Rail transit bridge seismic toughness grading evaluation standard construction method

Abstract

The application discloses a kind of track traffic bridge seismic toughness grading evaluation standard construction methods, comprising: determining the function target requirement after earthquake under different earthquake levels;Carry out seismic vulnerability and function vulnerability analysis, determine the structure damage grade and post-earthquake residual function under different earthquake intensity;Determine the repair procedure and repair path of track traffic bridge system component, calculate the repair quantity and component repair period, obtain the repair period of track traffic bridge system;Analysis obtains the traffic function in repair process;Draw ladder type function recovery function and calculate to obtain toughness index;Calculate the effective influence days of different damage grades under different earthquake intensity;Establish the relationship between damage grade and effective influence days, determine the effective influence days range of different damage degree grade, obtain the seismic toughness grading evaluation standard.The application reduces the number and calculation amount of bridge samples, accurately reflects the function recovery situation after earthquake, and is used to guide the seismic fortification of bridge.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering technology, and in particular to a method for constructing a seismic toughness grading evaluation standard for rail transit bridges. Background Technology

[0002] As lifeline projects for evacuating refugees from disaster areas and transporting relief supplies, bridges should not only ensure that they do not collapse under earthquake action, but also be put into use as soon as possible after the earthquake. Resilience is a reflection of the recovery ability of rail transit bridge systems under abnormal action, and usually includes resilience indicators such as direct loss, indirect loss, and recovery time. Therefore, it is necessary to carry out research on the seismic resilience evaluation standard of railway bridges.

[0003] Currently, rail transit bridges are shifting from performance-based design focused on "pre-earthquake prevention" and "earthquake protection" to resilient seismic design focused on "post-earthquake functional recovery." The current seismic toughness evaluation standard for bridges uses elastoplastic time-history analysis, considering multiple seismic waves and employing the Monte Carlo method to obtain extended engineering requirement parameters. It utilizes a component vulnerability database to calculate the damage state of building components, fully considering uncertainties such as ground motion, structural system, and component damage. Based on the component damage state, an evaluation system is established, including three building toughness evaluation indicators—personnel casualties, repair costs, and repair time—and multiple evaluation levels. These three indicators should use fitted values ​​with an 84% guarantee rate obtained from Monte Carlo simulations, and the number of Monte Carlo simulations should not be less than 1000. A clear grading standard for evaluation indicators is established according to the evaluation level to achieve seismic toughness assessment of individual buildings. Building repair costs are evaluated based on the comprehensive recovery of damaged components, and these costs include all direct expenses incurred in repairing, dismantling, and replacing damaged components.

[0004] The existing seismic toughness evaluation standards are derived from the evaluation of a large number of bridge samples. This requires statistical analysis of bridges built in different years, geological and intensity zones, different types of bridges, different pier heights and spans, and different seismic isolation measures. The calculation is extensive and difficult. Furthermore, the establishment of the toughness grading evaluation standards is too subjective and based on expert experience. The calculation of repair time and traffic function does not take into account the impact of the repair process under different damage conditions and the difference in the amount of repair work for different structures, making it difficult to quantitatively reflect the seismic toughness of the structure. Summary of the Invention

[0005] The purpose of this invention is to address the problems of existing methods for constructing seismic resilience evaluation standards, which rely heavily on the subjective experience of experts and require the evaluation of a large number of bridge samples, resulting in large computational loads and high difficulty. This invention provides a method for constructing a seismic resilience grading evaluation standard for rail transit bridges.

[0006] In a first aspect, the present invention provides a method for constructing a seismic toughness grading evaluation standard for rail transit bridges, comprising the following steps:

[0007] S1. Determine the post-earthquake functional objectives and requirements for rail transit bridge systems under different seismic levels;

[0008] S2. Conduct seismic vulnerability and functional vulnerability analysis of rail transit bridge systems to determine the structural damage level and post-earthquake residual function under different seismic intensities;

[0009] S3. Determine the repair procedures and repair paths for components of the rail transit bridge system based on different damage levels. Calculate the repair workload considering the overlap of repair procedures and combine this with the project budget quota to calculate the component repair period, thus obtaining the repair period for the rail transit bridge system. Analyze the post-earthquake residual function and repair path to obtain the traffic function throughout the repair process.

[0010] S4. Based on the repair period and traffic function, draw a stepped functional recovery function, and calculate the toughness index based on the functional recovery function;

[0011] S5. Based on the toughness index and the repair period of the rail transit bridge system, calculate the effective impact days for different damage levels under different earthquake intensities. The formula for calculating the effective impact days is as follows:

[0012]

[0013] Where ED represents the effective number of days of impact. R represents the repair period for the rail transit bridge system, and R is the toughness index.

[0014] S6. Establish the relationship between damage level and effective impact days of rail transit bridge system, analyze and determine the effective impact days range of different damage levels, and obtain the seismic toughness grading evaluation standard in combination with functional target requirements.

[0015] In the technical solution of this invention, the functional target requirements of the rail transit bridge system after an earthquake are first determined to obtain the qualitative requirements for grading. Then, based on the seismic vulnerability analysis model of the rail transit bridge, vulnerability and functional vulnerability analysis and functional loss analysis are carried out to obtain the structural damage level and post-earthquake residual function under different earthquake intensities. The analysis determines the repair procedures and repair paths of the rail transit bridge system components. The repair period of the components is obtained according to the repair procedures, repair paths and engineering budget quotas. The repair period of the rail transit bridge system under different earthquake intensities is further calculated. At the same time, the traffic function during the repair process under different earthquake intensities is obtained according to the post-earthquake residual function and repair path analysis. The toughness index is obtained according to the repair period and traffic function. The effective influence days of the seismic toughness evaluation index for different damage levels under different earthquake intensities are obtained. The effective influence days are used as the quantitative index for seismic toughness evaluation, thereby establishing the correlation between the post-earthquake functional performance (damage level) of the rail transit bridge system and the effective influence days. Based on the qualitative evaluation of functional target requirements and the quantitative evaluation of effective influence days, the seismic toughness grading evaluation standard of rail transit bridges is obtained.

[0016] Through the above technical solutions, a chain-linked model of seismic level (seismic intensity index) - functional objectives - effective impact days is established, and a seismic toughness grading evaluation standard is proposed. This solution analyzes the seismic vulnerability analysis model of rail transit bridge systems, reduces the number of bridge samples and the amount of calculation, reduces the reliance on experts' subjective experience to calculate the repair period, and uses the effective impact days range as a quantitative evaluation index to accurately reflect the post-earthquake functional recovery, thereby guiding the seismic fortification of bridges.

[0017] As a preferred embodiment of the present invention, in combination with existing seismic design specifications and bridge requirements for rail transit bridges, the functional target requirements of the bridge structure under minor, moderate and major earthquakes are determined, and the toughness level is divided into one-star, two-star, three-star and four-star.

[0018] As a preferred embodiment of the present invention, the functional objectives include the loss level of the rail transit bridge system and the bridge's reopening status after earthquake and repair.

[0019] As a preferred embodiment of the present invention, the earthquake intensity ranges from 0.05 to 0.95g, the difference between different earthquake intensities is 0.05 to 0.15g, and the difference between different earthquake intensities can be the same or different.

[0020] As a preferred embodiment of the present invention, when analyzing the post-earthquake functional performance of the rail transit bridge system, the longitudinal and transverse directions of the bridge are analyzed separately.

[0021] As a preferred embodiment of the present invention, the damage levels are divided into no damage, minor damage, moderate damage, severe loss, and complete destruction.

[0022] As a preferred embodiment of the present invention, the repair process of the rail transit bridge system components in step S3 is as follows:

[0023] When a bridge pier suffers minor damage, pressure grouting is used to repair the cracks. When a bridge pier suffers moderate damage, the plastic hinge zone of the bridge pier is reinforced by enlarging the cross section. When a bridge pier suffers severe damage, the entire height of the bridge pier is reinforced by enlarging the cross section. When a bridge pier is completely damaged, the bridge pier body is mechanically dismantled and rebuilt in situ.

[0024] When the support is slightly or moderately damaged, the support is reset and corrected by the top beam. When the support is severely or completely damaged, in addition to the reset and correction by the top beam, there is also the process of removing and installing the support.

[0025] When the main beam is slightly damaged, the repair process involves dismantling the track, removing the beam end expansion joints and track structure, and installing the beam end expansion joints and track structure. When the main beam is completely damaged, the repair process includes the installation and removal of the beam lifting machine, track dismantling, lifting the scrap beam, main beam prefabrication and transportation, main beam erection, and installation of expansion joints and track structure.

[0026] As a preferred embodiment of the present invention, the repair path for the rail transit bridge system is as follows:

[0027] When the bridge piers suffer moderate or severe damage, repair the bridge piers first, then repair the bearings and main beams.

[0028] When a bridge pier suffers minor damage, the main beam and supports, including the track and accessories, are repaired first, and then the bridge pier is repaired.

[0029] When the piers are not damaged, repair the main beams and supports as needed.

[0030] As a preferred embodiment of the present invention, in step S3, the engineering budget quota is adopted as the railway engineering budget quota - bridge and culvert engineering.

[0031] As a preferred embodiment of the present invention, the repair period for the rail transit bridge system includes assessment and decision-making time and functional restoration time, for

[0032]

[0033] in To assess decision-making time, This refers to the time required for the function to recover.

[0034] As a preferred embodiment of the present invention, the assessment and decision-making time includes the total time required for post-earthquake bridge inspection and assessment, repair plan formulation, and preparation of personnel, materials, and equipment.

[0035] As a preferred embodiment of the present invention, considering the overlap of the repair process, the functional recovery time is calculated under different damage levels. The formula for calculating the functional recovery time is as follows:

[0036] When the bridge pier is not damaged beyond the level of moderate damage:

[0037]

[0038] When the bridge pier is damaged beyond moderate level:

[0039]

[0040] In the formula Indicates the time required for the rail transit bridge system to restore its functionality. For the repair period of bridge pier components, For the repair period of the support components, The repair period for the main beam and auxiliary track structure components, Calculate the construction period for the preparatory stage before the repair of the main beam and auxiliary track structure. The construction period is calculated during the erection of the main beam and auxiliary track structure.

[0041] As a preferred embodiment of the present invention, the formula for calculating the toughness index is as follows:

[0042]

[0043] in As a resilience index; t 0 represents the time point when the earthquake occurred, and t2 represents the time point when the bridge function was restored; Q(t) This is the function to restore functionality.

[0044] As a preferred embodiment of the present invention, in the process of determining the effective impact days range for different damage levels, the median and average effective impact days under different earthquake intensities are statistically analyzed to obtain the effective impact days range corresponding to different damage levels.

[0045] In a second aspect, the present invention provides a method for evaluating the seismic toughness of rail transit bridges, comprising the following steps:

[0046] A seismic toughness grading evaluation standard for rail transit bridges was established using the above-mentioned method.

[0047] A seismic vulnerability analysis model for the target rail transit bridge system was established, and seismic response analysis was conducted to determine the post-earthquake functional performance of the rail transit bridge system under different seismic intensities.

[0048] Based on different damage levels, repair procedures, repair paths and engineering budget quotas for rail transit bridge systems are given. The post-earthquake repair period of rail transit bridge systems under different earthquake intensities is calculated. The toughness index is determined based on the functional recovery function. Based on the toughness index and repair period, the effective impact days of rail transit bridge systems under different post-earthquake functional performances are calculated.

[0049] Based on the seismic toughness grading evaluation standard, the seismic toughness level of the target rail transit bridge system is determined.

[0050] The present invention also provides an electronic device, including at least one processor and a memory communicatively connected to the at least one processor; the memory stores instructions that are executed by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to execute the above-described method for constructing a seismic toughness grading evaluation standard for rail transit bridges.

[0051] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0052] 1. This invention provides a method for constructing a seismic toughness grading evaluation standard. First, it establishes a correlation between seismic toughness grading at the "demand level" based on prior experience (current seismic design codes) and different earthquake levels and functional objectives. Then, through numerical simulation, it establishes a correlation between the functional performance of typical post-earthquake bridges and quantitative seismic toughness evaluation indicators at the "response level," ultimately constructing a quantitative seismic toughness evaluation standard suitable for rail transit bridges. This avoids the need for simulation analysis of a large number of sample bridges.

[0053] 2. The method for constructing a seismic toughness grading evaluation standard in this invention provides a structured approach and method for calculating the repair period. That is, by providing standardized repair procedures for different degrees of damage to key components, repair paths for rail transit bridge systems, and engineering budget quota indicators, the calculation of the repair period is linked to the "workload" and "man-day consumption," and the impact of repair workload and overlapping repair procedures can be considered. It relies less on subjective judgment from experts, thereby maximizing the objective evaluation of the seismic toughness of rail transit bridges. Attached Figure Description

[0054] Figure 1 This is a flowchart of a method for constructing a seismic toughness grading evaluation standard for rail transit bridges according to the present invention;

[0055] Figure 2 This is the finite element model for the seismic vulnerability analysis of bridges in this invention;

[0056] Figure 3 This is a diagram showing the post-earthquake damage levels of the bridge along the longitudinal direction.

[0057] Figure 4 Probability map of damage level exceeding the standard for the longitudinal earthquake-induced rail transit bridge system;

[0058] Figure 5 Damage level diagram of the transverse earthquake-induced rail transit bridge system;

[0059] Figure 6 This is a probability map showing the exceedance of damage levels for a transverse earthquake-prone rail transit bridge system.

[0060] Figure 7 Diagram showing the bridge pier repair process;

[0061] Figure 8 This is a diagram illustrating the repair process of the bearing.

[0062] Figure 9 Diagram showing the repair process of the main beam and its auxiliary track structure;

[0063] Figure 10 Repair route map for rail transit bridge system;

[0064] Figure 11 This is a diagram showing the probability of passage for bridges of different seismic intensities under a longitudinal earthquake.

[0065] Figure 12 This is a diagram showing the probability of traffic flow for rail transit bridges under different seismic intensities during transverse earthquakes.

[0066] Figure 13 A graph showing the function recovery of rail transit bridges;

[0067] Figure 14 The toughness index is the stress index for different seismic intensities under a longitudinal earthquake.

[0068] Figure 15 This is a diagram showing the distribution of toughness indices under different seismic intensity levels during a bridging earthquake.

[0069] Figure 16 Toughness index diagrams for different earthquake intensities under transverse bridge earthquakes;

[0070] Figure 17 Distribution of toughness index under different seismic intensity levels during transverse bridge earthquakes;

[0071] Figure 18 A map showing the effective number of days of impact for different earthquake intensities along the bridge direction;

[0072] Figure 19 A map showing the distribution of effective impact days for different earthquake intensities under the direction of the bridge;

[0073] Figure 20 Effective impact days for different earthquake intensities under transverse earthquakes;

[0074] Figure 21 A graph showing the relationship between damage level and effective number of days of impact;

[0075] Figure 22 A map showing the median number of days of effective impact on rail transit bridges under earthquakes.

[0076] Figure 23 A map showing the effective impact days of earthquakes on rail transit bridges (95% guarantee rate).

[0077] Figure 24 This is a map showing the average number of days the earthquake had an effective impact on rail transit bridges. Detailed Implementation

[0078] The present invention will now be described in further detail with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0079] Unless otherwise specified, the use of terms such as "upper," "lower," "left," "right," "center," "inner," and "outer" to indicate orientation or positional relationships in the description of specific embodiments of the present invention is based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationship in which the product / equipment / device is typically placed during use. These terms are merely for the purpose of facilitating the description of the present invention or simplifying the description in specific embodiments, enabling those skilled in the art to quickly understand the solution, and do not indicate or imply that a particular device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship. Therefore, they should not be construed as limitations on the present invention.

[0080] Furthermore, the use of terms such as "horizontal," "vertical," "suspended," "parallel," and "coaxial" does not imply that the corresponding device / component / element must be absolutely horizontal, vertical, suspended, parallel, or coaxial. Slight tilt or deviation is permissible, as long as it does not affect the normal function of the relevant component. For example, "horizontal" simply means that its direction is more horizontal relative to "vertical," not that the structure must be perfectly horizontal; a slight tilt is acceptable. "Coaxial" means that two components are set as coaxially as possible, allowing them to move coaxially or approximately coaxially when their relative positions change. Alternatively, it can be simplified to mean that the corresponding device / component / element, when set in a "horizontal," "vertical," "suspended," "parallel," or "coaxial" direction, can have an error / deviation of ±10% relative to the corresponding direction, more preferably within ±8%, more preferably within ±6%, more preferably within ±5%, and more preferably within ±4%. For example, the deviation in the "coaxial" direction is controlled within 0.2-1mm, preferably within 0.2-0.5mm. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its function in the solution of the present invention.

[0081] Furthermore, the use of terms such as "first," "second," and "third" in terminology is merely for distinguishing descriptions of identical or similar components and should not be interpreted as emphasizing or implying the relative importance of a particular component.

[0082] Furthermore, in the description of the embodiments of the present invention, "several", "more than", and "a number of" represent at least two. The number can be any number, such as 2, 3, 4, 5, 6, 7, 8, or 9, and can even exceed nine.

[0083] Furthermore, in the description of the technical solution of this invention, unless otherwise explicitly specified / limited / restricted, the terms "set up," "install," "connect," "link," "provided with," "laid out," and "arranged" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to common connection methods in the art, such as welding, riveting, bolting, and threaded connections. Such connections can be mechanical, electrical, or communication connections; they can be direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components.

[0084] Example 1

[0085] The existing building seismic toughness evaluation standard is based on elastoplastic time history analysis and a localized component vulnerability database. It has established an evaluation system that includes three building toughness evaluation indicators, namely casualties, repair costs and repair time, and three levels (three-star, two-star and one-star) of evaluation grades. The standard has clearly defined evaluation indicator grading standards according to the evaluation grades, and has proposed clear repair paths and calculation methods for the post-earthquake repair time of building structures.

[0086] Table 1. Levels of Repair Cost Indicators

[0087]

[0088] Table 2. Levels of Repair Time Indicators

[0089]

[0090] Table 3 Levels of Personnel Loss Indicators

[0091]

[0092] The aforementioned seismic toughness evaluation criteria were derived through extensive assessments of bridge samples or expert questionnaires, involving significant computational complexity and difficulty. Literature review reveals that factors influencing building function include recovery time, repair costs, and personnel loss. However, for railway bridges, functional recovery prioritizes the speed of post-earthquake functional recovery (recovery time) and is less correlated with personnel loss. Post-earthquake functional recovery for railway bridges primarily focuses on repair time and strategies to achieve rapid repair. Therefore, this invention provides a method for constructing a seismic toughness grading evaluation standard for rail transit bridges, such as… Figure 1 As shown, it includes the following steps:

[0093] Step S1: Determine the post-earthquake functional objectives of rail transit bridge systems under different seismic levels.

[0094] Based on existing seismic design codes and bridge requirements for rail transit bridges, the functional target requirements for bridge structures under minor, moderate, and major earthquakes are determined. The toughness level is divided into one-star, two-star, three-star, and four-star. The functional target requirements include the loss level of the rail transit bridge system and the bridge's post-earthquake and post-repair traffic conditions, as shown in Table 4.

[0095] Table 4. Post-earthquake functional target requirements for bridges under different seismic levels

[0096]

[0097] Assuming that bridges meeting existing seismic design codes have acceptable toughness—meaning they can meet the functional objectives of no damage in minor earthquakes, repairability in moderate earthquakes, and no collapse in major earthquakes—their toughness level is defined as two stars, indicating acceptable toughness. For certain special bridges or major national engineering projects, engineers may raise the seismic fortification requirements, such as cable-stayed bridges, suspension bridges, or the CZ Railway. In these cases, the required functional objective is minor repair in moderate earthquakes and repairability in major earthquakes. Based on this, a good toughness functional objective is defined, resulting in a three-star bridge toughness level. Furthermore, considering the development of socio-economic levels and the improvement of seismic technology, an excellent toughness objective is also established, meeting the requirements of no damage in moderate earthquakes and minor repair in major earthquakes; the bridge toughness level is four stars. Finally, for bridges that do not meet the code requirements, an insufficient toughness situation is defined, resulting in a one-star bridge toughness level.

[0098] S2. Conduct seismic vulnerability and functional vulnerability analysis of rail transit bridge systems to determine the structural damage level and post-earthquake residual function under different seismic intensities;

[0099] In conducting seismic vulnerability and functional vulnerability analysis, a seismic vulnerability analysis model for rail transit bridges is established to perform seismic response analysis and determine the functional performance required by the corresponding functional objectives, including the damage level of each component, the damage level of the rail transit bridge system, and its probability. This embodiment selects a typical simply supported beam rail transit bridge in the mountainous region of southwest China for seismic vulnerability analysis, calculating the damage level and probability of the bridge under different seismic intensity indices (PGA). The selected bridge is as follows: Figure 2 As shown, from ground level upwards, the structure consists of reinforced concrete piers, supports, main beams, sliding layers, base plates, CA mortar layers, track slabs, fasteners, and tracks. Rigid arms are incorporated into the main beams and piers. Specifically, this embodiment uses fiber elements to simulate the reinforced concrete piers, elastic beam elements to simulate the main beams and tracks, and nonlinear spring elements to simulate the supports, sliding layers, CA mortar layers, and fasteners. The bridge is a 12-span simply supported T-beam (32.6m×1 + 24.6m×2 + 32.6m×9). Including the two dead beams, the weight per meter of the main beam is approximately 34.2t. The pier height varies between 7m and 25m, using round-ended solid piers with a top cross-sectional dimension of 7.8m×1.8m. When the pier height exceeds 15m, a variable cross-section design is adopted with an outer slope of 2.5%. The pier cross-section reinforcement ratio is approximately 0.52%, and the pier bottom volumetric stirrup ratio is 0.3%. The bridge piers are simulated using fiber elements, with concrete grade C35 and main reinforcement grade HRB400.

[0100] Located in an 8-degree seismic zone with a seismic intensity of 0.3g, the bridge employs friction pendulum bearings and anti-falling beam blocks as its seismic isolation and mitigation measures. Different models of friction pendulum bearings are used for the 32m and 24m spans, with parameter information shown in Table 5. The specific arrangement is as follows: one end has a fixed bearing, and the other end has a longitudinal movable bearing. The side beams have transverse movable bearings installed at the fixed ends of the middle beams, and multiple movable bearings at the other ends. The movement of the friction pendulum bearings is controlled by pins. When the bearing pin exceeds its design bearing capacity (displacement of 2mm), the pin is sheared, and the bearing begins to function as a seismic isolation element. The friction pendulum bearings were simulated using singleFPBearing elements in OpenSEES, and the anti-falling beam blocks were simulated using ElasticPPGap elements.

[0101] Table 5. Parameters of Friction Pendulum Support

[0102]

[0103] The seismic motion was selected from 100 near-fault seismic waves in the PEER database, with amplitudes adjusted from 0.05g to 0.95g, representing 10 seismic intensity levels. The amplitude ratio of vertical to horizontal ground motion was set at 0.67. Modal analysis showed that the bridge's first and 20th natural frequencies were 1.31Hz and 3.33Hz, respectively, and these two frequencies were used to determine the Ruili damping parameters in the time history analysis.

[0104] 2.1 Seismic vulnerability analysis and functional vulnerability analysis along the bridge direction

[0105] For the numerous and widespread simply supported railway bridges, the key components affecting their post-earthquake traffic function mainly fall into three categories: piers, bearings, and main beams and auxiliary track structures. In conducting seismic vulnerability analysis, the damage degree of different components was graded and evaluated, with damage levels divided into five levels: no damage, minor damage, moderate damage, severe damage, and complete damage. A simply supported railway beam bridge is a series system composed of piers, bearings, main beams, and tracks. Its post-earthquake damage level can be taken as the average of the actual system function, or it can be calculated by determining the loss weights and damage levels of each key component through expert investigation. When evaluating the damage level of components, the existing damage levels of piers, bearings, main beams, and track structures are used. This embodiment shows the damage ratios of rail transit bridge systems at different damage levels under longitudinal seismic loading at various seismic intensities. Figure 3 As shown, with increasing PGA (Programme Forecast Aggregate), the damage to rail transit bridge systems becomes more severe. Specifically, when the PGA is 0.15g, the probability of minor and moderate damage exceeds 90%. When the PGA is 0.35g, the probability of severe damage reaches approximately 20%, and the probability of complete failure reaches approximately 5%, requiring track closure for repair. This means that under design earthquake conditions, there is approximately a 25% probability of track closure. When the PGA is 0.55g, even under rare earthquake conditions, the probability of track closure exceeds 60%.

[0106] The exceedance probability of damage proportions for rail transit bridges under various seismic intensity levels under longitudinal seismic loading is presented in the following table. Figure 4 Under frequent earthquakes (PGA=0.11g), the probability of exceeding the limit for minor damage is 55%, and the probability of exceeding the limit for moderate damage in rail transit bridge systems is 15%. Under design earthquakes (PGA=0.30g), the probability of exceeding the limit for minor damage in rail transit bridge systems is 100%, the probability of exceeding the limit for moderate damage is 80%, and the probability of exceeding the limit for severe damage is 15%. Under rare earthquakes (PGA=0.51g), the probability of exceeding the limit for moderate damage in rail transit bridge systems is close to 100%, and the probability of exceeding the limit for severe damage is 30%.

[0107] In estimating the residual function of railway bridges after an earthquake, the functional loss is mainly determined by different bridge damage levels to obtain the residual function after the earthquake.

[0108] 2.2 Seismic vulnerability analysis and functional vulnerability analysis of the transverse bridge

[0109] Damage ratios of different damage levels for rail transit bridges under transverse seismic loading at various seismic intensity levels, for example. Figure 5It can be seen that, compared with earthquakes along the bridge direction, earthquakes across the bridge cause less damage. For example, when the PGA is 0.15g, the proportion of minor damage exceeds 90%, while the probability of moderate or above damage is zero; when the PGA is 0.25g, the probability of minor damage is almost 100%, and no moderate damage occurs; even at 0.45g, the probability of minor damage exceeds 60%, but the proportion of severe damage and complete destruction is about 20%.

[0110] The exceedance probability of damage to rail transit bridges under transverse seismic loading at various seismic intensities is presented below. Figure 6 Under frequent earthquakes (PGA=0.11g), the probability of exceeding the limit for minor damage to the rail transit bridge system is 60%, and the probability of exceeding the limit for moderate damage is almost zero. Under design earthquakes (PGA=0.30g), the probability of exceeding the limit for minor damage to the rail transit bridge system is 100%, the probability of exceeding the limit for minor and moderate damage is about 10%, and the probability of exceeding the limit for severe damage is about 3%, all of which are at a low level. Under rare earthquakes (PGA=0.51g), the probability of exceeding the limit for moderate damage to the rail transit bridge system is close to 50%, and the probability of exceeding the limit for severe damage is close to 30%, which is similar to the probability of exceeding the limit under longitudinal earthquake action.

[0111] Step S3: Based on different damage levels, provide the repair procedures and repair paths for the components of the rail transit bridge system. Consider the overlap of the repair procedures and calculate the repair workload. Combine the engineering budget quota to calculate the repair period of the components and obtain the repair period of the rail transit bridge system. Based on the post-earthquake residual function and repair path analysis, obtain the traffic function during the repair process.

[0112] 3.1 Repair procedures for bridge piers

[0113] For minor damage to bridge piers, pressure grouting is used to repair cracks; for moderate damage, the plastic hinge zone is reinforced using the enlarged section method; for severe damage, the entire pier height is reinforced using the enlarged section method; and for complete damage, the pier body is mechanically dismantled and rebuilt in situ. The repair procedures and their overlaps for bridge pier components under different damage levels are as follows: Figure 7 When the damage level is moderate, the repair process is as follows: roughening, rebar installation, installation of pier steel bars, and concrete pouring of the pier body. The installation of pier steel bars is carried out simultaneously during the roughening and rebar installation processes.

[0114] 3.2 Repair procedure for bearings

[0115] For minor and moderate damage to the bearing, the support is repositioned and straightened using the top beam. For severe and complete damage, additional steps are required, including bearing removal and installation. Figure 8 .

[0116] 3.3 Repair procedures for the main beam and its auxiliary track structure

[0117] When the main beam is slightly damaged, the process involves dismantling the track, removing the expansion joints and track structure at the beam ends, and then installing the expansion joints and track structure again. When the main beam is completely damaged, the process includes installing and dismantling the beam lifting machine, dismantling the track, removing the scrap beam, prefabricating and transporting the main beam, erecting the main beam, and installing the expansion joints and track structure. Figure 9 .

[0118] 3.4 Repair Path for Rail Transit Bridge Systems

[0119] The repair sequence of rail transit bridge systems mainly depends on the degree of seismic damage to the substructure piers. The repair path for each stage is determined based on the damage level of the piers, such as... Figure 10 , Figure 13 As shown below:

[0120] (1) When the pier is damaged to a medium or higher degree, there may be a large residual displacement at the top of the pier and the stiffness is severely degraded. Repair the pier first and then repair the bearing and main beam (red repair path).

[0121] (2) When the pier is slightly damaged and the bearing capacity of the pier is not significantly reduced, the main beam and support, including the track and accessories, should be repaired first, and then the pier should be repaired (black repair path). This is most beneficial for the system to quickly restore the emergency passage function, meet the needs of disaster relief and rescue and reduce indirect economic losses.

[0122] (3) When the piers are not damaged, the main beams and supports can be repaired as needed (blue repair path).

[0123] Then, the repair work volume of the rail transit bridge system is calculated by considering the overlapping of repair procedures. The repair period for key components and the rail transit bridge system is then calculated based on the engineering budget quota. The component repair period includes the pier repair period, bearing repair period, and main beam and auxiliary track structure repair period. It should be noted that the repair work volume in this embodiment is calculated based on the seismic vulnerability classification, and the corresponding repair procedure "man-days" consumption is obtained by consulting the corresponding quota standards based on the actual situation of this bridge project.

[0124] (1) Construction period for bridge pier repair

[0125] In the case of minor damage, although the reduction in pier stiffness may affect train speed and passage, it will not lead to a track closure overall. The repair work will not affect train operation on the bridge. Therefore, the repair period for this type of component is considered to be 0 days. =0 days, in the formula The actual repair time for all minor damage to the bridge piers.

[0126] Under moderate damage, the critical path for repairing a single component is: reinforcement fabrication and installation → concrete pouring. To meet the minimum curing time required for repairing bridge pier components, the repair period for this type of component is the greater of the calculated period and 28 days.

[0127] =Max 同类受损构件 (V) H2 ×8.43 man-days / 10m 3 +W G2 ×4.56 man-days / t) ÷ ÷α

[0128] = Max( (28 days)

[0129] The average number of workers required to repair a moderately damaged bridge pier. The calculated construction period for repairing moderately damaged bridge piers, The actual construction period for repairing moderately damaged bridge piers. If the overall damage to the bridge still meets the minimum traffic function requirements, construction will be carried out during the maintenance window of the operating line, in which case α=0.25 (maintenance window time 6 hours / 24 hours); otherwise, α=1.

[0130] Under severe damage, the critical path for repair work is the same as that for piers with moderate damage, namely:

[0131] =Max 同类受损构件 (V) H3 ×8.43 man-days / 10m 3 +W G3 ×4.56 man-days / t) ÷

[0132] =Max( (28 days)

[0133] In the formula , These are the calculated and actual construction periods for the repair of severely damaged bridge piers, respectively. The average number of manpower required to repair severely damaged bridge piers, Calculation of the construction period for repairing severely damaged bridge piers. The actual construction period for repairing the severely damaged bridge piers.

[0134] Under complete damage, the critical path for repair work is the same as that for piers with moderate damage, namely:

[0135] =Max 同类受损构件 (V) H4×8.43 man-days / 10m 3 +W G4 ×4.56 man-days / t) ÷

[0136] =Max( (28 days)

[0137] In the formula , These are the calculated and actual construction periods for repairing completely damaged bridge piers, respectively. The average number of workers required to repair severely damaged bridge piers. Calculate the construction period for repairing the completely damaged bridge pier. To determine the actual construction period for repairing the completely damaged bridge pier, V H2 V H3 V H4 W represents the amount of concrete used under different damage levels. G2 W G3 W G4 This indicates the amount of steel reinforcement used under different damage levels.

[0138] Since it is assumed that similar components will be repaired simultaneously, the repair period for bridge pier components is... It can be obtained by the following formula:

[0139]

[0140] (2) Support repair period

[0141] For minor / moderate damage, the repair time for the bearing is calculated as follows:

[0142] =Max 同类受损构件 ((LB f1 / 2 +LG 1 / 2 ()×10.36 man-days / m + 17.70 man-days / single-line hole)÷

[0143] In the formula , The actual construction period for repairing bearings with minor or moderate damage is as follows: LB represents the number of workers required for each repair procedure. f1 / 2 For the amount of work requiring vertical jacking due to support damage, LG 1 / 2 The amount of horizontal top beam work required to reposition the main beam.

[0144] For severe / complete damage, the repair time for the bearing is calculated as follows:

[0145] =Max 同类受损构件 ((LBf3 (+LG3)×10.36 man-days / m +WB3×6.44 man-days / t +NB3×17.70 man-days / unit)÷

[0146] =Max 同类受损构件 (WB4 × 6.44 man-days / t + NB4 × 17.70 man-days / unit) ÷

[0147] In the formula The actual construction period for repairing severely or completely damaged bearings, respectively. To correspond to the number of workers required for the repair process, NB3 and NB4 represent the total number of supports under the main beam, and WB3 and WB4 represent the weight of the supports. LB f3 LG3 represents the vertical lifting displacement of the main beam, while LG4 represents the horizontal reset displacement.

[0148] Since it is assumed that similar components are repaired simultaneously, the repair period for support components is... It can be obtained by the following formula.

[0149]

[0150] (3) Repair period of main beam and auxiliary track structure

[0151] As mentioned above, since the main beam is not a component that is easily damaged by vibration, it will generally not suffer serious damage unless a beam falls off. Therefore, the main beam is only divided into two states: minor damage (damage to expansion joints or track slabs) and complete damage (requiring reconstruction).

[0152] For minor damage, the rails need to be unloaded during repair, interrupting train traffic. The repair time is calculated as follows:

[0153] ÷

[0154] In the formula LG T4 For the length of the track slab that needs to be removed / installed, For the weight of the expansion joint, For the length of the expansion joint repair, To reduce the volume of the track slab, This represents the number of workers required for the corresponding repair process.

[0155] For complete damage, where the main beam suffers severe damage leading to track breakage, the key technical route for repair includes two parts: preparatory work before repair and main beam erection. The first part's duration is the maximum of either "installing the beam lifting machine, dismantling the track, and removing the scrap beam" or "prefabricating and transporting the main beam." The second part's duration is the maximum of either "erecting the main beam and dismantling the beam lifting machine" or "erecting one main beam, installing expansion joints, and installing the track structure." It should be noted that the beam lifting machine is only installed and dismantled once, and the dismantling of the beam lifting machine is counted as 40% of the total man-days for this process. The repair duration is calculated as follows:

[0156]

[0157]

[0158]

[0159] In the formula, The total construction period for the repair of the main beam and auxiliary structures, The project duration is calculated for the preparation phase before repair. Calculate the construction period during the main beam erection stage. The number of workers required for the corresponding repair process.

[0160] Since it is assumed that similar components will be repaired simultaneously, the repair period for the main beam and auxiliary track structure components is... It can be obtained by the following formula.

[0161]

[0162] The repair period for bridges after an earthquake is calculated by multiplying the labor input quota for each process by the amount of work and dividing by the average number of laborers required. The average number of laborers required for the repair of piers, supports, and main beams with different degrees of damage can be taken as the average of the expert questionnaire survey results, as shown in Table 6 below.

[0163] Table 6. Average number of manpower required for component repair (questionnaire survey)

[0164]

[0165] In this embodiment, the repair period for bridge seismically damaged components calculated based on the given repair scheme and engineering budget quota is shown in Table 7, and it is compared with the results obtained from existing literature through a questionnaire survey.

[0166] Table 7 Repair period (days) for bridge components damaged by seismic activity

[0167]

[0168] For the repair of rail transit bridge systems, the damage level of the rail transit bridge system, the repair procedures for each component, and the repair paths between each component must be considered. The post-earthquake repair period for rail transit bridge systems, also known as the track closure duration, includes assessment and decision-making time and functional restoration time. The formula for calculating the repair period is:

[0169]

[0170] in To assess decision-making time, This refers to the time required for the function to recover.

[0171] The assessment and decision-making time includes the total time required for post-earthquake bridge inspection and assessment, repair plan development, and the preparation of personnel, materials, and equipment. Previous researchers have provided assessment and decision-making times for highway bridges with different damage levels based on expert questionnaires and other methods. The assessment and decision-making time mainly depends on the bridge's size and the degree of damage, while also considering local transportation conditions and the availability of post-earthquake repair resources. These factors are not significantly different for highway bridges and railway bridges; therefore, expert questionnaires yielded assessment and decision-making times of 6 days, 13 days, 22 days, and 30 days for four different damage levels (minor, moderate, severe, and complete damage).

[0172] The formula for calculating the function recovery time is:

[0173] When the bridge pier is not damaged beyond the level of moderate damage:

[0174]

[0175] When the bridge pier is damaged beyond moderate level:

[0176]

[0177] In the formula Indicates the time required for the rail transit bridge system to restore its functionality. For the repair period of bridge pier components, For the repair period of the support components, The repair period for the main beam and auxiliary track structure components, Calculate the construction period for the preparatory stage before the repair of the main beam and auxiliary track structure. The construction period is calculated during the erection of the main beam and auxiliary track structure.

[0178] Based on the analysis of post-earthquake residual functions and repair paths, the traffic function during the repair process is obtained. In estimating the post-earthquake residual functions and functional recovery during the repair process, this embodiment uses the following simplified algorithm to estimate the post-earthquake functional recovery process of railway beam bridges to obtain the traffic function. However, it should be noted that, under conditions of sufficient computing power, it can be obtained according to the vehicle-bridge coupled vibration analysis.

[0179] The vehicle speed is used to measure the traffic function of the rail transit bridge system. In determining the traffic function, the mechanical models of the damaged bearings, damaged bridge piers, and track irregularities are analyzed using seismic response analysis. The mechanical models of the damaged bearings and damaged bridge piers are then incorporated into the vehicle-track-bridge analysis model. The track irregularities are superimposed with the initial irregularities to analyze the post-earthquake traffic function of the rail transit bridge system and obtain the maximum safe operating speed Ve after the earthquake. The residual function Qr after the earthquake is calculated according to the following formula:

[0180] Qr = Ve / V0

[0181] In the formula, V0 is the original design speed.

[0182] To more clearly and intuitively demonstrate and define the traffic function of the post-earthquake rail transit bridge system, based on a design speed of 200 km / h... km / h Taking a railway line as an example, according to the Track Inspection - Dynamic Inspection Standard for Track Geometry (TB / T 3355-2023), the management of local peak dynamic deviation of track alignment irregularities can be handled as shown in the table below. That is, the maximum safe operating speed of vehicles on the bridge after an earthquake can be predicted based on the track irregularity indicators, as shown in Table 8 below.

[0183] Table 8 Definition and control indicators of impaired traffic function

[0184]

[0185] It should be noted that when the train speed needs to be reduced to below 45 km / h, normal scheduling requirements cannot be met; therefore, the functional loss ratio is 100% at this point. To simplify the study, the resilience evaluation example uses the following simplified algorithm to estimate the post-earthquake functional recovery process of railway beam bridges:

[0186] (1) When any component of the system (main beam, pier or support) is seriously damaged, the track structure is also likely to be seriously damaged, so the residual function is 0.

[0187] (2) When any component of the system suffers moderate damage, the system stiffness degrades significantly. To meet safety requirements, it is conservatively assumed that the train operates at 30% of its normal speed (60 km / h ÷ 200 km / h). After the supports (track and accessories) and main beam are repaired, the function is assumed to be 60% of the original (120 km / h ÷ 200 km / h).

[0188] (3) When any component of the system suffers minor damage, the function is assumed to be 80% of the original (160 km / h ÷ 200 km / h). The system function is considered to be fully restored as long as the supports, main beams and track structure are repaired.

[0189] (4) When repairing the track structure, traffic must be completely interrupted, at which point the function is reduced to 0.

[0190] According to the expert questionnaire results, rail transit bridge systems are permitted to operate at maximum speed under undamaged conditions, and at limited speeds under moderate and severe damage conditions. Based on the damage proportions of rail transit bridge systems at different damage levels under various seismic intensities during longitudinal earthquakes, the probability of bridge passage is obtained as follows: Figure 11 As can be seen, the probability of passage decreases with increasing PGA under different conditions. Specifically, under frequent earthquakes (PGA=0.11g), the probability of passage at the required speed is approximately 50%; under design earthquakes (PGA=0.30g), the rail transit bridge system completely fails to meet the requirements for speed-limited passage, and the probability of passage at the speed limit is approximately 85%, which means the probability of track closure is approximately 15%; under rare earthquakes (PGA=0.51g), the probability of passage at the speed limit decreases to 40%, meaning the probability of track closure is approximately 60%. The results indicate that under longitudinal earthquake action, when PGA=0.1g, the expected post-earthquake passage capability is approximately 50%, while when PGA exceeds 0.3g, post-earthquake passage capability is almost impossible.

[0191] The probability of bridges remaining passable under transverse earthquake conditions is as follows: Figure 12 As can be seen, the probability of passage under different conditions decreases with increasing PGA. Specifically, under frequent earthquakes (PGA=0.11g), the probability of passage at speed is approximately 40%, lower than the probability corresponding to earthquakes along the bridge direction (50%). Under design earthquakes (PGA=0.30g), the rail transit bridge system completely fails to meet the requirements for speed-limited passage, and the probability of passage at speed limits is approximately 90%, higher than the probability corresponding to earthquakes along the bridge direction (85%). Under rare earthquakes (PGA=0.51g), the probability of passage at speed limits decreases to 53%, higher than the probability corresponding to earthquakes along the bridge direction (40%). Overall, the probability of passage under transverse earthquakes is higher than that under longitudinal earthquakes. According to the functional vulnerability analysis results of the rail transit bridge system, under transverse earthquake action, the expected post-earthquake passage function is approximately 45% when PGA=0.1g, while when PGA exceeds 0.3g, post-earthquake passage is almost impossible.

[0192] S4. Based on the repair period and traffic function, draw a stepped functional recovery function, and calculate the toughness index based on the functional recovery function.

[0193] Based on the repair schedule of different repair procedures in the rail transit bridge system, and considering the traffic function during the repair process, a stepped function recovery function is plotted, such as... Figure 13 As shown.

[0194] Using toughness index RThe resilience index is used to quantify the system's functional loss and recovery ability under a certain intensity of seismic activity. It can be understood as reflecting the degree of functional recovery per unit time, and is obtained by integrating the functional recovery function and dividing it by the repair time. The calculation formula is as follows:

[0195]

[0196] in As a resilience index; t 0 represents the time point when the earthquake occurred, and t2 represents the time point when the bridge function was restored; Q(t) The functional recovery function, Q(t)=1, indicates complete functional normality, while Q(t)=0 indicates complete functional loss. A step function is used to reflect the functional recovery process of the rail transit bridge. The functional recovery curve, represented by the functional recovery function, reflects the real-time change in structural function from loss to complete recovery after an earthquake. It mainly includes three parts: structural traffic function Qr, functional repair path, and functional recovery time Tre. The functional repair path can be expressed using the functional recovery function Q(t), quantifying the post-earthquake functional recovery of the structure. For traffic function, the residual traffic function value of the railway bridge is quantified by vehicle speed loss. The post-earthquake functional recovery function is a quantitative function expressing the functional repair path, directly reflecting the quantitative relationship between post-earthquake repair strategies, repair methods, resource input, and the degree and time of structural functional recovery. Existing functional recovery functions are continuous functions, typically employing ideal recovery functions proposed by Cimellaro based on actual recovery data or types and considering varying levels of rescue resources: linear, exponential, trigonometric, and step-type recovery functions. However, existing linear, exponential, trigonometric, and step-type recovery functions fail to reflect the impact of structural repair order. Therefore, a functional recovery function considering the repair order of components is needed. While the impact of different component repair orders on the seismic toughness of bridges has been explored, the damage state of components and the damage evolution pattern of railway bridges have not been fully considered. Furthermore, according to expert surveys, 72.5% of railway experts prefer to use step-type functions to reflect the functional recovery process of railway bridges. Therefore, this invention innovatively proposes a functional recovery function that considers the repair order of components and the post-earthquake traffic function of structural damage; it is step-type, not continuous.

[0197] 4.1 Seismic toughness index along the bridge direction

[0198] Calculate the toughness index of rail transit bridges under longitudinal earthquakes, such as Figure 14As shown, it can be seen that, overall, the toughness index of rail transit bridges under longitudinal earthquakes decreases with increasing seismic intensity, but it exhibits a significant spanning characteristic, due to the large differences in repair time among various key components. To better understand the toughness index, it is divided into six levels based on the overall results: R<0.25, 0.25≤R<0.45, 0.45≤R<0.65, 0.65≤R<0.85, 0.85≤R<0.95, and 0.95≤R. The proportions of each level are shown in the figure. Figure 15 As shown, when PGA is 0.15g and 0.25g, the toughness index of rail transit bridges under longitudinal earthquakes is mostly concentrated in the ranges of [0.25, 0.45) and [0.65, 0.85). When PGA reaches 0.35g, the toughness index of rail transit bridges under longitudinal earthquakes in the ranges of [0.25, 0.45) and [0.65, 0.85) decreases to about 75%, and there is about a 25% probability that the toughness is below 0.25 (extremely low toughness). As PGA increases, the probability of toughness below 0.25 gradually increases, and when PGA reaches 0.55g, the probability reaches about 70%.

[0199] 4.2 Transverse seismic toughness index

[0200] The toughness index of rail transit bridges under transverse earthquakes is as follows: Figure 16 As shown, it can be seen that, overall, similar to longitudinal earthquakes, the toughness index of rail transit bridges decreases with increasing earthquake intensity under transverse earthquakes, but it exhibits a significant spanning characteristic, due to the large differences in repair time among various key components. The toughness distribution of each level is shown in the figure below. Figure 17 As shown, when PGA is 0.15g and 0.25g, the toughness index of rail transit bridges under transverse earthquakes is mostly concentrated in the ranges of [0.45, 0.65) and [0.65, 0.85), which is consistent with but different from the longitudinal earthquake. When PGA reaches 0.35g, the toughness index of rail transit bridges under longitudinal earthquakes in the ranges of [0.45, 0.65) and [0.65, 0.85) decreases to about 80%, and there is about a 20% probability that the toughness is below 0.25 (extremely low toughness). As PGA increases, the probability of toughness below 0.25 gradually increases, reaching about 55% when PGA reaches 0.55g, which is lower than the corresponding probability value for the longitudinal direction. Overall, the toughness index of rail transit bridges under transverse earthquakes is higher than that for the longitudinal direction.

[0201] S5. Based on the toughness index and the repair period of the rail transit bridge system, calculate the effective impact days for different damage levels under different earthquake intensities. The formula for calculating the effective impact days is as follows: :

[0202]

[0203] Among them, ED is the effective influence days, is the repair duration, which is the difference between the time point of earthquake occurrence and the time point of bridge function restoration.

[0204] 5.1 Effective influence days of structural damage under longitudinal earthquake action

[0205] According to the above calculation, the effective influence days of rail transit bridges under longitudinal earthquake are as Figure 18 shown. It can be seen that within the frequent earthquake (PGA less than 0.11g), rail transit bridges under longitudinal earthquake can achieve speed passing; in the range of PGA from 0.11g to 0.30g, the effective influence days obtained from some ground motion samples reach 30 days and 55 days; in the range of PGA from 0.30g to 0.51g, the effective influence days obtained from some ground motion samples reach about 100 days; when PGA exceeds 0.51g, that is, above the rare earthquake, there are more ground motion samples with effective influence days exceeding 90 days, and as PGA increases, the number of samples with effective influence days exceeding 90 days increases. The median value of the effective influence days under longitudinal earthquake shows that under the frequent earthquake, the median value of the effective influence days is almost 0, that is, under the frequent earthquake, rail transit bridges can meet the speed passing; under the design earthquake, the median value of the effective influence days reaches 30 days, and under the rare earthquake, the median value of the effective influence days is 42 days.

[0206] In order to better grasp the situation of the effective influence days of rail transit bridges under longitudinal earthquake, according to the overall results, the effective influence days are divided into six grades, namely ED = 0, 0 < ED ≤ 3, 3 < ED ≤ 30, 30 < ED ≤ 60, 60 < ED ≤ 100, 100 < ED, as Figure 19 shown. It can be seen that when PGA is 0.15g, the proportion of samples with effective influence days less than 3 days reaches more than 70%; when PGA is 0.25g, the proportion of samples with effective influence days less than 3 days is almost zero, and the proportion of effective influence days in the range of 3 to 30 days exceeds 50%; the proportion of effective influence days in the range of 3 to 30 days is more than 50% in the range of PGA from 0.25g to 0.45g; when PGA reaches 0.35g, the proportion of samples with effective influence days exceeding 100 days reaches 5%, and this proportion increases as PGA increases.

[0207] 5.2 Effective influence days of structural damage under transverse earthquake action

[0208] The effective influence days of rail transit bridges under transverse earthquake are as Figure 20As shown, generally speaking, the effective impact days of rail transit bridges under transverse earthquakes are lower than those under longitudinal earthquakes. During frequent earthquakes (PGA less than or equal to 0.11g), rail transit bridges can operate at speeds under transverse earthquakes. In the PGA range of 0.11g to 0.30g, the effective impact days obtained for most ground motion samples are relatively small. In the PGA range of 0.30g to 0.51g, the effective impact days obtained for some ground motion samples reach around 100 days, but for most ground motion samples, the effective impact days are less than 10 days. When the PGA exceeds 0.51g, i.e., above the level of rare earthquakes, a significant number of ground motion samples have effective impact days exceeding 90 days, and the number of samples with effective impact days exceeding 90 days increases with increasing PGA. The median effective impact days under transverse earthquakes indicate that under frequent earthquakes, the median effective impact days are almost 0, meaning that rail transit bridges can meet the speed requirements under frequent earthquakes. Under design earthquakes, the median effective impact days reach 4.81 days, and under rare earthquakes, the median effective impact days are about 15 days, both of which are less than the median effective impact days under longitudinal earthquakes.

[0209] Step S6: Establish the relationship between the damage level and the effective number of days of impact for the rail transit bridge system, analyze and determine the effective number of days of impact for different damage levels, and obtain the seismic toughness grading evaluation standard in combination with functional target requirements.

[0210] This invention selects simply supported beam bridges for rail transit for modeling and analysis. Based on the analysis results, the relationship between the damage level and the effective number of days of impact for rail transit bridge systems is established as follows: Figure 21 As shown, it can be found that the effective number of days of impact corresponding to the loss level under longitudinal seismic action is generally greater than that corresponding to transverse seismic action. This is mainly because the damage to the rail transit bridge system corresponding to longitudinal seismic action includes the loss of key components such as piers and bearings, while the loss level of key components such as piers in the rail transit bridge system under transverse seismic action is lower, and therefore the repair time is shorter.

[0211] Based on the above results, the comparison between the damage level and the effective impact days of the rail transit bridge system is summarized in Table 9, and based on this comparison table, the toughness level classification is summarized in Table 10. Because the method for constructing the bridge seismic toughness evaluation standard of this invention utilizes prior experience (seismic design codes), it is independent of factors such as the bridge's construction year, geological conditions, and intensity zone, and is only related to the bridge type. Therefore, it can significantly reduce the number of samples analyzed. It should be noted that the results shown in this table are applicable to simply supported beam bridges in rail transit. For other structural types of bridges such as continuous beams and rigid frame bridges, steps S1-S6 above should be used to determine the damage level and effective impact days of different bridge types, thereby obtaining the seismic toughness grading evaluation standard for different bridge types.

[0212] Table 9 Comparison of Damage Levels and Effective Impact Days for Rail Transit Bridge Systems

[0213]

[0214] Table 10 Seismic toughness classification evaluation criteria for rail transit bridge systems

[0215]

[0216] The median, average, and standard values ​​(95% guarantee rate) of the seismic toughness index (effective impact days) of bridges under different seismic intensity indices were statistically evaluated, and a seismic toughness classification evaluation was carried out.

[0217] (1) Resilience assessment based on median value

[0218] The median effective impact days and their envelope diagrams for rail transit bridges under earthquakes in the longitudinal and transverse directions are calculated as follows: Figure 22 As shown, the effective impact days envelope diagram for earthquakes in both directions exhibits a multi-segment structure. Under frequent earthquake conditions, the median effective impact days is 0, meeting the design objective of "minor earthquakes causing no damage." Under design earthquake conditions, the median effective impact days is approximately 30, meeting the "two-star" resilience level. Under rare earthquake conditions, the median effective impact days is approximately 45, meeting the "two-star" resilience level.

[0219] (2) Resilience evaluation based on 95% guarantee rate

[0220] The number of effective impact days with a 95% guarantee rate in all seismic motion samples is as follows: Figure 23 As shown, the effective impact days with a 95% guarantee rate are relatively high compared to the median effective impact days. Under frequent earthquakes, the effective impact days are 5, which does not meet the design target of "no damage in minor earthquakes," and its resilience level is "one-star." Under design earthquakes, the effective impact days are approximately 70, meeting the "one-star" resilience level, i.e., insufficient resilience. Under rare earthquakes, the effective impact days are approximately 100, also meeting the "one-star" resilience level, i.e., insufficient resilience. It can be observed that the resilience level obtained using a 95% guarantee rate is too low, indicating that this strategy is relatively conservative.

[0221] (3) Resilience evaluation based on mean

[0222] The mean number of effective impact days in all seismic motion samples is as follows: Figure 24As shown, the value is close to the median of the effective impact days. Under frequent earthquake conditions, the average effective impact days is 4.1, which does not meet the design target of "no damage in minor earthquakes," and its resilience level is "one-star." Under design earthquake conditions, the average effective impact days is approximately 30, meeting the resilience level of "two-star," meaning the resilience is acceptable. Under rare earthquake conditions, the average effective impact days is approximately 60, also meeting the resilience level of "two-star," meaning the resilience is acceptable. It can be observed that the resilience level obtained using the average is quite close to the resilience level obtained using the median.

[0223] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for constructing a seismic toughness grading evaluation standard for rail transit bridges, characterized in that, Includes the following steps: S1. Determine the post-earthquake functional objectives and requirements for rail transit bridge systems under different seismic levels; S2. Conduct seismic vulnerability and functional vulnerability analysis of rail transit bridge systems to determine the structural damage level and post-earthquake residual function under different seismic intensities; S3. Determine the repair procedures and repair paths for components of the rail transit bridge system based on different damage levels. Calculate the repair work volume by considering the overlap of repair procedures. Combine this with the engineering budget quota to calculate the component repair period and obtain the repair period for the rail transit bridge system. Based on the analysis of post-earthquake residual functions and repair paths, the accessibility throughout the repair process was obtained; S4. Based on the repair period and traffic function, draw a stepped functional recovery function, and calculate the toughness index based on the functional recovery function; S5. Based on the toughness index and the repair period of the rail transit bridge system, calculate the effective impact days for different damage levels under different earthquake intensities. The formula for calculating the effective impact days is as follows: Where ED represents the effective number of days of impact. The repair period for the rail transit bridge system is given by R; R is the toughness index. S6. Establish the relationship between damage level and effective impact days of rail transit bridge system, analyze and determine the effective impact days range of different damage levels, and obtain the seismic toughness grading evaluation standard in combination with functional target requirements.

2. The method for constructing a seismic toughness grading evaluation standard for rail transit bridges according to claim 1, characterized in that, Based on existing seismic design codes and bridge requirements for rail transit bridges, the functional target requirements for bridge structures under minor, moderate, and major earthquakes are determined. The toughness level is divided into one-star, two-star, three-star, and four-star. The functional target requirements include the loss level of the rail transit bridge system and the bridge's post-earthquake and post-repair traffic conditions.

3. A method for constructing a seismic toughness grading evaluation standard for rail transit bridges according to any one of claims 1, characterized in that, In step S3, the repair procedures for the components of the rail transit bridge system are as follows: When a bridge pier suffers minor damage, pressure grouting is used to repair the cracks. When a bridge pier suffers moderate damage, the plastic hinge zone of the bridge pier is reinforced by enlarging the cross section. When a bridge pier suffers severe damage, the entire height of the bridge pier is reinforced by enlarging the cross section. When a bridge pier is completely damaged, the bridge pier body is mechanically dismantled and rebuilt in situ. When the support is slightly or moderately damaged, the support is reset and corrected by the top beam. When the support is severely or completely damaged, in addition to the reset and correction by the top beam, there is also the process of removing and installing the support. When the main beam is slightly damaged, the repair process involves dismantling the track, removing the beam end expansion joints and track structure, and installing the beam end expansion joints and track structure. When the main beam is completely damaged, the repair process includes the installation and removal of the beam lifting machine, track dismantling, lifting the scrap beam, main beam prefabrication and transportation, main beam erection, and installation of expansion joints and track structure.

4. The method for constructing a seismic toughness grading evaluation standard for rail transit bridges according to claim 1, characterized in that, The repair path for rail transit bridge systems is determined based on the damage level of the piers, as follows: When the bridge piers suffer moderate or severe damage, repair the bridge piers first, then repair the bearings and main beams. When a bridge pier suffers minor damage, repair the main beam and supports first, including the track and accessories, and then repair the bridge pier. When the piers are not damaged, repair the main beams and supports as needed.

5. A method for constructing a seismic toughness grading evaluation standard for rail transit bridges according to any one of claims 1-4, characterized in that, The post-earthquake repair period for rail transit bridge systems includes assessment and decision-making time and functional restoration time.

6. The method for constructing a seismic toughness grading evaluation standard for rail transit bridges according to claim 5, characterized in that, The assessment and decision-making time includes the total time required for post-earthquake bridge inspection and assessment, repair plan development, and preparation of personnel, materials, and equipment.

7. The method for constructing a seismic toughness grading evaluation standard for rail transit bridges according to claim 5, characterized in that, Considering the workflow overlap of the repair process, the functional recovery time is calculated under different damage levels. The formula for calculating the functional recovery time is: When the bridge pier is not damaged beyond the level of moderate damage: When the bridge pier is damaged beyond moderate level: In the formula Indicates the time required for the rail transit bridge system to restore its functionality. For the repair period of bridge pier components, For the repair period of the support components, The repair period for the main beam and auxiliary track structure components, Calculate the construction period for the preparatory stage before the repair of the main beam and auxiliary track structure. The construction period is calculated during the erection of the main beam and auxiliary track structure.

8. A method for constructing a seismic toughness grading evaluation standard for rail transit bridges according to any one of claims 1-4, characterized in that, In determining the effective impact days range for different damage levels, the median and average effective impact days under different earthquake intensities were statistically analyzed to obtain the effective impact days range corresponding to different damage levels.

9. A method for evaluating the seismic toughness of rail transit bridges, characterized in that, Includes the following steps: A seismic toughness grading evaluation standard for rail transit bridges is established using the construction method of any one of claims 1-8. A seismic vulnerability analysis model for the target rail transit bridge system was established, and seismic response analysis was conducted to determine the post-earthquake functional performance of the rail transit bridge system under different seismic intensities. Based on different structural damage levels, repair procedures, repair paths, and engineering budget quotas for rail transit bridge systems are given. The post-earthquake repair period and traffic function of rail transit bridge systems under different earthquake intensities are calculated. Based on this, the functional recovery function is plotted and the toughness index is calculated. Based on the toughness index and repair period, the effective impact days of rail transit bridge systems under different post-earthquake functional performances are calculated. Based on the seismic toughness grading evaluation standard, the seismic toughness level of the target rail transit bridge system is determined.

10. An electronic device comprising at least one processor and a memory communicatively connected to said at least one processor; said memory storing instructions executable by said at least one processor, characterized in that, The instructions are executed by the at least one processor to enable the at least one processor to execute the method for constructing a seismic toughness grading evaluation standard for rail transit bridges as described in any one of claims 1-8.

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