Rail transit bridge anti-seismic toughness grading evaluation standard construction method

Abstract

The invention discloses a rail transit bridge shock resistance toughness grading evaluation standard construction method. The method comprises the following steps: determining post-earthquake function target requirements under different seismic levels; carrying out earthquake vulnerability and function vulnerability analysis, and determining structural damage levels and post-earthquake residual functions under different earthquake intensities; determining a component repairing procedure and a repairing path of the rail transit bridge system, calculating to obtain a repairing work amount and a component repairing period, and obtaining a repairing period of the rail transit bridge system; analyzing to obtain a passing function in the repairing process; drawing a stepped function recovery function and calculating to obtain a toughness index; calculating the number of effective influence days of different damage levels under different seismic intensities; and establishing a relationship between damage grades and effective influence days, determining an effective influence day range of different damage degree grades, and obtaining an anti-seismic toughness grading evaluation standard. According to the method, the number and calculation amount of bridge samples are reduced, the post-earthquake function recovery condition is accurately reflected, and the method is used for guiding earthquake fortification of the bridge.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge engineering, and in particular to a method for constructing a graded evaluation standard for seismic toughness of rail transit bridges. Background Art

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

[0003] Rail transit bridges are currently transitioning from performance-based design for "pre-earthquake prevention" and "earthquake protection" to resilient seismic design for "post-earthquake functional recovery." The current building seismic resilience evaluation standard for bridges uses an elasto-plastic time-history analysis method, taking into account multiple seismic waves and employing the Monte Carlo method to derive expanded engineering requirement parameters. This standard utilizes a component vulnerability database to calculate the damage state of building components, fully accounting for uncertainties such as ground motion, structural systems, and component damage. Based on the component damage state, a multi-level evaluation system is established, including three building resilience evaluation indicators: casualties, repair costs, and repair time. These three indicators should use fitted values ​​with an 84% assurance rate derived from Monte Carlo simulations, with a minimum of 1,000 Monte Carlo simulations. A clearly defined grading system for evaluation indicators is used to assess the seismic resilience of individual buildings. Building repair costs are assessed based on the comprehensive restoration of earthquake-damaged components, consisting of the direct costs incurred for repairing, removing, and replacing damaged components.

[0004] The existing seismic toughness evaluation standards are obtained through the evaluation of a large number of bridge samples. It is necessary to conduct statistical analysis on bridges of different construction years, different geological and intensity zones, different types of bridges, different pier heights and spans, and different seismic isolation measures. The calculation is large and difficult. In addition, the establishment of the toughness grading evaluation standards is too subjective to experts' experience. The calculation of repair period and traffic function does not take into account the repair process under different damage conditions and the impact of different structural repair project quantities, making it difficult to quantitatively reflect the seismic toughness of the structure. Summary of the Invention

[0005] The purpose of the present invention is to solve the problem that the existing method of constructing resilience evaluation standards requires a lot of reliance on the subjective experience of experts and requires the use of a large number of bridge samples for evaluation, resulting in large amounts of calculations and high difficulty, and to provide a method for constructing a graded evaluation standard for seismic resilience of rail transit bridges.

[0006] In a first aspect, the present invention provides a method for constructing a graded evaluation standard for seismic toughness of rail transit bridges, comprising the following steps: S1. Determine the post-earthquake functional requirements of rail transit bridge systems under different earthquake levels; S2. Conduct seismic vulnerability and functional vulnerability analysis of rail transit bridge systems to determine the structural damage levels and post-earthquake residual functions under different earthquake intensities; S3. Determine the repair process and path for rail transit bridge system components based on different damage levels. Calculate the repair workload by taking into account the overlap of repair process flows. Calculate the component repair duration based on the project budget quota to determine the repair duration for the rail transit bridge system. Analyze the post-earthquake residual function and repair path to determine the traffic function throughout the repair process. S4. Draw a step-type function recovery function based on the repair period and traffic function, and calculate the resilience index based on the function recovery function; S5. Calculate the effective impact days for different damage levels under different earthquake intensities based on the resilience index and the repair period of the rail transit bridge system. The calculation formula for the effective impact days is:

[0007] ED is the effective effect days, is the repair period of the rail transit bridge system, and R is the resilience index; S6. Establish the relationship between the damage level and effective impact days of rail transit bridge systems, analyze and determine the effective impact days range for different damage levels, and derive the seismic toughness grading evaluation standard based on functional target requirements.

[0008] In the technical solution of the present invention, the functional target requirements of the rail transit bridge system after an earthquake are first determined to obtain qualitative requirements for classification. 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 structural damage levels and post-earthquake residual functions under different earthquake intensities. The repair process and repair path of the rail transit bridge system components are determined by analysis. The component repair period is obtained based on the repair process, repair path, and engineering budget quota. 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 analyzed based on the post-earthquake residual function and repair path. The toughness index is obtained based on the repair period and traffic function. The effective impact days, a seismic toughness evaluation index for different damage levels under different earthquake intensities, is obtained. The effective impact days are used as a quantitative indicator for seismic toughness evaluation, thereby establishing a correlation between the post-earthquake functional performance (damage level) of the rail transit bridge system and the effective impact days. Based on the qualitative evaluation of the functional target requirements and the quantitative evaluation of the effective impact days, a graded evaluation standard for the seismic toughness of rail transit bridges is obtained.

[0009] Through the above-mentioned technical solution, a chain-related model of earthquake level (seismic intensity index)-functional target-effective impact days is established, and a seismic resilience grading evaluation standard is proposed. This solution analyzes the seismic vulnerability analysis model of the rail transit bridge system, reduces the number of bridge samples and the amount of calculation, reduces the use of experts' subjective experience to calculate the repair period, and uses the effective impact days range as a quantitative evaluation indicator to accurately reflect the post-earthquake functional recovery and guide the seismic fortification of bridges.

[0010] As a preferred solution of the present invention, combined with the existing rail transit bridge seismic design specifications and bridge requirements, the functional target requirements of the bridge structure under small earthquakes, moderate earthquakes and large earthquakes are determined, and the toughness levels are divided into one star, two stars, three stars and four stars.

[0011] As a preferred solution of the present invention, the functional target requirements include the loss level of the rail transit bridge system and the traffic conditions of the bridge after the earthquake and after repair.

[0012] As a preferred embodiment of the present invention, the range of earthquake intensity is 0.05~0.95g, the difference between different earthquake intensities is 0.05~0.15g, and the differences between different earthquake intensities can be the same or different.

[0013] As a preferred solution of the present invention, when analyzing the functional performance of the rail transit bridge system after an earthquake, the longitudinal direction and the transverse direction of the bridge are analyzed separately.

[0014] As a preferred embodiment of the present invention, the damage levels are divided into no damage, slight damage, moderate damage, severe loss and complete destruction.

[0015] As a preferred embodiment of the present invention, in step S3, the rail transit bridge system component repair process is as follows: When a pier is slightly damaged, pressure grouting is used to repair cracks. When a pier is moderately damaged, the plastic hinge area of ​​the pier is reinforced by enlarging the cross section. When a pier is severely damaged, the entire pier height is reinforced by enlarging the cross section. When a pier is completely damaged, the pier body is mechanically dismantled and rebuilt in situ. When the bearing is slightly or moderately damaged, the top beam is used to reset and correct the bearing. When the bearing is seriously or completely damaged, in addition to the top beam reset and correction, there are also processes for dismantling and installing the bearing. When the main beam is slightly damaged, the line is dismantled, the expansion joints and track structure at the beam ends are removed, and the expansion joints and track structure at the beam ends are installed. When the main beam is completely damaged, the repair includes the installation and removal of the beam lifting machine, line dismantling, lifting of the waste beam, prefabrication and transportation of the main beam, erection of the main beam, and installation of the expansion joints and track structure.

[0016] As a preferred solution of the present invention, the repair path of the rail transit bridge system is as follows: When the bridge piers are moderately damaged or above, repair the piers first and then the bearings and main beams; When minor damage occurs to the bridge piers, first repair the main beams and supports, including the tracks and accessories, and then repair the bridge piers; When there is no damage to the bridge piers, repair the main beams and supports as needed.

[0017] As a preferred solution of the present invention, in step S3, the engineering budget quota adopts the railway engineering budget quota - bridge and culvert engineering.

[0018] As a preferred solution of the present invention, the repair period of the rail transit bridge system includes the evaluation decision time and the function recovery time.

[0019] in To assess decision time, Function recovery time.

[0020] As a preferred solution 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.

[0021] As a preferred solution of the present invention, the functional recovery time under different damage levels is calculated by taking into account the overlap of the repair process. The functional recovery time calculation formula is: When the bridge pier is not damaged beyond the moderate level:

[0022] When the bridge pier is damaged beyond moderate level:

[0023] In the formula Indicates the functional recovery time of the rail transit bridge system, The repair period for the pier components is is the repair period of the supporting components, The repair period for the main beam and auxiliary track structural components is Calculate the construction period for the preparatory stage before repair of the main beam and auxiliary track structure. Calculate the construction period for the erection phase of the main beam and auxiliary track structures.

[0024] As a preferred embodiment of the present invention, the toughness index calculation formula is as follows:

[0025] in is the toughness index; t0 is the time point of earthquake occurrence, and t2 is the time point of bridge function recovery; Q(t) It is a function to restore the function.

[0026] As a preferred solution of the present invention, in the process of determining the effective impact days range for different damage severity levels, the median and average values ​​of the effective impact days under different earthquake intensities are counted to obtain the effective impact days range corresponding to different damage severity levels.

[0027] In a second aspect, the present invention provides a method for evaluating the seismic toughness of a rail transit bridge, comprising the following steps: The seismic toughness grading evaluation standard is established by using the above-mentioned method for constructing the seismic toughness grading evaluation standard for rail transit bridges; Establish a rail transit bridge seismic vulnerability analysis model for the target rail transit bridge system, conduct seismic response analysis, and determine the post-earthquake functional performance of the rail transit bridge system under different earthquake intensities; The repair process, repair path, and engineering budget quota for rail transit bridge systems are given according to different damage levels. 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 the repair period, the effective impact days under different post-earthquake functional performance of rail transit bridge systems are calculated. According to the seismic toughness grading evaluation standard, the seismic toughness level of the target rail transit bridge system is determined.

[0028] The present invention also provides an electronic device comprising at least one processor and a memory communicatively connected to the at least one processor; the memory stores instructions to be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the above-mentioned method for constructing a grading evaluation standard for seismic toughness of rail transit bridges.

[0029] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention proposes a method for constructing a graded seismic resilience evaluation standard. First, by leveraging prior experience (current seismic design specifications), a correlation between seismic resilience grading and functional objectives at the "demand level" is established. Then, through numerical simulation, a correlation is established between the functional performance of typical post-earthquake bridges and quantitative seismic resilience evaluation indicators at the "response level." Ultimately, a quantitative seismic resilience evaluation standard applicable to rail transit bridges is constructed. This avoids the need for simulation analysis of a large number of sample bridges.

[0030] 2. The calculation of the repair period in the method for constructing the seismic toughness grading evaluation standard of the present invention provides a structured idea and method. That is, by providing standardized repair procedures for key components under different degrees of damage, the repair path of the rail transit bridge system and the engineering budget quota indicators, the calculation of the repair period is linked to the "project volume" and "man-day consumption", and can consider the impact of the overlap of the repair project volume and the repair procedures, with less reliance on the subjective experience of experts, thereby maximizing the objective evaluation of the seismic toughness of rail bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 This is a flow chart of a method for constructing a graded evaluation standard for seismic toughness of rail transit bridges according to the present invention; Figure 2 A finite element model for bridge seismic vulnerability analysis according to the present invention; Figure 3 This is the post-earthquake damage level diagram of the bridge along the bridge direction; Figure 4 This is the damage level exceedance probability diagram of the rail transit bridge system under the along-bridge earthquake; Figure 5 This is the damage level diagram of rail transit bridge system in transverse bridge direction earthquake; Figure 6 The exceedance probability diagram of the damage level of the rail transit bridge system in the transverse direction earthquake; Figure 7 This is a diagram of the bridge pier repair process; Figure 8 This is the bearing repair process diagram; Figure 9 Repair process diagram of the main beam and its auxiliary track structure; Figure 10 Develop a repair path map for the rail transit bridge system; Figure 11 The traffic probability diagram of the bridge with different seismic intensity levels under the earthquake in the longitudinal direction of the bridge; Figure 12 The probability map of rail transit bridge traffic under different earthquake intensity levels in the transverse direction of the bridge; Figure 13 Function diagram for restoring rail transit bridge function; Figure 14 is the resilience index of different seismic intensity levels under earthquakes along the bridge direction; Figure 15 This is the distribution diagram of toughness index at different seismic intensity levels under earthquakes along the bridge direction; Figure 16 Toughness index diagram of different seismic intensity levels under transverse bridge earthquake; Figure 17 Distribution of toughness index at different seismic intensity levels under transverse bridge earthquakes; Figure 18 This is the effective impact days diagram of different earthquake intensity levels under the earthquake in the along-bridge direction; Figure 19 This is the distribution diagram of the effective impact days of different earthquake intensity levels under the earthquake in the along-bridge direction; Figure 20 The effective impact days diagram of different earthquake intensity levels under transverse bridge earthquakes; Figure 21 This is the relationship between damage level and effective impact days; Figure 22 This is the effective impact days of rail transit bridges under earthquakes (median value); Figure 23 This is a map of the effective impact days of rail transit bridges under earthquakes (95% assurance rate); Figure 24 This is the effective impact days of rail transit bridges under earthquakes (mean). DETAILED DESCRIPTION

[0032] The present invention will be further described in detail below with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments, as all technologies implemented based on the present invention fall within the scope of the present invention.

[0033] Unless otherwise specified, in the description of the specific embodiments of the present invention, the terms indicating the orientation or positional relationship, such as "upper", "lower", "left", "right", "center", "inside", and "outside", are based on the expressions of the orientation or positional relationship shown in the accompanying drawings, or are the orientation or positional relationship in which the invented product / device / apparatus is placed when it is conventionally used. These terms of orientation or positional relationship are merely for the purpose of facilitating the description of the scheme of the present invention or simplifying the description of the specific embodiments to facilitate the rapid understanding of the scheme by technicians, and do not indicate or imply that a specific device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship, and therefore should not be understood as limiting the present invention.

[0034] Furthermore, the use of terms such as "horizontal," "vertical," "overhanging," "parallel," and "coaxial" does not necessarily require that the corresponding devices / components / elements be absolutely horizontal, vertical, overhanging, parallel, or coaxial. Rather, they may be slightly tilted or have deviations, as long as they do not affect the normal function of the relevant components. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but rather that it can be slightly tilted. "Coaxial" means that the two components are arranged as coaxially as possible, so that they move in a coaxial or approximately coaxial manner when their relative positions change. Alternatively, it can be simplified to mean that the corresponding devices / components / elements are arranged in a "horizontal," "vertical," "overhanging," "parallel," or "coaxial" direction, and can have an error / deviation of ±10% relative to the corresponding direction, more preferably within an error / deviation of ±8%, more preferably within an error / deviation of ±6%, more preferably within an error / deviation of ±5%, and more preferably within an error / deviation of ±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 role in the solution of the present invention.

[0035] In addition, the expressions “first”, “second”, “third”, etc. in the terms are merely used to distinguish the description of the same or similar components, and should not be understood as emphasizing or implying the relative importance of specific components.

[0036] In addition, in the description of the embodiments of the present invention, "several," "plurality," and "a number" represent at least two. It can also be any number such as two, three, four, five, six, seven, eight, nine, or even more than nine.

[0037] Furthermore, in the description of the technical solution of the present invention, unless otherwise expressly specified, defined, or limited, the terms "disposed," "installed," "connected," "connected," "provided with," "laid," and "arranged" should be understood broadly. For example, they may refer to fixed connections, detachable connections, or integral connections. They may be welded, riveted, bolted, threaded, or other commonly used connection methods in the art. Such connections may be mechanical, electrical, or communicative; they may be direct, indirect via an intermediate medium, or internally connected between two components.

[0038] Example 1 The existing building seismic resilience evaluation standard is based on elastic-plastic time-history analysis and a localized component vulnerability library. It has established an evaluation system with three building resilience evaluation indicators, namely casualties, repair costs, and repair time, and a three-level (three-star, two-star, and one-star) evaluation grade. It has also divided the evaluation indicator grading standards according to the evaluation grades, and proposed a clear repair path and calculation method for the post-earthquake repair time of building structures.

[0039] Table 1 Levels of repair cost indicators

[0040] Table 2 Levels of repair time indicators

[0041] Table 3 Levels of personnel loss indicators

[0042] The above-mentioned seismic resilience evaluation standards are obtained through evaluation of a large number of bridge samples or expert questionnaire surveys, which require large amounts of calculations and are difficult to perform. Literature research shows that factors affecting building functions include recovery time, repair costs, and personnel losses. However, for railway bridges, functional recovery focuses more on the speed of post-earthquake functional recovery (recovery time), and is not strongly correlated with personnel losses. For the post-earthquake functional recovery of railway bridges, the main focus is on repair time and repair strategies to achieve repairs as quickly as possible. Therefore, the present invention provides a method for constructing a graded evaluation standard for seismic resilience of rail transit bridges, such as Figure 1 As shown, the following steps are included: Step S1: Determine the post-earthquake functional target requirements of the rail transit bridge system under different earthquake levels.

[0043] Combined with existing rail transit bridge seismic design specifications and bridge requirements, the functional target requirements of bridge structures under small, moderate, and major earthquakes are determined. The toughness levels are divided into one star, two stars, three stars, and four stars. The functional target requirements include the loss level of the rail transit bridge system and the traffic conditions of the bridge after the earthquake and after repair, as shown in Table 4.

[0044] Table 4 Post-earthquake functional requirements of bridges under different earthquake levels

[0045] Assuming that bridges meeting existing seismic design specifications have acceptable resilience, meaning they can meet the functional objectives of no damage in minor earthquakes, repairable in moderate earthquakes, and surviving major earthquakes under different earthquake levels, the bridge's resilience rating is two stars, indicating acceptable resilience. For certain special bridges or major national engineering projects, engineers may raise the seismic fortification requirements, such as for cable-stayed and suspension bridges, or for CZ railways. In these cases, the required functional objectives are minor repairs in moderate earthquakes and repairability in major earthquakes. Based on this, a good resilience functional objective is defined, resulting in a three-star bridge resilience rating. Furthermore, considering the development of socioeconomic levels and improvements in seismic technology, an excellent resilience objective is established, meeting the requirements of no damage in moderate earthquakes and minor repairs in major earthquakes, resulting in a four-star bridge resilience rating. Finally, for bridges that do not meet the requirements of the specifications, insufficient resilience is defined, and the bridge resilience rating is one star.

[0046] S2. Conduct seismic vulnerability and functional vulnerability analysis of rail transit bridge systems to determine the structural damage levels and post-earthquake residual functions under different earthquake intensities; In the seismic vulnerability and functional vulnerability analysis, a seismic vulnerability analysis model for rail transit bridges is established, and seismic response analysis is performed to determine the functional performance corresponding to the functional target requirements, including the damage level of each component, the damage level and probability of the rail transit bridge system. In this example, a typical rail transit simply supported beam bridge in the mountainous area of ​​southwest China is selected for seismic vulnerability analysis. The damage level and probability of the bridge under different seismic intensity indices (PGA) are calculated. The selected bridge is as follows: Figure 2 As shown, from the ground upward, the structure consists of reinforced concrete piers, bearings, main beams, sliding layer, base plate, CA mortar layer, track slab, fasteners, and tracks. Rigid arms are incorporated into the main beams and piers. 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 bearings, sliding layer, CA mortar layer, and fasteners. The bridge consists of 12 simply supported T-beams (32.6m × 1 + 24.6m × 2 + 32.6m × 9). The main beams, including the two constants, weigh approximately 34.2 tons per linear meter. Pier heights vary from 7m to 25m. Round-ended solid piers are used, with a 7.8m × 1.8m cross-section at the top. Pier heights exceeding 15m are designed as variable cross-sections with an external slope of 2.5%. The pier cross-section reinforcement ratio is approximately 0.52%, and the volumetric stirrup ratio at the pier base is 0.3%. The bridge piers are simulated using fiber elements, the concrete grade is C35, and the main reinforcement grade is HRB400.

[0047] Located in an 8-magnitude 0.3g earthquake zone, the bridge utilizes a combination of friction pendulum bearings and anti-drop beam blocks for seismic isolation. Different types of friction pendulum bearings are used for the 32m and 24m spans, with their parameters shown in Table 5. The specific arrangement involves a fixed bearing at one end and a longitudinal movable bearing at the other. The side beams are all equipped with transverse movable bearings at the fixed end of the center beam and multiple movable bearings at the other end. The friction pendulum bearings utilize pins to control their mobility. When the bearing pins exceed their design bearing capacity (displacement of 2mm), the pins shear off, and the bearings begin to function as seismic isolation devices. The friction pendulum bearings are modeled using the singleFPBearing element in OPENSEES, while the anti-drop beam blocks are modeled using the ElasticPPGap element.

[0048] Table 5 Friction pendulum support parameters

[0049] The seismic motions were selected from 100 near-fault seismic waves in the PEER database, with amplitudes adjusted from 0.05g to 0.95g, encompassing 10 seismic intensity levels. The amplitude ratio of vertical to horizontal seismic motions was set at 0.67. Modal analysis revealed that the first and 20th natural frequencies of the bridge were 1.31Hz and 3.33Hz, respectively. These frequencies were used in the time-history analysis to determine the Ruili damping parameters.

[0050] 2.1 Seismic vulnerability analysis along the bridge and functional vulnerability analysis For the large number and wide range of simply supported railway bridges, the key components that affect their post-earthquake traffic functions mainly include three categories: piers, supports, main beams, and auxiliary track structures. When conducting earthquake vulnerability analysis, the degree of damage of different components was graded and evaluated, and the damage levels were divided into 5 levels, namely no damage, slight damage, moderate damage, severe damage, and complete damage. The railway simply supported beam bridge is a series system composed of piers, supports, main beams and tracks. Its post-earthquake damage level can be taken as the average of the actual function of the system, or it can be calculated by determining the loss weights of each key component of the bridge and the damage level of the components through expert surveys. When evaluating the damage level of the components, the damage level of the existing piers, supports, main beams and track structures is used for evaluation. In this embodiment, the damage ratio of the rail transit bridge system at different damage levels under the action of earthquakes in the direction of the bridge at various seismic intensity levels is as follows: Figure 3 As shown in the figure, as the PGA increases, rail transit bridge system damage becomes more severe. When the PGA is 0.15g, the combined probability of minor and moderate damage exceeds 90%. At a PGA of 0.35g, the probability of severe damage reaches approximately 20%, while the probability of complete failure, requiring track repair, reaches approximately 5%. This means that under the design earthquake, there is approximately a 25% probability of track failure. At a PGA of 0.55g, under rare earthquake conditions, the probability of track failure exceeds 60%.

[0051] The exceedance probability of the damage ratio of rail transit bridges at each earthquake intensity level under the action of the longitudinal earthquake is shown in Figure 4 Under the condition of frequent earthquakes (PGA=0.11g), the probability of exceeding minor damage reaches 55%, and the probability of exceeding moderate damage for rail transit bridge systems reaches 15%; under the condition of design earthquakes (PGA=0.30g), the probability of exceeding minor damage for rail transit bridge systems reaches 100%, the probability of exceeding moderate damage reaches 80%, and the probability of exceeding severe damage reaches 15%; under the condition of rare earthquakes (PGA=0.51g), the probability of exceeding moderate damage for rail transit bridge systems is close to 100%, and the probability of exceeding severe damage reaches 30%.

[0052] In estimating the residual function of railway bridges after an earthquake, the functional loss is mainly determined by using different bridge earthquake damage levels to obtain the residual function after an earthquake.

[0053] 2.2 Transverse seismic vulnerability analysis and functional vulnerability analysis The damage ratios of rail transit bridges at different damage levels under transverse earthquakes are as follows: Figure 5 It can be seen that compared with earthquakes along the bridge, the degree of damage caused by earthquakes across the bridge is smaller. For example, when the PGA is 0.15g, the proportion of minor damage exceeds 90%, and the probability of moderate damage or above is zero; when the PGA is 0.25g, the probability of minor damage is almost 100%, and no moderate damage occurs; even when it reaches 0.45g, the probability of minor damage exceeds 60%, but the proportion of severe damage and complete destruction is about 20%.

[0054] The exceedance probability of damage to rail transit bridges at various earthquake intensity levels under transverse earthquakes is shown in Figure 6 Under the condition of frequent earthquakes (PGA=0.11g), the probability of exceeding minor damage of rail transit bridge system reaches 60%, and the probability of exceeding moderate damage of rail transit bridge system is almost zero; under the condition of design earthquake (PGA=0.30g), the probability of exceeding minor damage of rail transit bridge system reaches 100%, and the probability of exceeding minor damage and moderate damage are both about 10%, and the probability of exceeding severe damage is about 3%, both of which are at a low level; under the condition of rare earthquakes (PGA=0.51g), the probability of exceeding moderate damage of rail transit bridge system is close to 50%, and the probability of exceeding severe damage is close to 30%, which is similar to the probability of exceeding under the action of earthquake along the bridge.

[0055] Step S3: According to different damage levels, the repair process and repair path of the rail transit bridge system components are given. The repair project volume is calculated by taking into account the overlap of the repair process flow, and the repair period of the components is calculated in combination with the project budget quota to obtain the repair period of the rail transit bridge system; the traffic function during the repair process is obtained based on the post-earthquake residual function and the repair path analysis.

[0056] 3.1 Repair process of bridge piers For minor damage to the pier, pressure grouting is used to repair cracks. For moderate damage, the plastic hinge area of ​​the pier is reinforced by enlarging the cross section. For severe damage, the entire pier height is reinforced by enlarging the cross section. For complete damage, the pier body is mechanically dismantled and rebuilt in situ. The repair procedures and overlaps of pier components at different damage levels are as follows: Figure 7 When the damage level is medium, the repair process is roughening, planting reinforcement, pier body reinforcement installation, and pier body concrete pouring. Among them, the pier body reinforcement installation is carried out simultaneously during the repair of roughening and planting reinforcement.

[0057] 3.2 Repair process of bearing If the bearing is slightly or moderately damaged, the top beam is reset and the bearing is corrected. If it is severely or completely damaged, there is also a process of removing and installing the bearing, such as Figure 8 .

[0058] 3.3 Repair process of main beam and its auxiliary track structure When the main beam is slightly damaged, the line is dismantled, the expansion joints and track structures at the beam ends are removed, and the expansion joints and track structures at the beam ends are installed. When the main beam is completely damaged, the process includes the installation and removal of the beam hoist, line dismantling, lifting the waste beam, prefabrication and transportation of the main beam, erection of the main beam, installation of the expansion joints and track structures, etc. Figure 9 .

[0059] 3.4 Repair Paths for Rail Transit Bridge Systems The repair sequence of rail transit bridge systems mainly depends on the degree of earthquake damage to the substructure piers. The repair path at each stage is determined according to the damage level of the piers, such as Figure 10 、 Figure 13 As shown below: (1) When the piers are moderately damaged or above, the pier top may have large residual displacement and the stiffness is severely degraded. The piers should be repaired first, followed by the bearings and main beams (red repair path); (2) When the bridge piers are slightly damaged and the bearing capacity of the bridge piers is not significantly reduced, the main beams and supports, including the tracks and accessories, should be repaired first, and then the bridge piers should be repaired (black repair path). This is most beneficial for the system to quickly restore the emergency passage function, meet the needs of emergency rescue and reduce indirect economic losses.

[0060] (3) When the bridge piers are not damaged, the main beams and supports can be repaired as needed (blue repair path).

[0061] The repair process flow is then considered to calculate the repair workload for the rail transit bridge system. The repair duration for key components and the rail transit bridge system is then calculated based on the project budget quota. This component repair duration includes the repair duration for piers, bearings, and main beams and associated track structures. It should be noted that the repair workload in this example is calculated based on the seismic vulnerability classification, and the corresponding repair process "man-day" consumption is obtained by querying the corresponding quota standards based on the actual situation of this bridge project.

[0062] (1) Bridge pier repair period In the case of minor damage, although the reduction in pier stiffness may affect the speed of trains, it will generally not lead to track closures and the repair work will not affect traffic on the bridge. Therefore, the repair period for this type of component is considered to be 0 days. =0 days, where The actual repair period for all slightly damaged bridge piers.

[0063] For moderate damage, the critical repair path for a single component is pier reinforcement fabrication and installation → pier concrete pouring. To meet the minimum curing time required for pier component repair, the repair period for this type of component is the maximum of the calculated duration and 28 days.

[0064] =Max 同类受损构件 (V H2 ×8.43 working days / 10m 3 +W G2 ×4.56 working days / t)÷ ÷α =Max( , 28 days) The average number of man-hours required to repair a moderately damaged bridge pier. To calculate the construction period for repairing moderately damaged bridge piers, The actual construction period for repairing moderately damaged piers is α = 0.25 (6 hours of window time / 24 hours) if the overall bridge damage still meets the minimum traffic function requirements and the operating line window time is used for construction. In other cases, α = 1.

[0065] In the case of severe damage, the key lines of the repair project are the same as those for moderately damaged piers, namely: =Max 同类受损构件 (V H3 ×8.43 working days / 10m 3 +W G3 ×4.56 working days / t)÷

[0066] =Max( , 28 days) In the formula 、 are the calculated construction period and actual construction period for repairing severely damaged bridge piers, The average number of manpower required to repair severely damaged bridge piers is: Calculate the construction period for repairing severely damaged bridge piers. The actual construction period for repairing severely damaged bridge piers.

[0067] Under complete damage, the critical lines of the repair project are the same as those for moderately damaged piers, namely: =Max 同类受损构件 (V H4 ×8.43 working days / 10m 3 +W G4 ×4.56 working days / t)÷

[0068] =Max( , 28 days) In the formula 、 are the calculated construction period and actual construction period for repairing completely damaged piers, Average number of man-hours required to repair severely damaged bridge piers. Calculate the construction period for repairing completely damaged bridge piers. The actual construction period for repairing completely damaged piers is V H2 、V H3 、V H4 Indicates the amount of concrete under different damage levels, W G2 、W G3 、W G4 Indicates the amount of steel bars used under different damage levels.

[0069] Since it is assumed that similar components are repaired at the same time, the repair period of the pier components is It can be obtained by the following formula:

[0070] (2) Bearing repair period For minor / moderate damage, the bearing repair period is calculated as follows: =Max 同类受损构件 ((LB f1 / 2 +LG 1 / 2 )×10.36 man-days / m+17.70 man-days / single hole)÷

[0071] In the formula 、 are the actual duration of repair work for slightly or moderately damaged bearings, is the manpower required for the corresponding repair process, LB f1 / 2 The amount of work that needs to be vertically lifted due to support damage, LG 1 / 2 The amount of horizontal top beam work required to reset the main beam.

[0072] For severe / complete damage, the bearing repair period is calculated as follows: =Max 同类受损构件 ((LB f3 +LG3)×10.36 working days / m+WB3×6.44 working days / t+NB3×17.70 working days / piece)÷

[0073] =Max 同类受损构件(WB4×6.44 working days / t+NB4×17.70 working days / piece)÷

[0074] In the formula are the actual duration of repairing severely or completely damaged bearings, LB is the number of workers for the corresponding repair process, NB3 and NB4 are the number of all supports under the main beam, and WB3 and WB4 are the weight of the supports. f3 LG3 is the vertical lifting displacement of the main beam, and LG4 is the horizontal reset displacement.

[0075] Since it is assumed that similar components are repaired at the same time, the repair period of the support components is It can be obtained by pressing the formula.

[0076]

[0077] (3) Repair period of main beam and auxiliary track structure As mentioned above, the main beam and its auxiliary track structure are not easily damaged by earthquakes and generally will not suffer serious damage unless the beam falls. Therefore, the main beam is only divided into two states: slightly damaged (damaged expansion joints or track plates) and completely damaged (requires reconstruction).

[0078] For minor damage, rails must be laid out during repairs, which will interrupt train traffic. The repair period is calculated as follows:

[0079] In the formula The actual duration of the repair of the slightly damaged main beam and auxiliary track structure is LG T4 The length of track plate to be removed / installed, is the weight of the expansion joint, Repair length for expansion joints, To remove the track slab volume, is the manpower required for the corresponding repair process.

[0080] For complete damage, where the main beam is severely damaged, resulting in track rupture, the key technical route for repair includes two parts: the pre-repair preparation phase and the main beam erection phase. The duration of the first part is the maximum of "installing the beam hoist, dismantling the line, and lifting the waste beam" or "prefabricating and transporting the main beam." The duration of the second part is the maximum of "erecting the main beam, removing the beam hoist" or "erecting a single-hole main beam, installing the expansion joint, and installing the track structure." It should be noted that the beam hoist is only installed and removed once, and the removal of the beam hoist is counted as 40% of the total working days of this process. The repair duration is calculated as follows:

[0081]

[0082]

[0083] Where, The total construction period for repairing the main beam and auxiliary structures is: Calculate the duration for the pre-repair preparation phase. Calculate the construction period for the main beam erection stage. The number of man-hours required for the corresponding repair process.

[0084] Since it is assumed that similar components are repaired at the same time, the repair period of the main beam and auxiliary track structure components is It can be obtained by pressing the formula.

[0085]

[0086] The post-earthquake bridge repair period is calculated by multiplying the labor quota for each process by the project volume and dividing it by the average labor input. The average labor input for repairing piers, bearings, and main beam structures with varying degrees of damage can be taken as the average of the expert questionnaire results, as shown in Table 6 below.

[0087] Table 6 Average manpower input for component repair (questionnaire survey)

[0088] In this example, the repair period for earthquake-damaged bridge components calculated based on the given repair plan and engineering budget quota is shown in Table 7, and is compared with the results obtained through questionnaire surveys in existing literature.

[0089] Table 7 Repair period for earthquake-damaged bridge components (days)

[0090] When repairing rail transit bridge systems, it is necessary to consider the damage level of the rail transit bridge system, the repair process of each component, and the repair path between each component. The repair period of the rail transit bridge system after an earthquake is the length of time the track is disconnected, including the evaluation and decision-making time and the function recovery time. The repair period is calculated as follows:

[0091] in To assess decision time, Function recovery time.

[0092] 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 calculated assessment and decision-making times for highway bridges at different damage levels based on expert questionnaires and other methods. This time depends primarily on the bridge's size and the extent of the earthquake damage, while also considering local transportation conditions and the availability of post-earthquake repair resources. These factors do not differ significantly between highway and railway bridges. Therefore, the expert questionnaires yielded assessment and decision-making times of 6, 13, 22, and 30 days for four different damage levels (minor, moderate, severe, and complete damage), respectively.

[0093] The formula for calculating functional recovery time is: When the bridge pier is not damaged beyond the moderate level:

[0094] When the bridge pier is damaged beyond moderate level:

[0095] In the formula Indicates the functional recovery time of the rail transit bridge system, The repair period for the pier components is is the repair period of the supporting components, The repair period for the main beam and auxiliary track structural components is Calculate the construction period for the preparatory stage before repair of the main beam and auxiliary track structure. Calculate the construction period for the erection phase of the main beam and auxiliary track structures.

[0096] The accessibility during the repair process is determined based on the post-earthquake residual function and repair path analysis. This embodiment uses the following simplified algorithm to estimate the post-earthquake functional recovery process of railway beam bridges to determine the accessibility. However, it should be noted that with sufficient computing power, the accessibility can be determined using vehicle-bridge coupled vibration analysis.

[0097] The vehicle speed is used to measure the traffic function of the rail transit bridge system. In the process of determining the traffic function, the mechanical models of the damaged bearings, the damaged pier components, and the track irregularities are analyzed through earthquake response. The mechanical models of the damaged bearings and the damaged pier components are 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 driving speed Ve after the earthquake. The post-earthquake residual function Qr is calculated according to the following formula: Qr=Ve / V0 Where V0 is the original design driving speed.

[0098] In order to more clearly and intuitively display and define the traffic function of the rail transit bridge system after the earthquake, the design speed is 200 km / h Taking the railway line in [the context of a separate text] as an example, according to the Track Inspection - Track Geometry Dynamic Inspection Standard (TB / T 3355-2023), the management of local peak dynamic deviations of track irregularity geometry can be handled according to the following table. In other words, the maximum safe speed for vehicles on the axle after an earthquake can be inferred based on track irregularity indicators, as shown in Table 8 below.

[0099] Table 8 Definition and control indicators of traffic function damage

[0100] It should be noted that when the speed needs to be reduced to below 45 km / h, normal dispatching requirements can no longer be met, so the functional loss ratio is 100%. To simplify the study, the following simplified algorithm is used in the resilience evaluation example to estimate the functional recovery process of railway beam bridges after earthquakes: (1) When any component of the system (main beam, pier or support) is severely damaged, the track structure is likely to be severely damaged, so the residual function is 0.

[0101] (2) When any component of the system suffers moderate damage, the system stiffness degrades significantly. To meet safety requirements, we conservatively assume that the train is traveling at 30% of its normal speed (60 km / h ÷ 200 km / h). After the supports (tracks and accessories) and main beams are repaired, the function is assumed to be 60% of the original speed (120 km / h ÷ 200 km / h).

[0102] (3) When any component of the system is slightly damaged, the function is assumed to be 80% of the original (160 km / h ÷ 200 km / h). As long as the support, main beam and track structure are repaired, the system function is considered to be fully restored.

[0103] (4) When repairing the track structure, traffic must be completely interrupted and the function is reduced to 0.

[0104] According to the results of the expert questionnaire survey, the rail transit bridge system is open to traffic at full speed when it is intact, and is open to traffic at limited speed when it is moderately damaged or severely damaged. Based on the damage ratio of the rail transit bridge system at different damage levels under different earthquake intensity levels in the along-bridge earthquake, the traffic probability of the bridge is obtained as follows: Figure 11, it can be seen that the probability of passage under different conditions decreases with increasing PGA. For example, under a frequent earthquake (PGA = 0.11g), the probability of reaching full-speed passage is approximately 50%. Under a design earthquake (PGA = 0.30g), the rail transit bridge system completely fails to meet full-speed passage requirements, and the probability of speed-restricted passage is approximately 85%, which means the probability of track closure is approximately 15%. Under a rare earthquake (PGA = 0.51g), the probability of speed-restricted passage decreases to 40%, resulting in a track closure probability of approximately 60%. The results show that under a longitudinal earthquake with a PGA of 0.1g, the expected post-earthquake passage function is approximately 50%, while a PGA exceeding 0.3g makes post-earthquake passage function almost impossible.

[0105] The conditional traffic probability of the bridge under the transverse earthquake is as follows: Figure 12 As can be seen in the figure, the probability of passage under different conditions decreases with increasing PGA. Under a frequent earthquake (PGA = 0.11g), the probability of reaching speed is approximately 40%, lower than the probability corresponding to an earthquake in the along-bridge direction (50%). Under a design earthquake (PGA = 0.30g), the rail transit bridge system completely fails to meet the requirements for reaching speed, and the probability of speed-restricted passage is approximately 90%, higher than the probability corresponding to an earthquake in the along-bridge direction (85%). Under a rare earthquake (PGA = 0.51g), the probability of speed-restricted passage decreases to 53%, higher than the probability corresponding to an earthquake in the along-bridge direction (40%). Overall, the probability of conditional passage under transverse earthquakes is higher than that under longitudinal earthquakes. The functional vulnerability analysis of rail transit bridge systems shows that the expected post-earthquake passage function under a transverse earthquake with a PGA of 0.1g is approximately 45%, while a PGA exceeding 0.3g makes post-earthquake passage virtually impossible.

[0106] S4. Draw a step-type functional recovery function based on the repair period and traffic function, and calculate the resilience index based on the functional recovery function.

[0107] According to the repair period of different repair processes of the rail transit bridge system and the traffic function during the repair process, a step-type function recovery function is drawn, such as Figure 13 shown.

[0108] Adopting the resilience index R To quantify the system's functional loss and recovery ability under a certain intensity of earthquake motion, the resilience index can be understood as reflecting the degree of functional recovery per unit time. It is obtained by integrating the functional recovery function and dividing it by the repair period. The calculation formula is as follows:

[0109] in is the toughness index; t0 is the time point of earthquake occurrence, and t2 is the time point of bridge function recovery; Q(t) The function recovery function, Q(t) = 1, indicates full function, and Q(t) = 0, indicates complete loss of function. A step-shaped function is used to reflect the functional recovery process of rail transit bridges. The functional recovery curve represented by the functional recovery function reflects in real time the process from structural loss to complete recovery after an earthquake. It mainly includes three components: the structural traffic function Qr, the functional repair path, and the 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 functional expression of the functional repair path, directly reflecting the quantitative relationship between post-earthquake repair strategies, repair methods, and resource inputs, and the degree and time of structural functional recovery. In the prior art, the functional recovery function is a continuous function. Cimellaro's ideal recovery function, proposed based on real-world recovery data or types and taking into account varying levels of rescue resource availability, is typically used: linear, exponential, trigonometric, and step-shaped recovery functions. However, these existing linear, exponential, trigonometric, and step-shaped recovery functions fail to reflect the impact of the structural repair sequence. Therefore, a functional recovery function that considers the component repair sequence is needed. This study explored the impact of different component repair sequences on the seismic resilience of bridges, but failed to consider the component damage state or the damage evolution pattern of railway bridges. Furthermore, according to an expert questionnaire survey, 72.5% of railway experts prefer to use a step-shaped function to reflect the functional recovery process of railway bridges. Therefore, this paper innovatively proposes a functional recovery function that considers both the component repair sequence and the post-earthquake traffic function of structural damage. This function is step-shaped, not continuous.

[0110] 4.1 Earthquake resilience index along the bridge Calculate the resilience index of rail transit bridges under longitudinal earthquakes as follows: Figure 14 As shown in the figure, it can be seen that, in general, the toughness index of rail transit bridges under longitudinal earthquakes decreases with the increase of earthquake motion intensity, but it has a large span feature, which is due to the large difference in the repair time of each key component. In order to better understand the situation of the toughness index, the toughness index is divided into six levels according to the overall results, namely R<0.25, 0.25≤R<0.45, 0.45≤R<0.65, 0.65≤R<0.85, 0.85≤R<0.95, 0.95≤R, and the proportion of each level is shown in the figure. Figure 15As shown in the figure, it can be seen that when the PGA is 0.15g and 0.25g, the resilience index of rail transit bridges under longitudinal earthquakes is mostly concentrated in the range of [0.25, 0.45) and [0.65, 0.85); when the PGA reaches 0.35g, the resilience index of rail transit bridges under longitudinal earthquakes in the range of [0.25, 0.45) and [0.65, 0.85) decreases to about 75%, and there is about a 25% probability that the resilience is below 0.25 (extremely low resilience); as the PGA increases, the probability of the toughness being below 0.25 gradually increases, and when the PGA reaches 0.55g, the probability reaches about 70%.

[0111] 4.2 Transverse earthquake resilience index The resilience index of rail transit bridges under transverse earthquakes is as follows: Figure 16 As shown in the figure, it can be seen that, in general, similar to the longitudinal earthquake, the toughness index of rail transit bridges under transverse earthquakes decreases with the increase of earthquake intensity, but it has a large span feature. The reason is that the repair time of each key component varies greatly. The distribution of toughness at each level is shown in the figure. Figure 17 As shown in the figure, when the PGA is 0.15g and 0.25g, the resilience index of rail transit bridges under transverse earthquakes is mostly concentrated in the intervals [0.45, 0.65) and [0.65, 0.85), which is consistent with the longitudinal earthquake. When the PGA reaches 0.35g, the resilience index of rail transit bridges under longitudinal earthquakes in the intervals [0.45, 0.65) and [0.65, 0.85) decreases to approximately 80%, and there is a probability of about 20% that the resilience is below 0.25 (extremely low resilience). As the PGA increases, the probability of the toughness being below 0.25 gradually increases. When the PGA reaches 0.55g, the probability reaches approximately 55%, which is lower than the corresponding probability value for the longitudinal earthquake. Overall, the resilience index of rail transit bridges under transverse earthquakes is higher than that for the longitudinal earthquake.

[0112] S5. Calculate the effective impact days for different damage levels under different earthquake intensities based on the toughness index and the repair period of the rail transit bridge system. The calculation formula for the effective impact days is: :

[0113] ED is the effective effect days, is the repair period, which is the difference between the time when the earthquake occurred and the time when the bridge function was restored.

[0114] 5.1 Effective impact days of structural damage under earthquake action along the bridge According to the above calculation, the effective impact days of rail transit bridges under the earthquake in the longitudinal direction are as follows: Figure 18As shown, it can be seen that during frequent earthquakes (PGA less than 0.11g), rail transit bridges can achieve speed passing under longitudinal earthquakes; 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 rare earthquakes, 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 earthquakes indicates that under frequent earthquakes, the median value of the effective influence days is almost 0, that is, under frequent earthquakes, rail transit bridges can meet the requirement of speed passing; under design earthquakes, the median value of the effective influence days reaches 30 days, and under rare earthquakes, the median value of the effective influence days is 42 days.

[0115] To better understand the situation of the effective influence days of rail transit bridges under longitudinal earthquakes, according to the overall results, the effective influence days are divided into six levels, 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.

[0116] 5.2 Effective Influence Days of Structural Damage under Transverse Earthquake Action The effective influence days of rail transit bridges under transverse earthquakes are as Figure 20As shown in the figure, it can be seen that, in general, the effective impact days of rail transit bridges under transverse earthquakes are lower than those corresponding to longitudinal earthquakes. In the frequent earthquake range (PGA ≤ 0.11g), rail transit bridges can all reach full speed under transverse earthquakes. In the PGA range of 0.11g to 0.30g, the effective impact days of most seismic motion samples are relatively small. In the PGA range of 0.30g to 0.51g, some seismic motion samples have an effective impact day of approximately 100 days, but most seismic motion samples have an effective impact day of less than 10 days. When the PGA exceeds 0.51g, that is, when the PGA is above rare earthquakes, many seismic motion samples have an effective impact day of more than 90 days, and the number of samples with an effective impact day of more than 90 days increases with increasing PGA. The median value of the effective impact days under transverse earthquakes shows that under frequent earthquakes, the median value of the effective impact days is almost 0, that is, under frequent earthquakes, the rail transit bridge can meet the requirements of high-speed traffic; under design earthquakes, the median value of the effective impact days reaches 4.81 days, and under rare earthquakes, the median value of the effective impact days is about 15 days, both of which are smaller than the median value of the effective impact days under longitudinal earthquakes.

[0117] Step S6: Establish the relationship between the damage level and effective impact days of the rail transit bridge system, analyze and determine the effective impact day ranges of different damage levels, and obtain the seismic toughness grading evaluation standard in combination with the functional target requirements.

[0118] The present invention selects a rail transit simply supported beam bridge for modeling analysis. Based on the above analysis results, the relationship between the damage level and the effective impact days of the rail transit bridge system is established as follows: Figure 21 As shown in the figure, it can be found that the effective impact days corresponding to the loss level under the action of longitudinal earthquakes are generally greater than those corresponding to transverse earthquakes. This is mainly because the damage to the rail transit bridge system corresponding to the longitudinal earthquake includes the loss of key components such as piers and supports, while the loss level of key components such as piers in the rail transit bridge system under the action of transverse earthquakes is lower, so the repair time is shorter.

[0119] Based on the above results, the comparison between the degree of damage and the effective impact days of the rail transit bridge system is summarized in Table 9, and based on this comparison table, the toughness grade classification is summarized in Table 10. Because the method of constructing the bridge seismic toughness evaluation standard in the present invention draws on prior experience (seismic specifications), it is independent of factors such as the bridge 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 rail transit simply supported beam bridges. For other structural types of bridges such as continuous beams and rigid frame bridges, the above steps S1-S6 should be used to determine the damage level and effective impact days of different types of bridges, thereby obtaining the seismic toughness grading evaluation standard for different types of bridges.

[0120] Table 9 Comparison of damage levels and effective impact days for rail transit bridge systems

[0121] Table 10 Evaluation criteria for seismic toughness classification of rail transit bridge systems

[0122] The median, average and standard value (95% guarantee rate) of the seismic resilience index (effective impact days) of bridges under different earthquake intensity indices are statistically evaluated, and a graded evaluation of seismic resilience is carried out.

[0123] (1) Toughness evaluation based on median value Calculate the median value of the effective impact days of rail transit bridges under longitudinal and transverse earthquakes and their envelope diagrams as shown in the figure below. Figure 22 As shown in the figure, the envelope of the effective impact days for earthquakes in both directions is multi-segmented. In the case of frequent earthquakes, the median effective impact days is 0, meeting the "minor earthquake no damage" defense goal; in the case of design earthquakes, the median effective impact days is approximately 30, meeting the "two-star" resilience level; and in the case of rare earthquakes, the median effective impact days is approximately 45, meeting the "two-star" resilience level.

[0124] (2) Toughness evaluation based on 95% assurance rate The number of effective impact days with a 95% assurance rate in all earthquake motion samples is as follows: Figure 23 As shown, the effective impact days with a 95% assurance rate have a higher value relative to the median effective impact days. In the case of frequent earthquakes, the effective impact days are 5, which does not meet the design goal of "no damage in small earthquakes" and results in a "one-star" resilience rating. In the case of design earthquakes, the effective impact days are approximately 70, meeting the "one-star" resilience rating, indicating insufficient resilience. In the case of rare earthquakes, the effective impact days are approximately 100, meeting the "one-star" resilience rating, indicating insufficient resilience. It can be seen that the resilience rating obtained using the 95% assurance rate is low, indicating that this strategy is conservative.

[0125] (3) Resilience evaluation based on mean The average number of effective impact days in all earthquake motion samples is as follows: Figure 24As shown, its value is close to the median value of the effective impact days. Under frequent earthquakes, the mean effective impact days is 4.1, which does not meet the design goal of "no damage from minor earthquakes" and results in a "one-star" resilience rating. Under design earthquakes, the mean effective impact days is approximately 30, meeting the "two-star" resilience rating, indicating acceptable resilience. Under rare earthquakes, the mean effective impact days is approximately 60, meeting the "two-star" resilience rating, indicating acceptable resilience. It can be seen that the resilience rating obtained using the mean value is relatively close to the resilience rating obtained using the median value.

[0126] 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 and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for constructing a graded evaluation standard for seismic toughness of rail transit bridges, characterized in that: The following steps are involved: S1. Determine the post-earthquake functional requirements of rail transit bridge systems under different earthquake levels; S2. Conduct seismic vulnerability and functional vulnerability analysis of rail transit bridge systems to determine the structural damage levels and post-earthquake residual functions under different earthquake intensities; S3. Determine the repair process and repair path for rail transit bridge system components based on different damage levels, calculate the repair project volume by taking into account the overlap of the repair process flow, and calculate the component repair duration based on the project budget quota to obtain the repair duration of the rail transit bridge system; The traffic function during the entire restoration process was obtained based on the analysis of the post-earthquake residual function and restoration path; S4. Draw a step-type function recovery function based on the repair period and traffic function, and calculate the resilience index based on the function recovery function; S5. Calculate the effective impact days for different damage levels under different earthquake intensities based on the resilience index and the repair period of the rail transit bridge system. The calculation formula for the effective impact days is: ED is the effective effect days, is the repair period of the rail transit bridge system; R is the resilience index; S6. Establish the relationship between the damage level and effective impact days of rail transit bridge systems, analyze and determine the effective impact days range for different damage levels, and derive the seismic toughness grading evaluation standard based on functional target requirements.

2. A method for constructing a graded evaluation standard for seismic toughness of rail transit bridges according to claim 1, characterized in that: Combined with the existing rail transit bridge seismic design specifications and bridge requirements, the functional target requirements of the bridge structure under small earthquakes, moderate earthquakes and major earthquakes are determined. The toughness levels are divided into one star, two stars, three stars and four stars. The functional target requirements include the loss level of the rail transit bridge system and the traffic conditions of the bridge after the earthquake and after repair.

3. A method for constructing a graded evaluation standard for seismic toughness of rail transit bridges according to any one of claim 1, characterized in that: In step S3, the rail transit bridge system component repair process is as follows: When a pier is slightly damaged, pressure grouting is used to repair cracks. When a pier is moderately damaged, the plastic hinge area of ​​the pier is reinforced by enlarging the cross section. When a pier is severely damaged, the entire pier height is reinforced by enlarging the cross section. When a pier is completely damaged, the pier body is mechanically dismantled and rebuilt in situ. When the bearing is slightly or moderately damaged, the top beam is used to reset and correct the bearing. When the bearing is seriously or completely damaged, in addition to the top beam reset and correction, there are also processes for dismantling and installing the bearing. When the main beam is slightly damaged, the line is dismantled, the expansion joints and track structure at the beam ends are removed, and the expansion joints and track structure at the beam ends are installed. When the main beam is completely damaged, the repair includes the installation and removal of the beam lifting machine, line dismantling, lifting of the waste beam, prefabrication and transportation of the main beam, erection of the main beam, and installation of the expansion joints and track structure.

4. A method for constructing a graded evaluation standard for seismic toughness of 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 bridge piers, as follows: When the bridge piers are moderately damaged or above, repair the piers first and then the bearings and main beams; When minor damage occurs to the bridge piers, first repair the main beams and supports, including the tracks and accessories, and then repair the bridge piers; When there is no damage to the bridge piers, repair the main beams and supports as needed.

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

6. A method for constructing a graded evaluation standard for seismic toughness of 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 formulation, and preparation of personnel, materials, and equipment.

7. A method for constructing a graded evaluation standard for seismic toughness of rail transit bridges according to claim 5, characterized in that: Considering the overlap of repair process, the function recovery time under different damage levels is calculated. The function recovery time calculation formula is: When the bridge pier is not damaged beyond the moderate level: When the bridge pier is damaged beyond the moderate level: In the formula Indicates the functional recovery time of the rail transit bridge system, The repair period for the pier components is is the repair period of the supporting components, The repair period for the main beam and auxiliary track structural components is Calculate the construction period for the preparatory stage before repair of the main beam and auxiliary track structure. Calculate the construction period for the erection phase of the main beam and auxiliary track structures.

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

9. A method for evaluating the seismic toughness of rail transit bridges, characterized in that: The following steps are involved: A seismic toughness grading evaluation standard is established by using a method for constructing a seismic toughness grading evaluation standard for rail transit bridges as described in any one of claims 1 to 8; Establish a rail transit bridge seismic vulnerability analysis model for the target rail transit bridge system, conduct seismic response analysis, and determine the post-earthquake functional performance of the rail transit bridge system under different earthquake intensities; Based on different structural damage levels, the repair process, repair path and engineering budget quota of the rail transit bridge system are given. The post-earthquake repair period and the traffic function of the rail transit bridge system during the entire repair process are calculated under different earthquake intensities. Based on this, the functional recovery function is drawn and the toughness index is calculated. Based on the toughness index and repair period, the effective impact days under different post-earthquake functional performance of the rail transit bridge system are calculated. According to 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 the at least one processor; the memory storing instructions executed by the at least one processor, characterized in that: The instruction is executed by the at least one processor so that the at least one processor can execute the method for constructing a graded evaluation standard for seismic toughness of rail transit bridges as described in any one of claims 1-8.

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