based on the dynamic increment analysis method to obtain the seismic vulnerability curve of the vulnerable components; then, a method based on reliability theory is used to study the system vulnerability of the asymmetric special-shaped arch bridge under the action of three-way combined earthquakes.

[0043] Furthermore, the step S5 of carrying out the vulnerability analysis of the large-span asymmetric special-shaped steel arch bridge system specifically includes the following steps:

[0044] S51. Average strain is used as the damage index of asymmetric special-shaped steel arch bridges;

[0045] S52, select the curve fitting method based on the capacity demand ratio model to perform regression analysis on the vulnerability curve;

[0046] Based on the capacity demand ratio model, if the structural response Sd is greater than the structural capacity Sc, the structure will be damaged, and the damage exceedance probability Pf is expressed as follows:

[0047]

[0048] Taking the logarithm of both sides of the formula, the above formula can be expressed as:

[0049]

[0050] If the structural response Sd and the structural capacity Sc both obey the lognormal distribution, then ln(Sd / Sc) will obey the normal distribution. Given the symmetry of the normal distribution density function, the damage exceedance probability Pf can be written as:

[0051]

[0052] In the above formula, the regression mean λ and regression standard deviation σ are introduced to standardize ln(Sd / Sc), and the above formula can be written as:

[0053]

[0054] Since ln(Sd / Sc) has been standardized, the random variable ln(Sd / Sc) will obey the standard normal distribution, as shown in the following formula (5-5). The damage exceedance probability Pf can be expressed by the distribution function of the standard normal distribution as formula (5-6):

[0055]

[0056] Similarly, due to the symmetry of the standard normal distribution density function, the damage exceedance probability Pf can be simplified as:

[0057]

[0058] Among them, considering that the quadratic polynomial regression has higher solution accuracy, λ can be obtained by regression solution of the following formula, where a, b, c are regression coefficients, and IM is the ground motion intensity parameter:

[0059]

[0060] σ can be solved by formula (5-9), where Sr is the residual sum of squares of each discrete point relative to the regression curve. The calculation formula is shown in (5-10), and n is the number of discrete points:

[0061]

[0062] S53, modulating the peak ground acceleration PGA of the selected 15 seismic waves to the maximum PGA in the incremental dynamic analysis process, and sequentially inputting them into the full-bridge space model for time history analysis, i.e., inputting them in a three-way combination mode; counting the components in the structure that are damaged more times under the action of the 15 seismic waves, which are called vulnerable components;

[0063] S54. Each of the 15 groups of seismic records was modulated 8 times to obtain 120 groups of seismic records, and nonlinear time history analysis was performed using a three-way combined input method. The 120 groups of seismic response results of 12 typical vulnerable components were statistically analyzed, and a total of 1440 maximum plastic strain data were extracted. A total of 36 IDA curves were fitted according to the damage limit, that is, one for each component with slight damage, moderate damage, and severe damage. According to the IDA curves of each component, the regression mean λ and regression standard deviation σ corresponding to different damage states of each vulnerable component were obtained, and then the damage exceedance probability Pf of the vulnerable component was obtained.

[0064] S55. Calculate the damage probability of each single member:

[0065] S56. System vulnerability analysis: The failure probability of the system is calculated using the first-order limit method based on the series system. Since the correlation between the failure modes is between the two cases of complete correlation and complete independence, the failure probability of the system when all components in the structure are completely correlated is the lower limit of the failure probability interval, and the failure probability when all components are completely independent is the upper limit of the interval. The limit interval of the structural failure probability is:

[0066]

[0067] In the formula, Pfs represents the failure probability of the system, Pfi represents the failure probability of the i-th component, and n is the number of components;

[0068] S57. Based on the vulnerability curves of each component calculated by the capacity-demand ratio model, the system vulnerability curve is drawn, and the system failure probability of the asymmetric special-shaped arch bridge is further calculated using the first-order limit method. By comparing the degree of agreement between the system vulnerability curve and the vulnerability curve of a single component, the most vulnerable component in the special-shaped arch bridge system is obtained, thereby optimizing the seismic design of this type of bridge.

[0069] Beneficial effects: The present invention uses a full-bridge numerical analysis model and compares it with the dynamic test results to verify that the finite element model of a large-span asymmetric special-shaped steel arch bridge can better reflect the dynamic response of the bridge. This method for analyzing the seismic performance of the finite element model of a large-span asymmetric special-shaped steel arch bridge is developed to improve the accuracy and credibility of the seismic vulnerability assessment of asymmetric large-span special-shaped steel arch bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] The accompanying drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the accompanying drawings:

[0071] Figure 1 A flowchart of the steps of the seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge according to an embodiment of the present invention;

[0072] Figure 2 It is a schematic diagram of the arrangement of measuring points in the seismic vulnerability assessment method of an asymmetric large-span special-shaped steel arch bridge according to an embodiment of the present invention;

[0073] Figure 3 A schematic diagram of a spatial finite element model of a large-span asymmetric special-shaped steel arch bridge established based on the finite element calculation software Midas Civil in the seismic vulnerability assessment method of the asymmetric large-span special-shaped steel arch bridge described in an embodiment of the present invention;

[0074] Figure 4 Schematic diagram of the comparison between the dynamic response results of the bridge dynamic test and the time history analysis results of the finite element simulation in the seismic vulnerability assessment method of the asymmetric large-span special-shaped steel arch bridge according to the embodiment of the present invention Figure 1 (Working condition 1-30-N);

[0075] Figure 5 Schematic diagram of the comparison between the dynamic response results of the bridge dynamic test and the time history analysis results of the finite element simulation in the seismic vulnerability assessment method of the asymmetric large-span special-shaped steel arch bridge according to the embodiment of the present invention Figure 2 (Working condition 1-45-N);

[0076] Figure 6The dynamic acceleration spectrum of the three-way seismic wave selected after the Taft seismic wave correction for time history analysis in the seismic vulnerability assessment method of the asymmetric large-span special-shaped steel arch bridge described in the embodiment of the present invention;

[0077] Figure 7 A schematic diagram of model parameters with different rise-to-span ratios for finding key control factors of seismic performance in the seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge according to an embodiment of the present invention;

[0078] Figure 8 A schematic diagram of different arch rib height difference model parameters for finding key control factors of seismic performance in the seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge according to an embodiment of the present invention;

[0079] Fig. 9 A schematic diagram of different arch rib inclination model parameters for finding key control factors of seismic performance in the seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge according to an embodiment of the present invention;

[0080] Fig.10 It is a schematic diagram of different arch foot outward displacement model parameters for finding the key control factor of seismic performance in the seismic vulnerability assessment method of an asymmetric large-span special-shaped steel arch bridge according to an embodiment of the present invention;

[0081] Fig.11 A schematic diagram of model parameters of different arch positions for finding key control factors of seismic performance in the seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge according to an embodiment of the present invention;

[0082] Fig.12 A distribution diagram of seismic damage levels of steel components in the seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge according to an embodiment of the present invention;

[0083] Fig.13 A schematic diagram of vulnerable components of an asymmetric special-shaped arch bridge in the seismic vulnerability assessment method of an asymmetric large-span special-shaped steel arch bridge according to an embodiment of the present invention;

[0084] Fig.14 The IDA curves corresponding to the capacity demand ratio models of the north bank arch foot and the middle arch foot under different damage states in the seismic vulnerability assessment method of the asymmetric large-span special-shaped steel arch bridge described in the embodiment of the present invention;

[0085] Fig.15 It is a vulnerability curve of an asymmetric special-shaped arch bridge system in the seismic vulnerability assessment method of an asymmetric large-span special-shaped steel arch bridge described in an embodiment of the present invention. DETAILED DESCRIPTION

[0086] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0087] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments.

[0088] Example 1

[0089] See also Figure 1 :A seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge includes the following steps:

[0090] S1: Conduct dynamic testing of large-span asymmetric special-shaped steel arch bridges;

[0091] S2: Establish a full-bridge numerical analysis model and compare and verify it with the dynamic test results;

[0092] S3: Conduct seismic response analysis of large-span asymmetric special-shaped steel arch bridges;

[0093] S4: Conduct vulnerability analysis of typical components of large-span asymmetric special-shaped steel arch bridges;

[0094] S5: Conduct vulnerability analysis of large-span asymmetric special-shaped steel arch bridge systems.

[0095] This embodiment uses a full-bridge numerical analysis model and compares it with the dynamic test results to verify that the finite element model of a large-span asymmetric special-shaped steel arch bridge can better reflect the dynamic response of the bridge. This method for analyzing the seismic performance of the finite element model of a large-span asymmetric special-shaped steel arch bridge is developed to improve the accuracy and credibility of the seismic vulnerability assessment of asymmetric large-span special-shaped steel arch bridges.

[0096] In a specific example, the step S1 of carrying out a dynamic test of a large-span asymmetric special-shaped steel arch bridge includes the following steps:

[0097] S11. Place a vehicle with counterweight (J6P dump truck can be used) on each of the two lanes of the bridge, and consider the three parameters of vehicle speed, vehicle direction and vehicle spacing in advance;

[0098] S12. According to the structural characteristics of the large-span asymmetric special-shaped steel arch bridge, the acceleration sensor is arranged above the outer longitudinal beam, such as Figure 2 As shown: the measuring points are arranged asymmetrically on the north and south sides, with measuring point B arranged at the mid-span on one side and measuring points A, C, and D arranged at the mid-span, 1 / 4 span, and 3 / 4 span positions on the other side, respectively, for bridge dynamic testing.

[0099] In a specific example, the step S2 of establishing a full-bridge numerical analysis model and comparing and verifying it with the power test results includes the following steps:

[0100] S21: See Figure 3:Based on the finite element calculation software Midas Civil, a spatial finite element model of a large-span asymmetric special-shaped steel arch bridge is established. The arch bridge structure is discretized into spatial bar system units. According to the stress characteristics of the arch bridge, the tension unit is simulated by truss unit, and the bridge deck system, arch ribs, wind bracing, hangers, diagonal braces, and tie rods are simulated by beam units.

[0101] S22: See Figure 4-5 : Obtain the dynamic response results of the bridge dynamic test, compare them with the time-history analysis results of the finite element simulation, verify that the dynamic response results of the bridge are in good agreement, and use this to carry out seismic performance research.

[0102] The dynamic performance test and model verification method of the asymmetric large-span special-shaped steel arch bridge in this embodiment provides a theoretical and factual basis for subsequent earthquake vulnerability assessment.

[0103] In a specific example, the step S3 of carrying out seismic response analysis of a large-span asymmetric special-shaped steel arch bridge includes the following steps:

[0104] S31: seismic wave selection and input;

[0105] S32: One-dimensional earthquake response analysis;

[0106] S33: Multidimensional seismic response analysis.

[0107] In a specific example, the S31 seismic wave selection and input includes the following steps:

[0108] S311. Use the analog seismic wave method to select the seismic acceleration time history, that is, select strong earthquake records with similar geological environment, magnitude and spectrum characteristics to the site of the bridge to be built for input, refer to the engineering geological report and the "Evaluation Rules for Seismic Performance of Highway Bridges" (JTG / T 2231-02), and use the Taft seismic wave (1952, Taft Lincoln School, Kern County) for time history analysis after correction. The main characteristics of the seismic wave and the amplitude adjustment coefficient are shown in the table below. The corrected three-way seismic wave is as follows: Figure 6 As shown (taking E1 time course analysis as an example);

[0109]

[0110] S312. When conducting time-history analysis on the special-shaped arch bridge structure, the Rayleigh damping in proportional damping is used to calculate the damping ratio, and the frequencies of the first and ninth-order modes with larger participating masses in the X and Y directions of the first ten vibration modes are selected as typical frequencies, and the damping ratio ξ=0.0444 is obtained; the direct integration method is used for both E1 and E2 time-history analyses, with an analysis time of 20s and an analysis step of 0.02s. The vertical seismic action is taken as 65% of the acceleration of the horizontal seismic action.

[0111] In a specific example, the S32 one-dimensional earthquake response analysis includes the following steps:

[0112] S321. Using the method of inputting seismic waves separately from three orthogonal directions, namely longitudinal, transverse and vertical, a consistent excitation E1 and E2 time history analysis is performed on the model considering pile-soil interaction to analyze the displacement response and internal force response of the main control section of the special-shaped arch bridge under one-dimensional earthquake action.

[0113] S322. In view of the asymmetric structural characteristics of the special-shaped arch bridge, the 1 / 4 arch rib, 1 / 2 arch rib, 3 / 4 arch rib, arch feet on the north and south banks, and the top of the diagonal brace and tie rod of the side arch and the middle arch are selected as control points; among them, the side arch, diagonal brace and tie rod use the structural data of the east side of the bridge;

[0114] S323. Conduct one-dimensional earthquake dynamic response analysis, and obtain the displacement and internal force time history curves of the longitudinal, transverse, vertical side arch and middle arch control sections.

[0115] In a specific example, in S3, the S33 multi-dimensional earthquake action response analysis includes:

[0116] S331. According to the Code for Seismic Design of Buildings (GB 50011), the ground motions in three orthogonal directions are combined in a ratio of 1:0.85:0.65;

[0117] S332, perform consistent excitation E1 time history analysis to extract the displacement response and internal force response of some control sections of the large-span asymmetric special-shaped steel arch bridge under multi-dimensional earthquake action;

[0118] S333, conduct time history analysis considering the effect of dead load, that is, the load combination is the addition of Taft seismic wave and dead load; the seismic wave adopts the three-way combination input reflecting the most unfavorable state of the structure, and the dead load adopts the time-varying static load mode;

[0119] S334. Perform consistent excitation E1 and E2 time history analysis to extract the dynamic response results of some control sections of the large-span asymmetric special-shaped steel arch bridge under multi-dimensional seismic action considering the action of constant load.

[0120] In a specific example, the step S4 of carrying out the vulnerability analysis of typical components of the large-span asymmetric special-shaped steel arch bridge specifically refers to: comprehensively comparing the seismic performance of the asymmetric large-span special-shaped steel arch bridge under one-dimensional earthquake action, multi-dimensional earthquake action and multi-dimensional earthquake action considering the action of dead load; and in order to explore the application possibility and prospect of the large-span asymmetric special-shaped steel arch bridge structure in higher defense areas, the characteristics of the complex structure of the special-shaped arch bridge are disassembled, and the influencing factors of the seismic performance of the special-shaped arch bridge are analyzed from the perspective of structural design, and the key control factors of the seismic performance of the special-shaped arch bridge are found;

[0121] See also Figure 7-11 :The key control factors for seismic performance include:

[0122] S41. Based on the original design of unequal heights between the middle arch and the side arch, the rise heights of the side arch and the middle arch are increased and decreased synchronously. The modified Taft wave under the strong earthquake level is selected in the previous article. The dynamic response results of each key control section are analyzed under the multi-dimensional earthquake action response considering the effect of the dead load.

[0123] S42. By reducing the mid-arch rise height and establishing the arch rib height difference, the dynamic response results of each key control section are extracted under the same earthquake action response;

[0124] S43. Reasonable arch rib inclination angle can reasonably improve the dynamic characteristics of the arch bridge and enhance the overall stability. By adjusting the arch rib inclination design angle, other design parameters are kept unchanged on the basis of reasonable structural stress, and the dynamic response results of each arch rib control section under different arch rib inclination angles are extracted;

[0125] S44, arch foot area offset, adjust the asymmetry of the arch rib curve in the xy and xx planes, and extract the dynamic response results of each arch rib control section under different arch foot outward displacements;

[0126] S45. The arch crown position is adjusted, the axis of the arch rib curve in the XZ plane is adjusted, and the dynamic response results of each arch rib control section under different arch crown positions are extracted.

[0127] In a specific example, the step S5 of conducting a system vulnerability analysis of a large-span asymmetric special-shaped steel arch bridge specifically refers to: seismic vulnerability analysis of a three-dimensional special-shaped steel arch bridge. As a probabilistic risk analysis method, seismic vulnerability analysis can provide a more reasonable evaluation basis for the seismic optimization design of bridges. 15 time-history waves are selected from the PEER database based on the bridge site characteristics, and the average strain is used as the performance indicator. The time-history analysis of the asymmetric special-shaped arch bridge is performed based on the dynamic increment analysis method to obtain the seismic vulnerability curve of the vulnerable component; then, a method based on reliability theory is used to study the system vulnerability of the asymmetric special-shaped arch bridge under the action of a three-way combined earthquake.

[0128] In a specific example, the step S5 of carrying out the vulnerability analysis of the large-span asymmetric special-shaped steel arch bridge system specifically includes the following steps:

[0129] S51. Average strain is used as the damage index of asymmetric special-shaped steel arch bridges. The strain limit values ​​corresponding to different damage states of steel are divided as shown in the table below, where εy represents the yield strain of steel and ε is the absolute value of the average reaction compressive strain within the effective failure length range. Fig.12 This is the distribution diagram of earthquake damage level of steel components.

[0130]

[0131] S52, select the curve fitting method based on the capacity demand ratio model to perform regression analysis on the vulnerability curve;

[0132] Based on the capacity demand ratio model, if the structural response Sd is greater than the structural capacity Sc (assuming that the structural response Sd and the structural capacity Sc obey the log-normal distribution), the structure will be damaged, and the damage exceedance probability Pf is expressed as follows:

[0133]

[0134] Taking the logarithm of both sides of the formula, the above formula can be expressed as:

[0135]

[0136] If the structural response Sd and the structural capacity Sc both obey the lognormal distribution, then ln(Sd / Sc) will obey the normal distribution. Given the symmetry of the normal distribution density function, the damage exceedance probability Pf can be written as:

[0137]

[0138] In the above formula, the regression mean λ and regression standard deviation σ are introduced to standardize ln(Sd / Sc), and the above formula can be written as:

[0139]

[0140] Since ln(Sd / Sc) has been standardized, the random variable ln(Sd / Sc) will obey the standard normal distribution, as shown in the following formula (5-5). The damage exceedance probability Pf can be expressed by the distribution function of the standard normal distribution as formula (5-6):

[0141]

[0142] Similarly, due to the symmetry of the standard normal distribution density function, the damage exceedance probability Pf can be simplified as:

[0143]

[0144] Among them, considering that the quadratic polynomial regression has higher solution accuracy, λ can be obtained by regression solution of the following formula, where a, b, c are regression coefficients, and IM is the ground motion intensity parameter:

[0145]

[0146] σ can be solved by formula (5-9), where Sr is the residual sum of squares of each discrete point relative to the regression curve. The calculation formula is shown in (5-10), and n is the number of discrete points:

[0147]

[0148] S53, the peak ground acceleration PGA of the selected 15 seismic waves is modulated to the maximum PGA (1.6g) in the incremental dynamic analysis process, and is sequentially input into the full-bridge spatial model for time history analysis, i.e., input in a three-way combination mode; the components in the structure that are damaged more times under the action of the 15 seismic waves are counted, and are called vulnerable components, such as Fig.13 As shown;

[0149] S54. Each of the 15 groups of seismic records was modulated 8 times to obtain 120 groups of seismic records, and nonlinear time history analysis was performed using a three-way combined input method. The 120 groups of seismic response results of 12 typical vulnerable components were statistically analyzed, and a total of 1440 maximum plastic strain data were extracted. A total of 36 IDA curves were fitted according to the damage limit, that is, one for each component with slight damage, moderate damage, and severe damage. According to the IDA curves of each component, the regression mean λ and regression standard deviation σ corresponding to different damage states of each vulnerable component were obtained, and then the damage exceedance probability Pf of the vulnerable component was obtained.

[0150] S55. Calculate the damage probability of each single member: Taking the seismic vulnerability analysis of the arch foot as an example, the main vulnerable components are the arch feet on both sides of the middle arch. The fitting results of the capacity demand ratio model of the north bank arch foot and the middle arch foot under different damage states are shown in the table below, and the corresponding IDA curve is shown in Fig.14 .

[0151]

[0152] S56. System vulnerability analysis: The first-order limit method based on the series system is used to calculate the failure probability of the system. Since the correlation between the failure modes is between the two cases of complete correlation and complete independence, the failure probability of the system when all components in the structure are completely correlated is the lower limit of the failure probability interval, and the failure probability when all components are completely independent is the upper limit of the interval. The limit interval of the structural failure probability is obtained as

[108] :

[0153]

[0154] In the formula, Pfs represents the failure probability of the system, Pfi represents the failure probability of the i-th component, and n is the number of components;

[0155] S57, see Fig.15 :Based on the vulnerability curves of each component calculated by the capacity-demand ratio model, the system vulnerability curve is drawn, and the first-order limit method is used to further calculate the system failure probability of the asymmetric special-shaped arch bridge; by comparing the degree of agreement between the system vulnerability curve and the vulnerability curve of a single component, the most vulnerable component in the special-shaped arch bridge system is obtained, thereby optimizing the seismic design of this type of bridge.

[0156] In summary, the present invention develops a vulnerability assessment method for a novel structural system such as asymmetric large-span special-shaped steel arch bridges in the field of bridge engineering, provides a dynamic performance test and model verification method for a large-span special-shaped steel arch bridge, enriches the considerations at the level of seismic performance optimization design of asymmetric large-span special-shaped steel arch bridges, and enables designers to more comprehensively consider the parameters affecting the seismic performance design of this type of bridge; through multi-dimensional seismic action response analysis, the seismic performance and seismic response laws of asymmetric large-span special-shaped steel arch bridges are clarified, and the seismic vulnerability of asymmetric large-span special-shaped steel arch bridges is more systematically evaluated. Therefore, the method provided in this embodiment has important significance and value for urban resilience disaster prevention, optimizing bridge seismic design, and enriching bridge vulnerability assessment methods.

[0157] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge, characterized in that: The process includes the following steps: S1: Conduct dynamic testing of large-span asymmetric special-shaped steel arch bridges; S2: Establish a full-bridge numerical analysis model and compare and verify it with the dynamic test results; S3: Conduct seismic response analysis of large-span asymmetric special-shaped steel arch bridges; S4: Conduct vulnerability analysis of typical components of large-span asymmetric special-shaped steel arch bridges; the step S4 of conducting vulnerability analysis of typical components of large-span asymmetric special-shaped steel arch bridges specifically refers to: comprehensively comparing the seismic performance of asymmetric large-span special-shaped steel arch bridges under one-dimensional earthquake action, multi-dimensional earthquake action and multi-dimensional earthquake action considering the action of dead load; and in order to explore the application possibility and prospect of large-span asymmetric special-shaped steel arch bridge structures in higher defense areas, the characteristics of the complex structure of the special-shaped arch bridge will be disassembled, and the influencing factors of the seismic performance of the special-shaped arch bridge will be analyzed from the perspective of structural design, and the key control factors of the seismic performance of the special-shaped arch bridge will be found; S5: Conduct system vulnerability analysis of large-span asymmetric special-shaped steel arch bridges; the step S5 of conducting system vulnerability analysis of large-span asymmetric special-shaped steel arch bridges specifically refers to: seismic vulnerability analysis of three-dimensional special-shaped steel arch bridges. As a probabilistic risk analysis method, seismic vulnerability analysis can provide a more reasonable evaluation basis for the seismic optimization design of bridges. 15 time-history waves are selected from the PEER database for bridge site characteristics. The average strain is used as the performance indicator. The time-history analysis of the asymmetric special-shaped arch bridge is performed based on the dynamic increment analysis method to obtain the seismic vulnerability curve of the vulnerable components; then, a method based on reliability theory is used to study the system vulnerability of the asymmetric special-shaped arch bridge under the action of three-way combined earthquakes.

2. The seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge according to claim 1 is characterized in that: The step S1 of carrying out the dynamic test of the large-span asymmetric special-shaped steel arch bridge comprises the following steps: S11. Arrange a vehicle with a counterweight on each of the two lanes of the bridge, taking into account the three parameters of vehicle speed, vehicle direction and vehicle spacing; S12. According to the structural characteristics of the large-span asymmetric special-shaped steel arch bridge, the acceleration sensor is arranged above the outer longitudinal beam, and the measuring points are arranged asymmetrically on the north and south sides accordingly. On one side, the measuring point B is arranged at the mid-span, and on the other side, the measuring points A, C, and D are arranged at the mid-span, 1 / 4 span, and 3 / 4 span positions respectively to carry out bridge dynamic testing.

3. The seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge according to claim 1 is characterized in that: The step S2 of establishing a full-bridge numerical analysis model and comparing and verifying it with the power test results includes the following steps: S21: Based on the finite element calculation software Midas Civil, a spatial finite element model of a large-span asymmetric special-shaped steel arch bridge is established. The arch bridge structure is discretized into spatial bar system units. According to the stress characteristics of the arch bridge, the tension unit is simulated by truss unit, and the bridge deck system, arch ribs, wind bracing, hangers, diagonal braces, and tie rods are simulated by beam units. S22: Obtain the dynamic response results of the bridge dynamic test and compare them with the time history analysis results of the finite element simulation to verify that the dynamic response results of the bridge are in good agreement, so as to carry out seismic performance research.

4. The seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge according to claim 1 is characterized in that: The step S3 of carrying out seismic response analysis of a large-span asymmetric special-shaped steel arch bridge comprises the following steps: S31: seismic wave selection and input; S32: One-dimensional earthquake response analysis; S33: Multidimensional seismic response analysis.

5. The seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge according to claim 4 is characterized in that: The S31 seismic wave selection and input includes the following steps: S311. Use the analog seismic wave method to select the seismic acceleration time history, that is, select strong earthquake records with similar geological environment, magnitude and spectrum characteristics to the site of the bridge to be built as input, refer to the engineering geological report and the "Evaluation Rules for Seismic Performance of Highway Bridges" (JTG / T 2231-02), and use Taft seismic wave correction to perform time history analysis; S312. When conducting time-history analysis on the special-shaped arch bridge structure, the Rayleigh damping in proportional damping is used to calculate the damping ratio, and the frequencies of the first and ninth modes with larger participating masses in the X and Y directions of the first ten vibration modes are selected as typical frequencies, and the damping ratio ξ=0.0444 is obtained; the direct integration method is used for both E1 and E2 time-history analyses, with an analysis time of 20s and an analysis step of 0.02s. The vertical seismic action is taken as 65% of the acceleration of the horizontal seismic action.

6. The seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge according to claim 4 is characterized in that: The S32 one-dimensional earthquake response analysis includes the following steps: S321. Using the method of inputting seismic waves separately from three orthogonal directions, namely longitudinal, transverse and vertical, a consistent excitation E1 and E2 time history analysis is performed on the model considering pile-soil interaction to analyze the displacement response and internal force response of the main control section of the special-shaped arch bridge under one-dimensional earthquake action. S322. In view of the asymmetric structural characteristics of the special-shaped arch bridge, the 1 / 4 arch rib, 1 / 2 arch rib, 3 / 4 arch rib, arch feet on the north and south banks, and the top of the diagonal brace and tie rod of the side arch and the middle arch are selected as control points; among them, the side arch, diagonal brace and tie rod use the structural data of the east side of the bridge; S323. Conduct one-dimensional earthquake dynamic response analysis, and obtain the displacement and internal force time history curves of the longitudinal, transverse, vertical side arch and middle arch control sections.

7. The seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge according to claim 4 is characterized in that: In S3, the S33 multi-dimensional earthquake action response analysis includes: S331. According to the Code for Seismic Design of Buildings (GB 50011), the ground motions in three orthogonal directions are combined in a ratio of 1:0.85:0.65; S332, perform consistent excitation E1 time history analysis to extract the displacement response and internal force response of some control sections of the large-span asymmetric special-shaped steel arch bridge under multi-dimensional earthquake action; S333, conduct time history analysis considering the effect of dead load, that is, the load combination is the addition of Taft seismic wave and dead load; the seismic wave adopts the three-way combination input reflecting the most unfavorable state of the structure, and the dead load adopts the time-varying static load mode; S334. Perform consistent excitation E1 and E2 time history analysis to extract the dynamic response results of some control sections of the large-span asymmetric special-shaped steel arch bridge under multi-dimensional seismic action considering the action of constant load.

8. The seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge according to claim 1 is characterized in that: The key control factors for finding seismic performance include: S41. Based on the original design of unequal heights between the middle arch and the side arch, the rise heights of the side arch and the middle arch are increased and decreased synchronously. The modified Taft wave under the strong earthquake level is selected in the previous article. The dynamic response results of each key control section are analyzed under the multi-dimensional earthquake action response considering the effect of the dead load. S42. By reducing the mid-arch rise height and establishing the arch rib height difference, the dynamic response results of each key control section are extracted under the same earthquake action response; S43. Reasonable arch rib inclination angle can reasonably improve the dynamic characteristics of the arch bridge and enhance the overall stability. By adjusting the arch rib inclination design angle, other design parameters are kept unchanged on the basis of reasonable structural stress, and the dynamic response results of each arch rib control section under different arch rib inclination angles are extracted; S44, arch foot area offset, adjust the asymmetry of the arch rib curve in the xy and xx planes, and extract the dynamic response results of each arch rib control section under different arch foot outward displacements; S45. The arch crown position is adjusted, the axis of the arch rib curve in the XZ plane is adjusted, and the dynamic response results of each arch rib control section under different arch crown positions are extracted.

9. The seismic vulnerability assessment method for an asymmetric large-span special-shaped steel arch bridge according to claim 1, characterized in that: The step S5 of carrying out the vulnerability analysis of the large-span asymmetric special-shaped steel arch bridge system specifically includes the following steps: S51. Average strain is used as the damage index of asymmetric special-shaped steel arch bridges; S52, select the curve fitting method based on the capacity demand ratio model to perform regression analysis on the vulnerability curve; Based on the capacity demand ratio model, if the structural response Sd is greater than the structural capacity Sc, the structure will be damaged, and the damage exceedance probability Pf is expressed as follows: Taking the logarithm of both sides of the formula, the above formula can be expressed as: If the structural response Sd and the structural capacity Sc both obey the lognormal distribution, then ln(Sd / Sc) will obey the normal distribution. Given the symmetry of the normal distribution density function, the damage exceedance probability Pf can be written as: In the above formula, the regression mean λ and regression standard deviation σ are introduced to standardize ln(Sd / Sc), and the above formula can be written as: Since ln(Sd / Sc) has been standardized, the random variable ln(Sd / Sc) will obey the standard normal distribution, as shown in the following formula (5-5). The damage exceedance probability Pf can be expressed by the distribution function of the standard normal distribution as formula (5-6): Similarly, due to the symmetry of the standard normal distribution density function, the damage exceedance probability Pf can be simplified as: Among them, considering that the quadratic polynomial regression has higher solution accuracy, λ can be obtained by regression solution of the following formula, where a, b, c are regression coefficients, and IM is the ground motion intensity parameter: σ can be solved by formula (5-9), where Sr is the residual sum of squares of each discrete point relative to the regression curve. The calculation formula is shown in (5-10), and n is the number of discrete points: S53, modulating the peak ground acceleration PGA of the selected 15 seismic waves to the maximum PGA in the incremental dynamic analysis process, and sequentially inputting them into the full-bridge space model for time history analysis, i.e., inputting them in a three-way combination mode; counting the components in the structure that are damaged more times under the action of the 15 seismic waves, which are called vulnerable components; S54. Each of the 15 groups of seismic records was modulated 8 times to obtain 120 groups of seismic records, and nonlinear time history analysis was performed using a three-way combined input method. The 120 groups of seismic response results of 12 typical vulnerable components were statistically analyzed, and a total of 1440 maximum plastic strain data were extracted. A total of 36 IDA curves were fitted according to the damage limit, that is, one for each component with slight damage, moderate damage, and severe damage. According to the IDA curves of each component, the regression mean λ and regression standard deviation σ corresponding to different damage states of each vulnerable component were obtained, and then the damage exceedance probability Pf of the vulnerable component was obtained. S55. Calculate the damage probability of each single member: S56. System vulnerability analysis: The failure probability of the system is calculated using the first-order limit method based on the series system. Since the correlation between the failure modes is between the two cases of complete correlation and complete independence, the failure probability of the system when all components in the structure are completely correlated is the lower limit of the failure probability interval, and the failure probability when all components are completely independent is the upper limit of the interval. The limit interval of the structural failure probability is: In the formula, Pfs represents the failure probability of the system, Pfi represents the failure probability of the i-th component, and n is the number of components; S57. Based on the vulnerability curves of each component calculated by the capacity-demand ratio model, the system vulnerability curve is drawn, and the system failure probability of the asymmetric special-shaped arch bridge is further calculated using the first-order limit method. By comparing the degree of agreement between the system vulnerability curve and the vulnerability curve of a single component, the most vulnerable component in the special-shaped arch bridge system is obtained, thereby optimizing the seismic design of this type of bridge.

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